diff options
| -rw-r--r-- | src/ChangeLog | 11 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 13 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 1 | ||||
| -rw-r--r-- | src/algebra/string.spad.pamphlet | 275 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 55 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2718 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 4621 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 10 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8553 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 21198 |
10 files changed, 18735 insertions, 18720 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 67856a15..af7b76a7 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,16 @@ 2011-09-09 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/g-opt.boot (optIadd): Remork. + (optIsub): Likewise. + (optIdec): New. + * algebra/string.spad.pamphlet (IndexedString): Fold definition + into String. Remove. + (Character): Tidy. + (CharacterClass): Likewise. + * algebra/exposed.lsp.pamphlet: Do not expose ISTRING. + +2011-09-09 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/syntax.spad.pamphlet (Identifier): Remove CoercibleTo Symbol and CoercibleTo String properties. * algebra/symbol.spad.pamphlet (Symbol): Make RetractableTo Identifier. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index dab60382..e2d6afe9 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -127,7 +127,7 @@ oa_strap_0_sources = \ oa_strap_1_sources = $(oa_strap_0_sources) \ SRAGG ALAGG TBAGG KDAGG OPERCAT MATCAT ARR2CAT FFIELDC \ - SAOS ILIST ISTRING IBITS SEX FLOAT CCLASS REF UNISEG SEG VOID \ + SAOS ILIST IBITS SEX FLOAT CCLASS REF UNISEG SEG VOID \ ALIST SEX PATRES PATTERN BOP ARITY NONE IDENT SET FARRAY IFARRAY \ ANY SEXOF MATRIX IARRAY1 @@ -306,7 +306,6 @@ strap-0/LIST.$(FASLEXT): strap-0/LSAGG.$(FASLEXT) strap-0/PRIMARR.$(FASLEXT): strap-0/A1AGG.$(FASLEXT) strap-0/VECTOR.$(FASLEXT): strap-0/VECTCAT.$(FASLEXT) strap-0/CHAR.$(FASLEXT): strap-0/FSAGG.$(FASLEXT) -strap-0/STRING.$(FASLEXT): strap-0/SRAGG.$(FASLEXT) strap-0/STREAM.$(FASLEXT): strap-0/LZSTAGG.$(FASLEXT) strap-0/SUP.$(FASLEXT): strap-0/UPOLYC.$(FASLEXT) strap-0/FRAC.$(FASLEXT): strap-0/QFCAT.$(FASLEXT) @@ -454,8 +453,7 @@ strap-1/DIOPS.$(FASLEXT): strap-1/BGAGG.$(FASLEXT) strap-1/INT.$(FASLEXT) \ strap-1/CLAGG.$(FASLEXT) strap-1/CHAR.$(FASLEXT) strap-1/DIAGG.$(FASLEXT): strap-1/DIOPS.$(FASLEXT) strap-1/FSAGG.$(FASLEXT): strap-1/DIAGG.$(FASLEXT) strap-1/INS.$(FASLEXT) -strap-1/STRING.$(FASLEXT): strap-1/SRAGG.$(FASLEXT) strap-1/CHAR.$(FASLEXT) \ - strap-1/ISTRING.$(FASLEXT) +strap-1/STRING.$(FASLEXT): strap-1/SRAGG.$(FASLEXT) strap-1/CHAR.$(FASLEXT) strap-1/INT.$(FASLEXT): strap-1/STRING.$(FASLEXT) strap-1/ORDRING.$(FASLEXT) \ strap-1/MATRIX.$(FASLEXT) strap-1/PI.$(FASLEXT): strap-1/NNI.$(FASLEXT) @@ -480,9 +478,8 @@ strap-2/NNI.$(FASLEXT): strap-2/INT.$(FASLEXT) strap-2/PI.$(FASLEXT): strap-2/NNI.$(FASLEXT) strap-2/BOOLEAN.$(FASLEXT): strap-2/SINT.$(FASLEXT) strap-2/MAYBE.$(FASLEXT): strap-2/BOOLEAN.$(FASLEXT) -strap-2/ISTRING.$(FASLEXT): strap-2/INT.$(FASLEXT) strap-2/CHAR.$(FASLEXT): strap-2/PI.$(FASLEXT) -strap-2/STRING.$(FASLEXT): strap-2/CHAR.$(FASLEXT) strap-2/ISTRING.$(FASLEXT) +strap-2/STRING.$(FASLEXT): strap-2/CHAR.$(FASLEXT) strap-2/INT.$(FASLEXT) strap-2/LIST.$(FASLEXT): strap-2/ILIST.$(FASLEXT) strap-2/STRING.$(FASLEXT) strap-2/PRIMARR.$(FASLEXT): strap-2/INT.$(FASLEXT) strap-2/IARRAY1.$(FASLEXT): strap-2/PRIMARR.$(FASLEXT) @@ -789,8 +786,6 @@ $(OUT)/A1AGG.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/BOOLE-.$(FASLEXT) \ $(OUT)/FLAGG.$(FASLEXT) $(OUT)/LOGIC-.$(FASLEXT) \ $(OUT)/ORDTYPE-.$(FASLEXT) $(OUT)/SRAGG.$(FASLEXT): $(OUT)/A1AGG.$(FASLEXT) -$(OUT)/ISTRING.$(FASLEXT): $(OUT)/SRAGG.$(FASLEXT) \ - $(OUT)/DIFFSPC-.$(FASLEXT) $(OUT)/DIFFDOM-.$(FASLEXT) $(OUT)/STAGG.$(FASLEXT): $(OUT)/URAGG.$(FASLEXT) $(OUT)/LNAGG.$(FASLEXT) $(OUT)/LNAGG.$(FASLEXT): $(OUT)/SEGCAT.$(FASLEXT) $(OUT)/SEGCAT.$(FASLEXT): $(OUT)/KRCFROM.$(FASLEXT) @@ -898,7 +893,7 @@ axiom_algebra_layer_0 = \ FSAGG FSAGG- STAGG STAGG- CLAGG CLAGG- \ RCAGG RCAGG- SETAGG SETAGG- HOAGG HOAGG- \ TBAGG TBAGG- KDAGG KDAGG- DIAGG DIAGG- \ - DIOPS DIOPS- STRING ISTRING ILIST \ + DIOPS DIOPS- STRING ILIST \ LIST DIFFDOM DIFFDOM- DIFFSPC DIFFSPC- DIFFMOD \ LINEXP PATMAB REAL CHARZ LOGIC LOGIC- \ RTVALUE SYSPTR PDDOM PDDOM- PDSPC PDSPC- \ diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index 97cdea86..355586b8 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -940,7 +940,6 @@ (|IndexedList| . ILIST) (|IndexedMatrix| . IMATRIX) (|IndexedOneDimensionalArray| . IARRAY1) - (|IndexedString| . ISTRING) (|IndexedTwoDimensionalArray| . IARRAY2) (|IndexedVector| . IVECTOR) (|InnerAlgFactor| . IALGFACT) diff --git a/src/algebra/string.spad.pamphlet b/src/algebra/string.spad.pamphlet index f977ac10..16d128be 100644 --- a/src/algebra/string.spad.pamphlet +++ b/src/algebra/string.spad.pamphlet @@ -99,6 +99,8 @@ Character: OrderedFinite() with import %cdown: % -> % from Foreign Builtin import %c2i: % -> NNI from Foreign Builtin import %i2c: NNI -> % from Foreign Builtin + import %iinc: NNI -> PositiveInteger from Foreign Builtin + import %idec: PositiveInteger -> NNI from Foreign Builtin import %ccst: String -> % from Foreign Builtin import %s2c: String -> % from Foreign Builtin import %c2s: % -> String from Foreign Builtin @@ -110,8 +112,8 @@ Character: OrderedFinite() with a <= b == %cle(a,b) a >= b == %cge(a,b) size() == %ccstmax - index n == char((n - 1)::NNI) - lookup c == (1 + ord c)::PositiveInteger + index n == char %idec n + lookup c == %iinc ord c char(n: NNI) == %i2c n ord c == %c2i c random() == char(random(size())$NNI) @@ -197,6 +199,9 @@ CharacterClass: Join(SetCategory, ConvertibleTo String, ++ \spadfunFrom{alphanumeric?}{Character} is true. == add + import %iinc: Integer -> Integer from Foreign Builtin + import %idec: Integer -> Integer from Foreign Builtin + Rep := IndexedBits(0) N := size()$Character @@ -220,7 +225,7 @@ CharacterClass: Join(SetCategory, ConvertibleTo String, convert(cl):String == construct(convert(cl)@List(Character)) convert(cl:%):List(Character) == - [char(i) for i in 0..N-1 | cl.i] + [char(i) for i in 0..%idec N | cl.i] charClass(s: String) == cl := new(N, false) @@ -235,7 +240,7 @@ CharacterClass: Join(SetCategory, ConvertibleTo String, coerce(cl):OutputForm == (convert(cl)@String)::OutputForm -- Stuff to make a legal SetAggregate view - # a == (n := 0; for i in 0..N-1 | a.i repeat n := n+1; n) + # a == (n := 0; for i in 0..%idec N | a.i repeat n := %iinc n; n) empty():% == charClass [] brace():% == charClass [] @@ -243,188 +248,205 @@ CharacterClass: Join(SetCategory, ConvertibleTo String, remove!(c: Character, a:%) == (a(ord c) := false; a) inspect(a) == - for i in 0..N-1 | a.i repeat + for i in 0..%idec N | a.i repeat return char i error "Cannot take a character from an empty class." extract!(a) == - for i in 0..N-1 | a.i repeat + for i in 0..%idec N | a.i repeat a.i := false return char i error "Cannot take a character from an empty class." map(f, a) == b := new(N, false) - for i in 0..N-1 | a.i repeat b(ord f char i) := true + for i in 0..%idec N | a.i repeat b(ord f char i) := true b temp: % := new(N, false)$Rep map!(f, a) == fill!(temp, false) - for i in 0..N-1 | a.i repeat temp(ord f char i) := true + for i in 0..%idec N | a.i repeat temp(ord f char i) := true copyInto!(a, temp, 0) parts a == - [char i for i in 0..N-1 | a.i] + [char i for i in 0..%idec N | a.i] @ -\section{domain ISTRING IndexedString} -<<domain ISTRING IndexedString>>= -)abbrev domain ISTRING IndexedString -++ Authors: Stephen Watt, Michael Monagan, Manuel Bronstein 1986 .. 1991 --- The following Lisp dependencies are divided into two groups --- Those that are required --- MAKE-FULL-CVEC --- Those that can are included for efficiency only --- SUBSTRING STRPOS RPLACSTR + +\section{domain STRING String} +<<domain STRING String>>= +)abbrev domain STRING String ++ Description: -++ This domain implements low-level strings - -IndexedString(mn:Integer): Export == Implementation where - B ==> Boolean - C ==> Character - I ==> Integer - N ==> NonNegativeInteger - U ==> UniversalSegment Integer - - Export == StringAggregate() - Implementation == add - import %strlength: % -> N from Foreign Builtin - import %streq: (%,%) -> Boolean from Foreign Builtin - import %strlt: (%,%) -> Boolean from Foreign Builtin - import %ceq: (Character, Character) -> Boolean from Foreign Builtin - import %schar: (%,I) -> Character from Foreign Builtin - import %strconc: (%,%) -> % from Foreign Builtin - import %strcopy: % -> % from Foreign Builtin - import %strstc: (%,Integer,Character) -> Void from Foreign Builtin +++ This is the domain of character strings. +++ Authors: Stephen Watt, Michael Monagan, Manuel Bronstein 1986 .. 1991 + +String(): Public == Private where + Public == StringAggregate with + string: Integer -> % + ++ \spad{string i} returns the decimal representation of + ++ \spad{i} in a string + string: DoubleFloat -> % + ++ \spad{string f} returns the decimal representation of + ++ \spad{f} in a string + string: Identifier -> % + ++ \spad{string id} is the string representation of the + ++ identifier \spad{id} + Private == add + macro B == Boolean + macro C == Character + macro I == Integer + macro N == NonNegativeInteger + macro U == UniversalSegment Integer + + import %icst0: N from Foreign Builtin + import %icst1: N from Foreign Builtin + import %i2s: I -> % from Foreign Builtin + import %iinc: I -> I from Foreign Builtin + import %idec: I -> I from Foreign Builtin + import %f2s: DoubleFloat -> % from Foreign Builtin + import %sname: Identifier -> % from Foreign Builtin + import %strlength: % -> N from Foreign Builtin + import %streq: (%,%) -> B from Foreign Builtin + import %strlt: (%,%) -> B from Foreign Builtin + import %ceq: (C, C) -> B from Foreign Builtin + import %schar: (%,I) -> C from Foreign Builtin + import %strconc: (%,%) -> % from Foreign Builtin + import %strcopy: % -> % from Foreign Builtin + import %strstc: (%,I,C) -> Void from Foreign Builtin import %hash : % -> SingleInteger from Foreign Builtin + string(n: I) == %i2s n + string(f: DoubleFloat) == %f2s f + string(id: Identifier) == %sname id + c: Character cc: CharacterClass -- new n == makeString(n, space$C)$Lisp new(n, c) == makeString(n, c)$Lisp empty() == makeString(0@I)$Lisp - empty?(s) == %strlength s = 0 + empty?(s) == zero? %strlength s #s == %strlength s s = t == %streq(s,t) s < t == %strlt(s,t) concat(s:%,t:%) == %strconc(s,t) copy s == %strcopy s - insert(s:%, t:%, i:I) == concat(concat(s(mn..i-1), t), s(i..)) + insert(s:%, t:%, i:I) == concat(concat(s(1..%idec i), t), s(i..)) coerce(s:%):OutputForm == outputForm(s pretend String) - minIndex s == mn + minIndex s == %icst1 upperCase! s == map!(upperCase, s) lowerCase! s == map!(lowerCase, s) - latex s == concat("\mbox{``", concat(s pretend String, "''}")) + latex s == + concat("\mbox{``", concat(s pretend String, "''}")) replace(s, sg, t) == - l := lo(sg) - mn + l := %idec lo(sg) m := #s n := #t - h:I := if hasHi sg then hi(sg) - mn else maxIndex s - mn - negative? l or h >= m or h < l-1 => error "index out of range" - r := new((m-(h-l+1)+n)::N, space$C) - k: NonNegativeInteger := 0 - for i in 0..l-1 repeat + h:I := if hasHi sg then %idec hi(sg) else %idec maxIndex s + negative? l or h >= m or h < %idec l => error "index out of range" + r := new((m-%iinc(h-l)+n)::N, space$C) + k: NonNegativeInteger := %icst0 + for i in %icst0..%idec l repeat %strstc(r, k, %schar(s, i)) - k := k + 1 - for i in 0..n-1 repeat + k := %iinc(k) : N + for i in %icst0..%idec n repeat %strstc(r, k, %schar(t, i)) - k := k + 1 - for i in h+1..m-1 repeat + k := %iinc(k) : N + for i in %iinc h..%idec m repeat %strstc(r, k, %schar(s, i)) - k := k + 1 + k := %iinc(k) : N r setelt(s:%, i:I, c:C) == - i < mn or i > maxIndex(s) => error "index out of range" - %strstc(s, i - mn, c) + i < 1 or i > maxIndex(s) => error "index out of range" + %strstc(s, %idec i, c) c substring?(part, whole, startpos) == np:I := %strlength part nw:I := %strlength whole - negative?(startpos := startpos - mn) => error "index out of bounds" + negative?(startpos := %idec startpos) => error "index out of bounds" np > nw - startpos => false - for ip in 0..np-1 for iw in startpos.. repeat + for ip in %icst0..%idec np for iw in startpos.. repeat not %ceq(%schar(part, ip), %schar(whole, iw)) => return false true position(s:%, t:%, startpos:I) == - negative?(startpos := startpos - mn) => error "index out of bounds" - startpos >= %strlength t => mn - 1 + negative?(startpos := %idec startpos) => error "index out of bounds" + startpos >= %strlength t => %icst0 r:I := STRPOS(s, t, startpos, NIL$Lisp)$Lisp - %peq(r, NIL$Lisp)$Foreign(Builtin) => mn - 1 - r + mn + %peq(r, NIL$Lisp)$Foreign(Builtin) => %icst0 + %iinc r position(c: Character, t: %, startpos: I) == - negative?(startpos := startpos - mn) => error "index out of bounds" - startpos >= %strlength t => mn - 1 - for r in startpos..%strlength t - 1 repeat - if %ceq(%schar(t, r), c) then return r + mn - mn - 1 + negative?(startpos := %idec startpos) => error "index out of bounds" + startpos >= %strlength t => %icst0 + for r in startpos..%idec %strlength t repeat + if %ceq(%schar(t, r), c) then return %iinc r + %icst0 position(cc: CharacterClass, t: %, startpos: I) == - negative?(startpos := startpos - mn) => error "index out of bounds" - startpos >= %strlength t => mn - 1 - for r in startpos..%strlength t - 1 repeat - if member?(%schar(t,r), cc) then return r + mn - mn - 1 + negative?(startpos := %idec startpos) => error "index out of bounds" + startpos >= %strlength t => %icst0 + for r in startpos..%idec %strlength t repeat + if member?(%schar(t,r), cc) then return %iinc r + %icst0 suffix?(s, t) == (m := maxIndex s) > (n := maxIndex t) => false - substring?(s, t, mn + n - m) + substring?(s, t, %iinc(n - m)) split(s, c) == n := maxIndex s - i := mn - while i <= n and s.i = c repeat i := i + 1 + i := %icst1 + while i <= n and s.i = c repeat i := %iinc i l := empty()$List(%) j:Integer -- j is conditionally intialized - while i <= n and (j := position(c, s, i)) >= mn repeat - l := concat(s(i..j-1), l) + while i <= n and (j := position(c, s, i)) >= %icst1 repeat + l := concat(s(i..%idec j), l) i := j - while i <= n and s.i = c repeat i := i + 1 + while i <= n and s.i = c repeat i := %iinc i if i <= n then l := concat(s(i..n), l) reverse! l split(s, cc) == n := maxIndex s - i := mn - while i <= n and member?(s.i,cc) repeat i := i + 1 + i := %icst1 + while i <= n and member?(s.i,cc) repeat i := %iinc i l := empty()$List(%) j:Integer -- j is conditionally intialized - while i <= n and (j := position(cc, s, i)) >= mn repeat - l := concat(s(i..j-1), l) + while i <= n and (j := position(cc, s, i)) >= 1 repeat + l := concat(s(i..%idec j), l) i := j - while i <= n and member?(s.i,cc) repeat i := i + 1 + while i <= n and member?(s.i,cc) repeat i := %iinc i if i <= n then l := concat(s(i..n), l) reverse! l leftTrim(s, c) == n := maxIndex s - i := mn - while i <= n and s.i = c repeat i := i + 1 + i := %icst1 + while i <= n and s.i = c repeat i := %iinc i s(i..n) leftTrim(s, cc) == n := maxIndex s - i := mn - while i <= n and member?(s.i,cc) repeat i := i + 1 + i := %icst1 + while i <= n and member?(s.i,cc) repeat i := %iinc i s(i..n) rightTrim(s, c) == j := maxIndex s - while j >= mn and s.j = c repeat j := j - 1 + while j >= 1 and s.j = c repeat j := %idec j s(minIndex(s)..j) rightTrim(s, cc) == j := maxIndex s - while j >= mn and member?(s.j, cc) repeat j := j - 1 + while j >= %icst1 and member?(s.j, cc) repeat j := %idec j s(minIndex(s)..j) concat l == t := new(+/[#s for s in l], space$C) - i := mn + i := %icst1 for s in l repeat copyInto!(t, s, i) i := i + #s @@ -433,91 +455,51 @@ IndexedString(mn:Integer): Export == Implementation where copyInto!(y, x, s) == m := #x n := #y - s := s - mn + s := %idec s negative? s or s+m > n => error "index out of range" - RPLACSTR(y, s, m, x, 0, m)$Lisp + RPLACSTR(y, s, m, x, %icst0, m)$Lisp y elt(s:%, i:I) == - i < mn or i > maxIndex(s) => error "index out of range" - %schar(s, i - mn) + i < %icst1 or i > maxIndex(s) => error "index out of range" + %schar(s, %idec i) elt(s:%, sg:U) == - l := lo(sg) - mn - h := if hasHi sg then hi(sg) - mn else maxIndex s - mn + l := %idec lo(sg) + h := if hasHi sg then %idec hi(sg) else %idec maxIndex s negative? l or h >= #s => error "index out of bound" - SUBSTRING(s, l, max(0, h-l+1))$Lisp + SUBSTRING(s, l, max(%icst0, %iinc(h-l)))$Lisp hash s == %hash s - match(pattern,target,wildcard) == stringMatch(pattern,target,CHARACTER(wildcard)$Lisp)$Lisp + match(pattern,target,wildcard) == + stringMatch(pattern,target,CHARACTER(wildcard)$Lisp)$Lisp -@ - -Up to [[patch--40]] this read - -\begin{verbatim} - match(pattern,target,wildcard) == stringMatch(pattern,target,wildcard)$Lisp -\end{verbatim} - -which did not work (Issue~\#97), since [[wildcard]] is an Axiom-[[Character]], -not a Lisp-[[Character]]. The operation [[CHARACTER]] from [[Lisp]] performs -the coercion. - -<<domain ISTRING IndexedString>>= match?(pattern, target, dontcare) == n := maxIndex pattern p := position(dontcare, pattern, m := minIndex pattern)::N - p = m-1 => pattern = target - (p ~= m) and not prefix?(pattern(m..p-1), target) => false + p = %idec m => pattern = target + (p ~= m) and not prefix?(pattern(m..%idec p), target) => false i := p -- index into target - q := position(dontcare, pattern, p + 1)::N - while q ~= m-1 repeat - s := pattern(p+1..q-1) + q := position(dontcare, pattern, %iinc p)::N + while q ~= %idec m repeat + s := pattern(%iinc p..%idec q) i := position(s, target, i)::N - i = m-1 => return false + i = %idec m => return false i := i + #s p := q - q := position(dontcare, pattern, q + 1)::N - (p ~= n) and not suffix?(pattern(p+1..n), target) => false + q := position(dontcare, pattern, %iinc q)::N + (p ~= n) and not suffix?(pattern(%iinc p..n), target) => false true @ -\section{domain STRING String} -<<domain STRING String>>= -)abbrev domain STRING String -++ Description: -++ This is the domain of character strings. -MINSTRINGINDEX ==> 1 -- as of 3/14/90. - -String(): Public == Private where - Public == StringAggregate with - string: Integer -> % - ++ \spad{string i} returns the decimal representation of - ++ \spad{i} in a string - string: DoubleFloat -> % - ++ \spad{string f} returns the decimal representation of - ++ \spad{f} in a string - string: Identifier -> % - ++ \spad{string id} is the string representation of the - ++ identifier \spad{id} - Private == IndexedString(MINSTRINGINDEX) add - import %i2s: Integer -> % from Foreign Builtin - import %f2s: DoubleFloat -> % from Foreign Builtin - import %sname: Identifier -> % from Foreign Builtin - string(n: Integer) == %i2s n - string(f: DoubleFloat) == %f2s f - string(id: Identifier) == %sname id - -@ - \section{License} <<license>>= --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. --All rights reserved. --- Copyright (C) 2007-2010, Gabriel Dos Reis. +-- Copyright (C) 2007-2011, Gabriel Dos Reis. -- All rights reserved. -- --Redistribution and use in source and binary forms, with or without @@ -553,7 +535,6 @@ String(): Public == Private where <<domain CHAR Character>> <<domain CCLASS CharacterClass>> -<<domain ISTRING IndexedString>> <<domain STRING String>> @ \eject diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index f7dfa3f2..709e7b41 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -406,7 +406,7 @@ $VMsideEffectFreeOperators == %beq %blt %ble %bgt %bge %bitand %bitior %bitxor %bitnot %bcompl %ilength %ibit %icst0 %icst1 %icstmin %icstmax %imul %iadd %isub %igcd %ilcm %ipow %imin %imax %ieven? %iodd? %iinc - %irem %iquo %idivide %idec %irandom + %idec %irem %iquo %idivide %idec %irandom %feq %flt %fle %fgt %fge %fmul %fadd %fsub %fexp %fmin %fmax %float? %fpowi %fdiv %fneg %i2f %fminval %fmaxval %fbase %fprec %ftrunc %fsqrt %fpowf %flog %flog2 %flog10 %fmanexp %fNaN? @@ -742,11 +742,24 @@ optBge ['%bge,a,b] == optIadd(x is ['%iadd,a,b]) == integer? a and integer? b => a + b - integer? a and a = 0 => b - integer? b and b = 0 => a + integer? a => + a = 0 => b + b is [op,b1,b2] and op in '(%iadd %isub) => + integer? b1 => simplifyVMForm [op,['%iadd,a,b1],b2] + integer? b2 => simplifyVMForm ['%iadd,b1,[op,a,b2]] + x + x + integer? b => + b = 0 => a + a is [op,a1,a2] and op in '('%iadd %isub) => + integer? a1 => simplifyVMForm [op,['%iadd,a1,b],a2] + integer? a2 => simplifyVMForm ['%iadd,a1,[op,b,a2]] + x + x x optIinc(x is ['%iinc,a]) == + integer? a => a + 1 a is [op,b,c] and op in '(%isub %iadd) => integer? b => simplifyVMForm [op,[op,b,1],c] integer? c => simplifyVMForm [op,b,[op,c,1]] @@ -755,8 +768,40 @@ optIinc(x is ['%iinc,a]) == optIsub(x is ['%isub,a,b]) == integer? a and integer? b => a - b - integer? a and a = 0 => ['%ineg,b] - integer? b and b = 0 => a + integer? a => + a = 0 => ['%ineg,b] + b is ['%iadd,b1,b2] => + integer? b1 => simplifyVMForm ['%isub,['%isub,a,b1],b2] + integer? b2 => simplifyVMForm ['%isub,['%isub,a,b2],b1] + x + b is ['%isub,b1,b2] => + integer? b1 => simplifyVMForm ['%iadd,['%isub,a,b1],b2] + integer? b2 => simplifyVMForm ['%isub,['%iadd,a,b2],b1] + x + x + integer? b => + b = 0 => a + a is ['%iadd,a1,a2] => + integer? a1 => simplifyVMForm ['%iadd,['%isub,a1,b],a2] + integer? a2 => simplifyVMForm ['%iadd,a1,['%isub,a2,b]] + x + a is ['%isub,a1,a2] => + integer? a1 => simplifyVMForm ['%isub,['%isub,a1,b],a2] + integer? a2 => simplifyVMForm ['%isub,a1,['%iadd,a2,b]] + x + x + x + +optIdec(x is ['%idec,a]) == + integer? a => a - 1 + a is ['%iadd,b,c] => + integer? b => simplifyVMForm ['%iadd,['%isub,b,1],c] + integer? c => simplifyVMForm ['%iadd,b,['%isub,c,1]] + x + a is ['%isub,b,c] => + integer? b => simplifyVMForm ['%isub,['%isub,b,1],c] + integer? c => simplifyVMForm ['%isub,b,['%iadd,c,1]] + x x optImul(x is ['%imul,a,b]) == diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 79d968d3..ad6dab06 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2277006 . 3524522243) +(2275976 . 3524556579) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4422 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4418 . T) (-4423 . T) (-4417 . T)) +((-4421 . T) (-4419 . T) (-4418 . T) ((-4426 "*") . T) (-4417 . T) (-4422 . T) (-4416 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3495) +(-32 R -3494) ((|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 -1059) (QUOTE (-558))))) +((|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4425))) +((|HasAttribute| |#1| (QUOTE -4424))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -3495 UP UPUP -3013) +(-40 -3494 UP UPUP -3012) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3957 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) -(-41 R -3495) +((-4417 |has| (-419 |#2|) (-376)) (-4422 |has| (-419 |#2|) (-376)) (-4416 |has| (-419 |#2|) (-376)) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3956 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197)))))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -918) (QUOTE (-1197)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -657) (QUOTE (-558)))) (-3956 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -918) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197)))))) +(-41 R -3494) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-319)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) +((-4421 |has| |#1| (-569)) (-4419 . T) (-4418 . T)) ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4425 . T) (-4426 . T)) -((-3957 (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861)))) (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))))) +((-4424 . T) (-4425 . T)) +((-3956 (-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-860)))) (-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-860))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (|%list| (QUOTE -1058) (QUOTE (-558))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4422 . T)) +((-4421 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -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 -3495) +(-54 |Base| R -3494) ((|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},{}...,{}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},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -158,77 +158,77 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL (-58 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}"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL (-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's."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3970) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -3969) ((|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 -(-62 -3970) +(-62 -3969) ((|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 -(-63 -3970) +(-63 -3969) ((|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 -(-64 -3970) +(-64 -3969) ((|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 -(-65 -3970) +(-65 -3969) ((|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 -3970) +(-66 -3969) ((|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 -3970) +(-67 -3969) ((|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 -3970) +(-68 -3969) ((|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 -3970) +(-69 -3969) ((|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 -3970) +(-70 -3969) ((|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 -3970) +(-71 -3969) ((|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 -3970) +(-72 -3969) ((|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 -3970) +(-73 -3969) ((|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 -3970) +(-74 -3969) ((|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 -(-75 -3970) +(-75 -3969) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -3970) +(-78 -3969) ((|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 -(-79 -3970) +(-79 -3969) ((|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 -3970) +(-80 -3969) ((|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 -3970) +(-81 -3969) ((|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 -3970) +(-82 -3969) ((|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 -(-83 -3970) +(-83 -3969) ((|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 -(-84 -3970) +(-84 -3969) ((|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 -(-85 -3970) +(-85 -3969) ((|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 -(-86 -3970) +(-86 -3969) ((|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 -(-87 -3970) +(-87 -3969) ((|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 -(-88 -3970) +(-88 -3969) ((|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 -(-89 -3970) +(-89 -3969) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-376)))) (-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}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4425 . T)) +((-4424 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4425 . T) ((-4427 "*") . T) (-4426 . T) (-4422 . T) (-4420 . T) (-4419 . T) (-4418 . T) (-4423 . T) (-4417 . T) (-4416 . T) (-4415 . T) (-4414 . T) (-4413 . T) (-4421 . T) (-4424 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4412 . T)) +((-4424 . T) ((-4426 "*") . T) (-4425 . T) (-4421 . T) (-4419 . T) (-4418 . T) (-4417 . T) (-4422 . T) (-4416 . T) (-4415 . T) (-4414 . T) (-4413 . T) (-4412 . T) (-4420 . T) (-4423 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4411 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4422 . T)) +((-4421 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4427 "*")))) +((|HasAttribute| |#1| (QUOTE (-4426 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4425 . T)) +((-4424 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4426 . T)) +((-4425 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-558) (QUOTE (-928))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1040))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860))) (-3956 (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860)))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1172))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1197)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -657) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (|HasCategory| (-558) (QUOTE (-147))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-114) (QUOTE (-102)))) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| (-114) (QUOTE (-1121))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-860))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| (-114) (QUOTE (-1121))) (|HasCategory| (-114) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-114) (QUOTE (-102)))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-112 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -396,22 +396,22 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -3495 UP) +(-117 -3494 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 (-118 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-929))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1041))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-861))) (-3957 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-861)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1173))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1198)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-929)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-118 |#1|) (QUOTE (-928))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1040))) (|HasCategory| (-118 |#1|) (QUOTE (-841))) (|HasCategory| (-118 |#1|) (QUOTE (-860))) (-3956 (|HasCategory| (-118 |#1|) (QUOTE (-841))) (|HasCategory| (-118 |#1|) (QUOTE (-860)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1172))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1197)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-928)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4426))) +((|HasAttribute| |#1| (QUOTE -4425))) (-121 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -422,15 +422,15 @@ NIL NIL (-123 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"))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-125) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL (-126 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -438,24 +438,24 @@ NIL NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL NIL (-131) ((|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 `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-3957 (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-130) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-130) (QUOTE (-861))) (-3957 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-3956 (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-130) (QUOTE (-860))) (-3956 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -474,13 +474,13 @@ NIL NIL (-136) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4427 "*") . T)) +(((-4426 "*") . T)) NIL -(-137 |minix| -3020 R) +(-137 |minix| -3019 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -3020 S T$) +(-138 |minix| -3019 S T$) ((|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 @@ -502,8 +502,8 @@ NIL NIL (-143) ((|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}."))) -((-4425 . T) (-4415 . T) (-4426 . T)) -((-3957 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4424 . T) (-4414 . T) (-4425 . T)) +((-3956 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-860))) (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -518,7 +518,7 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4422 . T)) +((-4421 . T)) NIL (-148 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -526,9 +526,9 @@ NIL NIL (-149) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4422 . T)) +((-4421 . T)) NIL -(-150 -3495 UP UPUP) +(-150 -3494 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 @@ -539,14 +539,14 @@ NIL (-152 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasAttribute| |#1| (QUOTE -4425))) +((|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasAttribute| |#1| (QUOTE -4424))) (-153 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-154 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4420 . T) (-4419 . T) (-4422 . T)) +((-4419 . T) (-4418 . T) (-4421 . T)) NIL (-155) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -568,7 +568,7 @@ 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 -(-160 R -3495) +(-160 R -3494) ((|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})/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.} 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.} 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.} n!/(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 @@ -599,10 +599,10 @@ NIL (-167 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4421)) (|HasAttribute| |#2| (QUOTE -4424)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569)))) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-1040))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569)))) (-168 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4418 -3957 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-929)))) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4421 |has| |#1| (-6 -4421)) (-4424 |has| |#1| (-6 -4424)) (-1490 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 -3956 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-928)))) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4420 |has| |#1| (-6 -4420)) (-4423 |has| |#1| (-6 -4423)) (-1489 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-169 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4418 -3957 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-929)))) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4421 |has| |#1| (-6 -4421)) (-4424 |has| |#1| (-6 -4424)) (-1490 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . 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T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -630,7 +630,7 @@ NIL NIL (-175) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-176) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -638,7 +638,7 @@ NIL NIL (-177 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4427 "*") . T) (-4418 . T) (-4423 . T) (-4417 . T) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") . T) (-4417 . T) (-4422 . T) (-4416 . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-178) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -655,7 +655,7 @@ NIL (-181 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-965 |#2|) (|%list| (QUOTE -901) (|devaluate| |#1|)))) +((|HasCategory| (-964 |#2|) (|%list| (QUOTE -900) (|devaluate| |#1|)))) (-182 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -3495) +(-191 R -3494) ((|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 @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -3495 UP UPUP R) +(-219 -3494 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 -(-220 -3495 FP) +(-220 -3494 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 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 (-221) ((|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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-558) (QUOTE (-928))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1040))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860))) (-3956 (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860)))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1172))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1197)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -657) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (|HasCategory| (-558) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -3495) +(-223 R -3494) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -834,19 +834,19 @@ NIL NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) -((-4422 . T)) +((-4421 . T)) NIL -(-228 R -3495) +(-228 R -3494) ((|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 (-229) ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}."))) -((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4199 . T) (-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-230) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -854,19 +854,19 @@ NIL NIL (-231 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}"))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4426 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-233 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."))) -((-4426 . T)) +((-4425 . T)) NIL (-234 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4422 . T)) +((-4421 . T)) NIL (-235 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -878,7 +878,7 @@ NIL NIL (-237 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-238 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -890,33 +890,33 @@ NIL NIL (-240) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4422 . T)) +((-4421 . T)) NIL (-241 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4425))) +((|HasAttribute| |#1| (QUOTE -4424))) (-242 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4426 . T)) +((-4425 . T)) NIL (-243) ((|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 -(-244 S -3020 R) +(-244 S -3019 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4422)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1122)))) -(-245 -3020 R) +((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-814))) (|HasCategory| |#3| (QUOTE (-860))) (|HasAttribute| |#3| (QUOTE -4421)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-745))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (QUOTE (-1121)))) +(-245 -3019 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4419 |has| |#2| (-1070)) (-4420 |has| |#2| (-1070)) (-4422 |has| |#2| (-6 -4422)) (-4425 . T)) +((-4418 |has| |#2| (-1069)) (-4419 |has| |#2| (-1069)) (-4421 |has| |#2| (-6 -4421)) (-4424 . T)) NIL -(-246 -3020 R) +(-246 -3019 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."))) -((-4419 |has| |#2| (-1070)) (-4420 |has| |#2| (-1070)) (-4422 |has| |#2| (-6 -4422)) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-815))) 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(QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) +(-247 -3019 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 @@ -930,7 +930,7 @@ NIL NIL (-250) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4418 . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-251 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -938,20 +938,20 @@ NIL NIL (-252 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}"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 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's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-254 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-255 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4426 "*") |has| |#2| (-175)) (-4417 |has| |#2| (-569)) (-4422 |has| |#2| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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(QUOTE (-876)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-261 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-240)))) (-262 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL (-263 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL (-264 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -1023,15 +1023,15 @@ NIL (-273 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-239)))) +((|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-239)))) (-274 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL (-275 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"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . 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T) (-4418 . T) (-4421 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1'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 -(-287 R -3495) +(-287 R -3494) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -3495) +(-288 R -3494) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1103,10 +1103,10 @@ NIL (-293 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122)))) +((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121)))) (-294 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4426 . T)) +((-4425 . T)) NIL (-295 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1127,18 +1127,18 @@ NIL (-299 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4426))) +((|HasAttribute| |#1| (QUOTE -4425))) (-300 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -2247 -3938 |exactQuo|) +(-301 S R |Mod| -2246 -3937 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-302) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4418 . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-303) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1150,16 +1150,16 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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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(-485))) (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197))))) (-3956 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-310))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485)))) (-3956 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-745)))) (-3956 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-745)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4425 . T) (-4426 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1167,16 +1167,16 @@ NIL (-309 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1070)))) +((|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1069)))) (-310) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -3495 S) +(-311 -3494 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 -(-312 E -3495) +(-312 E -3494) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\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 @@ -1206,7 +1206,7 @@ NIL NIL (-319) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-320 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' 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 -(-322 -3495) +(-322 -3494) ((|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 @@ -1230,12 +1230,12 @@ NIL NIL (-325 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) 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(|HasCategory| $ (|%list| (QUOTE -1058) (QUOTE (-558))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -3495) +(-329 R -3494) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1254,8 +1254,8 @@ NIL NIL (-331 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."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1266,8 +1266,8 @@ NIL NIL (-334 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-4420 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-814)))) +((-4419 . T) (-4418 . T)) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-558) (QUOTE (-813)))) (-335 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1275,26 +1275,26 @@ NIL (-336 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-791) (QUOTE (-814)))) +((|HasCategory| (-790) (QUOTE (-813)))) (-337 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) (-338 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-339 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."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -3495) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -3494) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -3495) +(-341 -3494) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-342) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -3495 UP UPUP R) +(-346 -3494 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}'s are integers and the \\spad{P}'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 @@ -1320,37 +1320,37 @@ 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 -(-348 S -3495 UP UPUP R) +(-348 S -3494 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}'s are integers and the \\spad{P}'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 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 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 -(-349 -3495 UP UPUP R) +(-349 -3494 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}'s are integers and the \\spad{P}'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 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 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL (-350 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) (-351 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-352 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#3| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1058) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (|%list| (QUOTE -1058) (QUOTE (-558))))) (-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}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) -(-354 S -3495 UP UPUP) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| (-924 |#1|) (QUOTE (-147))) (|HasCategory| (-924 |#1|) (QUOTE (-381)))) (|HasCategory| (-924 |#1|) (QUOTE (-149))) (|HasCategory| (-924 |#1|) (QUOTE (-381))) (|HasCategory| (-924 |#1|) (QUOTE (-147)))) +(-354 S -3494 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -3495 UP UPUP) +(-355 -3494 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 |has| (-419 |#2|) (-376)) (-4422 |has| (-419 |#2|) (-376)) (-4416 |has| (-419 |#2|) (-376)) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-356 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) @@ -1358,16 +1358,16 @@ NIL NIL (-357 |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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| (-924 |#1|) (QUOTE (-147))) (|HasCategory| (-924 |#1|) (QUOTE (-381)))) (|HasCategory| (-924 |#1|) (QUOTE (-149))) (|HasCategory| (-924 |#1|) (QUOTE (-381))) (|HasCategory| (-924 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(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 @@ -1382,51 +1382,51 @@ NIL NIL (-363) ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-364 R UP -3495) +(-364 R UP -3494) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| (-924 |#1|) (QUOTE (-147))) (|HasCategory| (-924 |#1|) (QUOTE (-381)))) (|HasCategory| (-924 |#1|) (QUOTE (-149))) (|HasCategory| (-924 |#1|) (QUOTE (-381))) (|HasCategory| (-924 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|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(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-370 -3495 GF) +(-370 -3494 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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 -(-371 -3495 FP FPP) +(-371 -3494 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 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{ls}."))) NIL NIL (-374 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4422 . T)) +((-4421 . T)) NIL (-375 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1434,7 +1434,7 @@ NIL NIL (-376) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-377 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1450,7 +1450,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-569)))) (-380 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) +((-4421 |has| |#1| (-569)) (-4419 . T) (-4418 . T)) NIL (-381) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1462,15 +1462,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376)))) (-383 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL (-384 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122)))) +((|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121)))) (-385 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4425 . T)) +((-4424 . T)) NIL (-386 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1478,7 +1478,7 @@ NIL NIL (-387 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4419 . T) (-4418 . T)) NIL (-388 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1487,14 +1487,14 @@ NIL (-389 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) +((|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558))))) (-390 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL NIL (-391) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4408 . T) (-4416 . T) (-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4407 . T) (-4415 . T) (-4199 . T) (-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1506,11 +1506,11 @@ NIL NIL (-394 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4420 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-4419 . T) (-4418 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-395 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) ((|HasCategory| |#1| (QUOTE (-175)))) (-396) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1518,7 +1518,7 @@ NIL NIL (-397 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-398) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) @@ -1531,10 +1531,10 @@ NIL (-400 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-861)))) +((|HasCategory| |#1| (QUOTE (-860)))) (-401) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-402) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1546,13 +1546,13 @@ NIL NIL (-404 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-405) ((|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 -(-406 -3495 UP UPUP R) +(-406 -3494 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 @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-410 -3970 |returnType| -1537 |symbols|) +(-410 -3969 |returnType| -1536 |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 -(-411 -3495 UP) +(-411 -3494 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1586,28 +1586,28 @@ NIL NIL (-414) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4416))) +((|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4415))) (-416) ((|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(\"+\") 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'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'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\"."))) -((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4199 . T) (-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-417 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1243))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1243)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1242))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1242)))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-418 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL (-419 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4412 -12 (|has| |#1| (-6 -4423)) (|has| |#1| (-464)) (|has| |#1| (-6 -4412))) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464)))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +((-4411 -12 (|has| |#1| (-6 -4422)) (|has| |#1| (-464)) (|has| |#1| (-6 -4411))) (-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4411)) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464)))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-420 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1618,28 +1618,28 @@ NIL NIL (-422 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL (-423 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558))))) +((|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558))))) (-424 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-425 R -3495 UP A) +(-425 R -3494 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4422 . T)) +((-4421 . T)) NIL (-426 R1 F1 U1 A1 R2 F2 U2 A2) ((|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 -(-427 R -3495 UP A |ibasis|) +(-427 R -3494 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -1059) (|devaluate| |#2|)))) +((|HasCategory| |#4| (|%list| (QUOTE -1058) (|devaluate| |#2|)))) (-428 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1650,7 +1650,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-430 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) +((-4421 |has| |#1| (-569)) (-4419 . T) (-4418 . T)) NIL (-431 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)}."))) @@ -1659,10 +1659,10 @@ NIL (-432 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) +((|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547))))) (-433 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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}."))) -((-4422 -3957 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) ((-4427 "*") |has| |#1| (-569)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-569)) (-4417 |has| |#1| (-569))) +((-4421 -3956 (|has| |#1| (-1069)) (|has| |#1| (-485))) (-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) ((-4426 "*") |has| |#1| (-569)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-569)) (-4416 |has| |#1| (-569))) NIL (-434 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1679,36 +1679,36 @@ NIL (-437 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-381)))) +((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-381)))) (-438 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4425 . T) (-4415 . T) (-4426 . T)) +((-4424 . T) (-4414 . T) (-4425 . T)) NIL (-439 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-440 R -3495) +(-440 R -3494) ((|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 (-441 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4412 -12 (|has| |#1| (-6 -4412)) (|has| |#2| (-6 -4412))) (-4419 . T) (-4420 . T) (-4422 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#2| (QUOTE -4412)))) -(-442 R -3495) +((-4411 -12 (|has| |#1| (-6 -4411)) (|has| |#2| (-6 -4411))) (-4418 . T) (-4419 . T) (-4421 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4411)) (|HasAttribute| |#2| (QUOTE -4411)))) +(-442 R -3494) ((|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 -(-443 R -3495) +(-443 R -3494) ((|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 -(-444 R -3495) +(-444 R -3494) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -3495) +(-445 R -3494) ((|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 @@ -1716,10 +1716,10 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-447 R -3495 UP) +(-447 R -3494 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 -1059) (QUOTE (-48))))) +((|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-48))))) (-448) ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL @@ -1748,7 +1748,7 @@ 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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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'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 -(-455 R UP -3495) +(-455 R UP -3494) ((|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 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'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'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's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri'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 @@ -1786,16 +1786,16 @@ NIL NIL (-464) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-465 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4422 |has| (-419 (-965 |#1|)) (-569)) (-4420 . T) (-4419 . T)) -((|HasCategory| (-419 (-965 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-965 |#1|)) (QUOTE (-569)))) +((-4421 |has| (-419 (-964 |#1|)) (-569)) (-4419 . T) (-4418 . T)) +((|HasCategory| (-419 (-964 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-964 |#1|)) (QUOTE (-569)))) (-466 |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"))) -(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4426 "*") |has| |#2| (-175)) (-4417 |has| |#2| (-569)) (-4422 |has| |#2| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4422)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-467 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's conditional."))) NIL @@ -1822,7 +1822,7 @@ NIL NIL (-473 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,8 +1830,8 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-476 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -3495 R) +(-483 |lv| -3494 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4422 . T)) +((-4421 . T)) NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . 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T)) -((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) +((-4425 . 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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)}"))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-489) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-490) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1894,29 +1894,29 @@ NIL NIL (-491 |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."))) -((-4425 . T) (-4426 . 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Hall as given in Serre's book Lie Groups -- 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. 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-496 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}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -3495 UP UPUP R) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -3494 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}'s are integers and the \\spad{P}'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 @@ -1926,12 +1926,12 @@ NIL NIL (-499) ((|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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-558) (QUOTE (-928))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1040))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860))) (-3956 (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860)))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1172))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1197)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -657) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (|HasCategory| (-558) (QUOTE (-147))))) (-500 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4425)) (|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) +((|HasAttribute| |#1| (QUOTE -4424)) (|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-501 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,34 +1952,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -3495 UP |AlExt| |AlPol|) +(-506 -3494 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (|%list| (QUOTE -1058) (QUOTE (-558))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-509 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'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."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 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 -(-511 R UP -3495) +(-511 R UP -3494) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the 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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-512 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-114) (QUOTE (-102)))) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| (-114) (QUOTE (-1121))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-860))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| (-114) (QUOTE (-1121))) (|HasCategory| (-114) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-114) (QUOTE (-102)))) (-513 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1992,10 +1992,10 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-516 -3495 |Expon| |VarSet| |DPoly|) +(-516 -3494 |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 -631) (QUOTE (-1198))))) +((|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-1197))))) (-517 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -2007,11 +2007,11 @@ NIL (-519 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-520 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-521 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL @@ -2019,15 +2019,15 @@ NIL (-522 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-523 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-524 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-525 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL @@ -2039,39 +2039,39 @@ NIL (-527 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-814)))) +((|HasCategory| |#2| (QUOTE (-813)))) (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{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}"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-529) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-530 |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}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((-3957 (|HasCategory| (-593 |#1|) (QUOTE (-147))) (|HasCategory| (-593 |#1|) (QUOTE (-381)))) (|HasCategory| (-593 |#1|) (QUOTE (-149))) (|HasCategory| (-593 |#1|) (QUOTE (-381))) (|HasCategory| (-593 |#1|) (QUOTE (-147)))) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((-3956 (|HasCategory| (-593 |#1|) (QUOTE (-147))) (|HasCategory| (-593 |#1|) (QUOTE (-381)))) (|HasCategory| (-593 |#1|) (QUOTE (-149))) (|HasCategory| (-593 |#1|) (QUOTE (-381))) (|HasCategory| (-593 |#1|) (QUOTE (-147)))) (-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 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."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-533 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,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4426))) +((|HasAttribute| |#3| (QUOTE -4425))) (-534 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4426))) +((|HasAttribute| |#7| (QUOTE -4425))) (-535 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."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4426 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|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 @@ -2103,8 +2103,8 @@ NIL (-543 |Varset|) ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-791) (QUOTE (-1122))))) -(-544 K -3495 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-790) (QUOTE (-1121))))) +(-544 K -3494 |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 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 @@ -2128,7 +2128,7 @@ 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 -(-550 K -3495 |Par|) +(-550 K -3494 |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 @@ -2158,11 +2158,11 @@ NIL NIL (-557) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4422 . T) (-4423 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-558) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4412 . T) (-4416 . T) (-4411 . T) (-4422 . T) (-4423 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-559) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2182,13 +2182,13 @@ NIL NIL (-563 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) -(-564 R -3495) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) +(-564 R -3494) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-565 R0 -3495 UP UPUP R) +(-565 R0 -3494 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2198,7 +2198,7 @@ NIL NIL (-567 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4200 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4199 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-568 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2206,9 +2206,9 @@ NIL NIL (-569) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-570 R -3495) +(-570 R -3494) ((|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|)) #1="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},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2220,19 +2220,19 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-573 R -3495 L) +(-573 R -3494 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| #1="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| #1#)) (|:| |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| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="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|)) #4#) |#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 -678) (|devaluate| |#2|)))) +((|HasCategory| |#3| (|%list| (QUOTE -677) (|devaluate| |#2|)))) (-574) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-575 -3495 UP UPUP R) +(-575 -3494 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-576 -3495 UP) +(-576 -3494 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 @@ -2240,15 +2240,15 @@ 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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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 -(-578 R -3495 L) +(-578 R -3494 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| #1="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| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -678) (|devaluate| |#2|)))) -(-579 R -3495) +((|HasCategory| |#3| (|%list| (QUOTE -677) (|devaluate| |#2|)))) +(-579 R -3494) ((|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 -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1160)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-647))))) -(-580 -3495 UP) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1159)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-646))))) +(-580 -3494 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,27 +2256,27 @@ 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 -(-582 -3495) +(-582 -3494) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-583 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."))) -((-4200 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4199 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-585 R -3495) +(-585 R -3494) ((|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| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) -(-586 -3495 UP) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-646))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) +(-586 -3494 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|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#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|)) #1#) |#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 -(-587 R -3495) +(-587 R -3494) ((|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 @@ -2298,25 +2298,25 @@ NIL NIL (-592 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL (-593 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) (-594) ((|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 -(-595 -3495) +(-595 -3494) ((|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 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}."))) -((-4420 . T) (-4419 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-1198))))) -(-596 E -3495) +((-4419 . T) (-4418 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-1197))))) +(-596 E -3494) ((|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 -(-597 R -3495) +(-597 R -3494) ((|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},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2348,2861 +2348,2857 @@ NIL ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) NIL NIL -(-605 |mn|) -((|constructor| (NIL "This domain implements low-level strings"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-3957 (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-146) (QUOTE (-861))) (-3957 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) -(-606 E V R P) +(-605 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL -(-607 |Coef|) +(-606 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|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 (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) -(-608 |Coef|) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|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 (-1132))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) +(-607 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4427 "*") |has| |#1| (-569)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-569)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) ((|HasCategory| |#1| (QUOTE (-569)))) -(-609) +(-608) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) NIL NIL -(-610 A B) +(-609 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-611 A B C) +(-610 A B C) ((|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 -(-612 R -3495 FG) +(-611 R -3494 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL -(-613 S) +(-612 S) ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) NIL NIL -(-614 R |mn|) +(-613 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-615 S |Index| |Entry|) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-614 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#3| (QUOTE (-1122)))) -(-616 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#2| (QUOTE (-860))) (|HasAttribute| |#1| (QUOTE -4424)) (|HasCategory| |#3| (QUOTE (-1121)))) +(-615 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL NIL -(-617) +(-616) ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) NIL NIL -(-618 R A) +(-617 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)."))) -((-4422 -3957 (-2961 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4420 . T) (-4419 . T)) -((-3957 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) -(-619) +((-4421 -3956 (-2960 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4419 . T) (-4418 . T)) +((-3956 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +(-618) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL NIL -(-620) +(-619) ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) 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(|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-624) +(-623) ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) NIL NIL -(-625 |Entry|) +(-624 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) -(-626 S |Key| |Entry|) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (QUOTE (-1179))) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-860))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-102)))) +(-625 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL -(-627 |Key| |Entry|) +(-626 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4426 . T)) +((-4425 . T)) NIL -(-628 S) +(-627 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) -(-629 R S) +((|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) +(-628 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-630 S) +(-629 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-631 S) +(-630 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-632 -3495 UP) +(-631 -3494 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-633 S) +(-632 S) ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-634) +(-633) ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) NIL NIL -(-635 S) +(-634 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-636 A R S) +(-635 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-860)))) -(-637 S R) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-859)))) +(-636 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-638 R) +(-637 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4422 . T)) +((-4421 . T)) NIL -(-639 R -3495) +(-638 R -3494) ((|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 -(-640 R UP) +(-639 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4418 . T) (-4422 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) -(-641 R E V P TS ST) +((-4419 . T) (-4418 . T) ((-4426 "*") . T) (-4417 . T) (-4421 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558))))) +(-640 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) NIL NIL -(-642 OV E Z P) +(-641 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-643) +(-642) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-644 |VarSet| R |Order|) +(-643 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4422 . T)) +((-4421 . T)) NIL -(-645 R |ls|) +(-644 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-646 R -3495) +(-645 R -3494) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-647) +(-646) ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-648 |lv| -3495) +(-647 |lv| -3494) ((|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 -(-649) +(-648) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1180) (QUOTE (-861))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) -(-650 R A) +((-4425 . 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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)."))) -((-4422 -3957 (-2961 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4420 . T) (-4419 . T)) -((-3957 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) -(-651 S R) +((-4421 -3956 (-2960 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4419 . T) (-4418 . T)) +((-3956 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +(-650 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{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) -(-652 R) +(-651 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4419 . T) (-4418 . T)) NIL -(-653 R FE) +(-652 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|) #1="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|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL NIL -(-654 R) +(-653 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-655 |vars|) +(-654 |vars|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) NIL NIL -(-656 S R) +(-655 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2959 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) -(-657 K B) +((-2958 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +(-656 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-4420 . T) (-4419 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-655 |#2|) (QUOTE (-1122))))) -(-658 R) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-654 |#2|) (QUOTE (-1121))))) +(-657 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL -(-659 K B) +(-658 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL -(-660 S) +(-659 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) NIL NIL -(-661 S) +(-660 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-662 A B) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-661 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL NIL -(-663 A B) +(-662 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-664 A B C) +(-663 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-665 T$) +(-664 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-666 S) +(-665 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-667 S) +(-666 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-668 R) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-667 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL NIL -(-669 S E |un|) +(-668 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-670 A S) +(-669 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{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{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4426))) -(-671 S) +((|HasAttribute| |#1| (QUOTE -4425))) +(-670 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-672 M R S) +(-671 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4420 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-812)))) -(-673 R -3495 L) +((-4419 . T) (-4418 . T)) +((|HasCategory| |#1| (QUOTE (-811)))) +(-672 R -3494 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 -(-674 A -2888) +(-673 A -2887) ((|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}}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) -(-675 A) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +(-674 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) -(-676 A M) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +(-675 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) -(-677 S A) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +(-676 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) -(-678 A) +(-677 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-679 -3495 UP) +(-678 -3494 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)))) -(-680 A L) +(-679 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-681 S) +(-680 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-682) +(-681) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-683 R) +(-682 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-684 |VarSet| R) +(-683 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4419 . T) (-4418 . T)) ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) -(-685 A S) +(-684 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) NIL NIL -(-686 S) +(-685 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-687 -3495 |Row| |Col| M) +(-686 -3494 |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| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |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| #1#)) (|:| |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 -(-688 -3495) +(-687 -3494) ((|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'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|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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 -(-689 R E OV P) +(-688 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-690 |n| R) +(-689 |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."))) -((-4422 . T) (-4425 . T) (-4419 . T) (-4420 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4427 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-3957 (|HasAttribute| |#2| (QUOTE (-4427 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) -(-691) +((-4421 . T) (-4424 . T) (-4418 . T) (-4419 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4426 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-3956 (|HasAttribute| |#2| (QUOTE (-4426 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197))))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +(-690) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-692 |VarSet|) +(-691 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-693 A S) +(-692 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-694 S) +(-693 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-695 R) +(-694 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 -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-696) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-695) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL NIL -(-697 |VarSet|) +(-696 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL NIL -(-698 A) +(-697 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-699 A C) +(-698 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) NIL NIL -(-700 A B C) +(-699 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) NIL NIL -(-701) +(-700) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-702 A) +(-701 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-703 A C) +(-702 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-704 A B C) +(-703 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) NIL NIL -(-705 S R |Row| |Col|) +(-704 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4427 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) -(-706 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4426 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) +(-705 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL -(-707 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-706 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-708 R |Row| |Col| M) +(-707 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that m*n = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569)))) -(-709 R) +(-708 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."))) -((-4425 . T) (-4426 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-710 R) +((-4424 . T) (-4425 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4426 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-709 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{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-711 T$) +(-710 T$) ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-712 S -3495 FLAF FLAS) +(-711 S -3494 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,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{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 -(-713 R Q) +(-712 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-714) +(-713) ((|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"))) -((-4418 . T) (-4423 |has| (-719) (-376)) (-4417 |has| (-719) (-376)) (-1490 . T) (-4424 |has| (-719) (-6 -4424)) (-4421 |has| (-719) (-6 -4421)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . 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As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4426 . T)) +((-4425 . T)) NIL -(-716 U) +(-715 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-717) +(-716) ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? 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|)) #1="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|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-718 OV E -3495 PG) +(-717 OV E -3494 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 -(-719) +(-718) ((|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}"))) -((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4199 . T) (-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-720 R) +(-719 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) NIL NIL -(-721) +(-720) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4424 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4423 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-722 S D1 D2 I) +(-721 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-723 S) +(-722 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-724 S) +(-723 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-725 S T$) +(-724 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-726 S -3070 I) +(-725 S -3069 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 -(-727 E OV R P) +(-726 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) NIL NIL -(-728 R) +(-727 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-729 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-728 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-730) +(-729) ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-731 R |Mod| -2247 -3938 |exactQuo|) +(-730 R |Mod| -2246 -3937 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-732 R |Rep|) +(-731 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-733 IS E |ff|) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4420 |has| |#1| (-376)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-732 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-734 R M) +(-733 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) +((-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) (-4421 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-735 R |Mod| -2247 -3938 |exactQuo|) +(-734 R |Mod| -2246 -3937 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4422 . T)) +((-4421 . T)) NIL -(-736 S R) +(-735 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-737 R) +(-736 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL -(-738 -3495) +(-737 -3494) ((|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]]}."))) -((-4422 . T)) +((-4421 . T)) NIL -(-739 S) +(-738 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-740) +(-739) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-741 S) +(-740 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-742) +(-741) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-743 S R UP) +(-742 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) -(-744 R UP) +(-743 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4418 |has| |#1| (-376)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 |has| |#1| (-376)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-745 S) +(-744 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-746) +(-745) ((|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 -(-747 -3495 UP) +(-746 -3494 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 -(-748 |VarSet| E1 E2 R S PR PS) +(-747 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented "))) NIL NIL -(-749 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-748 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-750 E OV R PPR) +(-749 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-751 |vl| R) +(-750 |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."))) -(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-752 E OV R PRF) +(((-4426 "*") |has| |#2| (-175)) (-4417 |has| |#2| (-569)) (-4422 |has| |#2| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-877 |#1|) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4422)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(-751 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-753 E OV R P) +(-752 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-754 R S M) +(-753 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-755 R M) +(-754 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-861)))) -(-756 S) +((-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) (-4421 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-860)))) +(-755 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4425 . T) (-4415 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-757 S) +((-4424 . T) (-4414 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-756 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4415 . T) (-4426 . T)) +((-4414 . T) (-4425 . T)) NIL -(-758) +(-757) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL NIL -(-759 S) +(-758 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-760 |Coef| |Var|) +(-759 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-761 OV E R P) +(-760 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-762 E OV R P) +(-761 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-763 S R) +(-762 S R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) NIL NIL -(-764 R) +(-763 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL -(-765) +(-764) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{\\spad{manpageXXc02}}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) NIL NIL -(-766) +(-765) ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{\\spad{manpageXXc05}}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,ldfjac,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,b,eps,eta,ifail,f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) NIL NIL -(-767) +(-766) ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{\\spad{manpageXXc06}}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,n,x,ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,n,x,ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,y,ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,x,ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,n,init,x,y,trigm,trign,ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,n,init,x,y,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,n,x,y,ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,x,y,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,x,ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,x,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) NIL NIL -(-768) +(-767) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{\\spad{manpageXXd01}}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,a,b,maxcls,eps,lenwrk,mincls,wrkstr,ifail,functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,y,n,ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,a,b,maxpts,eps,lenwrk,minpts,ifail,functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,b,itype,n,gtype,ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,omega,key,epsabs,limlst,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,b,c,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,b,alfa,beta,key,epsabs,epsrel,lw,liw,ifail,g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,b,omega,key,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,inf,epsabs,epsrel,lw,liw,ifail,f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,b,npts,points,epsabs,epsrel,lw,liw,ifail,f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) NIL NIL -(-769) +(-768) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{\\spad{manpageXXd02}}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,mnp,numbeg,nummix,tol,init,iy,ijac,lwork,liwork,np,x,y,deleps,ifail,fcn,g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,m,k,tol,maxfun,match,elam,delam,hmax,maxit,ifail,coeffn,bdyval,monit,report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,m,k,tol,maxfun,match,elam,delam,hmax,maxit,ifail,coeffn,bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains \\spad{Asp12} and \\spad{Asp33} are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,b,n,tol,mnp,lw,liw,c,d,gam,x,np,ifail,fcnf,fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,v,n,a,b,tol,mnp,lw,liw,x,np,ifail,fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,m,n,relabs,iw,x,y,tol,ifail,g,fcn,pederv,output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (BDF),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,m,n,tol,relabs,x,y,ifail,g,fcn,output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,n,irelab,hmax,x,y,tol,ifail,g,fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,m,n,irelab,x,y,tol,ifail,fcn,output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) NIL NIL -(-770) +(-769) ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{\\spad{manpageXXd03}}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,xf,l,lbdcnd,bdxs,bdxf,ys,yf,m,mbdcnd,bdys,bdyf,zs,zf,n,nbdcnd,bdzs,bdzf,lambda,ldimf,mdimf,lwrk,f,ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,xmax,ymin,ymax,ngx,ngy,lda,scheme,ifail,pdef,bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,ngy,lda,maxit,acc,iout,a,rhs,ub,ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) NIL NIL -(-771) +(-770) ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{\\spad{manpageXXe01}}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,x,y,f,rnw,fnodes,px,py,ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,x,y,f,nw,nq,rnw,rnq,ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,x,y,f,triang,grads,px,py,ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,x,y,f,ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,my,x,y,f,ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,x,f,d,a,b,ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,x,f,ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,x,y,lck,lwrk,ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) NIL NIL -(-772) +(-771) ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{\\spad{manpageXXe02}}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,py,lamda,mu,m,x,y,npoint,nadres,ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,la,nplus2,toler,a,b,ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,my,px,py,x,y,lamda,mu,c,lwrk,liwrk,ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,px,py,x,y,lamda,mu,c,ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,m,x,y,f,w,s,nxest,nyest,lwrk,liwrk,nx,lamda,ny,mu,wrk,ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,mx,x,my,y,f,s,nxest,nyest,lwrk,liwrk,nx,lamda,ny,mu,wrk,iwrk,ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,px,py,x,y,f,w,mu,point,npoint,nc,nws,eps,lamda,ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,m,x,y,w,s,nest,lwrk,n,lamda,ifail,wrk,iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,lamda,c,ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,lamda,c,x,left,ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,lamda,c,x,ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,ncap7,x,y,w,lamda,ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,xmin,xmax,a,ia1,la,x,ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,xmin,xmax,a,ia1,la,qatm1,iaint1,laint,ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,xmin,xmax,a,ia1,la,iadif1,ladif,ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,kplus1,nrows,xmin,xmax,x,y,w,mf,xf,yf,lyf,ip,lwrk,liwrk,ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,a,xcap,ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,kplus1,nrows,x,y,w,ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) NIL NIL -(-773) +(-772) ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{\\spad{manpageXXe04}}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,m,n,fsumsq,s,lv,v,ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,nclin,ncnln,nrowa,nrowj,nrowr,a,bl,bu,liwork,lwork,sta,cra,der,fea,fun,hes,infb,infs,linf,lint,list,maji,majp,mini,minp,mon,nonf,opt,ste,stao,stac,stoo,stoc,ve,istate,cjac,clamda,r,x,ifail,confun,objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,msglvl,n,nclin,nctotl,nrowa,nrowh,ncolh,bigbnd,a,bl,bu,cvec,featol,hess,cold,lpp,orthog,liwork,lwork,x,istate,ifail,qphess)} is a comprehensive programming (QP) or linear programming (LP) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,msglvl,n,nclin,nctotl,nrowa,a,bl,bu,cvec,linobj,liwork,lwork,x,ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,ibound,liw,lw,bl,bu,x,ifail,funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,n,liw,lw,x,ifail,lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,n,liw,lw,x,ifail,lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,es,fu,it,lin,list,ma,op,pr,sta,sto,ve,x,ifail,objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) NIL NIL -(-774) +(-773) ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{\\spad{manpageXXf01}}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,m,n,ncolq,lda,theta,a,ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,wheret,m,n,a,lda,theta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,n,lda,a,ifail)} finds the QR factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,m,n,ncolq,lda,zeta,a,ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,wheret,m,n,a,lda,zeta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,n,lda,a,ifail)} finds the QR factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,avals,lal,nrow,ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,nz,licn,lirn,abort,avals,irn,icn,droptl,densw,ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,nz,licn,ivect,jvect,icn,ikeep,grow,eta,abort,idisp,avals,ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,nz,licn,lirn,pivot,lblock,grow,abort,a,irn,icn,ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) NIL NIL -(-775) +(-774) ((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{\\spad{manpageXXf02}}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldph,a,b,ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldpt,a,b,ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image,monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,ia,ib,eps1,matv,iv,a,b,ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)Bx where A and \\spad{B} are real,{} square matrices,{} using the QZ algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,n,alb,ub,m,iv,a,ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,iar,ai,iai,n,ivr,ivi,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,iai,n,ivr,ivi,ar,ai,ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,n,ivr,ivi,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,n,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,ib,n,iv,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)Bx,{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,ib,n,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)Bx,{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,ia,n,iv,ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,n,a,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) NIL NIL -(-776) +(-775) ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{\\spad{manpageXXf04}}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,n,damp,atol,btol,conlim,itnlim,msglvl,lrwork,liwork,b,ifail,aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,al,lal,d,nrow,ir,b,nrb,iselct,nrx,ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,b,precon,shift,itnlim,msglvl,lrwork,liwork,rtol,ifail,aprod,msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,nz,avals,licn,irn,lirn,icn,wkeep,ikeep,inform,b,acc,noits,ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,n,nra,tol,lwork,a,b,ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,n,d,e,b,ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,a,licn,icn,ikeep,mtype,idisp,rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A x=b,{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,ia,b,n,iaa,ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,b,n,a,ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,b,n,a,ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,b,ib,n,m,ic,a,ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) NIL NIL -(-777) +(-776) ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{\\spad{manpageXXf07}}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,n,nrhs,a,lda,ldb,b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,n,lda,a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,n,nrhs,a,lda,ipiv,ldb,b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A X=B,{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,n,lda,a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) NIL NIL -(-778) +(-777) ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,y,z,r,ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,y,ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)+n} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)+n} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,fnu,z,n,scale,ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)+n\\space{8}(nu)+n} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,z,scale,ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,z,scale,ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)+n} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)+n} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,x,tol,ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,ifail)} returns a value for the log,{} ln(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) NIL NIL -(-779) +(-778) ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) NIL NIL -(-780 S) +(-779 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-781) +(-780) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-782 S) +(-781 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-783) +(-782) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-784 |Par|) +(-783 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-785 -3495) +(-784 -3494) ((|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 -(-786 P -3495) +(-785 P -3494) ((|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''."))) NIL NIL -(-787 T$) +(-786 T$) NIL NIL NIL -(-788 UP -3495) +(-787 UP -3494) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL -(-789) +(-788) ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-790 R) +(-789 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-791) +(-790) ((|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."))) -(((-4427 "*") . T)) +(((-4426 "*") . T)) NIL -(-792 R -3495) +(-791 R -3494) ((|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 -(-793) +(-792) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-794 S) +(-793 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-795 R |PolR| E |PolE|) +(-794 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-796 R E V P TS) +(-795 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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 -(-797 -3495 |ExtF| |SUEx| |ExtP| |n|) +(-796 -3494 |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 -(-798 BP E OV R P) +(-797 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-799 |Par|) +(-798 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) NIL NIL -(-800 R |VarSet|) +(-799 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198))))) (-3957 (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))) (-2959 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))) (-2959 (|HasCategory| |#1| (QUOTE (-557)))) (-2959 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))) (-2959 (|HasCategory| |#1| (|%list| (QUOTE -38) (QUOTE (-558))))) (-2959 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-1198)))) (-2959 (|HasCategory| |#1| (|%list| (QUOTE -1012) (QUOTE (-558))))))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-801 R) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|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)}"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . 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T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-801 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-803 R) +(-802 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) -(-804 R E V P) +(-803 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-805 S) +(-804 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-175)))) -(-806) +((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-175)))) +(-805) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL NIL -(-807) +(-806) ((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-808) +(-807) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-809) +(-808) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-810 |Curve|) +(-809 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-811 S) +(-810 S) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-812) +(-811) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-813 S) +(-812 S) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-814) +(-813) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-815) +(-814) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-816) +(-815) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-817 S R) +(-816 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-381)))) -(-818 R) +((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-381)))) +(-817 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-819) +(-818) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-820 R) +(-819 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-3957 (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) -(-821 -3957 R OS S) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-3956 (|HasCategory| (-1016 |#1|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-1016 |#1|) (|%list| (QUOTE -1058) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1016 |#1|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1016 |#1|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558))))) +(-820 -3956 R OS S) ((|constructor| (NIL "\\spad{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 -(-822) +(-821) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-823 R -3495 L) +(-822 R -3494 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-824 R -3495) +(-823 R -3494) ((|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| #1="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| #1#) (|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| #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| #2#) (|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 -(-825) +(-824) ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE'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 -(-826 R -3495) +(-825 R -3494) ((|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 -(-827) +(-826) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE'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'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'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'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'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'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'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's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-828 -3495 UP UPUP R) +(-827 -3494 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 -(-829 -3495 UP L LQ) +(-828 -3494 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 -(-830) +(-829) ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-831 -3495 UP L LQ) +(-830 -3494 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-832 -3495 UP) +(-831 -3494 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|) #1="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}'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|) #1#)) (|:| |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}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-833 -3495 L UP A LO) +(-832 -3494 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 -(-834 -3495 UP) +(-833 -3494 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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-835 -3495 LO) +(-834 -3494 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-839 (-1197)) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-839 (-1197)) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-839 (-1197)) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-839 (-1197)) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-839 (-1197)) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-838 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4427 "*") |has| |#2| (-376)) (-4418 |has| |#2| (-376)) (-4423 |has| |#2| (-376)) (-4417 |has| |#2| (-376)) (-4422 . T) (-4420 . T) (-4419 . T)) +(((-4426 "*") |has| |#2| (-376)) (-4417 |has| |#2| (-376)) (-4422 |has| |#2| (-376)) (-4416 |has| |#2| (-376)) (-4421 . T) (-4419 . T) (-4418 . T)) ((|HasCategory| |#2| (QUOTE (-376)))) -(-840 S) +(-839 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) NIL NIL -(-841 S) +(-840 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-861)))) -(-842) +((|HasCategory| |#1| (QUOTE (-860)))) +(-841) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-843 P R) +(-842 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) -(-844 S) +(-843 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4425 . T) (-4415 . T) (-4426 . T)) +((-4424 . T) (-4414 . T) (-4425 . T)) NIL -(-845 R) +(-844 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."))) -((-4422 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) -(-846 R S) +((-4421 |has| |#1| (-859))) +((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3956 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3956 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) +(-845 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-847 R) +(-846 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) +((-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) (-4421 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-848 A S) +(-847 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-849 S) +(-848 S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-850) +(-849) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-851) +(-850) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) NIL NIL -(-852) +(-851) ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-853) +(-852) ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,cons,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) NIL NIL -(-854) +(-853) ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-855 R) +(-854 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4422 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) -(-856 R S) +((-4421 |has| |#1| (-859))) +((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3956 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3956 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) +(-855 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-857) +(-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-858 -3020 S) +(-857 -3019 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-859) +(-858) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-860) +(-859) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-4422 . T)) +((-4421 . T)) NIL -(-861) +(-860) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-862 T$ |f|) +(-861 T$ |f|) ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) -(-863 S) +((|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) +(-862 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-864) +(-863) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-865 S R) +(-864 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) -(-866 R) +(-865 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-867 R C) +(-866 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\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{\\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{\\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{\\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 (-376))) (|HasCategory| |#1| (QUOTE (-569)))) -(-868 R |sigma| -3662) +(-867 R |sigma| -3661) ((|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."))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) -(-869 |x| R |sigma| -3662) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +(-868 |x| R |sigma| -3661) ((|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}."))) -((-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) -(-870 R) +((-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) +(-869 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) -(-871) +(-870) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-872) +(-871) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-873) +(-872) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-874 S) +(-873 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-875) +(-874) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-876) +(-875) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-877) +(-876) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-878 |VariableList|) +(-877 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-879) +(-878) ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) NIL NIL -(-880 R |vl| |wl| |wtlevel|) +(-879 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) +((-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) (-4421 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) -(-881 R PS UP) +(-880 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-882 R |x| |pt|) +(-881 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-883 |p|) +(-882 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-884 |p|) +(-883 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-885 |p|) +(-884 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-883 |#1|) (QUOTE (-929))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-149))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-883 |#1|) (QUOTE (-1041))) (|HasCategory| (-883 |#1|) (QUOTE (-842))) (|HasCategory| (-883 |#1|) (QUOTE (-861))) (-3957 (|HasCategory| (-883 |#1|) (QUOTE (-842))) (|HasCategory| (-883 |#1|) (QUOTE (-861)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (QUOTE (-1173))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (QUOTE (-239))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (QUOTE (-240))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -526) (QUOTE (-1198)) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -883) (|devaluate| |#1|)) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (QUOTE (-319))) (|HasCategory| (-883 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-929)))) (|HasCategory| (-883 |#1|) (QUOTE (-147))))) -(-886 |p| PADIC) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-882 |#1|) (QUOTE (-928))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-882 |#1|) (QUOTE (-147))) (|HasCategory| (-882 |#1|) (QUOTE (-149))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-882 |#1|) (QUOTE (-1040))) (|HasCategory| (-882 |#1|) (QUOTE (-841))) (|HasCategory| (-882 |#1|) (QUOTE (-860))) (-3956 (|HasCategory| (-882 |#1|) (QUOTE (-841))) (|HasCategory| (-882 |#1|) (QUOTE (-860)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-882 |#1|) (QUOTE (-1172))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| (-882 |#1|) (QUOTE (-239))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-882 |#1|) (QUOTE (-240))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -526) (QUOTE (-1197)) (|%list| (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -882) (|devaluate| |#1|)) (|%list| (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-319))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-882 |#1|) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-882 |#1|) (QUOTE (-928)))) (|HasCategory| (-882 |#1|) (QUOTE (-147))))) +(-885 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-887 S T$) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1040))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-860))) (-3956 (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-860)))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1172))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(-886 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))))) -(-888) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))))) +(-887) ((|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'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's lowest value."))) NIL NIL -(-889) +(-888) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-890) +(-889) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-891 CF1 CF2) +(-890 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-892 |ComponentFunction|) +(-891 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-893 CF1 CF2) +(-892 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-894 |ComponentFunction|) +(-893 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-895) +(-894) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-896 CF1 CF2) +(-895 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-897 |ComponentFunction|) +(-896 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-898) +(-897) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-899 R) +(-898 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-900 R S L) +(-899 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-901 S) +(-900 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-902 |Base| |Subject| |Pat|) +(-901 |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 (-2959 (|HasCategory| |#2| (QUOTE (-1070)))) (-2959 (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (-2959 (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198))))) -(-903 R S) +((-12 (-2958 (|HasCategory| |#2| (QUOTE (-1069)))) (-2958 (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197)))))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (-2958 (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197)))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197))))) +(-902 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don'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},{}\\spad{e1}),{}...,{}(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 -(-904 R A B) +(-903 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}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) NIL NIL -(-905 R) +(-904 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-906 R -3070) +(-905 R -3069) ((|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 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 -(-907 R S) +(-906 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-908 |VarSet|) +(-907 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-909 UP R) +(-908 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-910 A T$ S) +(-909 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-911 T$ S) +(-910 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-912) +(-911) ((|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 -(-913 UP -3495) +(-912 UP -3494) ((|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 -(-914) +(-913) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **"))) NIL NIL -(-915) +(-914) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-916 R S) +(-915 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL -(-917 S) +(-916 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4422 . T)) +((-4421 . T)) NIL -(-918 A S) +(-917 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-919 S) +(-918 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-920 S) +(-919 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-921 S) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-920 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4422 . T)) -((-3957 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-861)))) -(-922 |n| R) +((-4421 . T)) +((-3956 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-860)))) +(-921 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-923 S) +(-922 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4422 . T)) +((-4421 . T)) NIL -(-924 S) +(-923 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-925 |p|) +(-924 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) -(-926 R E |VarSet| S) +(-925 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-927 R S) +(-926 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-928 S) +(-927 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-147)))) -(-929) +(-928) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-930 R0 -3495 UP UPUP R) +(-929 R0 -3494 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 -(-931 UP UPUP R) +(-930 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-932 UP UPUP) +(-931 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-933 R) +(-932 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-934 R) +(-933 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-935 E OV R P) +(-934 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-936) +(-935) ((|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'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-937 -3495) +(-936 -3494) ((|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 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 -(-938) +(-937) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4427 "*") . T)) +(((-4426 "*") . T)) NIL -(-939 R) +(-938 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-940) +(-939) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-941 |xx| -3495) +(-940 |xx| -3494) ((|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 -(-942 -3495 P) +(-941 -3494 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-943 R |Var| |Expon| GR) +(-942 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-944) +(-943) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-945 S) +(-944 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-946) +(-945) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-947) +(-946) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-948) +(-947) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-949 R -3495) +(-948 R -3494) ((|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 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-950 S A B) +(-949 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-951 S R -3495) +(-950 S R -3494) ((|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 -(-952 I) +(-951 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-953 S E) +(-952 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-954 S R L) +(-953 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-955 S E V R P) +(-954 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -901) (|devaluate| |#1|)))) -(-956 -3070) +((|HasCategory| |#3| (|%list| (QUOTE -900) (|devaluate| |#1|)))) +(-955 -3069) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-957 R -3495 -3070) +(-956 R -3494 -3069) ((|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 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 -(-958 S R Q) +(-957 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-959 S) +(-958 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-960 S R P) +(-959 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-961) +(-960) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-962 R) +(-961 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4426 . T) (-4425 . 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T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-962 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-964 |TheField| |ThePols|) +(-963 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-860)))) -(-965 R) +((|HasCategory| |#1| (QUOTE (-859)))) +(-964 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}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . 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(|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-967 |x| R) +(-966 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-968 S R E |VarSet|) +(-967 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the 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 gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-929))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) -(-969 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-928))) (|HasAttribute| |#2| (QUOTE -4422)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547))))) +(-968 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the 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 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 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 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}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-970 E V R P -3495) +(-969 E V R P -3494) ((|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},{}...,{}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 -(-971 E |Vars| R P S) +(-970 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-972 E V R P -3495) +(-971 E V R P -3494) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) -(-973) +(-972) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-974) +(-973) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-975 R E) +(-974 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4423))) -(-976 R L) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4422))) +(-975 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-977 S) +(-976 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-978 A B) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-977 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL -(-979) +(-978) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-980 -3495) +(-979 -3494) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL -(-981 I) +(-980 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-982) +(-981) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-983 A B) +(-982 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"))) -((-4422 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) -(-984) +((-4421 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-860))))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#2| (QUOTE (-745))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#2| (QUOTE (-745))))) (-12 (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#2| (QUOTE (-745)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-860))))) +(-983) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-985 T$) +(-984 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-986 T$) +(-985 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-987 S T$) +(-986 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-988) +(-987) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-989 S) +(-988 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL -(-990 R |polR|) +(-989 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-464)))) -(-991) +(-990) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-992) +(-991) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-993 S |Coef| |Expon| |Var|) +(-992 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-994 |Coef| |Expon| |Var|) +(-993 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-995) +(-994) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-996 S R E |VarSet| P) +(-995 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL ((|HasCategory| |#2| (QUOTE (-569)))) -(-997 R E |VarSet| P) +(-996 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4425 . T)) +((-4424 . T)) NIL -(-998 R E V P) +(-997 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-464)))) -(-999 K) +(-998 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-1000 |VarSet| E RC P) +(-999 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-1001 R) +(-1000 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1002 R1 R2) +(-1001 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-1003 R) +(-1002 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-1004 K) +(-1003 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-1005 R E OV PPR) +(-1004 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1006 K R UP -3495) +(-1005 K R UP -3494) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1007 R |Var| |Expon| |Dpoly|) +(-1006 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319))))) -(-1008 |vl| |nv|) +(-1007 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-1009 R E V P TS) +(-1008 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1010) +(-1009) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-1011 A S) +(-1010 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1173)))) -(-1012 S) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1040))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1172)))) +(-1011 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1013 A B R S) +(-1012 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-1014 |n| K) +(-1013 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-1015) +(-1014) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-1016 S) +(-1015 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL -(-1017 R) +(-1016 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.}"))) -((-4418 |has| |#1| (-302)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557)))) -(-1018 S R) +((-4417 |has| |#1| (-302)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-557)))) +(-1017 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-302)))) -(-1019 R) +((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-302)))) +(-1018 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4418 |has| |#1| (-302)) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4417 |has| |#1| (-302)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1020 QR R QS S) +(-1019 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-1021 S) +(-1020 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1022 S) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1021 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1023) +(-1022) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1024 -3495 UP UPUP |radicnd| |n|) +(-1023 -3494 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3957 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) -(-1025 |bb|) +((-4417 |has| (-419 |#2|) (-376)) (-4422 |has| (-419 |#2|) (-376)) (-4416 |has| (-419 |#2|) (-376)) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3956 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197)))))) (-3956 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -918) (QUOTE (-1197)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -657) (QUOTE (-558)))) (-3956 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -918) (QUOTE (-1197))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -916) (QUOTE (-1197)))))) +(-1024 |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."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) -(-1026) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-558) (QUOTE (-928))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1040))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860))) (-3956 (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-860)))) (|HasCategory| (-558) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1172))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1197)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -657) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (-3956 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-928)))) (|HasCategory| (-558) (QUOTE (-147))))) +(-1025) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-1027) +(-1026) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-1028 RP) +(-1027 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-1029 S) +(-1028 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-1030 A S) +(-1029 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-1122)))) -(-1031 S) +((|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#2| (QUOTE (-1121)))) +(-1030 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1032 S) +(-1031 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-1033) +(-1032) ((|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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) -((-4418 . T) (-4423 . T) (-4417 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4422 . T)) +((-4417 . T) (-4422 . T) (-4416 . T) (-4419 . T) (-4418 . T) ((-4426 "*") . T) (-4421 . T)) NIL -(-1034 R -3495) +(-1033 R -3494) ((|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 -(-1035 R -3495) +(-1034 R -3494) ((|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 -(-1036 -3495 UP) +(-1035 -3494 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 -(-1037 -3495 UP) +(-1036 -3494 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 -(-1038 S) +(-1037 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1039 F1 UP UPUP R F2) +(-1038 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-1040) +(-1039) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-1041) +(-1040) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1042 |Pol|) +(-1041 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1043 |Pol|) +(-1042 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1044) +(-1043) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-1045 |TheField|) +(-1044 |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"))) -((-4418 . T) (-4423 . T) (-4417 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4422 . T)) -((-3957 (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (QUOTE (-558))))) -(-1046 -3495 L) +((-4417 . T) (-4422 . T) (-4416 . T) (-4419 . T) (-4418 . T) ((-4426 "*") . T) (-4421 . T)) +((-3956 (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1058) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1058) (QUOTE (-558))))) +(-1045 -3494 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-1047 S) +(-1046 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1122)))) -(-1048 R E V P) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1047 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1049) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1048) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-1050 R) +(-1049 R) ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4427 "*")))) -(-1051 R) +((|HasAttribute| |#1| (QUOTE (-4426 "*")))) +(-1050 R) ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319)))) -(-1052 S) +(-1051 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1053 S) +(-1052 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-1054 S) +(-1053 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1055 -3495 |Expon| |VarSet| |FPol| |LFPol|) +(-1054 -3494 |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"))) -(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1056) +(-1055) ((|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.}"))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1198))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-861))) (|HasCategory| (-51) (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) -(-1057) +((-4424 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (QUOTE (-1197))) (|%list| (QUOTE |:|) (QUOTE -2285) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-860))) (|HasCategory| (-51) (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102)))) +(-1056) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1058 A S) +(-1057 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1059 S) +(-1058 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1060 Q R) +(-1059 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1061 R) +(-1060 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1062) +(-1061) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1063 UP) +(-1062 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1064 R) +(-1063 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-1065 T$) +(-1064 T$) ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-1066 T$) +(-1065 T$) ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1067 R |ls|) +(-1066 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-1122))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -800) (|devaluate| |#1|) (|%list| (QUOTE -878) (|devaluate| |#2|)))))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-878 |#2|) (QUOTE (-381))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-102)))) -(-1068) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| (-799 |#1| (-877 |#2|)) (QUOTE (-1121))) (|HasCategory| (-799 |#1| (-877 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -799) (|devaluate| |#1|) (|%list| (QUOTE -877) (|devaluate| |#2|)))))) (|HasCategory| (-799 |#1| (-877 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-799 |#1| (-877 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-877 |#2|) (QUOTE (-381))) (|HasCategory| (-799 |#1| (-877 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-799 |#1| (-877 |#2|)) (QUOTE (-102)))) +(-1067) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1069 S) +(-1068 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-1070) +(-1069) ((|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."))) -((-4422 . T)) +((-4421 . T)) NIL -(-1071 |xx| -3495) +(-1070 |xx| -3494) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1072 S) +(-1071 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-1073 S |m| |n| R |Row| |Col|) +(-1072 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL ((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-569))) (|HasCategory| |#4| (QUOTE (-175)))) -(-1074 |m| |n| R |Row| |Col|) +(-1073 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4425 . T) (-4420 . T) (-4419 . T)) +((-4424 . T) (-4419 . T) (-4418 . T)) NIL -(-1075 |m| |n| R) +(-1074 |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}."))) -((-4425 . T) (-4420 . T) (-4419 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-877))))) -(-1076 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4424 . T) (-4419 . T) (-4418 . T)) +((|HasCategory| |#3| (QUOTE (-175))) (-3956 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -629) (QUOTE (-876))))) +(-1075 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-1077 R) +(-1076 R) ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) NIL NIL -(-1078) +(-1077) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-1079 S T$) +(-1078 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1122)))) -(-1080 S) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1079 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1081) +(-1080) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1082 |TheField| |ThePolDom|) +(-1081 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1083) +(-1082) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4412 . T) (-4416 . T) (-4411 . T) (-4422 . T) (-4423 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1084) +(-1083) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1198))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-861))) (|HasCategory| (-51) (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) -(-1085 S R E V) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (QUOTE (-1197))) (|%list| (QUOTE |:|) (QUOTE -2285) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1121))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-860))) (|HasCategory| (-51) (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1197)) (|:| -2285 (-51))) (QUOTE (-102)))) +(-1084 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| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1012) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-1198))))) -(-1086 R E V) +((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1011) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-1197))))) +(-1085 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-1087) +(-1086) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1088 S |TheField| |ThePols|) +(-1087 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1089 |TheField| |ThePols|) +(-1088 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1090 R E V P TS) +(-1089 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1091 S R E V P) +(-1090 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1092 R E V P) +(-1091 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1093 R E V P TS) +(-1092 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1094) +(-1093) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1095) +(-1094) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1096 |Base| R -3495) +(-1095 |Base| R -3494) ((|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},{}...,{}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 -(-1097 |f|) +(-1096 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1098 |Base| R -3495) +(-1097 |Base| R -3494) ((|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 -(-1099 R |ls|) +(-1098 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1100 R UP M) +(-1099 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."))) -((-4418 |has| |#1| (-376)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))))) -(-1101 UP SAE UPA) +((-4417 |has| |#1| (-376)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))))) +(-1100 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1102 UP SAE UPA) +(-1101 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1103) +(-1102) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1104) +(-1103) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1105 S) +(-1104 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1106) +(-1105) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1107 R) +(-1106 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1108 R) +(-1107 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"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-1109 S) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-1108 (-1197)) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-1108 (-1197)) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-1108 (-1197)) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-1108 (-1197)) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-1108 (-1197)) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-1108 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1110 S) +(-1109 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1122)))) -(-1111 R S) +((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-1121)))) +(-1110 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-860)))) -(-1112) +((|HasCategory| |#1| (QUOTE (-859)))) +(-1111) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1113 S) +(-1112 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1110 |#1|) (QUOTE (-1122)))) -(-1114 R S) +((|HasCategory| (-1109 |#1|) (QUOTE (-1121)))) +(-1113 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1115 S) +(-1114 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1116 S L) +(-1115 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1117) +(-1116) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1118 S) +(-1117 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) -((-4425 . T) (-4415 . T) (-4426 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-1119 A S) +((-4424 . T) (-4414 . T) (-4425 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-1118 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1120 S) +(-1119 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4415 . T)) +((-4414 . T)) NIL -(-1121 S) +(-1120 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1122) +(-1121) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1123 |m| |n|) +(-1122 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1124) +(-1123) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1125 |Str| |Sym| |Int| |Flt| |Expr|) +(-1124 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to 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 Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1126 |Str| |Sym| |Int| |Flt| |Expr|) +(-1125 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1127 R FS) +(-1126 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1128 R E V P TS) +(-1127 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1129 R E V P TS) +(-1128 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1130 R E V P) +(-1129 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1131) +(-1130) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1132 S) +(-1131 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1133) +(-1132) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1134 |dimtot| |dim1| S) +(-1133 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4419 |has| |#3| (-1070)) (-4420 |has| |#3| (-1070)) (-4422 |has| |#3| (-6 -4422)) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-815))) 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(QUOTE (-1121))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) +(-1134 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-464)))) -(-1136) +(-1135) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) NIL NIL -(-1137) +(-1136) ((|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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1138 R -3495) +(-1137 R -3494) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) |#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|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1139 R) +(-1138 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1140) +(-1139) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1141) +(-1140) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4412 . T) (-4416 . T) (-4411 . T) (-4422 . T) (-4423 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1142 S) +(-1141 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4425 . T) (-4426 . T)) +((-4424 . T) (-4425 . T)) NIL -(-1143 S |ndim| R |Row| |Col|) +(-1142 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4427 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) -(-1144 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4426 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) +(-1143 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) -((-4425 . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4424 . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1145 R |Row| |Col| M) +(-1144 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1146 R |VarSet|) +(-1145 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."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-1147 |Coef| |Var| SMP) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-928)))) (-3956 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-1146 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1148 R E V P) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) +(-1147 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}"))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1149 UP -3495) +(-1148 UP -3494) ((|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 -(-1150 R) +(-1149 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1151 R) +(-1150 R) ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1152 R) +(-1151 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1153 S A) +(-1152 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-861)))) -(-1154 R) +((|HasCategory| |#1| (QUOTE (-860)))) +(-1153 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1155 R) +(-1154 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1156) +(-1155) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1157) +(-1156) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1158) +(-1157) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) NIL NIL -(-1159) +(-1158) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1160) +(-1159) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1161 V C) +(-1160 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1162 V C) +(-1161 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122))) (-3957 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) -(-1163 |ndim| R) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-1160 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1121))) (-3956 (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| (-1160 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1160 |#1| |#2|) (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| (-1160 |#1| |#2|) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-102)))) +(-1162 |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}."))) -((-4422 . T) (-4414 |has| |#2| (-6 (-4427 "*"))) (-4425 . T) (-4419 . T) (-4420 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4427 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-376))) (-3957 (|HasAttribute| |#2| (QUOTE (-4427 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) -(-1164 S) +((-4421 . T) (-4413 |has| |#2| (-6 (-4426 "*"))) (-4424 . T) (-4418 . T) (-4419 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4426 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-376))) (-3956 (|HasAttribute| |#2| (QUOTE (-4426 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197))))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +(-1163 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1165) +(-1164) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1166 R E V P TS) +(-1165 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1167 R E V P) +(-1166 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1168) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1167) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) NIL NIL -(-1169 S) +(-1168 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}."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1170 A S) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1169 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}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1171 S) +(-1170 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}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1172 |Key| |Ent| |dent|) +(-1171 |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."))) -((-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) -(-1173) +((-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) +(-1172) ((|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 non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1174) +(-1173) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1175 |Coef|) +(-1174 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1176 S) +(-1175 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4426 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1177 S) +((-4425 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1176 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1178 A B) +(-1177 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1179 A B C) +(-1178 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1180) -((|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-3957 (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-146) (QUOTE (-861))) (-3957 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) -(-1181 |Entry|) +(-1179) +((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| (-146) (QUOTE (-860))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-3956 (-12 (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| (-146) (QUOTE (-860))) (|HasCategory| (-146) (QUOTE (-1121)))) (|HasCategory| (-146) (QUOTE (-860))) (-3956 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-860))) (|HasCategory| (-146) (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1121))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +(-1180 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) -(-1182 A) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (QUOTE (-1179))) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 (-1179)) (|:| -2285 |#1|)) (QUOTE (-102)))) +(-1181 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) -(-1183 |Coef|) +(-1182 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1184 |Coef|) +(-1183 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1185 R UP) +(-1184 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-319)))) -(-1186 |n| R) +(-1185 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1194 E OV R P) +(-1193 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL -(-1195 |Coef| |var| |cen|) +(-1194 |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."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) -(-1196 |Coef| |var| |cen|) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1195 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) -(-1197) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-790)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-790)) (|devaluate| |#1|)))) (|HasCategory| (-790) (QUOTE (-1132))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-790))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-790))))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1196) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL NIL -(-1198) +(-1197) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1199 R) +(-1198 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1200 R) +(-1199 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4419 . T) (-4420 . T) (-4422 . 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T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3956 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-991) (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4422))) +(-1200) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1202) +(-1201) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1203) +(-1202) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1204 N) +(-1203 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1205 N) +(-1204 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) NIL NIL -(-1206) +(-1205) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1207 R) +(-1206 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1208) +(-1207) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1209 S) +(-1208 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1210 |Key| |Entry|) +(-1209 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4425 . T) (-4426 . T)) -((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) -(-1211 S) +((-4424 . T) (-4425 . T)) +((-12 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4289) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2285) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -630) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1121))) (-3956 (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876))))) (-3956 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4289 |#1|) (|:| -2285 |#2|)) (QUOTE (-102)))) +(-1210 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1212 S) +(-1211 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1213 R) +(-1212 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1214 S |Key| |Entry|) +(-1213 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1215 |Key| |Entry|) +(-1214 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4426 . T)) +((-4425 . T)) NIL -(-1216 |Key| |Entry|) +(-1215 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1217) +(-1216) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1218) +(-1217) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1219 S) +(-1218 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1220) +(-1219) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1221 R) +(-1220 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1222) +(-1221) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1223 S) +(-1222 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1224) +(-1223) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1225 S) +(-1224 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1226 S) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1225 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1227) +(-1226) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1228 R -3495) +(-1227 R -3494) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-1229 R |Row| |Col| M) +(-1228 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1230 R -3495) +(-1229 R -3494) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (|devaluate| |#1|))))) -(-1231 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -900) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -900) (|devaluate| |#1|))))) +(-1230 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1232 S R E V P) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) +(-1231 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-381)))) -(-1233 R E V P) +(-1232 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1234 |Curve|) +(-1233 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1235) +(-1234) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1236 S) +(-1235 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) -(-1237 -3495) +((|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) +(-1236 -3494) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL -(-1238) +(-1237) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1239) +(-1238) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1240 S) +(-1239 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) NIL -((|HasCategory| |#1| (QUOTE (-861)))) -(-1241) +((|HasCategory| |#1| (QUOTE (-860)))) +(-1240) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1242 S) +(-1241 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 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T) (-4421 . T)) NIL -(-1244) +(-1243) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1245) +(-1244) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1246) +(-1245) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1247) +(-1246) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 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A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) -(-1252 |Coef| UTS) +(-1251 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) 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(((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL -((|HasCategory| |#1| (QUOTE (-860)))) -(-1257 |x| R) +((|HasCategory| |#1| (QUOTE (-859)))) +(-1256 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4421 |has| |#2| (-376)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-1258 |x| R |y| S) +(((-4426 "*") |has| |#2| (-175)) (-4417 |has| |#2| (-569)) (-4420 |has| |#2| (-376)) (-4422 |has| |#2| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-391)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -900) (QUOTE (-558)))) (|HasCategory| (-1102) (|%list| (QUOTE -900) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558))))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (|%list| (QUOTE -904) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| (-1102) (|%list| (QUOTE -630) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -657) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (QUOTE (-558)))) (-3956 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3956 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-928)))) (-3956 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1172))) (|HasCategory| |#2| (|%list| (QUOTE -918) (QUOTE (-1197)))) (|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4422)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (-3956 (-12 (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(-1257 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1259 R Q UP) +(-1258 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1260 R UP) +(-1259 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1261 R UP) +(-1260 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1262 R U) +(-1261 R U) ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) NIL NIL -(-1263 S R) +(-1262 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1173)))) -(-1264 R) +((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1172)))) +(-1263 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4420 |has| |#1| (-376)) (-4422 |has| |#1| (-6 -4422)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-1265 R PR S PS) +(-1264 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1266 S |Coef| |Expon|) +(-1265 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#2|) (QUOTE (-1198)))))) -(-1267 |Coef| |Expon|) +((|HasCategory| |#2| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#2|) (QUOTE (-1197)))))) +(-1266 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1268 RC P) +(-1267 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1269 |Coef| |var| |cen|) +(-1268 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) -(-1270 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1269 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1271 |Coef|) +(-1270 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1272 S |Coef| ULS) +(-1271 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1273 |Coef| ULS) +(-1272 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1274 |Coef| ULS) +(-1273 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) -(-1275 R FE |var| |cen|) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4422 |has| |#1| (-376)) (-4416 |has| |#1| (-376)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3956 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) +(-1274 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((-4427 "*") |has| (-1269 |#2| |#3| |#4|) (-175)) (-4418 |has| (-1269 |#2| |#3| |#4|) (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-175))) (-3957 (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-569)))) -(-1276 A S) +(((-4426 "*") |has| (-1268 |#2| |#3| |#4|) (-175)) (-4417 |has| (-1268 |#2| |#3| |#4|) (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| (-1268 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-175))) (-3956 (|HasCategory| (-1268 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (|%list| (QUOTE -1058) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (|%list| (QUOTE -1058) (QUOTE (-558)))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-569)))) +(-1275 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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4426))) -(-1277 S) +((|HasAttribute| |#1| (QUOTE -4425))) +(-1276 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1278 |Coef| |var| |cen|) +(-1277 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) -(-1279 |Coef1| |Coef2| UTS1 UTS2) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3956 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -916) (QUOTE (-1197)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-790)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-790)) (|devaluate| |#1|)))) (|HasCategory| (-790) (QUOTE (-1132))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-790))))) (|HasSignature| |#1| (|%list| (QUOTE -4375) (|%list| (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-790))))) (|HasCategory| |#1| (QUOTE (-376))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1278 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1280 S |Coef|) +(-1279 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 (-979))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasSignature| |#2| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) -(-1281 |Coef|) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (|%list| (QUOTE -3483) (|%list| (|%list| (QUOTE -660) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4241) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) +(-1280 |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."))) -(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") |has| |#1| (-175)) (-4417 |has| |#1| (-569)) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1282 |Coef| UTS) +(-1281 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1283 -3495 UP L UTS) +(-1282 -3494 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-569)))) -(-1284) +(-1283) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1285 |sym|) +(-1284 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1286 S R) +(-1285 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1287 R) +((|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-745))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1286 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4426 . T) (-4425 . T)) +((-4425 . T) (-4424 . T)) NIL -(-1288 R) +(-1287 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4426 . T) (-4425 . T)) -((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-1289 A B) +((-4425 . T) (-4424 . T)) +((-3956 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3956 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-547)))) (-3956 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-860))) (-3956 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-558) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-745))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-1288 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1290) +(-1289) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1291) +(-1290) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1292) +(-1291) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1293) +(-1292) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1294) +(-1293) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1295 A S) +(-1294 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1296 S) +(-1295 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4420 . T) (-4419 . T)) +((-4419 . T) (-4418 . T)) NIL -(-1297 R) +(-1296 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*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 -(-1298 K R UP -3495) +(-1297 K R UP -3494) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1299) +(-1298) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1300) +(-1299) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1301 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1300 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) +((-4419 |has| |#1| (-175)) (-4418 |has| |#1| (-175)) (-4421 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1302 R E V P) +(-1301 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-4426 . T) (-4425 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1303 R) +((-4425 . T) (-4424 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -629) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1302 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) -((-4419 . T) (-4420 . T) (-4422 . T)) +((-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1304 |vl| R) +(-1303 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4422 . T) (-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4418))) -(-1305 R |VarSet| XPOLY) +((-4421 . T) (-4417 |has| |#2| (-6 -4417)) (-4419 . T) (-4418 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4417))) +(-1304 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1306 S -3495) +(-1305 S -3494) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1307 -3495) +(-1306 -3494) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +((-4416 . T) (-4422 . T) (-4417 . T) ((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL -(-1308 |vl| R) +(-1307 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) +((-4417 |has| |#2| (-6 -4417)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-1309 |VarSet| R) +(-1308 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -737) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4418))) -(-1310 R) +((-4417 |has| |#2| (-6 -4417)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -736) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4417))) +(-1309 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4418 |has| |#1| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4418))) -(-1311 |vl| R) +((-4417 |has| |#1| (-6 -4417)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4417))) +(-1310 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) +((-4417 |has| |#2| (-6 -4417)) (-4419 . T) (-4418 . T) (-4421 . T)) NIL -(-1312 R E) +(-1311 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4422 . T) (-4423 |has| |#1| (-6 -4423)) (-4418 |has| |#1| (-6 -4418)) (-4420 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasAttribute| |#1| (QUOTE -4423)) (|HasAttribute| |#1| (QUOTE -4418))) -(-1313 |VarSet| R) +((-4421 . T) (-4422 |has| |#1| (-6 -4422)) (-4417 |has| |#1| (-6 -4417)) (-4419 . T) (-4418 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4421)) (|HasAttribute| |#1| (QUOTE -4422)) (|HasAttribute| |#1| (QUOTE -4417))) +(-1312 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4418))) -(-1314) +((-4417 |has| |#2| (-6 -4417)) (-4419 . T) (-4418 . T) (-4421 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4417))) +(-1313) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1315 A) +(-1314 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1316 R |ls| |ls2|) +(-1315 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}. ") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1317 R) +(-1316 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1318 |p|) +(-1317 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) +(((-4426 "*") . T) (-4418 . T) (-4419 . T) (-4421 . T)) NIL NIL NIL @@ -5220,4 +5216,4 @@ NIL NIL NIL NIL -((-3 NIL 2276986 2276991 2276996 2277001) (-2 NIL 2276966 2276971 2276976 2276981) (-1 NIL 2276946 2276951 2276956 2276961) (0 NIL 2276926 2276931 2276936 2276941) (-1318 "ZMOD.spad" 2276735 2276748 2276864 2276921) (-1317 "ZLINDEP.spad" 2275833 2275844 2276725 2276730) (-1316 "ZDSOLVE.spad" 2265793 2265815 2275823 2275828) (-1315 "YSTREAM.spad" 2265288 2265299 2265783 2265788) (-1314 "YDIAGRAM.spad" 2264922 2264931 2265278 2265283) (-1313 "XRPOLY.spad" 2264142 2264162 2264778 2264847) (-1312 "XPR.spad" 2261937 2261950 2263860 2263959) (-1311 "XPOLYC.spad" 2261256 2261272 2261863 2261932) (-1310 "XPOLY.spad" 2260811 2260822 2261112 2261181) (-1309 "XPBWPOLY.spad" 2259250 2259270 2260585 2260654) (-1308 "XFALG.spad" 2256298 2256314 2259176 2259245) (-1307 "XF.spad" 2254761 2254776 2256200 2256293) (-1306 "XF.spad" 2253204 2253221 2254645 2254650) (-1305 "XEXPPKG.spad" 2252463 2252489 2253194 2253199) (-1304 "XDPOLY.spad" 2252077 2252093 2252319 2252388) (-1303 "XALG.spad" 2251745 2251756 2252033 2252072) (-1302 "WUTSET.spad" 2247715 2247732 2251346 2251373) (-1301 "WP.spad" 2246922 2246966 2247573 2247640) (-1300 "WHILEAST.spad" 2246720 2246729 2246912 2246917) (-1299 "WHEREAST.spad" 2246391 2246400 2246710 2246715) (-1298 "WFFINTBS.spad" 2244054 2244076 2246381 2246386) (-1297 "WEIER.spad" 2242276 2242287 2244044 2244049) (-1296 "VSPACE.spad" 2241949 2241960 2242244 2242271) (-1295 "VSPACE.spad" 2241642 2241655 2241939 2241944) (-1294 "VOID.spad" 2241319 2241328 2241632 2241637) (-1293 "VIEWDEF.spad" 2236520 2236529 2241309 2241314) (-1292 "VIEW3D.spad" 2220481 2220490 2236510 2236515) (-1291 "VIEW2D.spad" 2208380 2208389 2220471 2220476) (-1290 "VIEW.spad" 2206100 2206109 2208370 2208375) (-1289 "VECTOR2.spad" 2204739 2204752 2206090 2206095) (-1288 "VECTOR.spad" 2203239 2203250 2203490 2203517) (-1287 "VECTCAT.spad" 2201151 2201162 2203207 2203234) (-1286 "VECTCAT.spad" 2198870 2198883 2200928 2200933) (-1285 "VARIABLE.spad" 2198650 2198665 2198860 2198865) (-1284 "UTYPE.spad" 2198294 2198303 2198640 2198645) (-1283 "UTSODETL.spad" 2197589 2197613 2198250 2198255) (-1282 "UTSODE.spad" 2195805 2195825 2197579 2197584) (-1281 "UTSCAT.spad" 2193284 2193300 2195703 2195800) (-1280 "UTSCAT.spad" 2190383 2190401 2192804 2192809) (-1279 "UTS2.spad" 2189978 2190013 2190373 2190378) (-1278 "UTS.spad" 2184856 2184884 2188376 2188473) (-1277 "URAGG.spad" 2179577 2179588 2184846 2184851) (-1276 "URAGG.spad" 2174262 2174275 2179533 2179538) (-1275 "UPXSSING.spad" 2171880 2171906 2173316 2173449) (-1274 "UPXSCONS.spad" 2169558 2169578 2169931 2170080) (-1273 "UPXSCCA.spad" 2168129 2168149 2169404 2169553) (-1272 "UPXSCCA.spad" 2166842 2166864 2168119 2168124) (-1271 "UPXSCAT.spad" 2165431 2165447 2166688 2166837) (-1270 "UPXS2.spad" 2164974 2165027 2165421 2165426) (-1269 "UPXS.spad" 2162189 2162217 2163025 2163174) (-1268 "UPSQFREE.spad" 2160604 2160618 2162179 2162184) (-1267 "UPSCAT.spad" 2158399 2158423 2160502 2160599) (-1266 "UPSCAT.spad" 2155879 2155905 2157984 2157989) (-1265 "UPOLYC2.spad" 2155350 2155369 2155869 2155874) (-1264 "UPOLYC.spad" 2150430 2150441 2155192 2155345) (-1263 "UPOLYC.spad" 2145396 2145409 2150160 2150165) (-1262 "UPMP.spad" 2144328 2144341 2145386 2145391) (-1261 "UPDIVP.spad" 2143893 2143907 2144318 2144323) (-1260 "UPDECOMP.spad" 2142154 2142168 2143883 2143888) (-1259 "UPCDEN.spad" 2141371 2141387 2142144 2142149) (-1258 "UP2.spad" 2140735 2140756 2141361 2141366) (-1257 "UP.spad" 2137763 2137778 2138150 2138303) (-1256 "UNISEG2.spad" 2137260 2137273 2137719 2137724) (-1255 "UNISEG.spad" 2136613 2136624 2137179 2137184) (-1254 "UNIFACT.spad" 2135716 2135728 2136603 2136608) (-1253 "ULSCONS.spad" 2126628 2126648 2126998 2127147) (-1252 "ULSCCAT.spad" 2124365 2124385 2126474 2126623) (-1251 "ULSCCAT.spad" 2122210 2122232 2124321 2124326) (-1250 "ULSCAT.spad" 2120450 2120466 2122056 2122205) (-1249 "ULS2.spad" 2119964 2120017 2120440 2120445) (-1248 "ULS.spad" 2109535 2109563 2110480 2110909) (-1247 "UINT8.spad" 2109412 2109421 2109525 2109530) (-1246 "UINT64.spad" 2109288 2109297 2109402 2109407) (-1245 "UINT32.spad" 2109164 2109173 2109278 2109283) (-1244 "UINT16.spad" 2109040 2109049 2109154 2109159) (-1243 "UFD.spad" 2108105 2108114 2108966 2109035) (-1242 "UFD.spad" 2107232 2107243 2108095 2108100) (-1241 "UDVO.spad" 2106113 2106122 2107222 2107227) (-1240 "UDPO.spad" 2103694 2103705 2106069 2106074) (-1239 "TYPEAST.spad" 2103613 2103622 2103684 2103689) (-1238 "TYPE.spad" 2103545 2103554 2103603 2103608) (-1237 "TWOFACT.spad" 2102197 2102212 2103535 2103540) (-1236 "TUPLE.spad" 2101688 2101699 2102093 2102098) (-1235 "TUBETOOL.spad" 2098555 2098564 2101678 2101683) (-1234 "TUBE.spad" 2097202 2097219 2098545 2098550) (-1233 "TSETCAT.spad" 2085273 2085290 2097170 2097197) (-1232 "TSETCAT.spad" 2073330 2073349 2085229 2085234) (-1231 "TS.spad" 2071923 2071939 2072889 2072986) (-1230 "TRMANIP.spad" 2066287 2066304 2071611 2071616) (-1229 "TRIMAT.spad" 2065250 2065275 2066277 2066282) (-1228 "TRIGMNIP.spad" 2063777 2063794 2065240 2065245) (-1227 "TRIGCAT.spad" 2063289 2063298 2063767 2063772) (-1226 "TRIGCAT.spad" 2062799 2062810 2063279 2063284) (-1225 "TREE.spad" 2061245 2061256 2062277 2062304) (-1224 "TRANFUN.spad" 2061084 2061093 2061235 2061240) (-1223 "TRANFUN.spad" 2060921 2060932 2061074 2061079) (-1222 "TOPSP.spad" 2060595 2060604 2060911 2060916) (-1221 "TOOLSIGN.spad" 2060258 2060269 2060585 2060590) (-1220 "TEXTFILE.spad" 2058819 2058828 2060248 2060253) (-1219 "TEX1.spad" 2058375 2058386 2058809 2058814) (-1218 "TEX.spad" 2055569 2055578 2058365 2058370) (-1217 "TEMUTL.spad" 2055124 2055133 2055559 2055564) (-1216 "TBCMPPK.spad" 2053225 2053248 2055114 2055119) (-1215 "TBAGG.spad" 2052283 2052306 2053205 2053220) (-1214 "TBAGG.spad" 2051349 2051374 2052273 2052278) (-1213 "TANEXP.spad" 2050757 2050768 2051339 2051344) (-1212 "TALGOP.spad" 2050481 2050492 2050747 2050752) (-1211 "TABLEAU.spad" 2049962 2049973 2050471 2050476) (-1210 "TABLE.spad" 2047895 2047918 2048165 2048192) (-1209 "TABLBUMP.spad" 2044674 2044685 2047885 2047890) (-1208 "SYSTEM.spad" 2043902 2043911 2044664 2044669) (-1207 "SYSSOLP.spad" 2041385 2041396 2043892 2043897) (-1206 "SYSPTR.spad" 2041284 2041293 2041375 2041380) (-1205 "SYSNNI.spad" 2040507 2040518 2041274 2041279) (-1204 "SYSINT.spad" 2039911 2039922 2040497 2040502) (-1203 "SYNTAX.spad" 2036245 2036254 2039901 2039906) (-1202 "SYMTAB.spad" 2034313 2034322 2036235 2036240) (-1201 "SYMS.spad" 2030342 2030351 2034303 2034308) (-1200 "SYMPOLY.spad" 2029322 2029333 2029404 2029531) (-1199 "SYMFUNC.spad" 2028823 2028834 2029312 2029317) (-1198 "SYMBOL.spad" 2026318 2026327 2028813 2028818) (-1197 "SWITCH.spad" 2023089 2023098 2026308 2026313) (-1196 "SUTS.spad" 2020068 2020096 2021487 2021584) (-1195 "SUPXS.spad" 2017270 2017298 2018119 2018268) (-1194 "SUPFRACF.spad" 2016375 2016393 2017260 2017265) (-1193 "SUP2.spad" 2015767 2015780 2016365 2016370) (-1192 "SUP.spad" 2012409 2012420 2013182 2013335) (-1191 "SUMRF.spad" 2011383 2011394 2012399 2012404) (-1190 "SUMFS.spad" 2011012 2011029 2011373 2011378) (-1189 "SULS.spad" 2000570 2000598 2001528 2001957) (-1188 "SUCHTAST.spad" 2000339 2000348 2000560 2000565) (-1187 "SUCH.spad" 2000029 2000044 2000329 2000334) (-1186 "SUBSPACE.spad" 1992160 1992175 2000019 2000024) (-1185 "SUBRESP.spad" 1991330 1991344 1992116 1992121) (-1184 "STTFNC.spad" 1987798 1987814 1991320 1991325) (-1183 "STTF.spad" 1983897 1983913 1987788 1987793) (-1182 "STTAYLOR.spad" 1976542 1976553 1983772 1983777) (-1181 "STRTBL.spad" 1974557 1974574 1974706 1974733) (-1180 "STRING.spad" 1973224 1973233 1973544 1973571) (-1179 "STREAM3.spad" 1972797 1972812 1973214 1973219) (-1178 "STREAM2.spad" 1971925 1971938 1972787 1972792) (-1177 "STREAM1.spad" 1971631 1971642 1971915 1971920) (-1176 "STREAM.spad" 1968417 1968428 1971024 1971039) (-1175 "STINPROD.spad" 1967353 1967369 1968407 1968412) (-1174 "STEPAST.spad" 1966587 1966596 1967343 1967348) (-1173 "STEP.spad" 1965904 1965913 1966577 1966582) (-1172 "STBL.spad" 1963952 1963980 1964119 1964134) (-1171 "STAGG.spad" 1962651 1962662 1963942 1963947) (-1170 "STAGG.spad" 1961348 1961361 1962641 1962646) (-1169 "STACK.spad" 1960576 1960587 1960826 1960853) (-1168 "SRING.spad" 1960336 1960345 1960566 1960571) (-1167 "SREGSET.spad" 1958035 1958052 1959937 1959964) (-1166 "SRDCMPK.spad" 1956612 1956632 1958025 1958030) (-1165 "SRAGG.spad" 1951795 1951804 1956580 1956607) (-1164 "SRAGG.spad" 1946998 1947009 1951785 1951790) (-1163 "SQMATRIX.spad" 1944490 1944508 1945406 1945493) (-1162 "SPLTREE.spad" 1938956 1938969 1943752 1943779) (-1161 "SPLNODE.spad" 1935576 1935589 1938946 1938951) (-1160 "SPFCAT.spad" 1934385 1934394 1935566 1935571) (-1159 "SPECOUT.spad" 1932937 1932946 1934375 1934380) (-1158 "SPADXPT.spad" 1925028 1925037 1932927 1932932) (-1157 "spad-parser.spad" 1924493 1924502 1925018 1925023) (-1156 "SPADAST.spad" 1924194 1924203 1924483 1924488) (-1155 "SPACEC.spad" 1908409 1908420 1924184 1924189) (-1154 "SPACE3.spad" 1908185 1908196 1908399 1908404) (-1153 "SORTPAK.spad" 1907734 1907747 1908141 1908146) (-1152 "SOLVETRA.spad" 1905497 1905508 1907724 1907729) (-1151 "SOLVESER.spad" 1903953 1903964 1905487 1905492) (-1150 "SOLVERAD.spad" 1899979 1899990 1903943 1903948) (-1149 "SOLVEFOR.spad" 1898441 1898459 1899969 1899974) (-1148 "SNTSCAT.spad" 1898041 1898058 1898409 1898436) (-1147 "SMTS.spad" 1896323 1896349 1897600 1897697) (-1146 "SMP.spad" 1893726 1893746 1894116 1894243) (-1145 "SMITH.spad" 1892571 1892596 1893716 1893721) (-1144 "SMATCAT.spad" 1890689 1890719 1892515 1892566) (-1143 "SMATCAT.spad" 1888739 1888771 1890567 1890572) (-1142 "SKAGG.spad" 1887708 1887719 1888707 1888734) (-1141 "SINT.spad" 1886648 1886657 1887574 1887703) (-1140 "SIMPAN.spad" 1886376 1886385 1886638 1886643) (-1139 "SIGNRF.spad" 1885501 1885512 1886366 1886371) (-1138 "SIGNEF.spad" 1884787 1884804 1885491 1885496) (-1137 "SIGAST.spad" 1884204 1884213 1884777 1884782) (-1136 "SIG.spad" 1883566 1883575 1884194 1884199) (-1135 "SHP.spad" 1881510 1881525 1883522 1883527) (-1134 "SHDP.spad" 1868865 1868892 1869382 1869481) (-1133 "SGROUP.spad" 1868473 1868482 1868855 1868860) (-1132 "SGROUP.spad" 1868079 1868090 1868463 1868468) (-1131 "SGCF.spad" 1861218 1861227 1868069 1868074) (-1130 "SFRTCAT.spad" 1860164 1860181 1861186 1861213) (-1129 "SFRGCD.spad" 1859227 1859247 1860154 1860159) (-1128 "SFQCMPK.spad" 1854040 1854060 1859217 1859222) (-1127 "SFORT.spad" 1853479 1853493 1854030 1854035) (-1126 "SEXOF.spad" 1853322 1853362 1853469 1853474) (-1125 "SEXCAT.spad" 1851150 1851190 1853312 1853317) (-1124 "SEX.spad" 1851042 1851051 1851140 1851145) (-1123 "SETMN.spad" 1849502 1849519 1851032 1851037) (-1122 "SETCAT.spad" 1848987 1848996 1849492 1849497) (-1121 "SETCAT.spad" 1848470 1848481 1848977 1848982) (-1120 "SETAGG.spad" 1845019 1845030 1848450 1848465) (-1119 "SETAGG.spad" 1841576 1841589 1845009 1845014) (-1118 "SET.spad" 1839849 1839860 1840946 1840985) (-1117 "SEQAST.spad" 1839552 1839561 1839839 1839844) (-1116 "SEGXCAT.spad" 1838708 1838721 1839542 1839547) (-1115 "SEGCAT.spad" 1837633 1837644 1838698 1838703) (-1114 "SEGBIND2.spad" 1837331 1837344 1837623 1837628) (-1113 "SEGBIND.spad" 1837089 1837100 1837278 1837283) (-1112 "SEGAST.spad" 1836819 1836828 1837079 1837084) (-1111 "SEG2.spad" 1836254 1836267 1836775 1836780) (-1110 "SEG.spad" 1836067 1836078 1836173 1836178) (-1109 "SDVAR.spad" 1835343 1835354 1836057 1836062) (-1108 "SDPOL.spad" 1832598 1832609 1832889 1833016) (-1107 "SCPKG.spad" 1830687 1830698 1832588 1832593) (-1106 "SCOPE.spad" 1829864 1829873 1830677 1830682) (-1105 "SCACHE.spad" 1828560 1828571 1829854 1829859) (-1104 "SASTCAT.spad" 1828469 1828478 1828550 1828555) (-1103 "SAOS.spad" 1828341 1828350 1828459 1828464) (-1102 "SAERFFC.spad" 1828054 1828074 1828331 1828336) (-1101 "SAEFACT.spad" 1827755 1827775 1828044 1828049) (-1100 "SAE.spad" 1825189 1825205 1825800 1825935) (-1099 "RURPK.spad" 1822848 1822864 1825179 1825184) (-1098 "RULESET.spad" 1822301 1822325 1822838 1822843) (-1097 "RULECOLD.spad" 1822153 1822166 1822291 1822296) (-1096 "RULE.spad" 1820401 1820425 1822143 1822148) (-1095 "RTVALUE.spad" 1820136 1820145 1820391 1820396) (-1094 "RSTRCAST.spad" 1819853 1819862 1820126 1820131) (-1093 "RSETGCD.spad" 1816295 1816315 1819843 1819848) (-1092 "RSETCAT.spad" 1806263 1806280 1816263 1816290) (-1091 "RSETCAT.spad" 1796251 1796270 1806253 1806258) (-1090 "RSDCMPK.spad" 1794751 1794771 1796241 1796246) (-1089 "RRCC.spad" 1793135 1793165 1794741 1794746) (-1088 "RRCC.spad" 1791517 1791549 1793125 1793130) (-1087 "RPTAST.spad" 1791219 1791228 1791507 1791512) (-1086 "RPOLCAT.spad" 1770723 1770738 1791087 1791214) (-1085 "RPOLCAT.spad" 1749922 1749939 1770288 1770293) (-1084 "ROUTINE.spad" 1745323 1745332 1748071 1748098) (-1083 "ROMAN.spad" 1744651 1744660 1745189 1745318) (-1082 "ROIRC.spad" 1743731 1743763 1744641 1744646) (-1081 "RNS.spad" 1742707 1742716 1743633 1743726) (-1080 "RNS.spad" 1741769 1741780 1742697 1742702) (-1079 "RNGBIND.spad" 1740929 1740943 1741724 1741729) (-1078 "RNG.spad" 1740664 1740673 1740919 1740924) (-1077 "RMODULE.spad" 1740445 1740456 1740654 1740659) (-1076 "RMCAT2.spad" 1739865 1739922 1740435 1740440) (-1075 "RMATRIX.spad" 1738635 1738654 1738978 1739017) (-1074 "RMATCAT.spad" 1734214 1734245 1738591 1738630) (-1073 "RMATCAT.spad" 1729683 1729716 1734062 1734067) (-1072 "RLINSET.spad" 1729387 1729398 1729673 1729678) (-1071 "RINTERP.spad" 1729275 1729295 1729377 1729382) (-1070 "RING.spad" 1728745 1728754 1729255 1729270) (-1069 "RING.spad" 1728223 1728234 1728735 1728740) (-1068 "RIDIST.spad" 1727615 1727624 1728213 1728218) (-1067 "RGCHAIN.spad" 1726136 1726152 1727030 1727057) (-1066 "RGBCSPC.spad" 1725925 1725937 1726126 1726131) (-1065 "RGBCMDL.spad" 1725487 1725499 1725915 1725920) (-1064 "RFFACTOR.spad" 1724949 1724960 1725477 1725482) (-1063 "RFFACT.spad" 1724684 1724696 1724939 1724944) (-1062 "RFDIST.spad" 1723680 1723689 1724674 1724679) (-1061 "RF.spad" 1721354 1721365 1723670 1723675) (-1060 "RETSOL.spad" 1720773 1720786 1721344 1721349) (-1059 "RETRACT.spad" 1720201 1720212 1720763 1720768) (-1058 "RETRACT.spad" 1719627 1719640 1720191 1720196) (-1057 "RETAST.spad" 1719439 1719448 1719617 1719622) (-1056 "RESULT.spad" 1717001 1717010 1717588 1717615) (-1055 "RESRING.spad" 1716348 1716395 1716939 1716996) (-1054 "RESLATC.spad" 1715672 1715683 1716338 1716343) (-1053 "REPSQ.spad" 1715403 1715414 1715662 1715667) (-1052 "REPDB.spad" 1715110 1715121 1715393 1715398) (-1051 "REP2.spad" 1704824 1704835 1714952 1714957) (-1050 "REP1.spad" 1699044 1699055 1704774 1704779) (-1049 "REP.spad" 1696598 1696607 1699034 1699039) (-1048 "REGSET.spad" 1694390 1694407 1696199 1696226) (-1047 "REF.spad" 1693725 1693736 1694345 1694350) (-1046 "REDORDER.spad" 1692931 1692948 1693715 1693720) (-1045 "RECLOS.spad" 1691690 1691710 1692394 1692487) (-1044 "REALSOLV.spad" 1690830 1690839 1691680 1691685) (-1043 "REAL0Q.spad" 1688128 1688143 1690820 1690825) (-1042 "REAL0.spad" 1684972 1684987 1688118 1688123) (-1041 "REAL.spad" 1684844 1684853 1684962 1684967) (-1040 "RDUCEAST.spad" 1684565 1684574 1684834 1684839) (-1039 "RDIV.spad" 1684220 1684245 1684555 1684560) (-1038 "RDIST.spad" 1683787 1683798 1684210 1684215) (-1037 "RDETRS.spad" 1682651 1682669 1683777 1683782) (-1036 "RDETR.spad" 1680790 1680808 1682641 1682646) (-1035 "RDEEFS.spad" 1679889 1679906 1680780 1680785) (-1034 "RDEEF.spad" 1678899 1678916 1679879 1679884) (-1033 "RCFIELD.spad" 1676117 1676126 1678801 1678894) (-1032 "RCFIELD.spad" 1673421 1673432 1676107 1676112) (-1031 "RCAGG.spad" 1671357 1671368 1673411 1673416) (-1030 "RCAGG.spad" 1669220 1669233 1671276 1671281) (-1029 "RATRET.spad" 1668580 1668591 1669210 1669215) (-1028 "RATFACT.spad" 1668272 1668284 1668570 1668575) (-1027 "RANDSRC.spad" 1667591 1667600 1668262 1668267) (-1026 "RADUTIL.spad" 1667347 1667356 1667581 1667586) (-1025 "RADIX.spad" 1664126 1664140 1665672 1665765) (-1024 "RADFF.spad" 1661829 1661866 1661948 1662104) (-1023 "RADCAT.spad" 1661424 1661433 1661819 1661824) (-1022 "RADCAT.spad" 1661017 1661028 1661414 1661419) (-1021 "QUEUE.spad" 1660236 1660247 1660495 1660522) (-1020 "QUATCT2.spad" 1659856 1659875 1660226 1660231) (-1019 "QUATCAT.spad" 1658026 1658037 1659786 1659851) (-1018 "QUATCAT.spad" 1655944 1655957 1657706 1657711) (-1017 "QUAT.spad" 1654396 1654407 1654739 1654804) (-1016 "QUAGG.spad" 1653229 1653240 1654364 1654391) (-1015 "QQUTAST.spad" 1652997 1653006 1653219 1653224) (-1014 "QFORM.spad" 1652615 1652630 1652987 1652992) (-1013 "QFCAT2.spad" 1652307 1652324 1652605 1652610) (-1012 "QFCAT.spad" 1651009 1651020 1652209 1652302) (-1011 "QFCAT.spad" 1649293 1649306 1650495 1650500) (-1010 "QEQUAT.spad" 1648851 1648860 1649283 1649288) (-1009 "QCMPACK.spad" 1643765 1643785 1648841 1648846) (-1008 "QALGSET2.spad" 1641760 1641779 1643755 1643760) (-1007 "QALGSET.spad" 1637864 1637897 1641674 1641679) (-1006 "PWFFINTB.spad" 1635279 1635301 1637854 1637859) (-1005 "PUSHVAR.spad" 1634617 1634637 1635269 1635274) (-1004 "PTRANFN.spad" 1630752 1630763 1634607 1634612) (-1003 "PTPACK.spad" 1627839 1627850 1630742 1630747) (-1002 "PTFUNC2.spad" 1627661 1627676 1627829 1627834) (-1001 "PTCAT.spad" 1626915 1626926 1627629 1627656) (-1000 "PSQFR.spad" 1626229 1626254 1626905 1626910) (-999 "PSEUDLIN.spad" 1625115 1625125 1626219 1626224) (-998 "PSETPK.spad" 1611820 1611836 1624993 1624998) (-997 "PSETCAT.spad" 1606220 1606243 1611800 1611815) (-996 "PSETCAT.spad" 1600594 1600619 1606176 1606181) (-995 "PSCURVE.spad" 1599593 1599601 1600584 1600589) (-994 "PSCAT.spad" 1598376 1598405 1599491 1599588) (-993 "PSCAT.spad" 1597249 1597280 1598366 1598371) (-992 "PRTITION.spad" 1595947 1595955 1597239 1597244) (-991 "PRTDAST.spad" 1595666 1595674 1595937 1595942) (-990 "PRS.spad" 1585284 1585301 1595622 1595627) (-989 "PRQAGG.spad" 1584719 1584729 1585252 1585279) (-988 "PROPLOG.spad" 1584323 1584331 1584709 1584714) (-987 "PROPFUN2.spad" 1583946 1583959 1584313 1584318) (-986 "PROPFUN1.spad" 1583352 1583363 1583936 1583941) (-985 "PROPFRML.spad" 1581920 1581931 1583342 1583347) (-984 "PROPERTY.spad" 1581416 1581424 1581910 1581915) (-983 "PRODUCT.spad" 1579098 1579110 1579382 1579437) (-982 "PRINT.spad" 1578850 1578858 1579088 1579093) (-981 "PRIMES.spad" 1577111 1577121 1578840 1578845) (-980 "PRIMELT.spad" 1575232 1575246 1577101 1577106) (-979 "PRIMCAT.spad" 1574875 1574883 1575222 1575227) (-978 "PRIMARR2.spad" 1573642 1573654 1574865 1574870) (-977 "PRIMARR.spad" 1572481 1572491 1572651 1572678) (-976 "PREASSOC.spad" 1571863 1571875 1572471 1572476) (-975 "PR.spad" 1570228 1570240 1570927 1571054) (-974 "PPCURVE.spad" 1569365 1569373 1570218 1570223) (-973 "PORTNUM.spad" 1569156 1569164 1569355 1569360) (-972 "POLYROOT.spad" 1568005 1568027 1569112 1569117) (-971 "POLYLIFT.spad" 1567270 1567293 1567995 1568000) (-970 "POLYCATQ.spad" 1565396 1565418 1567260 1567265) (-969 "POLYCAT.spad" 1558898 1558919 1565264 1565391) (-968 "POLYCAT.spad" 1551696 1551719 1558064 1558069) (-967 "POLY2UP.spad" 1551148 1551162 1551686 1551691) (-966 "POLY2.spad" 1550745 1550757 1551138 1551143) (-965 "POLY.spad" 1548008 1548018 1548523 1548650) (-964 "POLUTIL.spad" 1546973 1547002 1547964 1547969) (-963 "POLTOPOL.spad" 1545721 1545736 1546963 1546968) (-962 "POINT.spad" 1544385 1544395 1544472 1544499) (-961 "PNTHEORY.spad" 1541087 1541095 1544375 1544380) (-960 "PMTOOLS.spad" 1539862 1539876 1541077 1541082) (-959 "PMSYM.spad" 1539411 1539421 1539852 1539857) (-958 "PMQFCAT.spad" 1539002 1539016 1539401 1539406) (-957 "PMPREDFS.spad" 1538464 1538486 1538992 1538997) (-956 "PMPRED.spad" 1537951 1537965 1538454 1538459) (-955 "PMPLCAT.spad" 1537028 1537046 1537880 1537885) (-954 "PMLSAGG.spad" 1536613 1536627 1537018 1537023) (-953 "PMKERNEL.spad" 1536192 1536204 1536603 1536608) (-952 "PMINS.spad" 1535772 1535782 1536182 1536187) (-951 "PMFS.spad" 1535349 1535367 1535762 1535767) (-950 "PMDOWN.spad" 1534639 1534653 1535339 1535344) (-949 "PMASSFS.spad" 1533614 1533630 1534629 1534634) (-948 "PMASS.spad" 1532632 1532640 1533604 1533609) (-947 "PLOTTOOL.spad" 1532412 1532420 1532622 1532627) (-946 "PLOT3D.spad" 1528876 1528884 1532402 1532407) (-945 "PLOT1.spad" 1528049 1528059 1528866 1528871) (-944 "PLOT.spad" 1522972 1522980 1528039 1528044) (-943 "PLEQN.spad" 1510374 1510401 1522962 1522967) (-942 "PINTERPA.spad" 1510158 1510174 1510364 1510369) (-941 "PINTERP.spad" 1509780 1509799 1510148 1510153) (-940 "PID.spad" 1508754 1508762 1509706 1509775) (-939 "PICOERCE.spad" 1508411 1508421 1508744 1508749) (-938 "PI.spad" 1508028 1508036 1508385 1508406) (-937 "PGROEB.spad" 1506637 1506651 1508018 1508023) (-936 "PGE.spad" 1498310 1498318 1506627 1506632) (-935 "PGCD.spad" 1497264 1497281 1498300 1498305) (-934 "PFRPAC.spad" 1496413 1496423 1497254 1497259) (-933 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1125860) (-726 "MKUCFUNC.spad" 1124012 1124030 1124467 1124472) (-725 "MKRECORD.spad" 1123600 1123613 1124002 1124007) (-724 "MKFUNC.spad" 1123007 1123017 1123590 1123595) (-723 "MKFLCFN.spad" 1121975 1121985 1122997 1123002) (-722 "MKBCFUNC.spad" 1121470 1121488 1121965 1121970) (-721 "MINT.spad" 1120909 1120917 1121372 1121465) (-720 "MHROWRED.spad" 1119420 1119430 1120899 1120904) (-719 "MFLOAT.spad" 1117940 1117948 1119310 1119415) (-718 "MFINFACT.spad" 1117340 1117362 1117930 1117935) (-717 "MESH.spad" 1115135 1115143 1117330 1117335) (-716 "MDDFACT.spad" 1113354 1113364 1115125 1115130) (-715 "MDAGG.spad" 1112645 1112655 1113334 1113349) (-714 "MCMPLX.spad" 1108010 1108018 1108624 1108825) (-713 "MCDEN.spad" 1107220 1107232 1108000 1108005) (-712 "MCALCFN.spad" 1104318 1104344 1107210 1107215) (-711 "MAYBE.spad" 1103618 1103629 1104308 1104313) (-710 "MATSTOR.spad" 1100934 1100944 1103608 1103613) (-709 "MATRIX.spad" 1099500 1099510 1099984 1100011) (-708 "MATLIN.spad" 1096868 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421197) (-304 "EP.spad" 414616 414626 418280 418285) (-303 "ENV.spad" 413294 413302 414606 414611) (-302 "ENTIRER.spad" 412962 412970 413238 413289) (-301 "EMR.spad" 412250 412291 412888 412957) (-300 "ELTAGG.spad" 410504 410523 412240 412245) (-299 "ELTAGG.spad" 408722 408743 410460 410465) (-298 "ELTAB.spad" 408197 408210 408712 408717) (-297 "ELFUTS.spad" 407632 407651 408187 408192) (-296 "ELEMFUN.spad" 407321 407329 407622 407627) (-295 "ELEMFUN.spad" 407008 407018 407311 407316) (-294 "ELAGG.spad" 404979 404989 406988 407003) (-293 "ELAGG.spad" 402887 402899 404898 404903) (-292 "ELABOR.spad" 402233 402241 402877 402882) (-291 "ELABEXPR.spad" 401165 401173 402223 402228) (-290 "EFUPXS.spad" 397941 397971 401121 401126) (-289 "EFULS.spad" 394777 394800 397897 397902) (-288 "EFSTRUC.spad" 392792 392808 394767 394772) (-287 "EF.spad" 387568 387584 392782 392787) (-286 "EAB.spad" 385868 385876 387558 387563) (-285 "E04UCFA.spad" 385404 385412 385858 385863) (-284 "E04NAFA.spad" 384981 384989 385394 385399) (-283 "E04MBFA.spad" 384561 384569 384971 384976) (-282 "E04JAFA.spad" 384097 384105 384551 384556) (-281 "E04GCFA.spad" 383633 383641 384087 384092) (-280 "E04FDFA.spad" 383169 383177 383623 383628) (-279 "E04DGFA.spad" 382705 382713 383159 383164) (-278 "E04AGNT.spad" 378579 378587 382695 382700) (-277 "DVARCAT.spad" 375469 375479 378569 378574) (-276 "DVARCAT.spad" 372357 372369 375459 375464) (-275 "DSMP.spad" 369653 369667 369958 370085) (-274 "DSEXT.spad" 368955 368965 369643 369648) (-273 "DSEXT.spad" 368161 368173 368851 368856) (-272 "DROPT1.spad" 367826 367836 368151 368156) (-271 "DROPT0.spad" 362691 362699 367816 367821) (-270 "DROPT.spad" 356650 356658 362681 362686) (-269 "DRAWPT.spad" 354823 354831 356640 356645) (-268 "DRAWHACK.spad" 354131 354141 354813 354818) (-267 "DRAWCX.spad" 351609 351617 354121 354126) (-266 "DRAWCURV.spad" 351156 351171 351599 351604) (-265 "DRAWCFUN.spad" 340688 340696 351146 351151) (-264 "DRAW.spad" 333564 333577 340678 340683) (-263 "DQAGG.spad" 331742 331752 333532 333559) (-262 "DPOLCAT.spad" 327099 327115 331610 331737) (-261 "DPOLCAT.spad" 322542 322560 327055 327060) (-260 "DPMO.spad" 314065 314081 314203 314416) (-259 "DPMM.spad" 305601 305619 305726 305939) (-258 "DOMTMPLT.spad" 305372 305380 305591 305596) (-257 "DOMCTOR.spad" 305127 305135 305362 305367) (-256 "DOMAIN.spad" 304238 304246 305117 305122) (-255 "DMP.spad" 301426 301441 301996 302123) (-254 "DMEXT.spad" 301293 301303 301394 301421) (-253 "DLP.spad" 300653 300663 301283 301288) (-252 "DLIST.spad" 299058 299068 299662 299689) (-251 "DLAGG.spad" 297475 297485 299048 299053) (-250 "DIVRING.spad" 297017 297025 297419 297470) (-249 "DIVRING.spad" 296603 296613 297007 297012) (-248 "DISPLAY.spad" 294793 294801 296593 296598) (-247 "DIRPROD2.spad" 293611 293629 294783 294788) (-246 "DIRPROD.spad" 280843 280859 281483 281582) (-245 "DIRPCAT.spad" 280036 280052 280739 280838) (-244 "DIRPCAT.spad" 278856 278874 279561 279566) (-243 "DIOSP.spad" 277681 277689 278846 278851) (-242 "DIOPS.spad" 276677 276687 277661 277676) (-241 "DIOPS.spad" 275647 275659 276633 276638) (-240 "DIFRING.spad" 275485 275493 275627 275642) (-239 "DIFFSPC.spad" 275064 275072 275475 275480) (-238 "DIFFSPC.spad" 274641 274651 275054 275059) (-237 "DIFFMOD.spad" 274130 274140 274609 274636) (-236 "DIFFDOM.spad" 273295 273306 274120 274125) (-235 "DIFFDOM.spad" 272458 272471 273285 273290) (-234 "DIFEXT.spad" 272277 272287 272438 272453) (-233 "DIAGG.spad" 271907 271917 272257 272272) (-232 "DIAGG.spad" 271545 271557 271897 271902) (-231 "DHMATRIX.spad" 269728 269738 270873 270900) (-230 "DFSFUN.spad" 263368 263376 269718 269723) (-229 "DFLOAT.spad" 259975 259983 263258 263363) (-228 "DFINTTLS.spad" 258206 258222 259965 259970) (-227 "DERHAM.spad" 256120 256152 258186 258201) (-226 "DEQUEUE.spad" 255315 255325 255598 255625) (-225 "DEGRED.spad" 254932 254946 255305 255310) (-224 "DEFINTRF.spad" 252514 252524 254922 254927) (-223 "DEFINTEF.spad" 251052 251068 252504 252509) (-222 "DEFAST.spad" 250436 250444 251042 251047) (-221 "DECIMAL.spad" 248400 248408 248761 248854) (-220 "DDFACT.spad" 246221 246238 248390 248395) (-219 "DBLRESP.spad" 245821 245845 246211 246216) (-218 "DBASIS.spad" 245447 245462 245811 245816) (-217 "DBASE.spad" 244111 244121 245437 245442) (-216 "DATAARY.spad" 243597 243610 244101 244106) (-215 "D03FAFA.spad" 243425 243433 243587 243592) (-214 "D03EEFA.spad" 243245 243253 243415 243420) (-213 "D03AGNT.spad" 242331 242339 243235 243240) (-212 "D02EJFA.spad" 241793 241801 242321 242326) (-211 "D02CJFA.spad" 241271 241279 241783 241788) (-210 "D02BHFA.spad" 240761 240769 241261 241266) (-209 "D02BBFA.spad" 240251 240259 240751 240756) (-208 "D02AGNT.spad" 235121 235129 240241 240246) (-207 "D01WGTS.spad" 233440 233448 235111 235116) (-206 "D01TRNS.spad" 233417 233425 233430 233435) (-205 "D01GBFA.spad" 232939 232947 233407 233412) (-204 "D01FCFA.spad" 232461 232469 232929 232934) (-203 "D01ASFA.spad" 231929 231937 232451 232456) (-202 "D01AQFA.spad" 231383 231391 231919 231924) (-201 "D01APFA.spad" 230823 230831 231373 231378) (-200 "D01ANFA.spad" 230317 230325 230813 230818) (-199 "D01AMFA.spad" 229827 229835 230307 230312) (-198 "D01ALFA.spad" 229367 229375 229817 229822) (-197 "D01AKFA.spad" 228893 228901 229357 229362) (-196 "D01AJFA.spad" 228416 228424 228883 228888) (-195 "D01AGNT.spad" 224483 224491 228406 228411) (-194 "CYCLOTOM.spad" 223989 223997 224473 224478) (-193 "CYCLES.spad" 220781 220789 223979 223984) (-192 "CVMP.spad" 220198 220208 220771 220776) (-191 "CTRIGMNP.spad" 218698 218714 220188 220193) (-190 "CTORKIND.spad" 218301 218309 218688 218693) (-189 "CTORCAT.spad" 217542 217550 218291 218296) (-188 "CTORCAT.spad" 216781 216791 217532 217537) (-187 "CTORCALL.spad" 216370 216380 216771 216776) (-186 "CTOR.spad" 216061 216069 216360 216365) (-185 "CSTTOOLS.spad" 215306 215319 216051 216056) (-184 "CRFP.spad" 209078 209091 215296 215301) (-183 "CRCEAST.spad" 208798 208806 209068 209073) (-182 "CRAPACK.spad" 207865 207875 208788 208793) (-181 "CPMATCH.spad" 207366 207381 207787 207792) (-180 "CPIMA.spad" 207071 207090 207356 207361) (-179 "COORDSYS.spad" 202080 202090 207061 207066) (-178 "CONTOUR.spad" 201507 201515 202070 202075) (-177 "CONTFRAC.spad" 197257 197267 201409 201502) (-176 "CONDUIT.spad" 197015 197023 197247 197252) (-175 "COMRING.spad" 196689 196697 196953 197010) (-174 "COMPPROP.spad" 196207 196215 196679 196684) (-173 "COMPLPAT.spad" 195974 195989 196197 196202) (-172 "COMPLEX2.spad" 195689 195701 195964 195969) (-171 "COMPLEX.spad" 191036 191046 191280 191541) (-170 "COMPILER.spad" 190585 190593 191026 191031) (-169 "COMPFACT.spad" 190187 190201 190575 190580) (-168 "COMPCAT.spad" 188259 188269 189921 190182) (-167 "COMPCAT.spad" 186056 186068 187720 187725) (-166 "COMMUPC.spad" 185804 185822 186046 186051) (-165 "COMMONOP.spad" 185337 185345 185794 185799) (-164 "COMMAAST.spad" 185100 185108 185327 185332) (-163 "COMM.spad" 184911 184919 185090 185095) (-162 "COMBOPC.spad" 183834 183842 184901 184906) (-161 "COMBINAT.spad" 182601 182611 183824 183829) (-160 "COMBF.spad" 180023 180039 182591 182596) (-159 "COLOR.spad" 178860 178868 180013 180018) (-158 "COLONAST.spad" 178526 178534 178850 178855) (-157 "CMPLXRT.spad" 178237 178254 178516 178521) (-156 "CLLCTAST.spad" 177899 177907 178227 178232) (-155 "CLIP.spad" 174007 174015 177889 177894) (-154 "CLIF.spad" 172662 172678 173963 174002) (-153 "CLAGG.spad" 169199 169209 172652 172657) (-152 "CLAGG.spad" 165604 165616 169059 169064) (-151 "CINTSLPE.spad" 164959 164972 165594 165599) (-150 "CHVAR.spad" 163097 163119 164949 164954) (-149 "CHARZ.spad" 163012 163020 163077 163092) (-148 "CHARPOL.spad" 162538 162548 163002 163007) (-147 "CHARNZ.spad" 162300 162308 162518 162533) (-146 "CHAR.spad" 159668 159676 162290 162295) (-145 "CFCAT.spad" 158996 159004 159658 159663) (-144 "CDEN.spad" 158216 158230 158986 158991) (-143 "CCLASS.spad" 156312 156320 157574 157613) (-142 "CATEGORY.spad" 155386 155394 156302 156307) (-141 "CATCTOR.spad" 155277 155285 155376 155381) (-140 "CATAST.spad" 154903 154911 155267 155272) (-139 "CASEAST.spad" 154617 154625 154893 154898) (-138 "CARTEN2.spad" 154007 154034 154607 154612) (-137 "CARTEN.spad" 149374 149398 153997 154002) (-136 "CARD.spad" 146669 146677 149348 149369) (-135 "CAPSLAST.spad" 146451 146459 146659 146664) (-134 "CACHSET.spad" 146075 146083 146441 146446) (-133 "CABMON.spad" 145630 145638 146065 146070) (-132 "BYTEORD.spad" 145305 145313 145620 145625) (-131 "BYTEBUF.spad" 143006 143014 144292 144319) (-130 "BYTE.spad" 142481 142489 142996 143001) (-129 "BTREE.spad" 141425 141435 141959 141986) (-128 "BTOURN.spad" 140301 140311 140903 140930) (-127 "BTCAT.spad" 139693 139703 140269 140296) (-126 "BTCAT.spad" 139105 139117 139683 139688) (-125 "BTAGG.spad" 138571 138579 139073 139100) (-124 "BTAGG.spad" 138057 138067 138561 138566) (-123 "BSTREE.spad" 136669 136679 137535 137562) (-122 "BRILL.spad" 134874 134885 136659 136664) (-121 "BRAGG.spad" 133830 133840 134864 134869) (-120 "BRAGG.spad" 132750 132762 133786 133791) (-119 "BPADICRT.spad" 130575 130587 130822 130915) (-118 "BPADIC.spad" 130247 130259 130501 130570) (-117 "BOUNDZRO.spad" 129903 129920 130237 130242) (-116 "BOP1.spad" 127361 127371 129893 129898) (-115 "BOP.spad" 122503 122511 127351 127356) (-114 "BOOLEAN.spad" 122051 122059 122493 122498) (-113 "BOOLE.spad" 121701 121709 122041 122046) (-112 "BOOLE.spad" 121349 121359 121691 121696) (-111 "BMODULE.spad" 121061 121073 121317 121344) (-110 "BITS.spad" 120435 120443 120650 120677) (-109 "BINDING.spad" 119856 119864 120425 120430) (-108 "BINARY.spad" 117825 117833 118181 118274) (-107 "BGAGG.spad" 117030 117040 117805 117820) (-106 "BGAGG.spad" 116243 116255 117020 117025) (-105 "BFUNCT.spad" 115807 115815 116223 116238) (-104 "BEZOUT.spad" 114947 114974 115757 115762) (-103 "BBTREE.spad" 111695 111705 114425 114452) (-102 "BASTYPE.spad" 111194 111202 111685 111690) (-101 "BASTYPE.spad" 110691 110701 111184 111189) (-100 "BALFACT.spad" 110150 110163 110681 110686) (-99 "AUTOMOR.spad" 109601 109610 110130 110145) (-98 "ATTREG.spad" 106324 106331 109353 109596) (-97 "ATTRBUT.spad" 102347 102354 106304 106319) (-96 "ATTRAST.spad" 102064 102071 102337 102342) (-95 "ATRIG.spad" 101534 101541 102054 102059) (-94 "ATRIG.spad" 101002 101011 101524 101529) (-93 "ASTCAT.spad" 100906 100913 100992 100997) (-92 "ASTCAT.spad" 100808 100817 100896 100901) (-91 "ASTACK.spad" 100018 100027 100286 100313) (-90 "ASSOCEQ.spad" 98852 98863 99974 99979) (-89 "ASP9.spad" 97933 97946 98842 98847) (-88 "ASP80.spad" 97255 97268 97923 97928) (-87 "ASP8.spad" 96298 96311 97245 97250) (-86 "ASP78.spad" 95749 95762 96288 96293) (-85 "ASP77.spad" 95118 95131 95739 95744) (-84 "ASP74.spad" 94210 94223 95108 95113) (-83 "ASP73.spad" 93481 93494 94200 94205) (-82 "ASP7.spad" 92641 92654 93471 93476) (-81 "ASP6.spad" 91508 91521 92631 92636) (-80 "ASP55.spad" 90017 90030 91498 91503) (-79 "ASP50.spad" 87834 87847 90007 90012) (-78 "ASP49.spad" 86833 86846 87824 87829) (-77 "ASP42.spad" 85248 85287 86823 86828) (-76 "ASP41.spad" 83835 83874 85238 85243) (-75 "ASP4.spad" 83130 83143 83825 83830) (-74 "ASP35.spad" 82118 82131 83120 83125) (-73 "ASP34.spad" 81419 81432 82108 82113) (-72 "ASP33.spad" 80979 80992 81409 81414) (-71 "ASP31.spad" 80119 80132 80969 80974) (-70 "ASP30.spad" 79011 79024 80109 80114) (-69 "ASP29.spad" 78477 78490 79001 79006) (-68 "ASP28.spad" 69750 69763 78467 78472) (-67 "ASP27.spad" 68647 68660 69740 69745) (-66 "ASP24.spad" 67734 67747 68637 68642) (-65 "ASP20.spad" 67198 67211 67724 67729) (-64 "ASP19.spad" 61884 61897 67188 67193) (-63 "ASP12.spad" 61298 61311 61874 61879) (-62 "ASP10.spad" 60569 60582 61288 61293) (-61 "ASP1.spad" 59950 59963 60559 60564) (-60 "ARRAY2.spad" 59189 59198 59428 59455) (-59 "ARRAY12.spad" 57902 57913 59179 59184) (-58 "ARRAY1.spad" 56565 56574 56911 56938) (-57 "ARR2CAT.spad" 52347 52368 56533 56560) (-56 "ARR2CAT.spad" 48149 48172 52337 52342) (-55 "ARITY.spad" 47521 47528 48139 48144) (-54 "APPRULE.spad" 46805 46827 47511 47516) (-53 "APPLYORE.spad" 46424 46437 46795 46800) (-52 "ANY1.spad" 45495 45504 46414 46419) (-51 "ANY.spad" 44346 44353 45485 45490) (-50 "ANTISYM.spad" 42791 42807 44326 44341) (-49 "ANON.spad" 42500 42507 42781 42786) (-48 "AN.spad" 40806 40813 42313 42406) (-47 "AMR.spad" 38991 39002 40704 40801) (-46 "AMR.spad" 37007 37020 38722 38727) (-45 "ALIST.spad" 33847 33868 34197 34224) (-44 "ALGSC.spad" 32982 33008 33719 33772) (-43 "ALGPKG.spad" 28765 28776 32938 32943) (-42 "ALGMFACT.spad" 27958 27972 28755 28760) (-41 "ALGMANIP.spad" 25442 25457 27785 27790) (-40 "ALGFF.spad" 23047 23074 23264 23420) (-39 "ALGFACT.spad" 22166 22176 23037 23042) (-38 "ALGEBRA.spad" 21999 22008 22122 22161) (-37 "ALGEBRA.spad" 21864 21875 21989 21994) (-36 "ALAGG.spad" 21376 21397 21832 21859) (-35 "AHYP.spad" 20757 20764 21366 21371) (-34 "AGG.spad" 19466 19473 20747 20752) (-33 "AGG.spad" 18139 18148 19422 19427) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2275956 2275961 2275966 2275971) (-2 NIL 2275936 2275941 2275946 2275951) (-1 NIL 2275916 2275921 2275926 2275931) (0 NIL 2275896 2275901 2275906 2275911) (-1317 "ZMOD.spad" 2275705 2275718 2275834 2275891) (-1316 "ZLINDEP.spad" 2274803 2274814 2275695 2275700) (-1315 "ZDSOLVE.spad" 2264763 2264785 2274793 2274798) (-1314 "YSTREAM.spad" 2264258 2264269 2264753 2264758) (-1313 "YDIAGRAM.spad" 2263892 2263901 2264248 2264253) (-1312 "XRPOLY.spad" 2263112 2263132 2263748 2263817) (-1311 "XPR.spad" 2260907 2260920 2262830 2262929) (-1310 "XPOLYC.spad" 2260226 2260242 2260833 2260902) (-1309 "XPOLY.spad" 2259781 2259792 2260082 2260151) (-1308 "XPBWPOLY.spad" 2258220 2258240 2259555 2259624) (-1307 "XFALG.spad" 2255268 2255284 2258146 2258215) (-1306 "XF.spad" 2253731 2253746 2255170 2255263) (-1305 "XF.spad" 2252174 2252191 2253615 2253620) (-1304 "XEXPPKG.spad" 2251433 2251459 2252164 2252169) (-1303 "XDPOLY.spad" 2251047 2251063 2251289 2251358) (-1302 "XALG.spad" 2250715 2250726 2251003 2251042) (-1301 "WUTSET.spad" 2246685 2246702 2250316 2250343) (-1300 "WP.spad" 2245892 2245936 2246543 2246610) (-1299 "WHILEAST.spad" 2245690 2245699 2245882 2245887) (-1298 "WHEREAST.spad" 2245361 2245370 2245680 2245685) (-1297 "WFFINTBS.spad" 2243024 2243046 2245351 2245356) (-1296 "WEIER.spad" 2241246 2241257 2243014 2243019) (-1295 "VSPACE.spad" 2240919 2240930 2241214 2241241) (-1294 "VSPACE.spad" 2240612 2240625 2240909 2240914) (-1293 "VOID.spad" 2240289 2240298 2240602 2240607) (-1292 "VIEWDEF.spad" 2235490 2235499 2240279 2240284) (-1291 "VIEW3D.spad" 2219451 2219460 2235480 2235485) (-1290 "VIEW2D.spad" 2207350 2207359 2219441 2219446) (-1289 "VIEW.spad" 2205070 2205079 2207340 2207345) (-1288 "VECTOR2.spad" 2203709 2203722 2205060 2205065) (-1287 "VECTOR.spad" 2202209 2202220 2202460 2202487) (-1286 "VECTCAT.spad" 2200121 2200132 2202177 2202204) (-1285 "VECTCAT.spad" 2197840 2197853 2199898 2199903) (-1284 "VARIABLE.spad" 2197620 2197635 2197830 2197835) (-1283 "UTYPE.spad" 2197264 2197273 2197610 2197615) (-1282 "UTSODETL.spad" 2196559 2196583 2197220 2197225) (-1281 "UTSODE.spad" 2194775 2194795 2196549 2196554) (-1280 "UTSCAT.spad" 2192254 2192270 2194673 2194770) (-1279 "UTSCAT.spad" 2189353 2189371 2191774 2191779) (-1278 "UTS2.spad" 2188948 2188983 2189343 2189348) (-1277 "UTS.spad" 2183826 2183854 2187346 2187443) (-1276 "URAGG.spad" 2178547 2178558 2183816 2183821) (-1275 "URAGG.spad" 2173232 2173245 2178503 2178508) (-1274 "UPXSSING.spad" 2170850 2170876 2172286 2172419) (-1273 "UPXSCONS.spad" 2168528 2168548 2168901 2169050) (-1272 "UPXSCCA.spad" 2167099 2167119 2168374 2168523) (-1271 "UPXSCCA.spad" 2165812 2165834 2167089 2167094) (-1270 "UPXSCAT.spad" 2164401 2164417 2165658 2165807) (-1269 "UPXS2.spad" 2163944 2163997 2164391 2164396) (-1268 "UPXS.spad" 2161159 2161187 2161995 2162144) (-1267 "UPSQFREE.spad" 2159574 2159588 2161149 2161154) (-1266 "UPSCAT.spad" 2157369 2157393 2159472 2159569) (-1265 "UPSCAT.spad" 2154849 2154875 2156954 2156959) (-1264 "UPOLYC2.spad" 2154320 2154339 2154839 2154844) (-1263 "UPOLYC.spad" 2149400 2149411 2154162 2154315) (-1262 "UPOLYC.spad" 2144366 2144379 2149130 2149135) (-1261 "UPMP.spad" 2143298 2143311 2144356 2144361) (-1260 "UPDIVP.spad" 2142863 2142877 2143288 2143293) (-1259 "UPDECOMP.spad" 2141124 2141138 2142853 2142858) (-1258 "UPCDEN.spad" 2140341 2140357 2141114 2141119) (-1257 "UP2.spad" 2139705 2139726 2140331 2140336) (-1256 "UP.spad" 2136733 2136748 2137120 2137273) (-1255 "UNISEG2.spad" 2136230 2136243 2136689 2136694) (-1254 "UNISEG.spad" 2135583 2135594 2136149 2136154) (-1253 "UNIFACT.spad" 2134686 2134698 2135573 2135578) (-1252 "ULSCONS.spad" 2125598 2125618 2125968 2126117) (-1251 "ULSCCAT.spad" 2123335 2123355 2125444 2125593) (-1250 "ULSCCAT.spad" 2121180 2121202 2123291 2123296) (-1249 "ULSCAT.spad" 2119420 2119436 2121026 2121175) (-1248 "ULS2.spad" 2118934 2118987 2119410 2119415) (-1247 "ULS.spad" 2108505 2108533 2109450 2109879) (-1246 "UINT8.spad" 2108382 2108391 2108495 2108500) (-1245 "UINT64.spad" 2108258 2108267 2108372 2108377) (-1244 "UINT32.spad" 2108134 2108143 2108248 2108253) (-1243 "UINT16.spad" 2108010 2108019 2108124 2108129) (-1242 "UFD.spad" 2107075 2107084 2107936 2108005) (-1241 "UFD.spad" 2106202 2106213 2107065 2107070) (-1240 "UDVO.spad" 2105083 2105092 2106192 2106197) (-1239 "UDPO.spad" 2102664 2102675 2105039 2105044) (-1238 "TYPEAST.spad" 2102583 2102592 2102654 2102659) (-1237 "TYPE.spad" 2102515 2102524 2102573 2102578) (-1236 "TWOFACT.spad" 2101167 2101182 2102505 2102510) (-1235 "TUPLE.spad" 2100658 2100669 2101063 2101068) (-1234 "TUBETOOL.spad" 2097525 2097534 2100648 2100653) (-1233 "TUBE.spad" 2096172 2096189 2097515 2097520) (-1232 "TSETCAT.spad" 2084243 2084260 2096140 2096167) (-1231 "TSETCAT.spad" 2072300 2072319 2084199 2084204) (-1230 "TS.spad" 2070893 2070909 2071859 2071956) (-1229 "TRMANIP.spad" 2065257 2065274 2070581 2070586) (-1228 "TRIMAT.spad" 2064220 2064245 2065247 2065252) (-1227 "TRIGMNIP.spad" 2062747 2062764 2064210 2064215) (-1226 "TRIGCAT.spad" 2062259 2062268 2062737 2062742) (-1225 "TRIGCAT.spad" 2061769 2061780 2062249 2062254) (-1224 "TREE.spad" 2060215 2060226 2061247 2061274) (-1223 "TRANFUN.spad" 2060054 2060063 2060205 2060210) (-1222 "TRANFUN.spad" 2059891 2059902 2060044 2060049) (-1221 "TOPSP.spad" 2059565 2059574 2059881 2059886) (-1220 "TOOLSIGN.spad" 2059228 2059239 2059555 2059560) (-1219 "TEXTFILE.spad" 2057789 2057798 2059218 2059223) (-1218 "TEX1.spad" 2057345 2057356 2057779 2057784) (-1217 "TEX.spad" 2054539 2054548 2057335 2057340) (-1216 "TEMUTL.spad" 2054094 2054103 2054529 2054534) (-1215 "TBCMPPK.spad" 2052195 2052218 2054084 2054089) (-1214 "TBAGG.spad" 2051253 2051276 2052175 2052190) (-1213 "TBAGG.spad" 2050319 2050344 2051243 2051248) (-1212 "TANEXP.spad" 2049727 2049738 2050309 2050314) (-1211 "TALGOP.spad" 2049451 2049462 2049717 2049722) (-1210 "TABLEAU.spad" 2048932 2048943 2049441 2049446) (-1209 "TABLE.spad" 2046865 2046888 2047135 2047162) (-1208 "TABLBUMP.spad" 2043644 2043655 2046855 2046860) (-1207 "SYSTEM.spad" 2042872 2042881 2043634 2043639) (-1206 "SYSSOLP.spad" 2040355 2040366 2042862 2042867) (-1205 "SYSPTR.spad" 2040254 2040263 2040345 2040350) (-1204 "SYSNNI.spad" 2039477 2039488 2040244 2040249) (-1203 "SYSINT.spad" 2038881 2038892 2039467 2039472) (-1202 "SYNTAX.spad" 2035215 2035224 2038871 2038876) (-1201 "SYMTAB.spad" 2033283 2033292 2035205 2035210) (-1200 "SYMS.spad" 2029312 2029321 2033273 2033278) (-1199 "SYMPOLY.spad" 2028292 2028303 2028374 2028501) (-1198 "SYMFUNC.spad" 2027793 2027804 2028282 2028287) (-1197 "SYMBOL.spad" 2025288 2025297 2027783 2027788) (-1196 "SWITCH.spad" 2022059 2022068 2025278 2025283) (-1195 "SUTS.spad" 2019038 2019066 2020457 2020554) (-1194 "SUPXS.spad" 2016240 2016268 2017089 2017238) (-1193 "SUPFRACF.spad" 2015345 2015363 2016230 2016235) (-1192 "SUP2.spad" 2014737 2014750 2015335 2015340) (-1191 "SUP.spad" 2011379 2011390 2012152 2012305) (-1190 "SUMRF.spad" 2010353 2010364 2011369 2011374) (-1189 "SUMFS.spad" 2009982 2009999 2010343 2010348) (-1188 "SULS.spad" 1999540 1999568 2000498 2000927) (-1187 "SUCHTAST.spad" 1999309 1999318 1999530 1999535) (-1186 "SUCH.spad" 1998999 1999014 1999299 1999304) (-1185 "SUBSPACE.spad" 1991130 1991145 1998989 1998994) (-1184 "SUBRESP.spad" 1990300 1990314 1991086 1991091) (-1183 "STTFNC.spad" 1986768 1986784 1990290 1990295) (-1182 "STTF.spad" 1982867 1982883 1986758 1986763) (-1181 "STTAYLOR.spad" 1975512 1975523 1982742 1982747) (-1180 "STRTBL.spad" 1973527 1973544 1973676 1973703) (-1179 "STRING.spad" 1972129 1972138 1972514 1972541) (-1178 "STREAM3.spad" 1971702 1971717 1972119 1972124) (-1177 "STREAM2.spad" 1970830 1970843 1971692 1971697) (-1176 "STREAM1.spad" 1970536 1970547 1970820 1970825) (-1175 "STREAM.spad" 1967322 1967333 1969929 1969944) (-1174 "STINPROD.spad" 1966258 1966274 1967312 1967317) (-1173 "STEPAST.spad" 1965492 1965501 1966248 1966253) (-1172 "STEP.spad" 1964809 1964818 1965482 1965487) (-1171 "STBL.spad" 1962857 1962885 1963024 1963039) (-1170 "STAGG.spad" 1961556 1961567 1962847 1962852) (-1169 "STAGG.spad" 1960253 1960266 1961546 1961551) (-1168 "STACK.spad" 1959481 1959492 1959731 1959758) (-1167 "SRING.spad" 1959241 1959250 1959471 1959476) (-1166 "SREGSET.spad" 1956940 1956957 1958842 1958869) (-1165 "SRDCMPK.spad" 1955517 1955537 1956930 1956935) (-1164 "SRAGG.spad" 1950700 1950709 1955485 1955512) (-1163 "SRAGG.spad" 1945903 1945914 1950690 1950695) (-1162 "SQMATRIX.spad" 1943395 1943413 1944311 1944398) (-1161 "SPLTREE.spad" 1937861 1937874 1942657 1942684) (-1160 "SPLNODE.spad" 1934481 1934494 1937851 1937856) (-1159 "SPFCAT.spad" 1933290 1933299 1934471 1934476) (-1158 "SPECOUT.spad" 1931842 1931851 1933280 1933285) (-1157 "SPADXPT.spad" 1923933 1923942 1931832 1931837) (-1156 "spad-parser.spad" 1923398 1923407 1923923 1923928) (-1155 "SPADAST.spad" 1923099 1923108 1923388 1923393) (-1154 "SPACEC.spad" 1907314 1907325 1923089 1923094) (-1153 "SPACE3.spad" 1907090 1907101 1907304 1907309) (-1152 "SORTPAK.spad" 1906639 1906652 1907046 1907051) (-1151 "SOLVETRA.spad" 1904402 1904413 1906629 1906634) (-1150 "SOLVESER.spad" 1902858 1902869 1904392 1904397) (-1149 "SOLVERAD.spad" 1898884 1898895 1902848 1902853) (-1148 "SOLVEFOR.spad" 1897346 1897364 1898874 1898879) (-1147 "SNTSCAT.spad" 1896946 1896963 1897314 1897341) (-1146 "SMTS.spad" 1895228 1895254 1896505 1896602) (-1145 "SMP.spad" 1892631 1892651 1893021 1893148) (-1144 "SMITH.spad" 1891476 1891501 1892621 1892626) (-1143 "SMATCAT.spad" 1889594 1889624 1891420 1891471) (-1142 "SMATCAT.spad" 1887644 1887676 1889472 1889477) (-1141 "SKAGG.spad" 1886613 1886624 1887612 1887639) (-1140 "SINT.spad" 1885553 1885562 1886479 1886608) (-1139 "SIMPAN.spad" 1885281 1885290 1885543 1885548) (-1138 "SIGNRF.spad" 1884406 1884417 1885271 1885276) (-1137 "SIGNEF.spad" 1883692 1883709 1884396 1884401) (-1136 "SIGAST.spad" 1883109 1883118 1883682 1883687) (-1135 "SIG.spad" 1882471 1882480 1883099 1883104) (-1134 "SHP.spad" 1880415 1880430 1882427 1882432) (-1133 "SHDP.spad" 1867770 1867797 1868287 1868386) (-1132 "SGROUP.spad" 1867378 1867387 1867760 1867765) (-1131 "SGROUP.spad" 1866984 1866995 1867368 1867373) (-1130 "SGCF.spad" 1860123 1860132 1866974 1866979) (-1129 "SFRTCAT.spad" 1859069 1859086 1860091 1860118) (-1128 "SFRGCD.spad" 1858132 1858152 1859059 1859064) (-1127 "SFQCMPK.spad" 1852945 1852965 1858122 1858127) (-1126 "SFORT.spad" 1852384 1852398 1852935 1852940) (-1125 "SEXOF.spad" 1852227 1852267 1852374 1852379) (-1124 "SEXCAT.spad" 1850055 1850095 1852217 1852222) (-1123 "SEX.spad" 1849947 1849956 1850045 1850050) (-1122 "SETMN.spad" 1848407 1848424 1849937 1849942) (-1121 "SETCAT.spad" 1847892 1847901 1848397 1848402) (-1120 "SETCAT.spad" 1847375 1847386 1847882 1847887) (-1119 "SETAGG.spad" 1843924 1843935 1847355 1847370) (-1118 "SETAGG.spad" 1840481 1840494 1843914 1843919) (-1117 "SET.spad" 1838754 1838765 1839851 1839890) (-1116 "SEQAST.spad" 1838457 1838466 1838744 1838749) (-1115 "SEGXCAT.spad" 1837613 1837626 1838447 1838452) (-1114 "SEGCAT.spad" 1836538 1836549 1837603 1837608) (-1113 "SEGBIND2.spad" 1836236 1836249 1836528 1836533) (-1112 "SEGBIND.spad" 1835994 1836005 1836183 1836188) (-1111 "SEGAST.spad" 1835724 1835733 1835984 1835989) (-1110 "SEG2.spad" 1835159 1835172 1835680 1835685) (-1109 "SEG.spad" 1834972 1834983 1835078 1835083) (-1108 "SDVAR.spad" 1834248 1834259 1834962 1834967) (-1107 "SDPOL.spad" 1831503 1831514 1831794 1831921) (-1106 "SCPKG.spad" 1829592 1829603 1831493 1831498) (-1105 "SCOPE.spad" 1828769 1828778 1829582 1829587) (-1104 "SCACHE.spad" 1827465 1827476 1828759 1828764) (-1103 "SASTCAT.spad" 1827374 1827383 1827455 1827460) (-1102 "SAOS.spad" 1827246 1827255 1827364 1827369) (-1101 "SAERFFC.spad" 1826959 1826979 1827236 1827241) (-1100 "SAEFACT.spad" 1826660 1826680 1826949 1826954) (-1099 "SAE.spad" 1824094 1824110 1824705 1824840) (-1098 "RURPK.spad" 1821753 1821769 1824084 1824089) (-1097 "RULESET.spad" 1821206 1821230 1821743 1821748) (-1096 "RULECOLD.spad" 1821058 1821071 1821196 1821201) (-1095 "RULE.spad" 1819306 1819330 1821048 1821053) (-1094 "RTVALUE.spad" 1819041 1819050 1819296 1819301) (-1093 "RSTRCAST.spad" 1818758 1818767 1819031 1819036) (-1092 "RSETGCD.spad" 1815200 1815220 1818748 1818753) (-1091 "RSETCAT.spad" 1805168 1805185 1815168 1815195) (-1090 "RSETCAT.spad" 1795156 1795175 1805158 1805163) (-1089 "RSDCMPK.spad" 1793656 1793676 1795146 1795151) (-1088 "RRCC.spad" 1792040 1792070 1793646 1793651) (-1087 "RRCC.spad" 1790422 1790454 1792030 1792035) (-1086 "RPTAST.spad" 1790124 1790133 1790412 1790417) (-1085 "RPOLCAT.spad" 1769628 1769643 1789992 1790119) (-1084 "RPOLCAT.spad" 1748827 1748844 1769193 1769198) (-1083 "ROUTINE.spad" 1744228 1744237 1746976 1747003) (-1082 "ROMAN.spad" 1743556 1743565 1744094 1744223) (-1081 "ROIRC.spad" 1742636 1742668 1743546 1743551) (-1080 "RNS.spad" 1741612 1741621 1742538 1742631) (-1079 "RNS.spad" 1740674 1740685 1741602 1741607) (-1078 "RNGBIND.spad" 1739834 1739848 1740629 1740634) (-1077 "RNG.spad" 1739569 1739578 1739824 1739829) (-1076 "RMODULE.spad" 1739350 1739361 1739559 1739564) (-1075 "RMCAT2.spad" 1738770 1738827 1739340 1739345) (-1074 "RMATRIX.spad" 1737540 1737559 1737883 1737922) (-1073 "RMATCAT.spad" 1733119 1733150 1737496 1737535) (-1072 "RMATCAT.spad" 1728588 1728621 1732967 1732972) (-1071 "RLINSET.spad" 1728292 1728303 1728578 1728583) (-1070 "RINTERP.spad" 1728180 1728200 1728282 1728287) (-1069 "RING.spad" 1727650 1727659 1728160 1728175) (-1068 "RING.spad" 1727128 1727139 1727640 1727645) (-1067 "RIDIST.spad" 1726520 1726529 1727118 1727123) (-1066 "RGCHAIN.spad" 1725041 1725057 1725935 1725962) (-1065 "RGBCSPC.spad" 1724830 1724842 1725031 1725036) (-1064 "RGBCMDL.spad" 1724392 1724404 1724820 1724825) (-1063 "RFFACTOR.spad" 1723854 1723865 1724382 1724387) (-1062 "RFFACT.spad" 1723589 1723601 1723844 1723849) (-1061 "RFDIST.spad" 1722585 1722594 1723579 1723584) (-1060 "RF.spad" 1720259 1720270 1722575 1722580) (-1059 "RETSOL.spad" 1719678 1719691 1720249 1720254) (-1058 "RETRACT.spad" 1719106 1719117 1719668 1719673) (-1057 "RETRACT.spad" 1718532 1718545 1719096 1719101) (-1056 "RETAST.spad" 1718344 1718353 1718522 1718527) (-1055 "RESULT.spad" 1715906 1715915 1716493 1716520) (-1054 "RESRING.spad" 1715253 1715300 1715844 1715901) (-1053 "RESLATC.spad" 1714577 1714588 1715243 1715248) (-1052 "REPSQ.spad" 1714308 1714319 1714567 1714572) (-1051 "REPDB.spad" 1714015 1714026 1714298 1714303) (-1050 "REP2.spad" 1703729 1703740 1713857 1713862) (-1049 "REP1.spad" 1697949 1697960 1703679 1703684) (-1048 "REP.spad" 1695503 1695512 1697939 1697944) (-1047 "REGSET.spad" 1693295 1693312 1695104 1695131) (-1046 "REF.spad" 1692630 1692641 1693250 1693255) (-1045 "REDORDER.spad" 1691836 1691853 1692620 1692625) (-1044 "RECLOS.spad" 1690595 1690615 1691299 1691392) (-1043 "REALSOLV.spad" 1689735 1689744 1690585 1690590) (-1042 "REAL0Q.spad" 1687033 1687048 1689725 1689730) (-1041 "REAL0.spad" 1683877 1683892 1687023 1687028) (-1040 "REAL.spad" 1683749 1683758 1683867 1683872) (-1039 "RDUCEAST.spad" 1683470 1683479 1683739 1683744) (-1038 "RDIV.spad" 1683125 1683150 1683460 1683465) (-1037 "RDIST.spad" 1682692 1682703 1683115 1683120) (-1036 "RDETRS.spad" 1681556 1681574 1682682 1682687) (-1035 "RDETR.spad" 1679695 1679713 1681546 1681551) (-1034 "RDEEFS.spad" 1678794 1678811 1679685 1679690) (-1033 "RDEEF.spad" 1677804 1677821 1678784 1678789) (-1032 "RCFIELD.spad" 1675022 1675031 1677706 1677799) (-1031 "RCFIELD.spad" 1672326 1672337 1675012 1675017) (-1030 "RCAGG.spad" 1670262 1670273 1672316 1672321) (-1029 "RCAGG.spad" 1668125 1668138 1670181 1670186) (-1028 "RATRET.spad" 1667485 1667496 1668115 1668120) (-1027 "RATFACT.spad" 1667177 1667189 1667475 1667480) (-1026 "RANDSRC.spad" 1666496 1666505 1667167 1667172) (-1025 "RADUTIL.spad" 1666252 1666261 1666486 1666491) (-1024 "RADIX.spad" 1663031 1663045 1664577 1664670) (-1023 "RADFF.spad" 1660734 1660771 1660853 1661009) (-1022 "RADCAT.spad" 1660329 1660338 1660724 1660729) (-1021 "RADCAT.spad" 1659922 1659933 1660319 1660324) (-1020 "QUEUE.spad" 1659141 1659152 1659400 1659427) (-1019 "QUATCT2.spad" 1658761 1658780 1659131 1659136) (-1018 "QUATCAT.spad" 1656931 1656942 1658691 1658756) (-1017 "QUATCAT.spad" 1654849 1654862 1656611 1656616) (-1016 "QUAT.spad" 1653301 1653312 1653644 1653709) (-1015 "QUAGG.spad" 1652134 1652145 1653269 1653296) (-1014 "QQUTAST.spad" 1651902 1651911 1652124 1652129) (-1013 "QFORM.spad" 1651520 1651535 1651892 1651897) (-1012 "QFCAT2.spad" 1651212 1651229 1651510 1651515) (-1011 "QFCAT.spad" 1649914 1649925 1651114 1651207) (-1010 "QFCAT.spad" 1648198 1648211 1649400 1649405) (-1009 "QEQUAT.spad" 1647756 1647765 1648188 1648193) (-1008 "QCMPACK.spad" 1642670 1642690 1647746 1647751) (-1007 "QALGSET2.spad" 1640665 1640684 1642660 1642665) (-1006 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1584158 1584185) (-987 "PROPLOG.spad" 1583229 1583237 1583615 1583620) (-986 "PROPFUN2.spad" 1582852 1582865 1583219 1583224) (-985 "PROPFUN1.spad" 1582258 1582269 1582842 1582847) (-984 "PROPFRML.spad" 1580826 1580837 1582248 1582253) (-983 "PROPERTY.spad" 1580322 1580330 1580816 1580821) (-982 "PRODUCT.spad" 1578004 1578016 1578288 1578343) (-981 "PRINT.spad" 1577756 1577764 1577994 1577999) (-980 "PRIMES.spad" 1576017 1576027 1577746 1577751) (-979 "PRIMELT.spad" 1574138 1574152 1576007 1576012) (-978 "PRIMCAT.spad" 1573781 1573789 1574128 1574133) (-977 "PRIMARR2.spad" 1572548 1572560 1573771 1573776) (-976 "PRIMARR.spad" 1571387 1571397 1571557 1571584) (-975 "PREASSOC.spad" 1570769 1570781 1571377 1571382) (-974 "PR.spad" 1569134 1569146 1569833 1569960) (-973 "PPCURVE.spad" 1568271 1568279 1569124 1569129) (-972 "PORTNUM.spad" 1568062 1568070 1568261 1568266) (-971 "POLYROOT.spad" 1566911 1566933 1568018 1568023) (-970 "POLYLIFT.spad" 1566176 1566199 1566901 1566906) (-969 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520573 520578) (-343 "FCOMP.spad" 518497 518507 519108 519113) (-342 "FC.spad" 508504 508512 518487 518492) (-341 "FAXF.spad" 501539 501553 508406 508499) (-340 "FAXF.spad" 494626 494642 501495 501500) (-339 "FARRAY.spad" 492602 492612 493635 493662) (-338 "FAMR.spad" 490746 490758 492500 492597) (-337 "FAMR.spad" 488874 488888 490630 490635) (-336 "FAMONOID.spad" 488558 488568 488828 488833) (-335 "FAMONC.spad" 486878 486890 488548 488553) (-334 "FAGROUP.spad" 486518 486528 486774 486801) (-333 "FACUTIL.spad" 484730 484747 486508 486513) (-332 "FACTFUNC.spad" 483932 483942 484720 484725) (-331 "EXPUPXS.spad" 480684 480707 481983 482132) (-330 "EXPRTUBE.spad" 477972 477980 480674 480679) (-329 "EXPRODE.spad" 475140 475156 477962 477967) (-328 "EXPR2UPS.spad" 471262 471275 475130 475135) (-327 "EXPR2.spad" 470967 470979 471252 471257) (-326 "EXPR.spad" 466052 466062 466766 467061) (-325 "EXPEXPAN.spad" 462796 462821 463428 463521) (-324 "EXITAST.spad" 462532 462540 462786 462791) (-323 "EXIT.spad" 462203 462211 462522 462527) (-322 "EVALCYC.spad" 461663 461677 462193 462198) (-321 "EVALAB.spad" 461243 461253 461653 461658) (-320 "EVALAB.spad" 460821 460833 461233 461238) (-319 "EUCDOM.spad" 458411 458419 460747 460816) (-318 "EUCDOM.spad" 456063 456073 458401 458406) (-317 "ESTOOLS2.spad" 455658 455672 456053 456058) (-316 "ESTOOLS1.spad" 455335 455346 455648 455653) (-315 "ESTOOLS.spad" 447213 447221 455325 455330) (-314 "ESCONT1.spad" 446954 446966 447203 447208) (-313 "ESCONT.spad" 443747 443755 446944 446949) (-312 "ES2.spad" 443260 443276 443737 443742) (-311 "ES1.spad" 442830 442846 443250 443255) (-310 "ES.spad" 435701 435709 442820 442825) (-309 "ES.spad" 428475 428485 435596 435601) (-308 "ERROR.spad" 425802 425810 428465 428470) (-307 "EQTBL.spad" 423796 423818 424005 424032) (-306 "EQ2.spad" 423514 423526 423786 423791) (-305 "EQ.spad" 418290 418300 421085 421197) (-304 "EP.spad" 414616 414626 418280 418285) (-303 "ENV.spad" 413294 413302 414606 414611) 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331610 331737) (-261 "DPOLCAT.spad" 322542 322560 327055 327060) (-260 "DPMO.spad" 314065 314081 314203 314416) (-259 "DPMM.spad" 305601 305619 305726 305939) (-258 "DOMTMPLT.spad" 305372 305380 305591 305596) (-257 "DOMCTOR.spad" 305127 305135 305362 305367) (-256 "DOMAIN.spad" 304238 304246 305117 305122) (-255 "DMP.spad" 301426 301441 301996 302123) (-254 "DMEXT.spad" 301293 301303 301394 301421) (-253 "DLP.spad" 300653 300663 301283 301288) (-252 "DLIST.spad" 299058 299068 299662 299689) (-251 "DLAGG.spad" 297475 297485 299048 299053) (-250 "DIVRING.spad" 297017 297025 297419 297470) (-249 "DIVRING.spad" 296603 296613 297007 297012) (-248 "DISPLAY.spad" 294793 294801 296593 296598) (-247 "DIRPROD2.spad" 293611 293629 294783 294788) (-246 "DIRPROD.spad" 280843 280859 281483 281582) (-245 "DIRPCAT.spad" 280036 280052 280739 280838) (-244 "DIRPCAT.spad" 278856 278874 279561 279566) (-243 "DIOSP.spad" 277681 277689 278846 278851) (-242 "DIOPS.spad" 276677 276687 277661 277676) (-241 "DIOPS.spad" 275647 275659 276633 276638) (-240 "DIFRING.spad" 275485 275493 275627 275642) (-239 "DIFFSPC.spad" 275064 275072 275475 275480) (-238 "DIFFSPC.spad" 274641 274651 275054 275059) (-237 "DIFFMOD.spad" 274130 274140 274609 274636) (-236 "DIFFDOM.spad" 273295 273306 274120 274125) (-235 "DIFFDOM.spad" 272458 272471 273285 273290) (-234 "DIFEXT.spad" 272277 272287 272438 272453) (-233 "DIAGG.spad" 271907 271917 272257 272272) (-232 "DIAGG.spad" 271545 271557 271897 271902) (-231 "DHMATRIX.spad" 269728 269738 270873 270900) (-230 "DFSFUN.spad" 263368 263376 269718 269723) (-229 "DFLOAT.spad" 259975 259983 263258 263363) (-228 "DFINTTLS.spad" 258206 258222 259965 259970) (-227 "DERHAM.spad" 256120 256152 258186 258201) (-226 "DEQUEUE.spad" 255315 255325 255598 255625) (-225 "DEGRED.spad" 254932 254946 255305 255310) (-224 "DEFINTRF.spad" 252514 252524 254922 254927) (-223 "DEFINTEF.spad" 251052 251068 252504 252509) (-222 "DEFAST.spad" 250436 250444 251042 251047) (-221 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"D01APFA.spad" 230823 230831 231373 231378) (-200 "D01ANFA.spad" 230317 230325 230813 230818) (-199 "D01AMFA.spad" 229827 229835 230307 230312) (-198 "D01ALFA.spad" 229367 229375 229817 229822) (-197 "D01AKFA.spad" 228893 228901 229357 229362) (-196 "D01AJFA.spad" 228416 228424 228883 228888) (-195 "D01AGNT.spad" 224483 224491 228406 228411) (-194 "CYCLOTOM.spad" 223989 223997 224473 224478) (-193 "CYCLES.spad" 220781 220789 223979 223984) (-192 "CVMP.spad" 220198 220208 220771 220776) (-191 "CTRIGMNP.spad" 218698 218714 220188 220193) (-190 "CTORKIND.spad" 218301 218309 218688 218693) (-189 "CTORCAT.spad" 217542 217550 218291 218296) (-188 "CTORCAT.spad" 216781 216791 217532 217537) (-187 "CTORCALL.spad" 216370 216380 216771 216776) (-186 "CTOR.spad" 216061 216069 216360 216365) (-185 "CSTTOOLS.spad" 215306 215319 216051 216056) (-184 "CRFP.spad" 209078 209091 215296 215301) (-183 "CRCEAST.spad" 208798 208806 209068 209073) (-182 "CRAPACK.spad" 207865 207875 208788 208793) (-181 "CPMATCH.spad" 207366 207381 207787 207792) (-180 "CPIMA.spad" 207071 207090 207356 207361) (-179 "COORDSYS.spad" 202080 202090 207061 207066) (-178 "CONTOUR.spad" 201507 201515 202070 202075) (-177 "CONTFRAC.spad" 197257 197267 201409 201502) (-176 "CONDUIT.spad" 197015 197023 197247 197252) (-175 "COMRING.spad" 196689 196697 196953 197010) (-174 "COMPPROP.spad" 196207 196215 196679 196684) (-173 "COMPLPAT.spad" 195974 195989 196197 196202) (-172 "COMPLEX2.spad" 195689 195701 195964 195969) (-171 "COMPLEX.spad" 191036 191046 191280 191541) (-170 "COMPILER.spad" 190585 190593 191026 191031) (-169 "COMPFACT.spad" 190187 190201 190575 190580) (-168 "COMPCAT.spad" 188259 188269 189921 190182) (-167 "COMPCAT.spad" 186056 186068 187720 187725) (-166 "COMMUPC.spad" 185804 185822 186046 186051) (-165 "COMMONOP.spad" 185337 185345 185794 185799) (-164 "COMMAAST.spad" 185100 185108 185327 185332) (-163 "COMM.spad" 184911 184919 185090 185095) (-162 "COMBOPC.spad" 183834 183842 184901 184906) (-161 "COMBINAT.spad" 182601 182611 183824 183829) (-160 "COMBF.spad" 180023 180039 182591 182596) (-159 "COLOR.spad" 178860 178868 180013 180018) (-158 "COLONAST.spad" 178526 178534 178850 178855) (-157 "CMPLXRT.spad" 178237 178254 178516 178521) (-156 "CLLCTAST.spad" 177899 177907 178227 178232) (-155 "CLIP.spad" 174007 174015 177889 177894) (-154 "CLIF.spad" 172662 172678 173963 174002) (-153 "CLAGG.spad" 169199 169209 172652 172657) (-152 "CLAGG.spad" 165604 165616 169059 169064) (-151 "CINTSLPE.spad" 164959 164972 165594 165599) (-150 "CHVAR.spad" 163097 163119 164949 164954) (-149 "CHARZ.spad" 163012 163020 163077 163092) (-148 "CHARPOL.spad" 162538 162548 163002 163007) (-147 "CHARNZ.spad" 162300 162308 162518 162533) (-146 "CHAR.spad" 159668 159676 162290 162295) (-145 "CFCAT.spad" 158996 159004 159658 159663) (-144 "CDEN.spad" 158216 158230 158986 158991) (-143 "CCLASS.spad" 156312 156320 157574 157613) (-142 "CATEGORY.spad" 155386 155394 156302 156307) (-141 "CATCTOR.spad" 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134869) (-120 "BRAGG.spad" 132750 132762 133786 133791) (-119 "BPADICRT.spad" 130575 130587 130822 130915) (-118 "BPADIC.spad" 130247 130259 130501 130570) (-117 "BOUNDZRO.spad" 129903 129920 130237 130242) (-116 "BOP1.spad" 127361 127371 129893 129898) (-115 "BOP.spad" 122503 122511 127351 127356) (-114 "BOOLEAN.spad" 122051 122059 122493 122498) (-113 "BOOLE.spad" 121701 121709 122041 122046) (-112 "BOOLE.spad" 121349 121359 121691 121696) (-111 "BMODULE.spad" 121061 121073 121317 121344) (-110 "BITS.spad" 120435 120443 120650 120677) (-109 "BINDING.spad" 119856 119864 120425 120430) (-108 "BINARY.spad" 117825 117833 118181 118274) (-107 "BGAGG.spad" 117030 117040 117805 117820) (-106 "BGAGG.spad" 116243 116255 117020 117025) (-105 "BFUNCT.spad" 115807 115815 116223 116238) (-104 "BEZOUT.spad" 114947 114974 115757 115762) (-103 "BBTREE.spad" 111695 111705 114425 114452) (-102 "BASTYPE.spad" 111194 111202 111685 111690) (-101 "BASTYPE.spad" 110691 110701 111184 111189) (-100 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"ASP49.spad" 86833 86846 87824 87829) (-77 "ASP42.spad" 85248 85287 86823 86828) (-76 "ASP41.spad" 83835 83874 85238 85243) (-75 "ASP4.spad" 83130 83143 83825 83830) (-74 "ASP35.spad" 82118 82131 83120 83125) (-73 "ASP34.spad" 81419 81432 82108 82113) (-72 "ASP33.spad" 80979 80992 81409 81414) (-71 "ASP31.spad" 80119 80132 80969 80974) (-70 "ASP30.spad" 79011 79024 80109 80114) (-69 "ASP29.spad" 78477 78490 79001 79006) (-68 "ASP28.spad" 69750 69763 78467 78472) (-67 "ASP27.spad" 68647 68660 69740 69745) (-66 "ASP24.spad" 67734 67747 68637 68642) (-65 "ASP20.spad" 67198 67211 67724 67729) (-64 "ASP19.spad" 61884 61897 67188 67193) (-63 "ASP12.spad" 61298 61311 61874 61879) (-62 "ASP10.spad" 60569 60582 61288 61293) (-61 "ASP1.spad" 59950 59963 60559 60564) (-60 "ARRAY2.spad" 59189 59198 59428 59455) (-59 "ARRAY12.spad" 57902 57913 59179 59184) (-58 "ARRAY1.spad" 56565 56574 56911 56938) (-57 "ARR2CAT.spad" 52347 52368 56533 56560) (-56 "ARR2CAT.spad" 48149 48172 52337 52342) (-55 "ARITY.spad" 47521 47528 48139 48144) (-54 "APPRULE.spad" 46805 46827 47511 47516) (-53 "APPLYORE.spad" 46424 46437 46795 46800) (-52 "ANY1.spad" 45495 45504 46414 46419) (-51 "ANY.spad" 44346 44353 45485 45490) (-50 "ANTISYM.spad" 42791 42807 44326 44341) (-49 "ANON.spad" 42500 42507 42781 42786) (-48 "AN.spad" 40806 40813 42313 42406) (-47 "AMR.spad" 38991 39002 40704 40801) (-46 "AMR.spad" 37007 37020 38722 38727) (-45 "ALIST.spad" 33847 33868 34197 34224) (-44 "ALGSC.spad" 32982 33008 33719 33772) (-43 "ALGPKG.spad" 28765 28776 32938 32943) (-42 "ALGMFACT.spad" 27958 27972 28755 28760) (-41 "ALGMANIP.spad" 25442 25457 27785 27790) (-40 "ALGFF.spad" 23047 23074 23264 23420) (-39 "ALGFACT.spad" 22166 22176 23037 23042) (-38 "ALGEBRA.spad" 21999 22008 22122 22161) (-37 "ALGEBRA.spad" 21864 21875 21989 21994) (-36 "ALAGG.spad" 21376 21397 21832 21859) (-35 "AHYP.spad" 20757 20764 21366 21371) (-34 "AGG.spad" 19466 19473 20747 20752) (-33 "AGG.spad" 18139 18148 19422 19427) (-32 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 7312a121..dc21210a 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,17 +1,17 @@ -(207264 . 3524522247) -((((-877)) . T)) -((((-877)) . T)) -((((-877)) . T)) -((((-877)) . T)) -((((-877)) . T)) -((((-1203)) . T)) -((((-877)) . T) (((-1203)) . T)) -((((-1203)) . T)) +(207056 . 3524556583) +((((-876)) . T)) +((((-876)) . T)) +((((-876)) . T)) +((((-876)) . T)) +((((-876)) . T)) +((((-1202)) . T)) +((((-876)) . T) (((-1202)) . T)) +((((-1202)) . T)) ((((-419 |#2|) |#3|) . T)) -((((-419 (-558))) |has| (-419 |#2|) (-1059 (-419 (-558)))) (((-558)) |has| (-419 |#2|) (-1059 (-558))) (((-419 |#2|)) . T)) +((((-419 (-558))) |has| (-419 |#2|) (-1058 (-419 (-558)))) (((-558)) |has| (-419 |#2|) (-1058 (-558))) (((-419 |#2|)) . T)) ((((-419 |#2|)) . T)) -((((-558)) |has| (-419 |#2|) (-658 (-558))) (((-419 |#2|)) . 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T)) ((((-419 (-558))) . T) (((-558)) . T)) ((((-558)) . T) (($) . T) (((-419 (-558))) . T)) ((((-558)) . T)) -((((-877)) . T)) +((((-876)) . T)) ((((-114)) . T)) ((((-114)) . T)) ((((-558) (-114)) . T)) ((((-558) (-114)) . T)) -((((-558) (-114)) . T) (((-1255 (-558)) $) . T)) +((((-558) (-114)) . T) (((-1254 (-558)) $) . T)) ((((-547)) . T)) ((((-114)) . T)) -((((-877)) . T)) +((((-876)) . T)) ((((-114)) . T)) ((((-114)) . T)) ((((-547)) . T)) -((((-877)) . T)) -((((-1198)) . T)) -((((-877)) . T)) +((((-876)) . T)) +((((-1197)) . T)) +((((-876)) . T)) ((($) . T)) -((((-877)) . T)) +((((-876)) . T)) ((($) . T) (((-558)) . T)) ((($) . T)) ((($ $) . T)) @@ -223,7 +223,7 @@ ((($) . T)) ((((-558)) . T) (($) . T)) (((|#1|) . T)) -((((-877)) . T)) +((((-876)) . T)) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-419 (-558))) . T)) @@ -234,7 +234,7 @@ ((((-118 |#1|)) . T) (((-419 (-558))) . T) (($) . T)) ((((-118 |#1|) (-118 |#1|)) . T) (((-419 (-558)) (-419 (-558))) . T) (($ $) . T)) ((((-118 |#1|)) . T)) -((((-1198) (-118 |#1|)) |has| (-118 |#1|) (-526 (-1198) (-118 |#1|))) (((-118 |#1|) (-118 |#1|)) |has| (-118 |#1|) (-321 (-118 |#1|)))) +((((-1197) (-118 |#1|)) |has| (-118 |#1|) (-526 (-1197) (-118 |#1|))) (((-118 |#1|) (-118 |#1|)) |has| (-118 |#1|) (-321 (-118 |#1|)))) ((((-118 |#1|)) |has| (-118 |#1|) (-321 (-118 |#1|)))) ((((-118 |#1|) $) |has| (-118 |#1|) (-298 (-118 |#1|) (-118 |#1|)))) ((((-118 |#1|)) . T)) @@ -247,63 +247,63 @@ ((((-118 |#1|)) . T)) (((|#1|) . T)) (((|#1|) . 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T)) -((((-547)) |has| |#4| (-631 (-547)))) +((((-547)) |has| |#4| (-630 (-547)))) (((|#4|) . T)) -(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1122)))) -(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1122)))) +(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1121)))) +(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1121)))) (((|#4|) . T)) -((((-877)) . T) (((-661 |#4|)) . T)) +((((-876)) . T) (((-660 |#4|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-175))) @@ -4137,15 +4128,15 @@ (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -((((-877)) . T)) +((((-876)) . T)) ((($) . T) (((-558)) . T) ((|#2|) . T)) ((($) . T) ((|#2|) . T)) (((|#2|) |has| |#2| (-175))) (((|#2|) |has| |#2| (-175))) -((((-841 |#1|)) . T)) -(((|#2|) . T) (((-558)) . T) (((-841 |#1|)) . T)) -(((|#2| (-841 |#1|)) . T)) -(((|#2| (-908 |#1|)) . T)) +((((-840 |#1|)) . T)) +(((|#2|) . T) (((-558)) . T) (((-840 |#1|)) . T)) +(((|#2| (-840 |#1|)) . T)) +(((|#2| (-907 |#1|)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-175))) (((|#2| |#2|) . T)) @@ -4155,12 +4146,12 @@ (((|#2|) |has| |#2| (-175))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-877)) . T)) +((((-876)) . T)) (((|#2|) . T) (($) . T) (((-558)) . T)) -((((-908 |#1|)) . T) ((|#2|) . T) (((-558)) . T) (((-841 |#1|)) . T)) -((((-908 |#1|)) . T) (((-841 |#1|)) . T)) +((((-907 |#1|)) . T) ((|#2|) . T) (((-558)) . T) (((-840 |#1|)) . T)) +((((-907 |#1|)) . T) (((-840 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-1198) |#1|) . T)) +((((-1197) |#1|) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| |#1|) . T)) (((|#1|) . T)) @@ -4169,11 +4160,11 @@ (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T) (($) . T)) -((((-877)) . T)) +((((-876)) . T)) (((|#1|) . T) (($) . T) (((-558)) . T)) -(((|#1|) . T) (((-558)) . T) (((-841 (-1198))) . T)) -((((-841 (-1198))) . T)) -((((-1198) |#1|) . T)) +(((|#1|) . T) (((-558)) . T) (((-840 (-1197))) . T)) +((((-840 (-1197))) . T)) +((((-1197) |#1|) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-175))) @@ -4185,7 +4176,7 @@ (((|#1|) . T)) (((|#2|) . T) ((|#1|) . T) (((-558)) . T)) (((|#1|) . T) (($) . T)) -((((-877)) . T)) +((((-876)) . T)) (((|#1|) . T) (($) . T) (((-558)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-175))) @@ -4196,20 +4187,20 @@ (((|#2|) |has| |#2| (-175))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-877)) . T)) +((((-876)) . T)) (((|#2|) . T) (($) . T) (((-558)) . T)) -(((|#2|) . T) (((-558)) . T) (((-841 |#1|)) . T)) -((((-841 |#1|)) . T)) +(((|#2|) . T) (((-558)) . T) (((-840 |#1|)) . T)) +((((-840 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-992)) . T)) -((((-992)) . T)) -((((-992)) . T) (((-877)) . T)) +((((-991)) . T)) +((((-991)) . T)) +((((-991)) . T) (((-876)) . T)) ((((-558)) . T)) ((($ $) . T)) ((($) . T)) ((($) . T)) -((((-877)) . T)) +((((-876)) . T)) ((((-558)) . T) (($) . T)) ((($) . T)) ((((-558)) . T)) -(((-3) T) ((-2) T) ((-1) T) ((0) T) ((-1318 . -175) T) ((-1318 . -633) 207246) ((-1318 . -746) T) ((-1318 . -1133) T) ((-1318 . -1078) T) ((-1318 . -1070) T) ((-1318 . -668) 207233) ((-1318 . -666) 207205) ((-1318 . -133) T) ((-1318 . -25) T) ((-1318 . -102) T) ((-1318 . -1238) T) ((-1318 . -630) 207187) ((-1318 . -1122) T) ((-1318 . -23) T) ((-1318 . -21) T) ((-1318 . -1077) 207174) ((-1318 . -1072) 207161) ((-1318 . -111) 207146) ((-1318 . -381) T) ((-1318 . -631) 207128) ((-1318 . -1173) T) ((-1314 . -1122) T) ((-1314 . -630) 207095) ((-1314 . -1238) T) ((-1314 . -102) T) ((-1314 . -502) 207077) ((-1314 . -633) 207059) ((-1313 . -1311) 207038) ((-1313 . -1059) 207015) ((-1313 . -633) 206964) ((-1313 . -1070) T) ((-1313 . -1078) T) ((-1313 . -1133) T) ((-1313 . -746) T) ((-1313 . -21) T) ((-1313 . -666) 206923) ((-1313 . -23) T) ((-1313 . -1122) T) ((-1313 . -630) 206905) ((-1313 . -1238) T) ((-1313 . -102) T) ((-1313 . -25) T) ((-1313 . -133) T) ((-1313 . -668) 206879) ((-1313 . -1303) 206863) ((-1313 . -737) 206833) ((-1313 . -660) 206803) ((-1313 . -1077) 206787) ((-1313 . -1072) 206771) ((-1313 . -111) 206750) ((-1313 . -38) 206720) ((-1313 . -1308) 206699) ((-1312 . -1070) T) ((-1312 . -1078) T) ((-1312 . -1133) T) ((-1312 . -746) T) ((-1312 . -21) T) ((-1312 . -666) 206658) ((-1312 . -23) T) ((-1312 . -1122) T) ((-1312 . -630) 206640) ((-1312 . -1238) T) ((-1312 . -102) T) ((-1312 . -25) T) ((-1312 . -133) T) ((-1312 . -668) 206614) ((-1312 . -633) 206570) ((-1312 . -1303) 206554) ((-1312 . -737) 206524) ((-1312 . -660) 206494) ((-1312 . -1077) 206478) ((-1312 . -1072) 206462) ((-1312 . -111) 206441) ((-1312 . -38) 206411) ((-1312 . -397) 206390) ((-1312 . -1059) 206374) ((-1310 . -1311) 206350) ((-1310 . -1059) 206324) ((-1310 . -633) 206270) ((-1310 . -1070) T) ((-1310 . -1078) T) ((-1310 . -1133) T) ((-1310 . -746) T) ((-1310 . -21) T) ((-1310 . -666) 206229) ((-1310 . -23) T) ((-1310 . -1122) T) ((-1310 . -630) 206211) ((-1310 . -1238) T) ((-1310 . -102) T) ((-1310 . -25) T) ((-1310 . -133) T) ((-1310 . -668) 206185) ((-1310 . -1303) 206169) ((-1310 . -737) 206139) ((-1310 . -660) 206109) ((-1310 . -1077) 206093) ((-1310 . -1072) 206077) ((-1310 . -111) 206056) ((-1310 . -38) 206026) ((-1310 . -1308) 206002) ((-1309 . -1311) 205981) ((-1309 . -1059) 205938) ((-1309 . -633) 205867) ((-1309 . -1070) T) ((-1309 . -1078) T) ((-1309 . -1133) T) ((-1309 . -746) T) ((-1309 . -21) T) ((-1309 . -666) 205826) ((-1309 . -23) T) ((-1309 . -1122) T) ((-1309 . -630) 205808) ((-1309 . -1238) T) ((-1309 . -102) T) ((-1309 . -25) T) ((-1309 . -133) T) ((-1309 . -668) 205782) ((-1309 . -1303) 205766) ((-1309 . -737) 205736) ((-1309 . -660) 205706) ((-1309 . -1077) 205690) ((-1309 . -1072) 205674) ((-1309 . -111) 205653) ((-1309 . -38) 205623) ((-1309 . -1308) 205602) ((-1309 . -397) 205574) ((-1304 . -397) 205546) ((-1304 . -633) 205495) ((-1304 . -1059) 205472) ((-1304 . -660) 205442) ((-1304 . -737) 205412) ((-1304 . -668) 205386) ((-1304 . -666) 205345) ((-1304 . -133) T) ((-1304 . -25) T) ((-1304 . -102) T) ((-1304 . -1238) T) ((-1304 . -630) 205327) ((-1304 . -1122) T) ((-1304 . -23) T) ((-1304 . -21) T) ((-1304 . -1077) 205311) ((-1304 . -1072) 205295) ((-1304 . -111) 205274) ((-1304 . -1311) 205253) ((-1304 . -1070) T) ((-1304 . -1078) T) ((-1304 . -1133) T) ((-1304 . -746) T) ((-1304 . -1303) 205237) ((-1304 . -38) 205207) ((-1304 . -1308) 205186) ((-1302 . -1233) 205155) ((-1302 . -630) 205117) ((-1302 . -153) 205101) ((-1302 . -34) T) ((-1302 . -1238) T) ((-1302 . -102) T) ((-1302 . -321) 205039) ((-1302 . -526) 204972) ((-1302 . -1122) T) ((-1302 . -501) 204956) ((-1302 . -631) 204917) ((-1302 . -997) 204886) ((-1301 . -1070) T) ((-1301 . -1078) T) ((-1301 . -1133) T) ((-1301 . -746) T) ((-1301 . -21) T) ((-1301 . -666) 204831) ((-1301 . -23) T) ((-1301 . -1122) T) ((-1301 . -630) 204800) ((-1301 . -1238) T) ((-1301 . -102) T) ((-1301 . -25) T) ((-1301 . -133) T) ((-1301 . -668) 204760) ((-1301 . -633) 204702) ((-1301 . -502) 204686) ((-1301 . -38) 204656) ((-1301 . -111) 204621) ((-1301 . -1072) 204591) ((-1301 . -1077) 204561) ((-1301 . -660) 204531) ((-1301 . -737) 204501) ((-1300 . -1104) T) ((-1300 . -502) 204482) ((-1300 . -630) 204448) ((-1300 . -633) 204429) ((-1300 . -1122) T) ((-1300 . -1238) T) ((-1300 . -102) T) ((-1300 . -93) T) ((-1299 . -1104) T) ((-1299 . -502) 204410) ((-1299 . -630) 204376) ((-1299 . -633) 204357) ((-1299 . -1122) T) ((-1299 . -1238) T) ((-1299 . -102) T) ((-1299 . -93) T) ((-1294 . -630) 204339) ((-1292 . -1122) T) ((-1292 . -630) 204321) ((-1292 . -1238) T) ((-1292 . -102) T) ((-1291 . -1122) T) ((-1291 . -630) 204303) ((-1291 . -1238) T) ((-1291 . -102) T) ((-1288 . -1287) 204287) ((-1288 . -385) 204271) ((-1288 . -864) 204250) ((-1288 . -861) 204229) ((-1288 . -153) 204213) ((-1288 . -34) T) ((-1288 . -1238) T) ((-1288 . -102) 204143) ((-1288 . -630) 204055) ((-1288 . -321) 203993) ((-1288 . -526) 203926) ((-1288 . -1122) 203876) ((-1288 . -501) 203860) ((-1288 . -631) 203821) ((-1288 . -298) 203773) ((-1288 . -616) 203750) ((-1288 . -300) 203727) ((-1288 . -671) 203711) ((-1288 . -19) 203695) ((-1285 . -1122) T) ((-1285 . -630) 203661) ((-1285 . -1238) T) ((-1285 . -102) T) ((-1278 . -1281) 203645) ((-1278 . -240) 203604) ((-1278 . -633) 203486) ((-1278 . -668) 203411) ((-1278 . -666) 203321) ((-1278 . -133) T) ((-1278 . -25) T) ((-1278 . -102) T) ((-1278 . -630) 203303) ((-1278 . -1122) T) ((-1278 . -23) T) ((-1278 . -21) T) ((-1278 . -746) T) ((-1278 . -1133) T) ((-1278 . -1078) T) ((-1278 . -1070) T) ((-1278 . -236) 203256) ((-1278 . -1238) T) ((-1278 . -239) 203215) ((-1278 . -298) 203180) ((-1278 . -917) 203093) ((-1278 . -911) 202981) ((-1278 . -919) 202894) ((-1278 . -994) 202863) ((-1278 . -38) 202760) ((-1278 . -111) 202622) ((-1278 . -1072) 202505) ((-1278 . -1077) 202388) ((-1278 . -660) 202285) ((-1278 . -737) 202182) ((-1278 . -147) 202161) ((-1278 . -149) 202140) ((-1278 . -175) 202091) ((-1278 . -569) 202070) ((-1278 . -302) 202049) ((-1278 . -47) 202026) ((-1278 . -1267) 202003) ((-1278 . -35) 201969) ((-1278 . -95) 201935) ((-1278 . -296) 201901) ((-1278 . -505) 201867) ((-1278 . -1227) 201833) ((-1278 . -1224) 201799) ((-1278 . -1023) 201765) ((-1275 . -338) 201709) ((-1275 . -1059) 201675) ((-1275 . -424) 201641) ((-1275 . -38) 201498) ((-1275 . -633) 201372) ((-1275 . -668) 201261) ((-1275 . -666) 201135) ((-1275 . -746) T) ((-1275 . -1133) T) ((-1275 . -1078) T) ((-1275 . -1070) T) ((-1275 . -111) 200985) ((-1275 . -1072) 200874) ((-1275 . -1077) 200763) ((-1275 . -21) T) ((-1275 . -23) T) ((-1275 . -1122) T) ((-1275 . -630) 200745) ((-1275 . -1238) T) ((-1275 . -102) T) ((-1275 . -25) T) ((-1275 . -133) T) ((-1275 . -660) 200602) ((-1275 . -737) 200459) ((-1275 . -147) 200420) ((-1275 . -149) 200381) ((-1275 . -175) T) ((-1275 . -569) T) ((-1275 . -302) T) ((-1275 . -47) 200325) ((-1274 . -1273) 200304) ((-1274 . -376) 200283) ((-1274 . -1243) 200262) ((-1274 . -940) 200241) ((-1274 . -569) 200192) ((-1274 . -175) 200123) ((-1274 . -633) 199936) ((-1274 . -737) 199777) ((-1274 . -660) 199618) ((-1274 . -38) 199459) ((-1274 . -464) 199438) ((-1274 . -319) 199417) ((-1274 . -668) 199314) ((-1274 . -666) 199196) ((-1274 . -746) T) ((-1274 . -1133) T) ((-1274 . -1078) T) ((-1274 . -1070) T) ((-1274 . -111) 199010) ((-1274 . -1072) 198845) ((-1274 . -1077) 198680) ((-1274 . -21) T) ((-1274 . -23) T) ((-1274 . -1122) T) ((-1274 . -630) 198662) ((-1274 . -1238) T) ((-1274 . -102) T) ((-1274 . -25) T) ((-1274 . -133) T) ((-1274 . -302) 198613) ((-1274 . -250) 198592) ((-1274 . -1023) 198558) ((-1274 . -1224) 198524) ((-1274 . -1227) 198490) ((-1274 . -505) 198456) ((-1274 . -296) 198422) ((-1274 . -95) 198388) ((-1274 . -35) 198354) ((-1274 . -1267) 198324) ((-1274 . -47) 198294) ((-1274 . -149) 198273) ((-1274 . -147) 198252) ((-1274 . -994) 198214) ((-1274 . -919) 198120) ((-1274 . -911) 198024) ((-1274 . -917) 197930) ((-1274 . -298) 197888) ((-1274 . -239) 197840) ((-1274 . -236) 197786) ((-1274 . -240) 197738) ((-1274 . -1271) 197722) ((-1274 . -1059) 197706) ((-1269 . -1273) 197667) ((-1269 . -376) 197646) ((-1269 . -1243) 197625) ((-1269 . -940) 197604) ((-1269 . -569) 197555) ((-1269 . -175) 197486) ((-1269 . -633) 197229) ((-1269 . -737) 197070) ((-1269 . -660) 196911) ((-1269 . -38) 196752) ((-1269 . -464) 196731) ((-1269 . -319) 196710) ((-1269 . -668) 196607) ((-1269 . -666) 196489) ((-1269 . -746) T) ((-1269 . -1133) T) ((-1269 . -1078) T) ((-1269 . -1070) T) ((-1269 . -111) 196303) ((-1269 . -1072) 196138) ((-1269 . -1077) 195973) ((-1269 . -21) T) ((-1269 . -23) T) ((-1269 . -1122) T) ((-1269 . -630) 195955) ((-1269 . -1238) T) ((-1269 . -102) T) ((-1269 . -25) T) ((-1269 . -133) T) ((-1269 . -302) 195906) ((-1269 . -250) 195885) ((-1269 . -1023) 195851) ((-1269 . -1224) 195817) ((-1269 . -1227) 195783) ((-1269 . -505) 195749) ((-1269 . -296) 195715) ((-1269 . -95) 195681) ((-1269 . -35) 195647) ((-1269 . -1267) 195617) ((-1269 . -47) 195587) ((-1269 . -149) 195566) ((-1269 . -147) 195545) ((-1269 . -994) 195507) ((-1269 . -919) 195413) ((-1269 . -911) 195294) ((-1269 . -917) 195200) ((-1269 . -298) 195158) ((-1269 . -239) 195110) ((-1269 . -236) 195056) ((-1269 . -240) 195008) ((-1269 . -1271) 194992) ((-1269 . -1059) 194927) ((-1257 . -1264) 194911) ((-1257 . -1173) 194889) ((-1257 . -631) NIL) ((-1257 . -321) 194876) ((-1257 . -526) 194822) ((-1257 . -338) 194799) ((-1257 . -1059) 194679) ((-1257 . -424) 194663) ((-1257 . -38) 194492) ((-1257 . -111) 194294) ((-1257 . -1072) 194117) ((-1257 . -1077) 193940) ((-1257 . -666) 193850) ((-1257 . -668) 193739) ((-1257 . -660) 193568) ((-1257 . -737) 193397) ((-1257 . -633) 193145) ((-1257 . -147) 193124) ((-1257 . -149) 193103) ((-1257 . -47) 193080) ((-1257 . -390) 193064) ((-1257 . -658) 193012) ((-1257 . -917) 192955) ((-1257 . -911) 192858) ((-1257 . -919) 192765) ((-1257 . -901) NIL) ((-1257 . -929) 192744) ((-1257 . -1243) 192723) ((-1257 . -969) 192692) ((-1257 . -940) 192671) ((-1257 . -569) 192582) ((-1257 . -302) 192493) ((-1257 . -175) 192384) ((-1257 . -464) 192315) ((-1257 . -319) 192294) ((-1257 . -298) 192221) ((-1257 . -240) T) ((-1257 . -133) T) ((-1257 . -25) T) ((-1257 . -102) T) ((-1257 . -630) 192203) ((-1257 . -1122) T) ((-1257 . -23) T) ((-1257 . -21) T) ((-1257 . -746) T) ((-1257 . -1133) T) ((-1257 . -1078) T) ((-1257 . -1070) T) ((-1257 . -236) 192190) ((-1257 . -1238) T) ((-1257 . -239) T) ((-1257 . -274) 192174) ((-1257 . -234) 192158) ((-1255 . -1115) 192142) ((-1255 . -635) 192126) ((-1255 . -1122) 192104) ((-1255 . -630) 192071) ((-1255 . -1238) 192049) ((-1255 . -102) 192027) ((-1255 . -1116) 191984) ((-1253 . -1252) 191963) ((-1253 . -1023) 191929) ((-1253 . -1224) 191895) ((-1253 . -1227) 191861) ((-1253 . -505) 191827) ((-1253 . -296) 191793) ((-1253 . -95) 191759) ((-1253 . -35) 191725) ((-1253 . -1267) 191702) ((-1253 . -47) 191679) ((-1253 . -633) 191427) ((-1253 . -737) 191241) ((-1253 . -660) 191055) ((-1253 . -668) 190863) ((-1253 . -666) 190718) ((-1253 . -1077) 190526) ((-1253 . -1072) 190334) ((-1253 . -111) 190116) ((-1253 . -38) 189930) ((-1253 . -994) 189899) ((-1253 . -298) 189799) ((-1253 . -1250) 189783) ((-1253 . -746) T) ((-1253 . -1133) T) ((-1253 . -1078) T) ((-1253 . -1070) T) ((-1253 . -21) T) ((-1253 . -23) T) ((-1253 . -1122) T) ((-1253 . -630) 189765) ((-1253 . -1238) T) ((-1253 . -102) T) ((-1253 . -25) T) ((-1253 . -133) T) ((-1253 . -147) 189690) ((-1253 . -149) 189615) ((-1253 . -631) 189286) ((-1253 . -234) 189256) ((-1253 . -917) 189107) ((-1253 . -919) 188904) ((-1253 . -911) 188699) ((-1253 . -274) 188669) ((-1253 . -239) 188528) ((-1253 . -236) 188381) ((-1253 . -240) 188286) ((-1253 . -376) 188265) ((-1253 . -1243) 188244) ((-1253 . -940) 188223) ((-1253 . -569) 188174) ((-1253 . -175) 188105) ((-1253 . -464) 188084) ((-1253 . -319) 188063) ((-1253 . -302) 188014) ((-1253 . -250) 187993) ((-1253 . -351) 187963) ((-1253 . -526) 187823) ((-1253 . -321) 187762) ((-1253 . -390) 187732) ((-1253 . -658) 187640) ((-1253 . -412) 187610) ((-1253 . -901) 187483) ((-1253 . -842) 187436) ((-1253 . -812) 187389) ((-1253 . -814) 187342) ((-1253 . -861) 187241) ((-1253 . -864) 187140) ((-1253 . -816) 187093) ((-1253 . -819) 187046) ((-1253 . -860) 186999) ((-1253 . -899) 186969) ((-1253 . -929) 186922) ((-1253 . -1041) 186874) ((-1253 . -1059) 186660) ((-1253 . -1173) 186612) ((-1253 . -1012) 186582) ((-1248 . -1252) 186543) ((-1248 . -1023) 186509) ((-1248 . -1224) 186475) ((-1248 . -1227) 186441) ((-1248 . -505) 186407) ((-1248 . -296) 186373) ((-1248 . -95) 186339) ((-1248 . -35) 186305) ((-1248 . -1267) 186282) ((-1248 . -47) 186259) ((-1248 . -633) 186054) ((-1248 . -737) 185850) ((-1248 . -660) 185646) ((-1248 . -668) 185498) ((-1248 . -666) 185335) ((-1248 . -1077) 185125) ((-1248 . -1072) 184915) ((-1248 . -111) 184661) ((-1248 . -38) 184457) ((-1248 . -994) 184426) ((-1248 . -298) 184254) ((-1248 . -1250) 184238) ((-1248 . -746) T) ((-1248 . -1133) T) ((-1248 . -1078) T) ((-1248 . -1070) T) ((-1248 . -21) T) ((-1248 . -23) T) ((-1248 . -1122) T) ((-1248 . -630) 184220) ((-1248 . -1238) T) ((-1248 . -102) T) ((-1248 . -25) T) ((-1248 . -133) T) ((-1248 . -147) 184127) ((-1248 . -149) 184034) ((-1248 . -631) NIL) ((-1248 . -234) 183986) ((-1248 . -917) 183819) ((-1248 . -919) 183580) ((-1248 . -911) 183316) ((-1248 . -274) 183268) ((-1248 . -239) 183091) ((-1248 . -236) 182908) ((-1248 . -240) 182795) ((-1248 . -376) 182774) ((-1248 . -1243) 182753) ((-1248 . -940) 182732) ((-1248 . -569) 182683) ((-1248 . -175) 182614) ((-1248 . -464) 182593) ((-1248 . -319) 182572) ((-1248 . -302) 182523) ((-1248 . -250) 182502) ((-1248 . -351) 182454) ((-1248 . -526) 182188) ((-1248 . -321) 182073) ((-1248 . -390) 182025) ((-1248 . -658) 181977) ((-1248 . -412) 181929) ((-1248 . -901) NIL) ((-1248 . -842) NIL) ((-1248 . -812) NIL) ((-1248 . -814) NIL) ((-1248 . -861) NIL) ((-1248 . -864) NIL) ((-1248 . -816) NIL) ((-1248 . -819) NIL) ((-1248 . -860) NIL) ((-1248 . -899) 181881) ((-1248 . -929) NIL) ((-1248 . -1041) NIL) ((-1248 . -1059) 181847) ((-1248 . -1173) NIL) ((-1248 . -1012) 181799) ((-1247 . -857) T) ((-1247 . -864) T) ((-1247 . -861) T) ((-1247 . -1122) T) ((-1247 . -630) 181781) ((-1247 . -1238) T) ((-1247 . -102) T) ((-1247 . -381) T) ((-1247 . -682) T) ((-1246 . -857) T) ((-1246 . -864) T) ((-1246 . -861) T) ((-1246 . -1122) T) ((-1246 . -630) 181763) ((-1246 . -1238) T) ((-1246 . -102) T) ((-1246 . -381) T) ((-1246 . -682) T) ((-1245 . -857) T) ((-1245 . -864) T) ((-1245 . -861) T) ((-1245 . -1122) T) ((-1245 . -630) 181745) ((-1245 . -1238) T) ((-1245 . -102) T) ((-1245 . -381) T) ((-1245 . -682) T) ((-1244 . -857) T) ((-1244 . -864) T) ((-1244 . -861) T) ((-1244 . -1122) T) ((-1244 . -630) 181727) ((-1244 . -1238) T) ((-1244 . -102) T) ((-1244 . -381) T) ((-1244 . -682) T) ((-1239 . -1104) T) ((-1239 . -502) 181708) ((-1239 . -630) 181674) ((-1239 . -633) 181655) ((-1239 . -1122) T) ((-1239 . -1238) T) ((-1239 . -102) T) ((-1239 . -93) T) ((-1236 . -502) 181632) ((-1236 . -630) 181573) ((-1236 . -633) 181550) ((-1236 . -1122) 181528) ((-1236 . -1238) 181506) ((-1236 . -102) 181484) ((-1231 . -760) 181460) ((-1231 . -35) 181426) ((-1231 . -95) 181392) ((-1231 . -296) 181358) ((-1231 . -505) 181324) ((-1231 . -1227) 181290) ((-1231 . -1224) 181256) ((-1231 . -1023) 181222) ((-1231 . -47) 181191) ((-1231 . -38) 181088) ((-1231 . -660) 180985) ((-1231 . -737) 180882) ((-1231 . -633) 180764) ((-1231 . -302) 180743) ((-1231 . -569) 180722) ((-1231 . -111) 180584) ((-1231 . -1072) 180467) ((-1231 . -1077) 180350) ((-1231 . -175) 180301) ((-1231 . -149) 180280) ((-1231 . -147) 180259) ((-1231 . -668) 180184) ((-1231 . -666) 180094) ((-1231 . -994) 180055) ((-1231 . -919) 180036) ((-1231 . -1238) T) ((-1231 . -911) 180015) ((-1231 . -1070) T) ((-1231 . -1078) T) ((-1231 . -1133) T) ((-1231 . -746) T) ((-1231 . -21) T) ((-1231 . -23) T) ((-1231 . -1122) T) ((-1231 . -630) 179997) ((-1231 . -102) T) ((-1231 . -25) T) ((-1231 . -133) T) ((-1231 . -917) 179978) ((-1231 . -526) 179945) ((-1231 . -321) 179932) ((-1225 . -1031) 179916) ((-1225 . -34) T) ((-1225 . -1238) T) ((-1225 . -102) 179866) ((-1225 . -630) 179798) ((-1225 . -321) 179736) ((-1225 . -526) 179669) ((-1225 . -1122) 179647) ((-1225 . -501) 179631) ((-1220 . -378) 179605) ((-1220 . -102) T) ((-1220 . -1238) T) ((-1220 . -630) 179587) ((-1220 . -1122) T) ((-1218 . -1122) T) ((-1218 . -630) 179569) ((-1218 . -1238) T) ((-1218 . -102) T) ((-1218 . -633) 179551) ((-1212 . -849) 179535) ((-1212 . -102) T) ((-1212 . -1238) T) ((-1212 . -630) 179517) ((-1212 . -1122) T) ((-1210 . -1215) 179496) ((-1210 . -233) 179446) ((-1210 . -107) 179396) ((-1210 . -321) 179200) ((-1210 . -526) 178960) ((-1210 . -501) 178897) ((-1210 . -153) 178847) ((-1210 . -631) NIL) ((-1210 . -242) 178797) ((-1210 . -627) 178776) ((-1210 . -300) 178755) ((-1210 . -1238) T) ((-1210 . -298) 178734) ((-1210 . -1122) T) ((-1210 . -630) 178716) ((-1210 . -102) T) ((-1210 . -34) T) ((-1210 . -616) 178695) ((-1206 . -1122) T) ((-1206 . -630) 178677) ((-1206 . -1238) T) ((-1206 . -102) T) ((-1205 . -857) T) ((-1205 . -864) T) ((-1205 . -861) T) ((-1205 . -1122) T) ((-1205 . -630) 178659) ((-1205 . -1238) T) ((-1205 . -102) T) ((-1205 . -381) T) ((-1205 . -682) T) ((-1204 . -857) T) ((-1204 . -864) T) ((-1204 . -861) T) ((-1204 . -1122) T) ((-1204 . -630) 178641) ((-1204 . -1238) T) ((-1204 . -102) T) ((-1204 . -381) T) ((-1203 . -1284) T) ((-1203 . -1122) T) ((-1203 . -630) 178608) ((-1203 . -1238) T) ((-1203 . -102) T) ((-1203 . -1059) 178544) ((-1203 . -633) 178480) ((-1202 . -630) 178462) ((-1201 . -630) 178444) ((-1200 . -338) 178421) ((-1200 . -1059) 178317) ((-1200 . -424) 178301) ((-1200 . -38) 178198) ((-1200 . -633) 178051) ((-1200 . -668) 177976) ((-1200 . -666) 177886) ((-1200 . -746) T) ((-1200 . -1133) T) ((-1200 . -1078) T) ((-1200 . -1070) T) ((-1200 . -111) 177748) ((-1200 . -1072) 177631) ((-1200 . -1077) 177514) ((-1200 . -21) T) ((-1200 . -23) T) ((-1200 . -1122) T) ((-1200 . -630) 177496) ((-1200 . -1238) T) ((-1200 . -102) T) ((-1200 . -25) T) ((-1200 . -133) T) ((-1200 . -660) 177393) ((-1200 . -737) 177290) ((-1200 . -147) 177269) ((-1200 . -149) 177248) ((-1200 . -175) 177199) ((-1200 . -569) 177178) ((-1200 . -302) 177157) ((-1200 . -47) 177134) ((-1198 . -861) T) ((-1198 . -630) 177116) ((-1198 . -1122) T) ((-1198 . -102) T) ((-1198 . -1238) T) ((-1198 . -864) T) ((-1198 . -631) 177038) ((-1198 . -633) 177004) ((-1198 . -1059) 176986) ((-1198 . -901) 176953) ((-1197 . -630) 176935) ((-1196 . -1281) 176919) ((-1196 . -240) 176878) ((-1196 . -633) 176760) ((-1196 . -668) 176685) ((-1196 . -666) 176595) ((-1196 . -133) T) ((-1196 . -25) T) ((-1196 . -102) T) ((-1196 . -630) 176577) ((-1196 . -1122) T) ((-1196 . -23) T) ((-1196 . -21) T) ((-1196 . -746) T) ((-1196 . -1133) T) ((-1196 . -1078) T) ((-1196 . -1070) T) ((-1196 . -236) 176530) ((-1196 . -1238) T) ((-1196 . -239) 176489) ((-1196 . -298) 176454) ((-1196 . -917) 176367) ((-1196 . -911) 176255) ((-1196 . -919) 176168) ((-1196 . -994) 176137) ((-1196 . -38) 176034) ((-1196 . -111) 175896) ((-1196 . -1072) 175779) ((-1196 . -1077) 175662) ((-1196 . -660) 175559) ((-1196 . -737) 175456) ((-1196 . -147) 175435) ((-1196 . -149) 175414) ((-1196 . -175) 175365) ((-1196 . -569) 175344) ((-1196 . -302) 175323) ((-1196 . -47) 175300) ((-1196 . -1267) 175277) ((-1196 . -35) 175243) ((-1196 . -95) 175209) ((-1196 . -296) 175175) ((-1196 . -505) 175141) ((-1196 . -1227) 175107) ((-1196 . -1224) 175073) ((-1196 . -1023) 175039) ((-1195 . -1273) 175000) ((-1195 . -376) 174979) ((-1195 . -1243) 174958) ((-1195 . -940) 174937) ((-1195 . -569) 174888) ((-1195 . -175) 174819) ((-1195 . -633) 174562) ((-1195 . -737) 174403) ((-1195 . -660) 174244) ((-1195 . -38) 174085) ((-1195 . -464) 174064) ((-1195 . -319) 174043) ((-1195 . -668) 173940) ((-1195 . -666) 173822) ((-1195 . -746) T) ((-1195 . -1133) T) ((-1195 . -1078) T) ((-1195 . -1070) T) ((-1195 . -111) 173636) ((-1195 . -1072) 173471) ((-1195 . -1077) 173306) ((-1195 . -21) T) ((-1195 . -23) T) ((-1195 . -1122) T) ((-1195 . -630) 173288) ((-1195 . -1238) T) ((-1195 . -102) T) ((-1195 . -25) T) ((-1195 . -133) T) ((-1195 . -302) 173239) ((-1195 . -250) 173218) ((-1195 . -1023) 173184) ((-1195 . -1224) 173150) ((-1195 . -1227) 173116) ((-1195 . -505) 173082) ((-1195 . -296) 173048) ((-1195 . -95) 173014) ((-1195 . -35) 172980) ((-1195 . -1267) 172950) ((-1195 . -47) 172920) ((-1195 . -149) 172899) ((-1195 . -147) 172878) ((-1195 . -994) 172840) ((-1195 . -919) 172746) ((-1195 . -911) 172627) ((-1195 . -917) 172533) ((-1195 . -298) 172491) ((-1195 . -239) 172443) ((-1195 . -236) 172389) ((-1195 . -240) 172341) ((-1195 . -1271) 172325) ((-1195 . -1059) 172260) ((-1192 . -1264) 172244) ((-1192 . -1173) 172222) ((-1192 . -631) NIL) ((-1192 . -321) 172209) ((-1192 . -526) 172155) ((-1192 . -338) 172132) ((-1192 . -1059) 172012) ((-1192 . -424) 171996) ((-1192 . -38) 171825) ((-1192 . -111) 171627) ((-1192 . -1072) 171450) ((-1192 . -1077) 171273) ((-1192 . -666) 171183) ((-1192 . -668) 171072) ((-1192 . -660) 170901) ((-1192 . -737) 170730) ((-1192 . -633) 170499) ((-1192 . -147) 170478) ((-1192 . -149) 170457) ((-1192 . -47) 170434) ((-1192 . -390) 170418) ((-1192 . -658) 170366) ((-1192 . -917) 170309) ((-1192 . -911) 170212) ((-1192 . -919) 170119) ((-1192 . -901) NIL) ((-1192 . -929) 170098) ((-1192 . -1243) 170077) ((-1192 . -969) 170046) ((-1192 . -940) 170025) ((-1192 . -569) 169936) ((-1192 . -302) 169847) ((-1192 . -175) 169738) ((-1192 . -464) 169669) ((-1192 . -319) 169648) ((-1192 . -298) 169575) ((-1192 . -240) T) ((-1192 . -133) T) ((-1192 . -25) T) ((-1192 . -102) T) ((-1192 . -630) 169557) ((-1192 . -1122) T) ((-1192 . -23) T) ((-1192 . -21) T) ((-1192 . -746) T) ((-1192 . -1133) T) ((-1192 . -1078) T) ((-1192 . -1070) T) ((-1192 . -236) 169544) ((-1192 . -1238) T) ((-1192 . -239) T) ((-1192 . -274) 169528) ((-1192 . -234) 169512) ((-1189 . -1252) 169473) ((-1189 . -1023) 169439) ((-1189 . -1224) 169405) ((-1189 . -1227) 169371) ((-1189 . -505) 169337) ((-1189 . -296) 169303) ((-1189 . -95) 169269) ((-1189 . -35) 169235) ((-1189 . -1267) 169212) ((-1189 . -47) 169189) ((-1189 . -633) 168984) ((-1189 . -737) 168780) ((-1189 . -660) 168576) ((-1189 . -668) 168428) ((-1189 . -666) 168265) ((-1189 . -1077) 168055) ((-1189 . -1072) 167845) ((-1189 . -111) 167591) ((-1189 . -38) 167387) ((-1189 . -994) 167356) ((-1189 . -298) 167184) ((-1189 . -1250) 167168) ((-1189 . -746) T) ((-1189 . -1133) T) ((-1189 . -1078) T) ((-1189 . -1070) T) ((-1189 . -21) T) ((-1189 . -23) T) ((-1189 . -1122) T) ((-1189 . -630) 167150) ((-1189 . -1238) T) ((-1189 . -102) T) ((-1189 . -25) T) ((-1189 . -133) T) ((-1189 . -147) 167057) ((-1189 . -149) 166964) ((-1189 . -631) NIL) ((-1189 . -234) 166916) ((-1189 . -917) 166749) ((-1189 . -919) 166510) ((-1189 . -911) 166246) ((-1189 . -274) 166198) ((-1189 . -239) 166021) ((-1189 . -236) 165838) ((-1189 . -240) 165725) ((-1189 . -376) 165704) ((-1189 . -1243) 165683) ((-1189 . -940) 165662) ((-1189 . -569) 165613) ((-1189 . -175) 165544) ((-1189 . -464) 165523) ((-1189 . -319) 165502) ((-1189 . -302) 165453) ((-1189 . -250) 165432) ((-1189 . -351) 165384) ((-1189 . -526) 165118) ((-1189 . -321) 165003) ((-1189 . -390) 164955) ((-1189 . -658) 164907) ((-1189 . -412) 164859) ((-1189 . -901) NIL) ((-1189 . -842) NIL) ((-1189 . -812) NIL) ((-1189 . -814) NIL) ((-1189 . -861) NIL) ((-1189 . -864) NIL) ((-1189 . -816) NIL) ((-1189 . -819) NIL) ((-1189 . -860) NIL) ((-1189 . -899) 164811) ((-1189 . -929) NIL) ((-1189 . -1041) NIL) ((-1189 . -1059) 164777) ((-1189 . -1173) NIL) ((-1189 . -1012) 164729) ((-1188 . -1104) T) ((-1188 . -502) 164710) ((-1188 . -630) 164676) ((-1188 . -633) 164657) ((-1188 . -1122) T) ((-1188 . -1238) T) ((-1188 . -102) T) ((-1188 . -93) T) ((-1187 . -1122) T) ((-1187 . -630) 164639) ((-1187 . -1238) T) ((-1187 . -102) T) ((-1186 . -1122) T) ((-1186 . -630) 164621) ((-1186 . -1238) T) ((-1186 . -102) T) ((-1181 . -1215) 164597) ((-1181 . -233) 164544) ((-1181 . -107) 164491) ((-1181 . -321) 164286) ((-1181 . -526) 164034) ((-1181 . -501) 163968) ((-1181 . -153) 163915) ((-1181 . -631) NIL) ((-1181 . -242) 163862) ((-1181 . -627) 163838) ((-1181 . -300) 163814) ((-1181 . -1238) T) ((-1181 . -298) 163790) ((-1181 . -1122) T) ((-1181 . -630) 163772) ((-1181 . -102) T) ((-1181 . -34) T) ((-1181 . -616) 163748) ((-1180 . -1165) T) ((-1180 . -385) 163730) ((-1180 . -864) T) ((-1180 . -861) T) ((-1180 . -153) 163712) ((-1180 . -34) T) ((-1180 . -1238) T) ((-1180 . -102) T) ((-1180 . -630) 163694) ((-1180 . -321) NIL) ((-1180 . -526) NIL) ((-1180 . -1122) T) ((-1180 . -501) 163676) ((-1180 . -631) NIL) ((-1180 . -298) 163626) ((-1180 . -616) 163601) ((-1180 . -300) 163576) ((-1180 . -671) 163558) ((-1180 . -19) 163540) ((-1176 . -694) 163524) ((-1176 . -671) 163508) ((-1176 . -300) 163485) ((-1176 . -298) 163437) ((-1176 . -616) 163414) ((-1176 . -631) 163375) ((-1176 . -501) 163359) ((-1176 . -1122) 163337) ((-1176 . -526) 163270) ((-1176 . -321) 163208) ((-1176 . -630) 163140) ((-1176 . -102) 163090) ((-1176 . -1238) T) ((-1176 . -34) T) ((-1176 . -153) 163074) ((-1176 . -1277) 163058) ((-1176 . -1031) 163042) ((-1176 . -1171) 163026) ((-1176 . -633) 163003) ((-1174 . -1104) T) ((-1174 . -502) 162984) ((-1174 . -630) 162950) ((-1174 . -633) 162931) ((-1174 . -1122) T) ((-1174 . -1238) T) ((-1174 . -102) T) ((-1174 . -93) T) ((-1172 . -1215) 162910) ((-1172 . -233) 162860) ((-1172 . -107) 162810) ((-1172 . -321) 162614) ((-1172 . -526) 162374) ((-1172 . -501) 162311) ((-1172 . -153) 162261) ((-1172 . -631) NIL) ((-1172 . -242) 162211) ((-1172 . -627) 162190) ((-1172 . -300) 162169) ((-1172 . -1238) T) ((-1172 . -298) 162148) ((-1172 . -1122) T) ((-1172 . -630) 162130) ((-1172 . -102) T) ((-1172 . -34) T) ((-1172 . -616) 162109) ((-1169 . -1142) 162093) ((-1169 . -501) 162077) ((-1169 . -1122) 162055) ((-1169 . -526) 161988) ((-1169 . -321) 161926) ((-1169 . -630) 161858) ((-1169 . -102) 161808) ((-1169 . -1238) T) ((-1169 . -34) T) ((-1169 . -107) 161792) ((-1167 . -1130) 161761) ((-1167 . -1233) 161730) ((-1167 . -630) 161692) ((-1167 . -153) 161676) ((-1167 . -34) T) ((-1167 . -1238) T) ((-1167 . -102) T) ((-1167 . -321) 161614) ((-1167 . -526) 161547) ((-1167 . -1122) T) ((-1167 . -501) 161531) ((-1167 . -631) 161492) ((-1167 . -997) 161461) ((-1167 . -1092) 161430) ((-1163 . -1144) 161375) ((-1163 . -501) 161359) ((-1163 . -526) 161292) ((-1163 . -321) 161230) ((-1163 . -34) T) ((-1163 . -1074) 161170) ((-1163 . -1059) 161066) ((-1163 . -633) 160984) ((-1163 . -424) 160968) ((-1163 . -658) 160916) ((-1163 . -668) 160854) ((-1163 . -390) 160838) ((-1163 . -240) 160817) ((-1163 . -236) 160762) ((-1163 . -239) 160713) ((-1163 . -274) 160697) ((-1163 . -911) 160618) ((-1163 . -919) 160541) ((-1163 . -917) 160500) ((-1163 . -234) 160484) ((-1163 . -737) 160416) ((-1163 . -660) 160348) ((-1163 . -666) 160307) ((-1163 . -133) T) ((-1163 . -25) T) ((-1163 . -102) T) ((-1163 . -1238) T) ((-1163 . -630) 160269) ((-1163 . -1122) T) ((-1163 . -23) T) ((-1163 . -21) T) ((-1163 . -1077) 160253) ((-1163 . -1072) 160237) ((-1163 . -111) 160216) ((-1163 . -1070) T) ((-1163 . -1078) T) ((-1163 . -1133) T) ((-1163 . -746) T) ((-1163 . -38) 160176) ((-1163 . -631) 160137) ((-1162 . -1031) 160108) ((-1162 . -34) T) ((-1162 . -1238) T) ((-1162 . -102) T) ((-1162 . -630) 160090) ((-1162 . -321) 160016) ((-1162 . -526) 159924) ((-1162 . -1122) T) ((-1162 . -501) 159895) ((-1161 . -1122) T) ((-1161 . -630) 159877) ((-1161 . -1238) T) ((-1161 . -102) T) ((-1156 . -1158) T) ((-1156 . -1284) T) ((-1156 . -93) T) ((-1156 . -102) T) ((-1156 . -1238) T) ((-1156 . -630) 159843) ((-1156 . -1122) T) ((-1156 . -633) 159824) ((-1156 . -502) 159805) ((-1156 . -1104) T) ((-1154 . -1155) 159789) ((-1154 . -102) T) ((-1154 . -1238) T) ((-1154 . -630) 159771) ((-1154 . -1122) T) ((-1147 . -760) 159750) ((-1147 . -35) 159716) ((-1147 . -95) 159682) ((-1147 . -296) 159648) ((-1147 . -505) 159614) ((-1147 . -1227) 159580) ((-1147 . -1224) 159546) ((-1147 . -1023) 159512) ((-1147 . -47) 159484) ((-1147 . -38) 159381) ((-1147 . -660) 159278) ((-1147 . -737) 159175) ((-1147 . -633) 159057) ((-1147 . -302) 159036) ((-1147 . -569) 159015) ((-1147 . -111) 158877) ((-1147 . -1072) 158760) ((-1147 . -1077) 158643) ((-1147 . -175) 158594) ((-1147 . -149) 158573) ((-1147 . -147) 158552) ((-1147 . -668) 158477) ((-1147 . -666) 158387) ((-1147 . -994) 158354) ((-1147 . -919) 158338) ((-1147 . -1238) T) ((-1147 . -911) 158320) ((-1147 . -1070) T) ((-1147 . -1078) T) ((-1147 . -1133) T) ((-1147 . -746) T) ((-1147 . -21) T) ((-1147 . -23) T) ((-1147 . -1122) T) ((-1147 . -630) 158302) ((-1147 . -102) T) ((-1147 . -25) T) ((-1147 . -133) T) ((-1147 . -917) 158286) ((-1147 . -526) 158256) ((-1147 . -321) 158243) ((-1146 . -969) 158210) ((-1146 . -633) 158002) ((-1146 . -1059) 157885) ((-1146 . -1243) 157864) ((-1146 . -929) 157843) ((-1146 . -901) 157702) ((-1146 . -919) 157686) ((-1146 . -911) 157668) ((-1146 . -917) 157652) ((-1146 . -526) 157604) ((-1146 . -464) 157555) ((-1146 . -658) 157503) ((-1146 . -668) 157392) ((-1146 . -390) 157376) ((-1146 . -47) 157348) ((-1146 . -38) 157197) ((-1146 . -660) 157046) ((-1146 . -737) 156895) ((-1146 . -302) 156826) ((-1146 . -569) 156757) ((-1146 . -111) 156579) ((-1146 . -1072) 156422) ((-1146 . -1077) 156265) ((-1146 . -175) 156176) ((-1146 . -149) 156155) ((-1146 . -147) 156134) ((-1146 . -666) 156044) ((-1146 . -133) T) ((-1146 . -25) T) ((-1146 . -102) T) ((-1146 . -1238) T) ((-1146 . -630) 156026) ((-1146 . -1122) T) ((-1146 . -23) T) ((-1146 . -21) T) ((-1146 . -1070) T) ((-1146 . -1078) T) ((-1146 . -1133) T) ((-1146 . -746) T) ((-1146 . -424) 156010) ((-1146 . -338) 155982) ((-1146 . -321) 155969) ((-1146 . -631) 155717) ((-1141 . -557) T) ((-1141 . -1243) T) ((-1141 . -1173) T) ((-1141 . -1059) 155699) ((-1141 . -631) 155614) ((-1141 . -1041) T) ((-1141 . -901) 155596) ((-1141 . -860) T) ((-1141 . -819) T) ((-1141 . -816) T) ((-1141 . -864) T) ((-1141 . -861) T) ((-1141 . -814) T) ((-1141 . -812) T) ((-1141 . -842) T) ((-1141 . -668) 155568) ((-1141 . -658) 155550) ((-1141 . -940) T) ((-1141 . -569) T) ((-1141 . -302) T) ((-1141 . -175) T) ((-1141 . -633) 155522) ((-1141 . -737) 155509) ((-1141 . -660) 155496) ((-1141 . -1077) 155483) ((-1141 . -1072) 155470) ((-1141 . -111) 155455) ((-1141 . -38) 155442) ((-1141 . -464) T) ((-1141 . -319) T) ((-1141 . -239) T) ((-1141 . -236) 155429) ((-1141 . -240) T) ((-1141 . -145) T) ((-1141 . -1070) T) ((-1141 . -1078) T) ((-1141 . -1133) T) ((-1141 . -746) T) ((-1141 . -21) T) ((-1141 . -666) 155401) ((-1141 . -23) T) ((-1141 . -1122) T) ((-1141 . -630) 155383) ((-1141 . -1238) T) ((-1141 . -102) T) ((-1141 . -25) T) ((-1141 . -133) T) ((-1141 . -149) T) ((-1141 . -857) T) ((-1141 . -381) T) ((-1141 . -113) T) ((-1141 . -682) T) ((-1137 . -1104) T) ((-1137 . -502) 155364) ((-1137 . -630) 155330) ((-1137 . -633) 155311) ((-1137 . -1122) T) ((-1137 . -1238) T) ((-1137 . -102) T) ((-1137 . -93) T) ((-1136 . -1122) T) ((-1136 . -630) 155293) ((-1136 . -1238) T) ((-1136 . -102) T) ((-1134 . -245) 155272) ((-1134 . -1296) 155242) ((-1134 . -819) 155221) ((-1134 . -816) 155200) ((-1134 . -864) 155151) ((-1134 . -861) 155102) ((-1134 . -814) 155081) ((-1134 . -815) 155060) ((-1134 . -737) 155002) ((-1134 . -660) 154924) ((-1134 . -300) 154901) ((-1134 . -298) 154878) ((-1134 . -501) 154862) ((-1134 . -526) 154795) ((-1134 . -321) 154733) ((-1134 . -34) T) ((-1134 . -616) 154710) ((-1134 . -1059) 154537) ((-1134 . -633) 154335) ((-1134 . -424) 154304) ((-1134 . -658) 154210) ((-1134 . -668) 154043) ((-1134 . -390) 154012) ((-1134 . -381) 153991) ((-1134 . -240) 153943) ((-1134 . -666) 153722) ((-1134 . -746) 153700) ((-1134 . -1133) 153678) ((-1134 . -1078) 153656) ((-1134 . -1070) 153634) ((-1134 . -236) 153525) ((-1134 . -239) 153422) ((-1134 . -274) 153391) ((-1134 . -911) 153258) ((-1134 . -919) 153127) ((-1134 . -917) 153059) ((-1134 . -234) 153028) ((-1134 . -630) 152721) ((-1134 . -1077) 152642) ((-1134 . -1072) 152543) ((-1134 . -111) 152459) ((-1134 . -133) 152330) ((-1134 . -25) 152163) ((-1134 . -102) 151895) ((-1134 . -1238) T) ((-1134 . -1122) 151647) ((-1134 . -23) 151499) ((-1134 . -21) 151410) ((-1127 . -408) T) ((-1127 . -1238) T) ((-1127 . -630) 151392) ((-1126 . -1125) 151356) ((-1126 . -102) T) ((-1126 . -630) 151338) ((-1126 . -1122) T) ((-1126 . -298) 151294) ((-1126 . -1238) T) ((-1126 . -635) 151209) ((-1124 . -1125) 151161) ((-1124 . -102) T) ((-1124 . -630) 151143) ((-1124 . -1122) T) ((-1124 . -298) 151099) ((-1124 . -1238) T) ((-1124 . -635) 151002) ((-1123 . -381) T) ((-1123 . -102) T) ((-1123 . -1238) T) ((-1123 . -630) 150984) ((-1123 . -1122) T) ((-1118 . -438) 150968) ((-1118 . -1120) 150952) ((-1118 . -381) 150931) ((-1118 . -242) 150915) ((-1118 . -631) 150876) ((-1118 . -153) 150860) ((-1118 . -501) 150844) ((-1118 . -1122) T) ((-1118 . -526) 150777) ((-1118 . -321) 150715) ((-1118 . -630) 150697) ((-1118 . -102) T) ((-1118 . -1238) T) ((-1118 . -34) T) ((-1118 . -107) 150681) ((-1118 . -233) 150665) ((-1117 . -1104) T) ((-1117 . -502) 150646) ((-1117 . -630) 150612) ((-1117 . -633) 150593) ((-1117 . -1122) T) ((-1117 . -1238) T) ((-1117 . -102) T) ((-1117 . -93) T) ((-1113 . -1238) T) ((-1113 . -1122) 150563) ((-1113 . -630) 150522) ((-1113 . -102) 150492) ((-1112 . -1104) T) ((-1112 . -502) 150473) ((-1112 . -630) 150439) ((-1112 . -633) 150420) ((-1112 . -1122) T) ((-1112 . -1238) T) ((-1112 . -102) T) ((-1112 . -93) T) ((-1110 . -1115) 150404) ((-1110 . -635) 150388) ((-1110 . -1122) 150366) ((-1110 . -630) 150333) ((-1110 . -1238) 150311) ((-1110 . -102) 150289) ((-1110 . -1116) 150247) ((-1109 . -277) 150231) ((-1109 . -633) 150215) ((-1109 . -1059) 150199) ((-1109 . -864) T) ((-1109 . -102) T) ((-1109 . -1122) T) ((-1109 . -630) 150181) ((-1109 . -861) T) ((-1109 . -236) 150168) ((-1109 . -1238) T) ((-1109 . -239) T) ((-1108 . -262) 150105) ((-1108 . -633) 149841) ((-1108 . -1059) 149668) ((-1108 . -631) NIL) ((-1108 . -338) 149629) ((-1108 . -424) 149613) ((-1108 . -38) 149462) ((-1108 . -111) 149284) ((-1108 . -1072) 149127) ((-1108 . -1077) 148970) ((-1108 . -666) 148880) ((-1108 . -668) 148769) ((-1108 . -660) 148618) ((-1108 . -737) 148467) ((-1108 . -147) 148446) ((-1108 . -149) 148425) ((-1108 . -175) 148336) ((-1108 . -569) 148267) ((-1108 . -302) 148198) ((-1108 . -47) 148159) ((-1108 . -390) 148143) ((-1108 . -658) 148091) ((-1108 . -464) 148042) ((-1108 . -526) 147905) ((-1108 . -917) 147840) ((-1108 . -911) 147735) ((-1108 . -919) 147634) ((-1108 . -901) NIL) ((-1108 . -929) 147613) ((-1108 . -1243) 147592) ((-1108 . -969) 147537) ((-1108 . -321) 147524) ((-1108 . -240) 147503) ((-1108 . -133) T) ((-1108 . -25) T) ((-1108 . -102) T) ((-1108 . -630) 147485) ((-1108 . -1122) T) ((-1108 . -23) T) ((-1108 . -21) T) ((-1108 . -746) T) ((-1108 . -1133) T) ((-1108 . -1078) T) ((-1108 . -1070) T) ((-1108 . -236) 147430) ((-1108 . -1238) T) ((-1108 . -239) 147381) ((-1108 . -274) 147365) ((-1108 . -234) 147349) ((-1106 . -630) 147331) ((-1103 . -861) T) ((-1103 . -630) 147313) ((-1103 . -1122) T) ((-1103 . -102) T) ((-1103 . -1238) T) ((-1103 . -864) T) ((-1103 . -631) 147294) ((-1100 . -744) 147273) ((-1100 . -1059) 147169) ((-1100 . -424) 147153) ((-1100 . -658) 147101) ((-1100 . -668) 146975) ((-1100 . -390) 146959) ((-1100 . -383) 146938) ((-1100 . -149) 146917) ((-1100 . -633) 146735) ((-1100 . -737) 146603) ((-1100 . -660) 146471) ((-1100 . -666) 146366) ((-1100 . -1077) 146276) ((-1100 . -1072) 146186) ((-1100 . -111) 146075) ((-1100 . -38) 145943) ((-1100 . -422) 145922) ((-1100 . -414) 145901) ((-1100 . -147) 145852) ((-1100 . -1173) 145831) ((-1100 . -363) 145810) ((-1100 . -381) 145761) ((-1100 . -250) 145712) ((-1100 . -302) 145663) ((-1100 . -319) 145614) ((-1100 . -464) 145565) ((-1100 . -569) 145516) ((-1100 . -940) 145467) ((-1100 . -1243) 145418) ((-1100 . -376) 145369) ((-1100 . -240) 145294) ((-1100 . -236) 145167) ((-1100 . -239) 145046) ((-1100 . -274) 145016) ((-1100 . -911) 144885) ((-1100 . -919) 144756) ((-1100 . -917) 144689) ((-1100 . -234) 144659) ((-1100 . -631) 144643) ((-1100 . -21) T) ((-1100 . -23) T) ((-1100 . -1122) T) ((-1100 . -630) 144625) ((-1100 . -1238) T) ((-1100 . -102) T) ((-1100 . -25) T) ((-1100 . -133) T) ((-1100 . -1070) T) ((-1100 . -1078) T) ((-1100 . -1133) T) ((-1100 . -746) T) ((-1100 . -175) T) ((-1098 . -1122) T) ((-1098 . -630) 144607) ((-1098 . -1238) T) ((-1098 . -102) T) ((-1098 . -298) 144586) ((-1097 . -1122) T) ((-1097 . -630) 144568) ((-1097 . -1238) T) ((-1097 . -102) T) ((-1096 . -1122) T) ((-1096 . -630) 144550) ((-1096 . -1238) T) ((-1096 . -102) T) ((-1096 . -298) 144529) ((-1096 . -1059) 144506) ((-1096 . -633) 144483) ((-1095 . -1238) T) ((-1094 . -1104) T) ((-1094 . -502) 144464) ((-1094 . -630) 144430) ((-1094 . -633) 144411) ((-1094 . -1122) T) ((-1094 . -1238) T) ((-1094 . -102) T) ((-1094 . -93) T) ((-1087 . -1104) T) ((-1087 . -502) 144392) ((-1087 . -630) 144358) ((-1087 . -633) 144339) ((-1087 . -1122) T) ((-1087 . -1238) T) ((-1087 . -102) T) ((-1087 . -93) T) ((-1084 . -1215) 144314) ((-1084 . -233) 144260) ((-1084 . -107) 144206) ((-1084 . -321) 144057) ((-1084 . -526) 143865) ((-1084 . -501) 143797) ((-1084 . -153) 143743) ((-1084 . -631) NIL) ((-1084 . -242) 143689) ((-1084 . -627) 143664) ((-1084 . -300) 143639) ((-1084 . -1238) T) ((-1084 . -298) 143614) ((-1084 . -1122) T) ((-1084 . -630) 143596) ((-1084 . -102) T) ((-1084 . -34) T) ((-1084 . -616) 143571) ((-1083 . -557) T) ((-1083 . -1243) T) ((-1083 . -1173) T) ((-1083 . -1059) 143553) ((-1083 . -631) 143468) ((-1083 . -1041) T) ((-1083 . -901) 143450) ((-1083 . -860) T) ((-1083 . -819) T) ((-1083 . -816) T) ((-1083 . -864) T) ((-1083 . -861) T) ((-1083 . -814) T) ((-1083 . -812) T) ((-1083 . -842) T) ((-1083 . -668) 143422) ((-1083 . -658) 143404) ((-1083 . -940) T) ((-1083 . -569) T) ((-1083 . -302) T) ((-1083 . -175) T) ((-1083 . -633) 143376) ((-1083 . -737) 143363) ((-1083 . -660) 143350) ((-1083 . -1077) 143337) ((-1083 . -1072) 143324) ((-1083 . -111) 143309) ((-1083 . -38) 143296) ((-1083 . -464) T) ((-1083 . -319) T) ((-1083 . -239) T) ((-1083 . -236) 143283) ((-1083 . -240) T) ((-1083 . -145) T) ((-1083 . -1070) T) ((-1083 . -1078) T) ((-1083 . -1133) T) ((-1083 . -746) T) ((-1083 . -21) T) ((-1083 . -666) 143255) ((-1083 . -23) T) ((-1083 . -1122) T) ((-1083 . -630) 143237) ((-1083 . -1238) T) ((-1083 . -102) T) ((-1083 . -25) T) ((-1083 . -133) T) ((-1083 . -149) T) ((-1083 . -635) 143218) ((-1082 . -1089) 143197) ((-1082 . -102) T) ((-1082 . -1238) T) ((-1082 . -630) 143179) ((-1082 . -1122) T) ((-1079 . -1238) T) ((-1079 . -1122) 143157) ((-1079 . -630) 143124) ((-1079 . -102) 143102) ((-1075 . -1074) 143042) ((-1075 . -660) 142984) ((-1075 . -737) 142926) ((-1075 . -34) T) ((-1075 . -321) 142864) ((-1075 . -526) 142797) ((-1075 . -501) 142781) ((-1075 . -668) 142765) ((-1075 . -666) 142734) ((-1075 . -133) T) ((-1075 . -25) T) ((-1075 . -102) T) ((-1075 . -1238) T) ((-1075 . -630) 142696) ((-1075 . -1122) T) ((-1075 . -23) T) ((-1075 . -21) T) ((-1075 . -1077) 142680) ((-1075 . -1072) 142664) ((-1075 . -111) 142643) ((-1075 . -1296) 142613) ((-1075 . -631) 142574) ((-1067 . -1092) 142503) ((-1067 . -997) 142432) ((-1067 . -631) 142374) ((-1067 . -501) 142339) ((-1067 . -1122) T) ((-1067 . -526) 142223) ((-1067 . -321) 142131) ((-1067 . -630) 142074) ((-1067 . -102) T) ((-1067 . -1238) T) ((-1067 . -34) T) ((-1067 . -153) 142039) ((-1067 . -1233) 141968) ((-1057 . -1104) T) ((-1057 . -502) 141949) ((-1057 . -630) 141915) ((-1057 . -633) 141896) ((-1057 . -1122) T) ((-1057 . -1238) T) ((-1057 . -102) T) ((-1057 . -93) T) ((-1056 . -1215) 141871) ((-1056 . -233) 141817) ((-1056 . -107) 141763) ((-1056 . -321) 141614) ((-1056 . -526) 141422) ((-1056 . -501) 141354) ((-1056 . -153) 141300) ((-1056 . -631) NIL) ((-1056 . -242) 141246) ((-1056 . -627) 141221) ((-1056 . -300) 141196) ((-1056 . -1238) T) ((-1056 . -298) 141171) ((-1056 . -1122) T) ((-1056 . -630) 141153) ((-1056 . -102) T) ((-1056 . -34) T) ((-1056 . -616) 141128) ((-1055 . -175) T) ((-1055 . -633) 141097) ((-1055 . -746) T) ((-1055 . -1133) T) ((-1055 . -1078) T) ((-1055 . -1070) T) ((-1055 . -668) 141071) ((-1055 . -666) 141030) ((-1055 . -133) T) ((-1055 . -25) T) ((-1055 . -102) T) ((-1055 . -1238) T) ((-1055 . -630) 141012) ((-1055 . -1122) T) ((-1055 . -23) T) ((-1055 . -21) T) ((-1055 . -1077) 140986) ((-1055 . -1072) 140960) ((-1055 . -111) 140927) ((-1055 . -38) 140911) ((-1055 . -660) 140895) ((-1055 . -737) 140879) ((-1048 . -1092) 140848) ((-1048 . -997) 140817) ((-1048 . -631) 140778) ((-1048 . -501) 140762) ((-1048 . -1122) T) ((-1048 . -526) 140695) ((-1048 . -321) 140633) ((-1048 . -630) 140595) ((-1048 . -102) T) ((-1048 . -1238) T) ((-1048 . -34) T) ((-1048 . -153) 140579) 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135246) ((-1015 . -1122) T) ((-1015 . -1238) T) ((-1015 . -102) T) ((-1015 . -93) T) ((-1014 . -21) T) ((-1014 . -666) 135228) ((-1014 . -23) T) ((-1014 . -1122) T) ((-1014 . -630) 135210) ((-1014 . -1238) T) ((-1014 . -102) T) ((-1014 . -25) T) ((-1014 . -133) T) ((-1014 . -298) 135177) ((-1010 . -630) 135159) ((-1007 . -1122) T) ((-1007 . -630) 135141) ((-1007 . -1238) T) ((-1007 . -102) T) ((-992 . -819) T) ((-992 . -816) T) ((-992 . -864) T) ((-992 . -861) T) ((-992 . -814) T) ((-992 . -23) T) ((-992 . -1122) T) ((-992 . -630) 135101) ((-992 . -1238) T) ((-992 . -102) T) ((-992 . -25) T) ((-992 . -133) T) ((-991 . -1104) T) ((-991 . -502) 135082) ((-991 . -630) 135048) ((-991 . -633) 135029) ((-991 . -1122) T) ((-991 . -1238) T) ((-991 . -102) T) ((-991 . -93) T) ((-985 . -988) T) ((-985 . -102) T) ((-985 . -630) 135011) ((-985 . -1122) T) ((-985 . -682) T) ((-985 . -1238) T) ((-985 . -113) T) ((-985 . -633) 134995) ((-984 . -630) 134977) ((-983 . -1122) T) ((-983 . -630) 134959) 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. -501) 127452) ((-920 . -1122) 127430) ((-920 . -526) 127363) ((-920 . -321) 127301) ((-920 . -630) 127212) ((-920 . -102) 127162) ((-920 . -1238) T) ((-920 . -34) T) ((-920 . -1031) 127146) ((-915 . -1122) T) ((-915 . -630) 127128) ((-915 . -1238) T) ((-915 . -102) T) ((-908 . -861) T) ((-908 . -630) 127110) ((-908 . -1122) T) ((-908 . -102) T) ((-908 . -1238) T) ((-908 . -864) T) ((-908 . -1059) 127087) ((-908 . -633) 127064) ((-905 . -1122) T) ((-905 . -630) 127046) ((-905 . -1238) T) ((-905 . -102) T) ((-905 . -1059) 127014) ((-905 . -633) 126982) ((-903 . -1122) T) ((-903 . -630) 126964) ((-903 . -1238) T) ((-903 . -102) T) ((-900 . -1122) T) ((-900 . -630) 126946) ((-900 . -1238) T) ((-900 . -102) T) ((-890 . -1104) T) ((-890 . -502) 126927) ((-890 . -630) 126893) ((-890 . -633) 126874) ((-890 . -1122) T) ((-890 . -1238) T) ((-890 . -102) T) ((-890 . -93) T) ((-890 . -1284) T) ((-888 . -1122) T) ((-888 . -630) 126856) ((-888 . -1238) T) ((-888 . -102) T) ((-887 . -1238) T) 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-631) 122918) ((-877 . -1122) T) ((-877 . -630) 122900) ((-877 . -1238) T) ((-877 . -102) T) ((-876 . -875) T) ((-876 . -176) T) ((-876 . -630) 122882) ((-872 . -861) T) ((-872 . -630) 122864) ((-872 . -1122) T) ((-872 . -102) T) ((-872 . -1238) T) ((-872 . -864) T) ((-869 . -866) 122848) ((-869 . -1059) 122744) ((-869 . -633) 122641) ((-869 . -424) 122625) ((-869 . -737) 122595) ((-869 . -660) 122565) ((-869 . -668) 122539) ((-869 . -666) 122498) ((-869 . -133) T) ((-869 . -25) T) ((-869 . -102) T) ((-869 . -1238) T) ((-869 . -630) 122480) ((-869 . -1122) T) ((-869 . -23) T) ((-869 . -21) T) ((-869 . -1077) 122464) ((-869 . -1072) 122448) ((-869 . -111) 122427) ((-869 . -1070) T) ((-869 . -1078) T) ((-869 . -1133) T) ((-869 . -746) T) ((-869 . -38) 122397) ((-868 . -866) 122381) ((-868 . -1059) 122277) ((-868 . -633) 122195) ((-868 . -424) 122179) ((-868 . -737) 122149) ((-868 . -660) 122119) ((-868 . -668) 122093) ((-868 . -666) 122052) ((-868 . -133) T) ((-868 . -25) T) ((-868 . -102) T) ((-868 . -1238) T) ((-868 . -630) 122034) ((-868 . -1122) T) ((-868 . -23) T) ((-868 . -21) T) ((-868 . -1077) 122018) ((-868 . -1072) 122002) ((-868 . -111) 121981) ((-868 . -1070) T) ((-868 . -1078) T) ((-868 . -1133) T) ((-868 . -746) T) ((-868 . -38) 121951) ((-862 . -864) T) ((-862 . -1238) T) ((-862 . -102) T) ((-862 . -502) 121935) ((-862 . -630) 121883) ((-862 . -633) 121867) ((-855 . -1122) T) ((-855 . -630) 121849) ((-855 . -1238) T) ((-855 . -102) T) ((-855 . -424) 121833) ((-855 . -633) 121701) ((-855 . -1059) 121597) ((-855 . -21) 121549) ((-855 . -666) 121466) ((-855 . -23) 121418) ((-855 . -25) 121370) ((-855 . -133) 121322) ((-855 . -860) 121301) ((-855 . -668) 121274) ((-855 . -1078) 121253) ((-855 . -1070) 121232) ((-855 . -819) 121211) ((-855 . -816) 121190) ((-855 . -864) 121169) ((-855 . -861) 121148) ((-855 . -814) 121127) ((-855 . -812) 121106) ((-855 . -1133) 121085) ((-855 . -746) 121064) ((-854 . -1122) T) ((-854 . -630) 121046) ((-854 . -1238) T) ((-854 . -102) T) ((-851 . -849) 121028) ((-851 . -102) T) ((-851 . -1238) T) ((-851 . -630) 121010) ((-851 . -1122) T) ((-847 . -1070) T) ((-847 . -1078) T) ((-847 . -1133) T) ((-847 . -746) T) ((-847 . -21) T) ((-847 . -666) 120955) ((-847 . -23) T) ((-847 . -1122) T) ((-847 . -630) 120937) ((-847 . -1238) T) ((-847 . -102) T) ((-847 . -25) T) ((-847 . -133) T) ((-847 . -668) 120897) ((-847 . -633) 120851) ((-847 . -1059) 120820) ((-847 . -298) 120799) ((-847 . -149) 120778) ((-847 . -147) 120757) ((-847 . -38) 120727) ((-847 . -111) 120692) ((-847 . -1072) 120662) ((-847 . -1077) 120632) ((-847 . -660) 120602) ((-847 . -737) 120572) ((-845 . -1122) T) ((-845 . -630) 120554) ((-845 . -1238) T) ((-845 . -102) T) ((-845 . -424) 120538) ((-845 . -633) 120406) ((-845 . -1059) 120302) ((-845 . -21) 120254) ((-845 . -666) 120171) ((-845 . -23) 120123) ((-845 . -25) 120075) ((-845 . -133) 120027) ((-845 . -860) 120006) ((-845 . -668) 119979) ((-845 . -1078) 119958) ((-845 . -1070) 119937) 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-633) 119313) ((-840 . -1059) 119297) ((-840 . -864) T) ((-840 . -102) T) ((-840 . -1122) T) ((-840 . -630) 119279) ((-840 . -861) T) ((-840 . -236) 119266) ((-840 . -1238) T) ((-840 . -239) T) ((-839 . -111) 119201) ((-839 . -1072) 119152) ((-839 . -1077) 119103) ((-839 . -21) T) ((-839 . -666) 119039) ((-839 . -23) T) ((-839 . -1122) T) ((-839 . -630) 119008) ((-839 . -1238) T) ((-839 . -102) T) ((-839 . -25) T) ((-839 . -133) T) ((-839 . -668) 118959) ((-839 . -240) T) ((-839 . -633) 118868) ((-839 . -746) T) ((-839 . -1133) T) ((-839 . -1078) T) ((-839 . -1070) T) ((-839 . -236) 118855) ((-839 . -239) T) ((-839 . -502) 118839) ((-839 . -376) 118818) ((-839 . -1243) 118797) ((-839 . -940) 118776) ((-839 . -569) 118755) ((-839 . -175) 118734) ((-839 . -737) 118671) ((-839 . -660) 118608) ((-839 . -38) 118545) ((-839 . -464) 118524) ((-839 . -319) 118503) ((-839 . -302) 118482) ((-839 . -250) 118461) ((-838 . -262) 118400) ((-838 . -633) 118137) ((-838 . -1059) 117965) ((-838 . -631) NIL) ((-838 . -338) 117927) ((-838 . -424) 117911) ((-838 . -38) 117760) ((-838 . -111) 117582) ((-838 . -1072) 117425) ((-838 . -1077) 117268) ((-838 . -666) 117178) ((-838 . -668) 117067) ((-838 . -660) 116916) ((-838 . -737) 116765) ((-838 . -147) 116744) ((-838 . -149) 116723) ((-838 . -175) 116634) ((-838 . -569) 116565) ((-838 . -302) 116496) ((-838 . -47) 116458) ((-838 . -390) 116442) ((-838 . -658) 116390) ((-838 . -464) 116341) ((-838 . -526) 116206) ((-838 . -917) 116142) ((-838 . -911) 116038) ((-838 . -919) 115938) ((-838 . -901) NIL) ((-838 . -929) 115917) ((-838 . -1243) 115896) ((-838 . -969) 115843) ((-838 . -321) 115830) ((-838 . -240) 115809) ((-838 . -133) T) ((-838 . -25) T) ((-838 . -102) T) ((-838 . -630) 115791) ((-838 . -1122) T) ((-838 . -23) T) ((-838 . -21) T) ((-838 . -746) T) ((-838 . -1133) T) ((-838 . -1078) T) ((-838 . -1070) T) ((-838 . -236) 115736) ((-838 . -1238) T) ((-838 . -239) 115687) ((-838 . -274) 115671) ((-838 . -234) 115655) ((-837 . -245) 115634) ((-837 . -1296) 115604) ((-837 . -819) 115583) ((-837 . -816) 115562) ((-837 . -864) 115513) ((-837 . -861) 115464) ((-837 . -814) 115443) ((-837 . -815) 115422) ((-837 . -737) 115364) ((-837 . -660) 115286) ((-837 . -300) 115263) ((-837 . -298) 115240) ((-837 . -501) 115224) ((-837 . -526) 115157) ((-837 . -321) 115095) ((-837 . -34) T) ((-837 . -616) 115072) ((-837 . -1059) 114899) ((-837 . -633) 114697) ((-837 . -424) 114666) ((-837 . -658) 114572) ((-837 . -668) 114405) ((-837 . -390) 114374) ((-837 . -381) 114353) ((-837 . -240) 114305) ((-837 . -666) 114084) ((-837 . -746) 114062) ((-837 . -1133) 114040) ((-837 . -1078) 114018) ((-837 . -1070) 113996) ((-837 . -236) 113887) ((-837 . -239) 113784) ((-837 . -274) 113753) ((-837 . -911) 113620) ((-837 . -919) 113489) ((-837 . -917) 113421) ((-837 . -234) 113390) ((-837 . -630) 113083) ((-837 . -1077) 113004) ((-837 . -1072) 112905) ((-837 . -111) 112821) ((-837 . -133) 112692) ((-837 . -25) 112525) ((-837 . -102) 112257) 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-526) 110711) ((-801 . -338) 110688) ((-801 . -1059) 110547) ((-801 . -424) 110531) ((-801 . -38) 110360) ((-801 . -111) 110162) ((-801 . -1072) 109985) ((-801 . -1077) 109808) ((-801 . -666) 109718) ((-801 . -668) 109607) ((-801 . -660) 109436) ((-801 . -737) 109265) ((-801 . -633) 109013) ((-801 . -147) 108992) ((-801 . -149) 108971) ((-801 . -47) 108948) ((-801 . -390) 108932) ((-801 . -658) 108880) ((-801 . -917) 108823) ((-801 . -911) 108726) ((-801 . -919) 108633) ((-801 . -901) NIL) ((-801 . -929) 108612) ((-801 . -1243) 108591) ((-801 . -969) 108560) ((-801 . -940) 108539) ((-801 . -569) 108450) ((-801 . -302) 108361) ((-801 . -175) 108252) ((-801 . -464) 108183) ((-801 . -319) 108162) ((-801 . -298) 108089) ((-801 . -240) T) ((-801 . -133) T) ((-801 . -25) T) ((-801 . -102) T) ((-801 . -630) 108050) ((-801 . -1122) T) ((-801 . -23) T) ((-801 . -21) T) ((-801 . -746) T) ((-801 . -1133) T) ((-801 . -1078) T) ((-801 . -1070) T) ((-801 . -236) 108037) ((-801 . -1238) T) ((-801 . -239) T) ((-801 . -274) 108021) ((-801 . -234) 108005) ((-800 . -1086) 107972) ((-800 . -631) 107606) ((-800 . -321) 107593) ((-800 . -526) 107545) ((-800 . -338) 107517) ((-800 . -1059) 107374) ((-800 . -424) 107358) ((-800 . -38) 107207) ((-800 . -633) 106973) ((-800 . -668) 106862) ((-800 . -666) 106772) ((-800 . -746) T) ((-800 . -1133) T) ((-800 . -1078) T) ((-800 . -1070) T) ((-800 . -111) 106594) ((-800 . -1072) 106437) ((-800 . -1077) 106280) ((-800 . -21) T) ((-800 . -23) T) ((-800 . -1122) T) ((-800 . -630) 106194) ((-800 . -1238) T) ((-800 . -102) T) ((-800 . -25) T) ((-800 . -133) T) ((-800 . -660) 106043) ((-800 . -737) 105892) ((-800 . -147) 105871) ((-800 . -149) 105850) ((-800 . -175) 105761) ((-800 . -569) 105692) ((-800 . -302) 105623) ((-800 . -47) 105595) ((-800 . -390) 105579) ((-800 . -658) 105527) ((-800 . -464) 105478) ((-800 . -917) 105462) ((-800 . -911) 105444) ((-800 . -919) 105428) ((-800 . -901) 105287) ((-800 . -929) 105266) ((-800 . -1243) 105245) ((-800 . -969) 105212) ((-793 . -1122) T) ((-793 . -630) 105194) ((-793 . -1238) T) ((-793 . -102) T) ((-791 . -815) T) ((-791 . -133) T) ((-791 . -25) T) ((-791 . -102) T) ((-791 . -1238) T) ((-791 . -630) 105176) ((-791 . -1122) T) ((-791 . -23) T) ((-791 . -814) T) ((-791 . -861) T) ((-791 . -864) T) ((-791 . -816) T) ((-791 . -819) T) ((-791 . -746) T) ((-791 . -1133) T) ((-789 . -1122) T) ((-789 . -630) 105158) ((-789 . -1238) T) ((-789 . -102) T) ((-756 . -757) 105142) ((-756 . -1120) 105126) ((-756 . -242) 105110) ((-756 . -631) 105071) ((-756 . -153) 105055) ((-756 . -501) 105039) ((-756 . -1122) T) ((-756 . -526) 104972) ((-756 . -321) 104910) ((-756 . -630) 104892) ((-756 . -102) T) ((-756 . -1238) T) ((-756 . -34) T) ((-756 . -107) 104876) ((-756 . -715) 104860) ((-755 . -1070) T) ((-755 . -1078) T) ((-755 . -1133) T) ((-755 . -746) T) ((-755 . -21) T) ((-755 . -666) 104805) ((-755 . -23) T) ((-755 . -1122) T) ((-755 . -630) 104787) ((-755 . -1238) T) ((-755 . -102) T) ((-755 . -25) T) ((-755 . -133) T) ((-755 . -668) 104747) ((-755 . -633) 104703) ((-755 . -1059) 104674) ((-755 . -149) 104653) ((-755 . -147) 104632) ((-755 . -38) 104602) ((-755 . -111) 104567) ((-755 . -1072) 104537) ((-755 . -1077) 104507) ((-755 . -660) 104477) ((-755 . -737) 104447) ((-755 . -381) 104400) ((-751 . -969) 104353) ((-751 . -633) 104138) ((-751 . -1059) 104014) ((-751 . -1243) 103993) ((-751 . -929) 103972) ((-751 . -901) NIL) ((-751 . -919) 103949) ((-751 . -911) 103924) ((-751 . -917) 103901) ((-751 . -526) 103839) ((-751 . -464) 103790) ((-751 . -658) 103738) ((-751 . -668) 103627) ((-751 . -390) 103611) ((-751 . -47) 103576) ((-751 . -38) 103425) ((-751 . -660) 103274) ((-751 . -737) 103123) ((-751 . -302) 103054) ((-751 . -569) 102985) ((-751 . -111) 102807) ((-751 . -1072) 102650) ((-751 . -1077) 102493) ((-751 . -175) 102404) ((-751 . -149) 102383) ((-751 . -147) 102362) ((-751 . -666) 102272) ((-751 . -133) T) ((-751 . -25) T) ((-751 . -102) T) ((-751 . -1238) T) 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101745) ((-734 . -149) 101724) ((-734 . -147) 101703) ((-734 . -38) 101673) ((-734 . -111) 101638) ((-734 . -1072) 101608) ((-734 . -1077) 101578) ((-734 . -660) 101548) ((-734 . -737) 101518) ((-733 . -861) T) ((-733 . -630) 101453) ((-733 . -1122) T) ((-733 . -102) T) ((-733 . -1238) T) ((-733 . -864) T) ((-733 . -502) 101403) ((-733 . -633) 101353) ((-732 . -1264) 101337) ((-732 . -1173) 101315) ((-732 . -631) NIL) ((-732 . -321) 101302) ((-732 . -526) 101248) ((-732 . -338) 101225) ((-732 . -1059) 101105) ((-732 . -424) 101089) ((-732 . -38) 100918) ((-732 . -111) 100720) ((-732 . -1072) 100543) ((-732 . -1077) 100366) ((-732 . -666) 100276) ((-732 . -668) 100165) ((-732 . -660) 99994) ((-732 . -737) 99823) ((-732 . -633) 99579) ((-732 . -147) 99558) ((-732 . -149) 99537) ((-732 . -47) 99514) ((-732 . -390) 99498) ((-732 . -658) 99446) ((-732 . -917) 99389) ((-732 . -911) 99292) ((-732 . -919) 99199) ((-732 . -901) NIL) ((-732 . -929) 99178) ((-732 . -1243) 99157) ((-732 . -969) 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T) ((-731 . -102) T) ((-731 . -25) T) ((-731 . -133) T) ((-731 . -302) T) ((-731 . -250) T) ((-730 . -1122) T) ((-730 . -630) 98174) ((-730 . -1238) T) ((-730 . -102) T) ((-721 . -401) T) ((-721 . -1059) 98156) ((-721 . -864) T) ((-721 . -861) T) ((-721 . -38) 98143) ((-721 . -633) 98115) ((-721 . -746) T) ((-721 . -1133) T) ((-721 . -1078) T) ((-721 . -1070) T) ((-721 . -111) 98100) ((-721 . -1072) 98087) ((-721 . -1077) 98074) ((-721 . -21) T) ((-721 . -666) 98046) ((-721 . -23) T) ((-721 . -1122) T) ((-721 . -630) 98028) ((-721 . -1238) T) ((-721 . -102) T) ((-721 . -25) T) ((-721 . -133) T) ((-721 . -668) 98000) ((-721 . -660) 97987) ((-721 . -737) 97974) ((-721 . -175) T) ((-721 . -302) T) ((-721 . -569) T) ((-721 . -557) T) ((-721 . -1243) T) ((-721 . -1173) T) ((-721 . -631) 97889) ((-721 . -1041) T) ((-721 . -901) 97871) ((-721 . -860) T) ((-721 . -819) T) ((-721 . -816) T) ((-721 . -814) T) ((-721 . -812) T) ((-721 . -842) T) ((-721 . -658) 97853) ((-721 . -940) T) ((-721 . 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. -133) T) ((-395 . -25) T) ((-395 . -102) T) ((-395 . -1238) T) ((-395 . -630) 55105) ((-395 . -1122) T) ((-395 . -23) T) ((-395 . -21) T) ((-395 . -1077) 55089) ((-395 . -1072) 55073) ((-395 . -111) 55052) ((-394 . -111) 55031) ((-394 . -1072) 55015) ((-394 . -1077) 54999) ((-394 . -21) T) ((-394 . -666) 54968) ((-394 . -23) T) ((-394 . -1122) T) ((-394 . -630) 54950) ((-394 . -1238) T) ((-394 . -102) T) ((-394 . -25) T) ((-394 . -133) T) ((-394 . -668) 54934) ((-394 . -521) 54913) ((-394 . -737) 54883) ((-394 . -660) 54853) ((-391 . -416) T) ((-391 . -149) T) ((-391 . -633) 54803) ((-391 . -668) 54768) ((-391 . -666) 54718) ((-391 . -133) T) ((-391 . -25) T) ((-391 . -102) T) ((-391 . -1238) T) ((-391 . -630) 54685) ((-391 . -1122) T) ((-391 . -23) T) ((-391 . -21) T) ((-391 . -746) T) ((-391 . -1133) T) ((-391 . -1078) T) ((-391 . -1070) T) ((-391 . -631) 54599) ((-391 . -376) T) ((-391 . -1243) T) ((-391 . -940) T) ((-391 . -569) T) ((-391 . -175) T) ((-391 . -737) 54564) ((-391 . 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. -1122) T) ((-163 . -630) 11257) ((-163 . -1238) T) ((-163 . -102) T) ((-159 . -25) T) ((-159 . -102) T) ((-159 . -1238) T) ((-159 . -630) 11239) ((-159 . -1122) T) ((-158 . -1104) T) ((-158 . -502) 11220) ((-158 . -630) 11186) ((-158 . -633) 11167) ((-158 . -1122) T) ((-158 . -1238) T) ((-158 . -102) T) ((-158 . -93) T) ((-156 . -1104) T) ((-156 . -502) 11148) ((-156 . -630) 11114) ((-156 . -633) 11095) ((-156 . -1122) T) ((-156 . -1238) T) ((-156 . -102) T) ((-156 . -93) T) ((-154 . -1070) T) ((-154 . -1078) T) ((-154 . -1133) T) ((-154 . -746) T) ((-154 . -21) T) ((-154 . -666) 11054) ((-154 . -23) T) ((-154 . -1122) T) ((-154 . -630) 11036) ((-154 . -1238) T) ((-154 . -102) T) ((-154 . -25) T) ((-154 . -133) T) ((-154 . -668) 11010) ((-154 . -633) 10979) ((-154 . -38) 10963) ((-154 . -111) 10942) ((-154 . -1072) 10926) ((-154 . -1077) 10910) ((-154 . -660) 10894) ((-154 . -737) 10878) ((-154 . -1296) 10862) ((-146 . -857) T) ((-146 . -864) T) ((-146 . -861) T) ((-146 . -1122) T) 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((-1300 . -632) 204494) ((-1300 . -502) 204478) ((-1300 . -38) 204448) ((-1300 . -111) 204413) ((-1300 . -1071) 204383) ((-1300 . -1076) 204353) ((-1300 . -659) 204323) ((-1300 . -736) 204293) ((-1299 . -1103) T) ((-1299 . -502) 204274) ((-1299 . -629) 204240) ((-1299 . -632) 204221) ((-1299 . -1121) T) ((-1299 . -1237) T) ((-1299 . -102) T) ((-1299 . -93) T) ((-1298 . -1103) T) ((-1298 . -502) 204202) ((-1298 . -629) 204168) ((-1298 . -632) 204149) ((-1298 . -1121) T) ((-1298 . -1237) T) ((-1298 . -102) T) ((-1298 . -93) T) ((-1293 . -629) 204131) ((-1291 . -1121) T) ((-1291 . -629) 204113) ((-1291 . -1237) T) ((-1291 . -102) T) ((-1290 . -1121) T) ((-1290 . -629) 204095) ((-1290 . -1237) T) ((-1290 . -102) T) ((-1287 . -1286) 204079) ((-1287 . -385) 204063) ((-1287 . -863) 204042) ((-1287 . -860) 204021) ((-1287 . -153) 204005) ((-1287 . -34) T) ((-1287 . -1237) T) ((-1287 . -102) 203935) ((-1287 . -629) 203847) ((-1287 . -321) 203785) ((-1287 . -526) 203718) ((-1287 . -1121) 203668) ((-1287 . -501) 203652) ((-1287 . -630) 203613) ((-1287 . -298) 203565) ((-1287 . -615) 203542) ((-1287 . -300) 203519) ((-1287 . -670) 203503) ((-1287 . -19) 203487) ((-1284 . -1121) T) ((-1284 . -629) 203453) ((-1284 . -1237) T) ((-1284 . -102) T) ((-1277 . -1280) 203437) ((-1277 . -240) 203396) ((-1277 . -632) 203278) ((-1277 . -667) 203203) ((-1277 . -665) 203113) ((-1277 . -133) T) ((-1277 . -25) T) ((-1277 . -102) T) ((-1277 . -629) 203095) ((-1277 . -1121) T) ((-1277 . -23) T) ((-1277 . -21) T) ((-1277 . -745) T) ((-1277 . -1132) T) ((-1277 . -1077) T) ((-1277 . -1069) T) ((-1277 . -236) 203048) ((-1277 . -1237) T) ((-1277 . -239) 203007) ((-1277 . -298) 202972) ((-1277 . -916) 202885) ((-1277 . -910) 202773) ((-1277 . -918) 202686) ((-1277 . -993) 202655) ((-1277 . -38) 202552) ((-1277 . -111) 202414) ((-1277 . -1071) 202297) ((-1277 . -1076) 202180) ((-1277 . -659) 202077) ((-1277 . -736) 201974) ((-1277 . -147) 201953) ((-1277 . -149) 201932) ((-1277 . -175) 201883) ((-1277 . -569) 201862) ((-1277 . -302) 201841) ((-1277 . -47) 201818) ((-1277 . -1266) 201795) ((-1277 . -35) 201761) ((-1277 . -95) 201727) ((-1277 . -296) 201693) ((-1277 . -505) 201659) ((-1277 . -1226) 201625) ((-1277 . -1223) 201591) ((-1277 . -1022) 201557) ((-1274 . -338) 201501) ((-1274 . -1058) 201467) ((-1274 . -424) 201433) ((-1274 . -38) 201290) ((-1274 . -632) 201164) ((-1274 . -667) 201053) ((-1274 . -665) 200927) ((-1274 . -745) T) ((-1274 . -1132) T) ((-1274 . -1077) T) ((-1274 . -1069) T) ((-1274 . -111) 200777) ((-1274 . -1071) 200666) ((-1274 . -1076) 200555) ((-1274 . -21) T) ((-1274 . -23) T) ((-1274 . -1121) T) ((-1274 . -629) 200537) ((-1274 . -1237) T) ((-1274 . -102) T) ((-1274 . -25) T) ((-1274 . -133) T) ((-1274 . -659) 200394) ((-1274 . -736) 200251) ((-1274 . -147) 200212) ((-1274 . -149) 200173) ((-1274 . -175) T) ((-1274 . -569) T) ((-1274 . -302) T) ((-1274 . -47) 200117) ((-1273 . -1272) 200096) ((-1273 . -376) 200075) ((-1273 . -1242) 200054) ((-1273 . -939) 200033) ((-1273 . -569) 199984) ((-1273 . -175) 199915) ((-1273 . -632) 199728) ((-1273 . -736) 199569) ((-1273 . -659) 199410) ((-1273 . -38) 199251) ((-1273 . -464) 199230) ((-1273 . -319) 199209) ((-1273 . -667) 199106) ((-1273 . -665) 198988) ((-1273 . -745) T) ((-1273 . -1132) T) ((-1273 . -1077) T) ((-1273 . -1069) T) ((-1273 . -111) 198802) ((-1273 . -1071) 198637) ((-1273 . -1076) 198472) ((-1273 . -21) T) ((-1273 . -23) T) ((-1273 . -1121) T) ((-1273 . -629) 198454) ((-1273 . -1237) T) ((-1273 . -102) T) ((-1273 . -25) T) ((-1273 . -133) T) ((-1273 . -302) 198405) ((-1273 . -250) 198384) ((-1273 . -1022) 198350) ((-1273 . -1223) 198316) ((-1273 . -1226) 198282) ((-1273 . -505) 198248) ((-1273 . -296) 198214) ((-1273 . -95) 198180) ((-1273 . -35) 198146) ((-1273 . -1266) 198116) ((-1273 . -47) 198086) ((-1273 . -149) 198065) ((-1273 . -147) 198044) ((-1273 . -993) 198006) ((-1273 . -918) 197912) ((-1273 . -910) 197816) ((-1273 . -916) 197722) ((-1273 . -298) 197680) ((-1273 . -239) 197632) ((-1273 . -236) 197578) ((-1273 . -240) 197530) ((-1273 . -1270) 197514) ((-1273 . -1058) 197498) ((-1268 . -1272) 197459) ((-1268 . -376) 197438) ((-1268 . -1242) 197417) ((-1268 . -939) 197396) ((-1268 . -569) 197347) ((-1268 . -175) 197278) ((-1268 . -632) 197021) ((-1268 . -736) 196862) ((-1268 . -659) 196703) ((-1268 . -38) 196544) ((-1268 . -464) 196523) ((-1268 . -319) 196502) ((-1268 . -667) 196399) ((-1268 . -665) 196281) ((-1268 . -745) T) ((-1268 . -1132) T) ((-1268 . -1077) T) ((-1268 . -1069) T) ((-1268 . -111) 196095) ((-1268 . -1071) 195930) ((-1268 . -1076) 195765) ((-1268 . -21) T) ((-1268 . -23) T) ((-1268 . -1121) T) ((-1268 . -629) 195747) ((-1268 . -1237) T) ((-1268 . -102) T) ((-1268 . -25) T) ((-1268 . -133) T) ((-1268 . -302) 195698) ((-1268 . -250) 195677) ((-1268 . -1022) 195643) ((-1268 . -1223) 195609) ((-1268 . -1226) 195575) ((-1268 . -505) 195541) ((-1268 . -296) 195507) ((-1268 . -95) 195473) ((-1268 . -35) 195439) ((-1268 . -1266) 195409) ((-1268 . -47) 195379) ((-1268 . -149) 195358) ((-1268 . -147) 195337) ((-1268 . -993) 195299) ((-1268 . -918) 195205) ((-1268 . -910) 195086) ((-1268 . -916) 194992) ((-1268 . -298) 194950) ((-1268 . -239) 194902) ((-1268 . -236) 194848) ((-1268 . -240) 194800) ((-1268 . -1270) 194784) ((-1268 . -1058) 194719) ((-1256 . -1263) 194703) ((-1256 . -1172) 194681) ((-1256 . -630) NIL) ((-1256 . -321) 194668) ((-1256 . -526) 194614) ((-1256 . -338) 194591) ((-1256 . -1058) 194471) ((-1256 . -424) 194455) ((-1256 . -38) 194284) ((-1256 . -111) 194086) ((-1256 . -1071) 193909) ((-1256 . -1076) 193732) ((-1256 . -665) 193642) ((-1256 . -667) 193531) ((-1256 . -659) 193360) ((-1256 . -736) 193189) ((-1256 . -632) 192937) ((-1256 . -147) 192916) ((-1256 . -149) 192895) ((-1256 . -47) 192872) ((-1256 . -390) 192856) ((-1256 . -657) 192804) ((-1256 . -916) 192747) ((-1256 . -910) 192650) ((-1256 . -918) 192557) ((-1256 . -900) NIL) ((-1256 . -928) 192536) ((-1256 . -1242) 192515) ((-1256 . -968) 192484) ((-1256 . -939) 192463) ((-1256 . -569) 192374) ((-1256 . -302) 192285) ((-1256 . -175) 192176) ((-1256 . -464) 192107) ((-1256 . -319) 192086) ((-1256 . -298) 192013) ((-1256 . -240) T) ((-1256 . -133) T) ((-1256 . -25) T) ((-1256 . -102) T) ((-1256 . -629) 191995) ((-1256 . -1121) T) ((-1256 . -23) T) ((-1256 . -21) T) ((-1256 . -745) T) ((-1256 . -1132) T) ((-1256 . -1077) T) ((-1256 . -1069) T) ((-1256 . -236) 191982) ((-1256 . -1237) T) ((-1256 . -239) T) ((-1256 . -274) 191966) ((-1256 . -234) 191950) ((-1254 . -1114) 191934) ((-1254 . -634) 191918) ((-1254 . -1121) 191896) ((-1254 . -629) 191863) ((-1254 . -1237) 191841) ((-1254 . -102) 191819) ((-1254 . -1115) 191776) ((-1252 . -1251) 191755) ((-1252 . -1022) 191721) ((-1252 . -1223) 191687) ((-1252 . -1226) 191653) ((-1252 . -505) 191619) ((-1252 . -296) 191585) ((-1252 . -95) 191551) ((-1252 . -35) 191517) ((-1252 . -1266) 191494) ((-1252 . -47) 191471) ((-1252 . -632) 191219) ((-1252 . -736) 191033) ((-1252 . -659) 190847) ((-1252 . -667) 190655) ((-1252 . -665) 190510) ((-1252 . -1076) 190318) ((-1252 . -1071) 190126) ((-1252 . -111) 189908) ((-1252 . -38) 189722) ((-1252 . -993) 189691) ((-1252 . -298) 189591) ((-1252 . -1249) 189575) ((-1252 . -745) T) ((-1252 . -1132) T) ((-1252 . -1077) T) ((-1252 . -1069) T) ((-1252 . -21) T) ((-1252 . -23) T) ((-1252 . -1121) T) ((-1252 . -629) 189557) ((-1252 . -1237) T) ((-1252 . -102) T) ((-1252 . -25) T) ((-1252 . -133) T) ((-1252 . -147) 189482) ((-1252 . -149) 189407) ((-1252 . -630) 189078) ((-1252 . -234) 189048) ((-1252 . -916) 188899) ((-1252 . -918) 188696) ((-1252 . -910) 188491) ((-1252 . -274) 188461) ((-1252 . -239) 188320) ((-1252 . -236) 188173) ((-1252 . -240) 188078) ((-1252 . -376) 188057) ((-1252 . -1242) 188036) ((-1252 . -939) 188015) ((-1252 . -569) 187966) ((-1252 . -175) 187897) ((-1252 . -464) 187876) ((-1252 . -319) 187855) ((-1252 . -302) 187806) ((-1252 . -250) 187785) ((-1252 . -351) 187755) ((-1252 . -526) 187615) ((-1252 . -321) 187554) ((-1252 . -390) 187524) ((-1252 . -657) 187432) ((-1252 . -412) 187402) ((-1252 . -900) 187275) ((-1252 . -841) 187228) ((-1252 . -811) 187181) ((-1252 . -813) 187134) ((-1252 . -860) 187033) ((-1252 . -863) 186932) ((-1252 . -815) 186885) ((-1252 . -818) 186838) ((-1252 . -859) 186791) ((-1252 . -898) 186761) ((-1252 . -928) 186714) ((-1252 . -1040) 186666) ((-1252 . -1058) 186452) ((-1252 . -1172) 186404) ((-1252 . -1011) 186374) ((-1247 . -1251) 186335) ((-1247 . -1022) 186301) ((-1247 . -1223) 186267) ((-1247 . -1226) 186233) ((-1247 . -505) 186199) ((-1247 . -296) 186165) ((-1247 . -95) 186131) ((-1247 . -35) 186097) ((-1247 . -1266) 186074) ((-1247 . -47) 186051) ((-1247 . -632) 185846) ((-1247 . -736) 185642) ((-1247 . -659) 185438) ((-1247 . -667) 185290) ((-1247 . -665) 185127) ((-1247 . -1076) 184917) ((-1247 . -1071) 184707) ((-1247 . -111) 184453) ((-1247 . -38) 184249) ((-1247 . -993) 184218) ((-1247 . -298) 184046) ((-1247 . -1249) 184030) ((-1247 . -745) T) ((-1247 . -1132) T) ((-1247 . -1077) T) ((-1247 . -1069) T) ((-1247 . -21) T) ((-1247 . -23) T) ((-1247 . -1121) T) ((-1247 . -629) 184012) ((-1247 . -1237) T) ((-1247 . -102) T) ((-1247 . -25) T) ((-1247 . -133) T) ((-1247 . -147) 183919) ((-1247 . -149) 183826) ((-1247 . -630) NIL) ((-1247 . -234) 183778) ((-1247 . -916) 183611) ((-1247 . -918) 183372) ((-1247 . -910) 183108) ((-1247 . -274) 183060) ((-1247 . -239) 182883) ((-1247 . -236) 182700) ((-1247 . -240) 182587) ((-1247 . -376) 182566) ((-1247 . -1242) 182545) ((-1247 . -939) 182524) ((-1247 . -569) 182475) ((-1247 . -175) 182406) ((-1247 . -464) 182385) ((-1247 . -319) 182364) ((-1247 . -302) 182315) ((-1247 . -250) 182294) ((-1247 . -351) 182246) ((-1247 . -526) 181980) ((-1247 . -321) 181865) ((-1247 . -390) 181817) ((-1247 . -657) 181769) ((-1247 . -412) 181721) ((-1247 . -900) NIL) ((-1247 . -841) NIL) ((-1247 . -811) NIL) ((-1247 . -813) NIL) ((-1247 . -860) NIL) ((-1247 . -863) NIL) ((-1247 . -815) NIL) ((-1247 . -818) NIL) ((-1247 . -859) NIL) ((-1247 . -898) 181673) ((-1247 . -928) NIL) ((-1247 . -1040) NIL) ((-1247 . -1058) 181639) ((-1247 . -1172) NIL) ((-1247 . -1011) 181591) ((-1246 . -856) T) ((-1246 . -863) T) ((-1246 . -860) T) ((-1246 . -1121) T) ((-1246 . -629) 181573) ((-1246 . -1237) T) ((-1246 . -102) T) ((-1246 . -381) T) ((-1246 . -681) T) ((-1245 . -856) T) ((-1245 . -863) T) ((-1245 . -860) T) ((-1245 . -1121) T) ((-1245 . -629) 181555) ((-1245 . -1237) T) ((-1245 . -102) T) ((-1245 . -381) T) ((-1245 . -681) T) ((-1244 . -856) T) ((-1244 . -863) T) ((-1244 . -860) T) ((-1244 . -1121) T) ((-1244 . -629) 181537) ((-1244 . -1237) T) ((-1244 . -102) T) ((-1244 . -381) T) ((-1244 . -681) T) ((-1243 . -856) T) ((-1243 . -863) T) ((-1243 . -860) T) ((-1243 . -1121) T) ((-1243 . -629) 181519) ((-1243 . -1237) T) ((-1243 . -102) T) ((-1243 . -381) T) ((-1243 . -681) T) ((-1238 . -1103) T) ((-1238 . -502) 181500) ((-1238 . -629) 181466) ((-1238 . -632) 181447) ((-1238 . -1121) T) ((-1238 . -1237) T) ((-1238 . -102) T) ((-1238 . -93) T) ((-1235 . -502) 181424) ((-1235 . -629) 181365) ((-1235 . -632) 181342) ((-1235 . -1121) 181320) ((-1235 . -1237) 181298) ((-1235 . -102) 181276) ((-1230 . -759) 181252) ((-1230 . -35) 181218) ((-1230 . -95) 181184) ((-1230 . -296) 181150) ((-1230 . -505) 181116) ((-1230 . -1226) 181082) ((-1230 . -1223) 181048) ((-1230 . -1022) 181014) ((-1230 . -47) 180983) ((-1230 . -38) 180880) ((-1230 . -659) 180777) ((-1230 . -736) 180674) ((-1230 . -632) 180556) ((-1230 . -302) 180535) ((-1230 . -569) 180514) ((-1230 . -111) 180376) ((-1230 . -1071) 180259) ((-1230 . -1076) 180142) ((-1230 . -175) 180093) ((-1230 . -149) 180072) ((-1230 . -147) 180051) ((-1230 . -667) 179976) ((-1230 . -665) 179886) ((-1230 . -993) 179847) ((-1230 . -918) 179828) ((-1230 . -1237) T) ((-1230 . -910) 179807) ((-1230 . -1069) T) ((-1230 . -1077) T) ((-1230 . -1132) T) ((-1230 . -745) T) ((-1230 . -21) T) ((-1230 . -23) T) ((-1230 . -1121) T) ((-1230 . -629) 179789) ((-1230 . -102) T) ((-1230 . -25) T) ((-1230 . -133) T) ((-1230 . -916) 179770) ((-1230 . -526) 179737) ((-1230 . -321) 179724) ((-1224 . -1030) 179708) ((-1224 . -34) T) ((-1224 . -1237) T) ((-1224 . -102) 179658) ((-1224 . -629) 179590) ((-1224 . -321) 179528) ((-1224 . -526) 179461) ((-1224 . -1121) 179439) ((-1224 . -501) 179423) ((-1219 . -378) 179397) ((-1219 . -102) T) ((-1219 . -1237) T) ((-1219 . -629) 179379) ((-1219 . -1121) T) ((-1217 . -1121) T) ((-1217 . -629) 179361) ((-1217 . -1237) T) ((-1217 . -102) T) ((-1217 . -632) 179343) ((-1211 . -848) 179327) ((-1211 . -102) T) ((-1211 . -1237) T) ((-1211 . -629) 179309) ((-1211 . -1121) T) ((-1209 . -1214) 179288) ((-1209 . -233) 179238) ((-1209 . -107) 179188) ((-1209 . -321) 178992) ((-1209 . -526) 178752) ((-1209 . -501) 178689) ((-1209 . -153) 178639) ((-1209 . -630) NIL) ((-1209 . -242) 178589) ((-1209 . -626) 178568) ((-1209 . -300) 178547) ((-1209 . -1237) T) ((-1209 . -298) 178526) ((-1209 . -1121) T) ((-1209 . -629) 178508) ((-1209 . -102) T) ((-1209 . -34) T) ((-1209 . -615) 178487) ((-1205 . -1121) T) ((-1205 . -629) 178469) ((-1205 . -1237) T) ((-1205 . -102) T) ((-1204 . -856) T) ((-1204 . -863) T) ((-1204 . -860) T) ((-1204 . -1121) T) ((-1204 . -629) 178451) ((-1204 . -1237) T) ((-1204 . -102) T) ((-1204 . -381) T) ((-1204 . -681) T) ((-1203 . -856) T) ((-1203 . -863) T) ((-1203 . -860) T) ((-1203 . -1121) T) ((-1203 . -629) 178433) ((-1203 . -1237) T) ((-1203 . -102) T) ((-1203 . -381) T) ((-1202 . -1283) T) ((-1202 . -1121) T) ((-1202 . -629) 178400) ((-1202 . -1237) T) ((-1202 . -102) T) ((-1202 . -1058) 178336) ((-1202 . -632) 178272) ((-1201 . -629) 178254) ((-1200 . -629) 178236) ((-1199 . -338) 178213) ((-1199 . -1058) 178109) ((-1199 . -424) 178093) ((-1199 . -38) 177990) ((-1199 . -632) 177843) ((-1199 . -667) 177768) ((-1199 . -665) 177678) ((-1199 . -745) T) ((-1199 . -1132) T) ((-1199 . -1077) T) ((-1199 . -1069) T) ((-1199 . -111) 177540) ((-1199 . -1071) 177423) ((-1199 . -1076) 177306) ((-1199 . -21) T) ((-1199 . -23) T) ((-1199 . -1121) T) ((-1199 . -629) 177288) ((-1199 . -1237) T) ((-1199 . -102) T) ((-1199 . -25) T) ((-1199 . -133) T) ((-1199 . -659) 177185) ((-1199 . -736) 177082) ((-1199 . -147) 177061) ((-1199 . -149) 177040) ((-1199 . -175) 176991) ((-1199 . -569) 176970) ((-1199 . -302) 176949) ((-1199 . -47) 176926) ((-1197 . -860) T) ((-1197 . -629) 176908) ((-1197 . -1121) T) ((-1197 . -102) T) ((-1197 . -1237) T) ((-1197 . -863) T) ((-1197 . -630) 176830) ((-1197 . -632) 176796) ((-1197 . -1058) 176778) ((-1197 . -900) 176745) ((-1196 . -629) 176727) ((-1195 . -1280) 176711) ((-1195 . -240) 176670) ((-1195 . -632) 176552) ((-1195 . -667) 176477) ((-1195 . -665) 176387) ((-1195 . -133) T) ((-1195 . -25) T) ((-1195 . -102) T) ((-1195 . -629) 176369) ((-1195 . -1121) T) ((-1195 . -23) T) ((-1195 . -21) T) ((-1195 . -745) T) ((-1195 . -1132) T) ((-1195 . -1077) T) ((-1195 . -1069) T) ((-1195 . -236) 176322) ((-1195 . -1237) T) ((-1195 . -239) 176281) ((-1195 . -298) 176246) ((-1195 . -916) 176159) ((-1195 . -910) 176047) ((-1195 . -918) 175960) ((-1195 . -993) 175929) ((-1195 . -38) 175826) ((-1195 . -111) 175688) ((-1195 . -1071) 175571) ((-1195 . -1076) 175454) ((-1195 . -659) 175351) ((-1195 . -736) 175248) ((-1195 . -147) 175227) ((-1195 . -149) 175206) ((-1195 . -175) 175157) ((-1195 . -569) 175136) ((-1195 . -302) 175115) ((-1195 . -47) 175092) ((-1195 . -1266) 175069) ((-1195 . -35) 175035) ((-1195 . -95) 175001) ((-1195 . -296) 174967) ((-1195 . -505) 174933) ((-1195 . -1226) 174899) ((-1195 . -1223) 174865) ((-1195 . -1022) 174831) ((-1194 . -1272) 174792) ((-1194 . -376) 174771) ((-1194 . -1242) 174750) ((-1194 . -939) 174729) ((-1194 . -569) 174680) ((-1194 . -175) 174611) ((-1194 . -632) 174354) ((-1194 . -736) 174195) ((-1194 . -659) 174036) ((-1194 . -38) 173877) ((-1194 . -464) 173856) ((-1194 . -319) 173835) ((-1194 . -667) 173732) ((-1194 . -665) 173614) ((-1194 . -745) T) ((-1194 . -1132) T) ((-1194 . -1077) T) ((-1194 . -1069) T) ((-1194 . -111) 173428) ((-1194 . -1071) 173263) ((-1194 . -1076) 173098) ((-1194 . -21) T) ((-1194 . -23) T) ((-1194 . -1121) T) ((-1194 . -629) 173080) ((-1194 . -1237) T) ((-1194 . -102) T) ((-1194 . -25) T) ((-1194 . -133) T) ((-1194 . -302) 173031) ((-1194 . -250) 173010) ((-1194 . -1022) 172976) ((-1194 . -1223) 172942) ((-1194 . -1226) 172908) ((-1194 . -505) 172874) ((-1194 . -296) 172840) ((-1194 . -95) 172806) ((-1194 . -35) 172772) ((-1194 . -1266) 172742) ((-1194 . -47) 172712) ((-1194 . -149) 172691) ((-1194 . -147) 172670) ((-1194 . -993) 172632) ((-1194 . -918) 172538) ((-1194 . -910) 172419) ((-1194 . -916) 172325) ((-1194 . -298) 172283) ((-1194 . -239) 172235) ((-1194 . -236) 172181) ((-1194 . -240) 172133) ((-1194 . -1270) 172117) ((-1194 . -1058) 172052) ((-1191 . -1263) 172036) ((-1191 . -1172) 172014) ((-1191 . -630) NIL) ((-1191 . -321) 172001) ((-1191 . -526) 171947) ((-1191 . -338) 171924) ((-1191 . -1058) 171804) ((-1191 . -424) 171788) ((-1191 . -38) 171617) ((-1191 . -111) 171419) ((-1191 . -1071) 171242) ((-1191 . -1076) 171065) ((-1191 . -665) 170975) ((-1191 . -667) 170864) ((-1191 . -659) 170693) ((-1191 . -736) 170522) ((-1191 . -632) 170291) ((-1191 . -147) 170270) ((-1191 . -149) 170249) ((-1191 . -47) 170226) ((-1191 . -390) 170210) ((-1191 . -657) 170158) ((-1191 . -916) 170101) ((-1191 . -910) 170004) ((-1191 . -918) 169911) ((-1191 . -900) NIL) ((-1191 . -928) 169890) ((-1191 . -1242) 169869) ((-1191 . -968) 169838) ((-1191 . -939) 169817) ((-1191 . -569) 169728) ((-1191 . -302) 169639) ((-1191 . -175) 169530) ((-1191 . -464) 169461) ((-1191 . -319) 169440) ((-1191 . -298) 169367) ((-1191 . -240) T) ((-1191 . -133) T) ((-1191 . -25) T) ((-1191 . -102) T) ((-1191 . -629) 169349) ((-1191 . -1121) T) ((-1191 . -23) T) ((-1191 . -21) T) ((-1191 . -745) T) ((-1191 . -1132) T) ((-1191 . -1077) T) ((-1191 . -1069) T) ((-1191 . -236) 169336) ((-1191 . -1237) T) ((-1191 . -239) T) ((-1191 . -274) 169320) ((-1191 . -234) 169304) ((-1188 . -1251) 169265) ((-1188 . -1022) 169231) ((-1188 . -1223) 169197) ((-1188 . -1226) 169163) ((-1188 . -505) 169129) ((-1188 . -296) 169095) ((-1188 . -95) 169061) ((-1188 . -35) 169027) ((-1188 . -1266) 169004) ((-1188 . -47) 168981) ((-1188 . -632) 168776) ((-1188 . -736) 168572) ((-1188 . -659) 168368) ((-1188 . -667) 168220) ((-1188 . -665) 168057) ((-1188 . -1076) 167847) ((-1188 . -1071) 167637) ((-1188 . -111) 167383) ((-1188 . -38) 167179) ((-1188 . -993) 167148) ((-1188 . -298) 166976) ((-1188 . -1249) 166960) ((-1188 . -745) T) ((-1188 . -1132) T) ((-1188 . -1077) T) ((-1188 . -1069) T) ((-1188 . -21) T) ((-1188 . -23) T) ((-1188 . -1121) T) ((-1188 . -629) 166942) ((-1188 . -1237) T) ((-1188 . -102) T) ((-1188 . -25) T) ((-1188 . -133) T) ((-1188 . -147) 166849) ((-1188 . -149) 166756) ((-1188 . -630) NIL) ((-1188 . -234) 166708) ((-1188 . -916) 166541) ((-1188 . -918) 166302) ((-1188 . -910) 166038) ((-1188 . -274) 165990) ((-1188 . -239) 165813) ((-1188 . -236) 165630) ((-1188 . -240) 165517) ((-1188 . -376) 165496) ((-1188 . -1242) 165475) ((-1188 . -939) 165454) ((-1188 . -569) 165405) ((-1188 . -175) 165336) ((-1188 . -464) 165315) ((-1188 . -319) 165294) ((-1188 . -302) 165245) ((-1188 . -250) 165224) ((-1188 . -351) 165176) ((-1188 . -526) 164910) ((-1188 . -321) 164795) ((-1188 . -390) 164747) ((-1188 . -657) 164699) ((-1188 . -412) 164651) ((-1188 . -900) NIL) ((-1188 . -841) NIL) ((-1188 . -811) NIL) ((-1188 . -813) NIL) ((-1188 . -860) NIL) ((-1188 . -863) NIL) ((-1188 . -815) NIL) ((-1188 . -818) NIL) ((-1188 . -859) NIL) ((-1188 . -898) 164603) ((-1188 . -928) NIL) ((-1188 . -1040) NIL) ((-1188 . -1058) 164569) ((-1188 . -1172) NIL) ((-1188 . -1011) 164521) ((-1187 . -1103) T) ((-1187 . -502) 164502) ((-1187 . -629) 164468) ((-1187 . -632) 164449) ((-1187 . -1121) T) ((-1187 . -1237) T) ((-1187 . -102) T) ((-1187 . -93) T) ((-1186 . -1121) T) ((-1186 . -629) 164431) ((-1186 . -1237) T) ((-1186 . -102) T) ((-1185 . -1121) T) ((-1185 . -629) 164413) ((-1185 . -1237) T) ((-1185 . -102) T) ((-1180 . -1214) 164389) ((-1180 . -233) 164336) ((-1180 . -107) 164283) ((-1180 . -321) 164078) ((-1180 . -526) 163826) ((-1180 . -501) 163760) ((-1180 . -153) 163707) ((-1180 . -630) NIL) ((-1180 . -242) 163654) ((-1180 . -626) 163630) ((-1180 . -300) 163606) ((-1180 . -1237) T) ((-1180 . -298) 163582) ((-1180 . -1121) T) ((-1180 . -629) 163564) ((-1180 . -102) T) ((-1180 . -34) T) ((-1180 . -615) 163540) ((-1179 . -1164) T) ((-1179 . -385) 163522) ((-1179 . -863) T) ((-1179 . -860) T) ((-1179 . -153) 163504) ((-1179 . -34) T) ((-1179 . -1237) T) ((-1179 . -102) T) ((-1179 . -629) 163486) ((-1179 . -321) NIL) ((-1179 . -526) NIL) ((-1179 . -1121) T) ((-1179 . -501) 163468) ((-1179 . -630) NIL) ((-1179 . -298) 163418) ((-1179 . -615) 163393) ((-1179 . -300) 163368) ((-1179 . -670) 163350) ((-1179 . -19) 163332) ((-1175 . -693) 163316) ((-1175 . -670) 163300) ((-1175 . -300) 163277) ((-1175 . -298) 163229) ((-1175 . -615) 163206) ((-1175 . -630) 163167) ((-1175 . -501) 163151) ((-1175 . -1121) 163129) ((-1175 . -526) 163062) ((-1175 . -321) 163000) ((-1175 . -629) 162932) ((-1175 . -102) 162882) ((-1175 . -1237) T) ((-1175 . -34) T) ((-1175 . -153) 162866) ((-1175 . -1276) 162850) ((-1175 . -1030) 162834) ((-1175 . -1170) 162818) ((-1175 . -632) 162795) ((-1173 . -1103) T) ((-1173 . -502) 162776) ((-1173 . -629) 162742) ((-1173 . -632) 162723) ((-1173 . -1121) T) ((-1173 . -1237) T) ((-1173 . -102) T) ((-1173 . -93) T) ((-1171 . -1214) 162702) ((-1171 . -233) 162652) ((-1171 . -107) 162602) ((-1171 . -321) 162406) ((-1171 . -526) 162166) ((-1171 . -501) 162103) ((-1171 . -153) 162053) ((-1171 . -630) NIL) ((-1171 . -242) 162003) ((-1171 . -626) 161982) ((-1171 . -300) 161961) ((-1171 . -1237) T) ((-1171 . -298) 161940) ((-1171 . -1121) T) ((-1171 . -629) 161922) ((-1171 . -102) T) ((-1171 . -34) T) ((-1171 . -615) 161901) ((-1168 . -1141) 161885) ((-1168 . -501) 161869) ((-1168 . -1121) 161847) ((-1168 . -526) 161780) ((-1168 . -321) 161718) ((-1168 . -629) 161650) ((-1168 . -102) 161600) ((-1168 . -1237) T) ((-1168 . -34) T) ((-1168 . -107) 161584) ((-1166 . -1129) 161553) ((-1166 . -1232) 161522) ((-1166 . -629) 161484) ((-1166 . -153) 161468) ((-1166 . -34) T) ((-1166 . -1237) T) ((-1166 . -102) T) ((-1166 . -321) 161406) ((-1166 . -526) 161339) ((-1166 . -1121) T) ((-1166 . -501) 161323) ((-1166 . -630) 161284) ((-1166 . -996) 161253) ((-1166 . -1091) 161222) ((-1162 . -1143) 161167) ((-1162 . -501) 161151) ((-1162 . -526) 161084) ((-1162 . -321) 161022) ((-1162 . -34) T) ((-1162 . -1073) 160962) ((-1162 . -1058) 160858) ((-1162 . -632) 160776) ((-1162 . -424) 160760) ((-1162 . -657) 160708) ((-1162 . -667) 160646) ((-1162 . -390) 160630) ((-1162 . -240) 160609) ((-1162 . -236) 160554) ((-1162 . -239) 160505) ((-1162 . -274) 160489) ((-1162 . -910) 160410) ((-1162 . -918) 160333) ((-1162 . -916) 160292) ((-1162 . -234) 160276) ((-1162 . -736) 160208) ((-1162 . -659) 160140) ((-1162 . -665) 160099) ((-1162 . -133) T) ((-1162 . -25) T) ((-1162 . -102) T) ((-1162 . -1237) T) ((-1162 . -629) 160061) ((-1162 . -1121) T) ((-1162 . -23) T) ((-1162 . -21) T) ((-1162 . -1076) 160045) ((-1162 . -1071) 160029) ((-1162 . -111) 160008) ((-1162 . -1069) T) ((-1162 . -1077) T) ((-1162 . -1132) T) ((-1162 . -745) T) ((-1162 . -38) 159968) ((-1162 . -630) 159929) ((-1161 . -1030) 159900) ((-1161 . -34) T) ((-1161 . -1237) T) ((-1161 . -102) T) ((-1161 . -629) 159882) ((-1161 . -321) 159808) ((-1161 . -526) 159716) ((-1161 . -1121) T) ((-1161 . -501) 159687) ((-1160 . -1121) T) ((-1160 . -629) 159669) ((-1160 . -1237) T) ((-1160 . -102) T) ((-1155 . -1157) T) ((-1155 . -1283) T) ((-1155 . -93) T) ((-1155 . -102) T) ((-1155 . -1237) T) ((-1155 . -629) 159635) ((-1155 . -1121) T) ((-1155 . -632) 159616) ((-1155 . -502) 159597) ((-1155 . -1103) T) ((-1153 . -1154) 159581) ((-1153 . -102) T) ((-1153 . -1237) T) ((-1153 . -629) 159563) ((-1153 . -1121) T) ((-1146 . -759) 159542) ((-1146 . -35) 159508) ((-1146 . -95) 159474) ((-1146 . -296) 159440) ((-1146 . -505) 159406) ((-1146 . -1226) 159372) ((-1146 . -1223) 159338) ((-1146 . -1022) 159304) ((-1146 . -47) 159276) ((-1146 . -38) 159173) ((-1146 . -659) 159070) ((-1146 . -736) 158967) ((-1146 . -632) 158849) ((-1146 . -302) 158828) ((-1146 . -569) 158807) ((-1146 . -111) 158669) ((-1146 . -1071) 158552) ((-1146 . -1076) 158435) ((-1146 . -175) 158386) ((-1146 . -149) 158365) ((-1146 . -147) 158344) ((-1146 . -667) 158269) ((-1146 . -665) 158179) ((-1146 . -993) 158146) ((-1146 . -918) 158130) ((-1146 . -1237) T) ((-1146 . -910) 158112) ((-1146 . -1069) T) ((-1146 . -1077) T) ((-1146 . -1132) T) ((-1146 . -745) T) ((-1146 . -21) T) ((-1146 . -23) T) ((-1146 . -1121) T) ((-1146 . -629) 158094) ((-1146 . -102) T) ((-1146 . -25) T) ((-1146 . -133) T) ((-1146 . -916) 158078) ((-1146 . -526) 158048) ((-1146 . -321) 158035) ((-1145 . -968) 158002) ((-1145 . -632) 157794) ((-1145 . -1058) 157677) ((-1145 . -1242) 157656) ((-1145 . -928) 157635) ((-1145 . -900) 157494) ((-1145 . -918) 157478) ((-1145 . -910) 157460) ((-1145 . -916) 157444) ((-1145 . -526) 157396) ((-1145 . -464) 157347) ((-1145 . -657) 157295) ((-1145 . -667) 157184) ((-1145 . -390) 157168) ((-1145 . -47) 157140) ((-1145 . -38) 156989) ((-1145 . -659) 156838) ((-1145 . -736) 156687) ((-1145 . -302) 156618) ((-1145 . -569) 156549) ((-1145 . -111) 156371) ((-1145 . -1071) 156214) ((-1145 . -1076) 156057) ((-1145 . -175) 155968) ((-1145 . -149) 155947) ((-1145 . -147) 155926) ((-1145 . -665) 155836) ((-1145 . -133) T) ((-1145 . -25) T) ((-1145 . -102) T) ((-1145 . -1237) T) ((-1145 . -629) 155818) ((-1145 . -1121) T) ((-1145 . -23) T) ((-1145 . -21) T) ((-1145 . -1069) T) ((-1145 . -1077) T) ((-1145 . -1132) T) ((-1145 . -745) T) ((-1145 . -424) 155802) ((-1145 . -338) 155774) ((-1145 . -321) 155761) ((-1145 . -630) 155509) ((-1140 . -557) T) ((-1140 . -1242) T) ((-1140 . -1172) T) ((-1140 . -1058) 155491) ((-1140 . -630) 155406) ((-1140 . -1040) T) ((-1140 . -900) 155388) ((-1140 . -859) T) ((-1140 . -818) T) ((-1140 . -815) T) ((-1140 . -863) T) ((-1140 . -860) T) ((-1140 . -813) T) ((-1140 . -811) T) ((-1140 . -841) T) ((-1140 . -667) 155360) ((-1140 . -657) 155342) ((-1140 . -939) T) ((-1140 . -569) T) ((-1140 . -302) T) ((-1140 . -175) T) ((-1140 . -632) 155314) ((-1140 . -736) 155301) ((-1140 . -659) 155288) ((-1140 . -1076) 155275) ((-1140 . -1071) 155262) ((-1140 . -111) 155247) ((-1140 . -38) 155234) ((-1140 . -464) T) ((-1140 . -319) T) ((-1140 . -239) T) ((-1140 . -236) 155221) ((-1140 . -240) T) ((-1140 . -145) T) ((-1140 . -1069) T) ((-1140 . -1077) T) ((-1140 . -1132) T) ((-1140 . -745) T) ((-1140 . -21) T) ((-1140 . -665) 155193) ((-1140 . -23) T) ((-1140 . -1121) T) ((-1140 . -629) 155175) ((-1140 . -1237) T) ((-1140 . -102) T) ((-1140 . -25) T) ((-1140 . -133) T) ((-1140 . -149) T) ((-1140 . -856) T) ((-1140 . -381) T) ((-1140 . -113) T) ((-1140 . -681) T) ((-1136 . -1103) T) ((-1136 . -502) 155156) ((-1136 . -629) 155122) ((-1136 . -632) 155103) ((-1136 . -1121) T) ((-1136 . -1237) T) ((-1136 . -102) T) ((-1136 . -93) T) ((-1135 . -1121) T) ((-1135 . -629) 155085) ((-1135 . -1237) T) ((-1135 . -102) T) ((-1133 . -245) 155064) ((-1133 . -1295) 155034) ((-1133 . -818) 155013) ((-1133 . -815) 154992) ((-1133 . -863) 154943) ((-1133 . -860) 154894) ((-1133 . -813) 154873) ((-1133 . -814) 154852) ((-1133 . -736) 154794) ((-1133 . -659) 154716) ((-1133 . -300) 154693) ((-1133 . -298) 154670) ((-1133 . -501) 154654) ((-1133 . -526) 154587) ((-1133 . -321) 154525) ((-1133 . -34) T) ((-1133 . -615) 154502) ((-1133 . -1058) 154329) ((-1133 . -632) 154127) ((-1133 . -424) 154096) ((-1133 . -657) 154002) ((-1133 . -667) 153835) ((-1133 . -390) 153804) ((-1133 . -381) 153783) ((-1133 . -240) 153735) ((-1133 . -665) 153514) ((-1133 . -745) 153492) ((-1133 . -1132) 153470) ((-1133 . -1077) 153448) ((-1133 . -1069) 153426) ((-1133 . -236) 153317) ((-1133 . -239) 153214) ((-1133 . -274) 153183) ((-1133 . -910) 153050) ((-1133 . -918) 152919) ((-1133 . -916) 152851) ((-1133 . -234) 152820) ((-1133 . -629) 152513) ((-1133 . -1076) 152434) ((-1133 . -1071) 152335) ((-1133 . -111) 152251) ((-1133 . -133) 152122) ((-1133 . -25) 151955) ((-1133 . -102) 151687) ((-1133 . -1237) T) ((-1133 . -1121) 151439) ((-1133 . -23) 151291) ((-1133 . -21) 151202) ((-1126 . -408) T) ((-1126 . -1237) T) ((-1126 . -629) 151184) ((-1125 . -1124) 151148) ((-1125 . -102) T) ((-1125 . -629) 151130) ((-1125 . -1121) T) ((-1125 . -298) 151086) ((-1125 . -1237) T) ((-1125 . -634) 151001) ((-1123 . -1124) 150953) ((-1123 . -102) T) ((-1123 . -629) 150935) ((-1123 . -1121) T) ((-1123 . -298) 150891) ((-1123 . -1237) T) ((-1123 . -634) 150794) ((-1122 . -381) T) ((-1122 . -102) T) ((-1122 . -1237) T) ((-1122 . -629) 150776) ((-1122 . -1121) T) ((-1117 . -438) 150760) ((-1117 . -1119) 150744) ((-1117 . -381) 150723) ((-1117 . -242) 150707) ((-1117 . -630) 150668) ((-1117 . -153) 150652) ((-1117 . -501) 150636) ((-1117 . -1121) T) ((-1117 . -526) 150569) ((-1117 . -321) 150507) ((-1117 . -629) 150489) ((-1117 . -102) T) ((-1117 . -1237) T) ((-1117 . -34) T) ((-1117 . -107) 150473) ((-1117 . -233) 150457) ((-1116 . -1103) T) ((-1116 . -502) 150438) ((-1116 . -629) 150404) ((-1116 . -632) 150385) ((-1116 . -1121) T) ((-1116 . -1237) T) ((-1116 . -102) T) ((-1116 . -93) T) ((-1112 . -1237) T) ((-1112 . -1121) 150355) ((-1112 . -629) 150314) ((-1112 . -102) 150284) ((-1111 . -1103) T) ((-1111 . -502) 150265) ((-1111 . -629) 150231) ((-1111 . -632) 150212) ((-1111 . -1121) T) ((-1111 . -1237) T) ((-1111 . -102) T) ((-1111 . -93) T) ((-1109 . -1114) 150196) ((-1109 . -634) 150180) ((-1109 . -1121) 150158) ((-1109 . -629) 150125) ((-1109 . -1237) 150103) ((-1109 . -102) 150081) ((-1109 . -1115) 150039) ((-1108 . -277) 150023) ((-1108 . -632) 150007) ((-1108 . -1058) 149991) ((-1108 . -863) T) ((-1108 . -102) T) ((-1108 . -1121) T) ((-1108 . -629) 149973) ((-1108 . -860) T) ((-1108 . -236) 149960) ((-1108 . -1237) T) ((-1108 . -239) T) ((-1107 . -262) 149897) ((-1107 . -632) 149633) ((-1107 . -1058) 149460) ((-1107 . -630) NIL) ((-1107 . -338) 149421) ((-1107 . -424) 149405) ((-1107 . -38) 149254) ((-1107 . -111) 149076) ((-1107 . -1071) 148919) ((-1107 . -1076) 148762) ((-1107 . -665) 148672) ((-1107 . -667) 148561) ((-1107 . -659) 148410) ((-1107 . -736) 148259) ((-1107 . -147) 148238) ((-1107 . -149) 148217) ((-1107 . -175) 148128) ((-1107 . -569) 148059) ((-1107 . -302) 147990) ((-1107 . -47) 147951) ((-1107 . -390) 147935) ((-1107 . -657) 147883) ((-1107 . -464) 147834) ((-1107 . -526) 147697) ((-1107 . -916) 147632) ((-1107 . -910) 147527) ((-1107 . -918) 147426) ((-1107 . -900) NIL) ((-1107 . -928) 147405) ((-1107 . -1242) 147384) ((-1107 . -968) 147329) ((-1107 . -321) 147316) ((-1107 . -240) 147295) ((-1107 . -133) T) ((-1107 . -25) T) ((-1107 . -102) T) ((-1107 . -629) 147277) ((-1107 . -1121) T) ((-1107 . -23) T) ((-1107 . -21) T) ((-1107 . -745) T) ((-1107 . -1132) T) ((-1107 . -1077) T) ((-1107 . -1069) T) ((-1107 . -236) 147222) ((-1107 . -1237) T) ((-1107 . -239) 147173) ((-1107 . -274) 147157) ((-1107 . -234) 147141) ((-1105 . -629) 147123) ((-1102 . -860) T) ((-1102 . -629) 147105) ((-1102 . -1121) T) ((-1102 . -102) T) ((-1102 . -1237) T) ((-1102 . -863) T) ((-1102 . -630) 147086) ((-1099 . -743) 147065) ((-1099 . -1058) 146961) ((-1099 . -424) 146945) ((-1099 . -657) 146893) ((-1099 . -667) 146767) ((-1099 . -390) 146751) ((-1099 . -383) 146730) ((-1099 . -149) 146709) ((-1099 . -632) 146527) ((-1099 . -736) 146395) ((-1099 . -659) 146263) ((-1099 . -665) 146158) ((-1099 . -1076) 146068) ((-1099 . -1071) 145978) ((-1099 . -111) 145867) ((-1099 . -38) 145735) ((-1099 . -422) 145714) ((-1099 . -414) 145693) ((-1099 . -147) 145644) ((-1099 . -1172) 145623) ((-1099 . -363) 145602) ((-1099 . -381) 145553) ((-1099 . -250) 145504) ((-1099 . -302) 145455) ((-1099 . -319) 145406) ((-1099 . -464) 145357) ((-1099 . -569) 145308) ((-1099 . -939) 145259) ((-1099 . -1242) 145210) ((-1099 . -376) 145161) ((-1099 . -240) 145086) ((-1099 . -236) 144959) ((-1099 . -239) 144838) ((-1099 . -274) 144808) ((-1099 . -910) 144677) ((-1099 . -918) 144548) ((-1099 . -916) 144481) ((-1099 . -234) 144451) ((-1099 . -630) 144435) ((-1099 . -21) T) ((-1099 . -23) T) ((-1099 . -1121) T) ((-1099 . -629) 144417) ((-1099 . -1237) T) ((-1099 . -102) T) ((-1099 . -25) T) ((-1099 . -133) T) ((-1099 . -1069) T) ((-1099 . -1077) T) ((-1099 . -1132) T) ((-1099 . -745) T) ((-1099 . -175) T) ((-1097 . -1121) T) ((-1097 . -629) 144399) ((-1097 . -1237) T) ((-1097 . -102) T) ((-1097 . -298) 144378) ((-1096 . -1121) T) ((-1096 . -629) 144360) ((-1096 . -1237) T) ((-1096 . -102) T) ((-1095 . -1121) T) ((-1095 . -629) 144342) ((-1095 . -1237) T) ((-1095 . -102) T) ((-1095 . -298) 144321) ((-1095 . -1058) 144298) ((-1095 . -632) 144275) ((-1094 . -1237) T) ((-1093 . -1103) T) ((-1093 . -502) 144256) ((-1093 . -629) 144222) ((-1093 . 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142656) ((-1074 . -526) 142589) ((-1074 . -501) 142573) ((-1074 . -667) 142557) ((-1074 . -665) 142526) ((-1074 . -133) T) ((-1074 . -25) T) ((-1074 . -102) T) ((-1074 . -1237) T) ((-1074 . -629) 142488) ((-1074 . -1121) T) ((-1074 . -23) T) ((-1074 . -21) T) ((-1074 . -1076) 142472) ((-1074 . -1071) 142456) ((-1074 . -111) 142435) ((-1074 . -1295) 142405) ((-1074 . -630) 142366) ((-1066 . -1091) 142295) ((-1066 . -996) 142224) ((-1066 . -630) 142166) ((-1066 . -501) 142131) ((-1066 . -1121) T) ((-1066 . -526) 142015) ((-1066 . -321) 141923) ((-1066 . -629) 141866) ((-1066 . -102) T) ((-1066 . -1237) T) ((-1066 . -34) T) ((-1066 . -153) 141831) ((-1066 . -1232) 141760) ((-1056 . -1103) T) ((-1056 . -502) 141741) ((-1056 . -629) 141707) ((-1056 . -632) 141688) ((-1056 . -1121) T) ((-1056 . -1237) T) ((-1056 . -102) T) ((-1056 . -93) T) ((-1055 . -1214) 141663) ((-1055 . -233) 141609) ((-1055 . -107) 141555) ((-1055 . -321) 141406) ((-1055 . -526) 141214) ((-1055 . -501) 141146) ((-1055 . -153) 141092) ((-1055 . -630) NIL) ((-1055 . -242) 141038) ((-1055 . -626) 141013) ((-1055 . -300) 140988) ((-1055 . -1237) T) ((-1055 . -298) 140963) ((-1055 . -1121) T) ((-1055 . -629) 140945) ((-1055 . -102) T) ((-1055 . -34) T) ((-1055 . -615) 140920) ((-1054 . -175) T) ((-1054 . -632) 140889) ((-1054 . -745) T) ((-1054 . -1132) T) ((-1054 . -1077) T) ((-1054 . -1069) T) ((-1054 . -667) 140863) ((-1054 . -665) 140822) ((-1054 . -133) T) ((-1054 . -25) T) ((-1054 . -102) T) ((-1054 . -1237) T) ((-1054 . -629) 140804) ((-1054 . -1121) T) ((-1054 . -23) T) ((-1054 . -21) T) ((-1054 . -1076) 140778) ((-1054 . -1071) 140752) ((-1054 . -111) 140719) ((-1054 . -38) 140703) ((-1054 . -659) 140687) ((-1054 . -736) 140671) ((-1047 . -1091) 140640) ((-1047 . -996) 140609) ((-1047 . -630) 140570) ((-1047 . -501) 140554) ((-1047 . -1121) T) ((-1047 . -526) 140487) ((-1047 . -321) 140425) ((-1047 . -629) 140387) ((-1047 . -102) T) ((-1047 . -1237) T) ((-1047 . -34) T) ((-1047 . -153) 140371) 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T) ((-1039 . -502) 139473) ((-1039 . -629) 139439) ((-1039 . -632) 139420) ((-1039 . -1121) T) ((-1039 . -1237) T) ((-1039 . -102) T) ((-1039 . -93) T) ((-1024 . -1011) 139402) ((-1024 . -1172) T) ((-1024 . -632) 139352) ((-1024 . -1058) 139312) ((-1024 . -630) 139242) ((-1024 . -1040) T) ((-1024 . -928) NIL) ((-1024 . -898) 139224) ((-1024 . -859) T) ((-1024 . -818) T) ((-1024 . -815) T) ((-1024 . -863) T) ((-1024 . -860) T) ((-1024 . -813) T) ((-1024 . -811) T) ((-1024 . -841) T) ((-1024 . -900) 139206) ((-1024 . -412) 139188) ((-1024 . -657) 139170) ((-1024 . -390) 139152) ((-1024 . -298) NIL) ((-1024 . -321) NIL) ((-1024 . -526) NIL) ((-1024 . -351) 139134) ((-1024 . -250) T) ((-1024 . -111) 139061) ((-1024 . -1071) 139011) ((-1024 . -1076) 138961) ((-1024 . -302) T) ((-1024 . -736) 138911) ((-1024 . -659) 138861) ((-1024 . -667) 138811) ((-1024 . -665) 138761) ((-1024 . -38) 138711) ((-1024 . -319) T) ((-1024 . -464) T) ((-1024 . -175) T) ((-1024 . -569) T) ((-1024 . -939) T) 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137969) ((-1023 . -910) 137876) ((-1023 . -274) 137853) ((-1023 . -239) 137790) ((-1023 . -236) 137721) ((-1023 . -240) 137693) ((-1023 . -376) T) ((-1023 . -1242) T) ((-1023 . -939) T) ((-1023 . -569) T) ((-1023 . -736) 137638) ((-1023 . -659) 137583) ((-1023 . -38) 137528) ((-1023 . -464) T) ((-1023 . -319) T) ((-1023 . -302) T) ((-1023 . -250) T) ((-1023 . -381) NIL) ((-1023 . -363) NIL) ((-1023 . -1172) NIL) ((-1023 . -147) 137500) ((-1023 . -414) NIL) ((-1023 . -422) 137472) ((-1023 . -149) 137444) ((-1023 . -383) 137416) ((-1023 . -390) 137393) ((-1023 . -657) 137327) ((-1023 . -424) 137304) ((-1023 . -1058) 137179) ((-1023 . -743) 137151) ((-1020 . -1015) 137135) ((-1020 . -501) 137119) ((-1020 . -1121) 137097) ((-1020 . -526) 137030) ((-1020 . -321) 136968) ((-1020 . -629) 136900) ((-1020 . -102) 136850) ((-1020 . -1237) T) ((-1020 . -34) T) ((-1020 . -107) 136834) ((-1016 . -1018) 136818) ((-1016 . -863) 136797) ((-1016 . -860) 136776) ((-1016 . -1058) 136672) ((-1016 . -424) 136656) ((-1016 . -657) 136604) ((-1016 . -667) 136506) ((-1016 . -390) 136490) ((-1016 . -298) 136448) ((-1016 . -321) 136413) ((-1016 . -526) 136325) ((-1016 . -351) 136309) ((-1016 . -38) 136257) ((-1016 . -111) 136132) ((-1016 . -1071) 136028) ((-1016 . -1076) 135924) ((-1016 . -665) 135847) ((-1016 . -659) 135795) ((-1016 . -736) 135743) ((-1016 . -632) 135633) ((-1016 . -302) 135584) ((-1016 . -250) 135563) ((-1016 . -240) 135542) ((-1016 . -236) 135487) ((-1016 . -239) 135438) ((-1016 . -274) 135422) ((-1016 . -910) 135343) ((-1016 . -918) 135266) ((-1016 . -916) 135225) ((-1016 . -234) 135209) ((-1016 . -630) 135170) ((-1016 . -149) 135149) ((-1016 . -147) 135128) ((-1016 . -133) T) ((-1016 . -25) T) ((-1016 . -102) T) ((-1016 . -1237) T) ((-1016 . -629) 135110) ((-1016 . -1121) T) ((-1016 . -23) T) ((-1016 . -21) T) ((-1016 . -1069) T) ((-1016 . -1077) T) ((-1016 . -1132) T) ((-1016 . -745) T) ((-1014 . -1103) T) ((-1014 . -502) 135091) ((-1014 . -629) 135057) ((-1014 . -632) 135038) ((-1014 . -1121) T) ((-1014 . -1237) T) ((-1014 . -102) T) ((-1014 . -93) T) ((-1013 . -21) T) ((-1013 . -665) 135020) ((-1013 . -23) T) ((-1013 . -1121) T) ((-1013 . -629) 135002) ((-1013 . -1237) T) ((-1013 . -102) T) ((-1013 . -25) T) ((-1013 . -133) T) ((-1013 . -298) 134969) ((-1009 . -629) 134951) ((-1006 . -1121) T) ((-1006 . -629) 134933) ((-1006 . -1237) T) ((-1006 . -102) T) ((-991 . -818) T) ((-991 . -815) T) ((-991 . -863) T) ((-991 . -860) T) ((-991 . -813) T) ((-991 . -23) T) ((-991 . -1121) T) ((-991 . -629) 134893) ((-991 . -1237) T) ((-991 . -102) T) ((-991 . -25) T) ((-991 . -133) T) ((-990 . -1103) T) ((-990 . -502) 134874) ((-990 . -629) 134840) ((-990 . -632) 134821) ((-990 . -1121) T) ((-990 . -1237) T) ((-990 . -102) T) ((-990 . -93) T) ((-984 . -987) T) ((-984 . -102) T) ((-984 . -629) 134803) ((-984 . -1121) T) ((-984 . -681) T) ((-984 . -1237) T) ((-984 . -113) T) ((-984 . -632) 134787) ((-983 . -629) 134769) ((-982 . -1121) T) ((-982 . -629) 134751) ((-982 . -1237) T) ((-982 . -102) T) ((-982 . -381) 134704) ((-982 . -745) 134603) ((-982 . -1132) 134502) ((-982 . -23) 134313) ((-982 . -25) 134124) ((-982 . -133) 133979) ((-982 . -485) 133932) ((-982 . -21) 133887) ((-982 . -665) 133831) ((-982 . -814) 133784) ((-982 . -813) 133737) ((-982 . -860) 133636) ((-982 . -863) 133535) ((-982 . -815) 133488) ((-982 . -818) 133441) ((-976 . -19) 133425) ((-976 . -670) 133409) ((-976 . -300) 133386) ((-976 . -298) 133338) ((-976 . -615) 133315) ((-976 . -630) 133276) ((-976 . -501) 133260) ((-976 . -1121) 133210) ((-976 . -526) 133143) ((-976 . -321) 133081) ((-976 . -629) 132993) ((-976 . -102) 132923) ((-976 . -1237) T) ((-976 . -34) T) ((-976 . -153) 132907) ((-976 . -860) 132886) ((-976 . -863) 132865) ((-976 . -385) 132849) ((-974 . -338) 132828) ((-974 . -1058) 132724) ((-974 . -424) 132708) ((-974 . -38) 132605) ((-974 . -632) 132458) ((-974 . -667) 132383) ((-974 . -665) 132293) ((-974 . -745) T) ((-974 . -1132) T) ((-974 . -1077) T) ((-974 . -1069) T) ((-974 . -111) 132155) ((-974 . -1071) 132038) ((-974 . -1076) 131921) ((-974 . -21) T) ((-974 . -23) T) ((-974 . -1121) T) ((-974 . -629) 131903) ((-974 . -1237) T) ((-974 . -102) T) ((-974 . -25) T) ((-974 . -133) T) ((-974 . -659) 131800) ((-974 . -736) 131697) ((-974 . -147) 131676) ((-974 . -149) 131655) ((-974 . -175) 131606) ((-974 . -569) 131585) ((-974 . -302) 131564) ((-974 . -47) 131543) ((-972 . -1121) T) ((-972 . -629) 131509) ((-972 . -1237) T) ((-972 . -102) T) ((-964 . -968) 131470) ((-964 . -632) 131259) ((-964 . -1058) 131139) ((-964 . -1242) 131118) ((-964 . -928) 131097) ((-964 . -900) 131022) ((-964 . -918) 131003) ((-964 . -910) 130982) ((-964 . -916) 130963) ((-964 . -526) 130909) ((-964 . -464) 130860) ((-964 . -657) 130808) ((-964 . -667) 130697) ((-964 . -390) 130681) ((-964 . -47) 130650) ((-964 . -38) 130499) ((-964 . -659) 130348) ((-964 . -736) 130197) ((-964 . -302) 130128) ((-964 . -569) 130059) ((-964 . -111) 129881) ((-964 . -1071) 129724) ((-964 . -1076) 129567) ((-964 . -175) 129478) ((-964 . -149) 129457) ((-964 . -147) 129436) ((-964 . -665) 129346) ((-964 . -133) T) ((-964 . -25) T) ((-964 . -102) T) ((-964 . -1237) T) ((-964 . -629) 129328) ((-964 . -1121) T) ((-964 . -23) T) ((-964 . -21) T) ((-964 . -1069) T) ((-964 . -1077) T) ((-964 . -1132) T) ((-964 . -745) T) ((-964 . -424) 129312) ((-964 . -338) 129281) ((-964 . -321) 129268) ((-964 . -630) 129129) ((-961 . -1000) 129113) ((-961 . -19) 129097) ((-961 . -670) 129081) ((-961 . -300) 129058) ((-961 . -298) 129010) ((-961 . -615) 128987) ((-961 . -630) 128948) ((-961 . -501) 128932) ((-961 . -1121) 128882) ((-961 . -526) 128815) ((-961 . -321) 128753) ((-961 . -629) 128665) ((-961 . -102) 128595) ((-961 . -1237) T) ((-961 . -34) T) ((-961 . -153) 128579) ((-961 . -860) 128558) ((-961 . -863) 128537) ((-961 . -385) 128521) ((-961 . -1286) 128505) ((-961 . -634) 128482) ((-945 . -994) T) ((-945 . -629) 128464) ((-943 . -973) T) ((-943 . -629) 128446) ((-937 . -815) T) ((-937 . -863) T) ((-937 . -860) T) ((-937 . -1121) T) ((-937 . -629) 128428) ((-937 . -1237) T) ((-937 . -102) T) ((-937 . -25) T) ((-937 . -745) T) ((-937 . -1132) T) ((-932 . -376) T) ((-932 . -1242) T) ((-932 . -939) T) ((-932 . -569) T) ((-932 . -175) T) ((-932 . -632) 128365) ((-932 . -736) 128317) ((-932 . -659) 128269) ((-932 . -38) 128221) ((-932 . -464) T) ((-932 . -319) T) ((-932 . -667) 128173) ((-932 . -665) 128110) ((-932 . -745) T) ((-932 . -1132) T) ((-932 . -1077) T) ((-932 . -1069) T) ((-932 . -111) 128041) ((-932 . -1071) 127993) ((-932 . -1076) 127945) ((-932 . -21) T) ((-932 . -23) T) ((-932 . -1121) T) ((-932 . -629) 127927) ((-932 . -1237) T) ((-932 . -102) T) ((-932 . -25) T) ((-932 . -133) T) ((-932 . -302) T) ((-932 . -250) T) ((-924 . -363) T) ((-924 . -1172) T) ((-924 . -381) T) ((-924 . -147) T) ((-924 . -376) T) ((-924 . -1242) T) ((-924 . -939) T) ((-924 . -569) T) ((-924 . -175) T) ((-924 . -632) 127877) ((-924 . -736) 127842) ((-924 . -659) 127807) ((-924 . -38) 127772) ((-924 . -464) T) ((-924 . -319) T) ((-924 . -111) 127721) ((-924 . -1071) 127686) ((-924 . -1076) 127651) ((-924 . -665) 127601) ((-924 . -667) 127566) ((-924 . -302) T) ((-924 . -250) T) ((-924 . -414) T) ((-924 . -239) T) ((-924 . -1237) T) ((-924 . -236) 127553) ((-924 . -1069) T) ((-924 . -1077) T) ((-924 . -1132) T) ((-924 . -745) T) ((-924 . -21) T) ((-924 . -23) T) ((-924 . -1121) T) ((-924 . -629) 127535) ((-924 . -102) T) ((-924 . -25) T) ((-924 . -133) T) ((-924 . -240) T) ((-924 . -341) 127522) ((-924 . -149) 127504) ((-924 . -1058) 127491) ((-924 . -1295) 127478) ((-924 . -1306) 127465) ((-924 . -630) 127447) ((-923 . -1121) T) ((-923 . -629) 127429) ((-923 . -1237) T) ((-923 . -102) T) ((-920 . -922) 127413) ((-920 . -863) 127364) ((-920 . -860) 127315) ((-920 . -745) T) ((-920 . -1121) T) ((-920 . -629) 127297) ((-920 . -102) T) ((-920 . -1132) T) ((-920 . -485) T) ((-920 . -1237) T) ((-920 . -298) 127276) ((-919 . -121) 127260) ((-919 . -501) 127244) ((-919 . -1121) 127222) ((-919 . -526) 127155) ((-919 . -321) 127093) ((-919 . -629) 127004) ((-919 . -102) 126954) ((-919 . -1237) T) ((-919 . -34) T) ((-919 . -1030) 126938) ((-914 . -1121) T) ((-914 . -629) 126920) ((-914 . -1237) T) ((-914 . -102) T) ((-907 . -860) T) ((-907 . -629) 126902) ((-907 . -1121) T) ((-907 . -102) T) ((-907 . -1237) T) ((-907 . -863) T) ((-907 . -1058) 126879) ((-907 . -632) 126856) ((-904 . -1121) T) ((-904 . -629) 126838) ((-904 . -1237) T) ((-904 . -102) T) ((-904 . -1058) 126806) ((-904 . -632) 126774) ((-902 . -1121) T) ((-902 . -629) 126756) ((-902 . -1237) T) ((-902 . -102) T) ((-899 . -1121) T) ((-899 . -629) 126738) ((-899 . -1237) T) ((-899 . -102) T) ((-889 . -1103) T) ((-889 . -502) 126719) ((-889 . -629) 126685) ((-889 . -632) 126666) ((-889 . -1121) T) ((-889 . -1237) T) ((-889 . -102) T) ((-889 . -93) T) ((-889 . -1283) T) ((-887 . -1121) T) ((-887 . -629) 126648) ((-887 . -1237) T) ((-887 . -102) T) ((-886 . -1237) T) ((-886 . -629) 126520) ((-886 . -1121) 126471) ((-886 . -102) 126422) ((-885 . -1011) 126406) ((-885 . -1172) 126384) ((-885 . -1058) 126248) ((-885 . -632) 126146) ((-885 . -630) 125947) ((-885 . -1040) 125925) ((-885 . -928) 125904) ((-885 . -898) 125888) ((-885 . -859) 125867) ((-885 . -818) 125846) ((-885 . -815) 125825) ((-885 . -863) 125776) ((-885 . -860) 125727) ((-885 . -813) 125706) ((-885 . -811) 125685) ((-885 . -841) 125664) ((-885 . -900) 125589) ((-885 . -412) 125573) ((-885 . -657) 125521) ((-885 . -667) 125437) ((-885 . -390) 125421) ((-885 . -298) 125379) ((-885 . -321) 125344) ((-885 . -526) 125256) ((-885 . -351) 125240) ((-885 . -250) T) ((-885 . -111) 125171) ((-885 . -1071) 125123) ((-885 . -1076) 125075) ((-885 . -302) T) ((-885 . -736) 125027) ((-885 . -659) 124979) ((-885 . -665) 124916) ((-885 . -38) 124868) ((-885 . -319) T) ((-885 . -464) T) ((-885 . -175) T) ((-885 . -569) T) ((-885 . -939) T) ((-885 . -1242) T) ((-885 . -376) T) ((-885 . -240) 124847) ((-885 . -236) 124792) ((-885 . -239) 124743) ((-885 . -274) 124727) ((-885 . -910) 124648) ((-885 . -918) 124571) ((-885 . -916) 124530) ((-885 . -234) 124514) ((-885 . -149) 124493) ((-885 . -147) 124472) ((-885 . -133) T) ((-885 . -25) T) ((-885 . -102) T) ((-885 . -1237) T) ((-885 . -629) 124454) ((-885 . -1121) T) ((-885 . -23) T) ((-885 . -21) T) ((-885 . -1069) T) ((-885 . -1077) T) ((-885 . -1132) T) ((-885 . -745) T) ((-884 . -1011) 124431) ((-884 . -1172) NIL) ((-884 . -1058) 124408) ((-884 . -632) 124338) ((-884 . -630) NIL) ((-884 . -1040) NIL) ((-884 . -928) NIL) ((-884 . -898) 124315) ((-884 . -859) NIL) ((-884 . -818) NIL) ((-884 . -815) NIL) ((-884 . -863) NIL) ((-884 . -860) NIL) ((-884 . -813) NIL) ((-884 . -811) NIL) ((-884 . -841) NIL) ((-884 . -900) NIL) ((-884 . -412) 124292) ((-884 . -657) 124269) ((-884 . -667) 124214) ((-884 . -390) 124191) ((-884 . -298) 124121) ((-884 . -321) 124065) ((-884 . -526) 123928) ((-884 . -351) 123905) ((-884 . -250) T) ((-884 . -111) 123822) ((-884 . -1071) 123767) ((-884 . -1076) 123712) ((-884 . -302) T) ((-884 . -736) 123657) ((-884 . -659) 123602) ((-884 . -665) 123532) ((-884 . -38) 123477) ((-884 . -319) T) ((-884 . -464) T) ((-884 . -175) T) ((-884 . -569) T) ((-884 . -939) T) ((-884 . -1242) T) ((-884 . -376) T) ((-884 . -240) NIL) ((-884 . -236) NIL) ((-884 . -239) NIL) ((-884 . -274) 123454) ((-884 . -910) NIL) ((-884 . -918) NIL) ((-884 . -916) NIL) ((-884 . -234) 123431) ((-884 . -149) T) ((-884 . -147) NIL) ((-884 . -133) T) ((-884 . -25) T) ((-884 . -102) T) ((-884 . -1237) T) ((-884 . -629) 123413) ((-884 . -1121) T) ((-884 . -23) T) ((-884 . -21) T) ((-884 . -1069) T) ((-884 . -1077) T) ((-884 . -1132) T) ((-884 . -745) T) ((-882 . -883) 123397) ((-882 . -939) T) ((-882 . -569) T) ((-882 . -302) T) ((-882 . -175) T) ((-882 . -632) 123369) ((-882 . -736) 123356) ((-882 . -659) 123343) ((-882 . -1076) 123330) ((-882 . -1071) 123317) ((-882 . -111) 123302) ((-882 . -38) 123289) ((-882 . -464) T) ((-882 . -319) T) ((-882 . -1069) T) ((-882 . -1077) T) ((-882 . -1132) T) ((-882 . -745) T) ((-882 . -21) T) ((-882 . -665) 123261) ((-882 . -23) T) ((-882 . -1121) T) ((-882 . -629) 123243) ((-882 . -1237) T) ((-882 . -102) T) ((-882 . -25) T) ((-882 . -133) T) ((-882 . -667) 123230) ((-882 . -149) T) ((-879 . -1069) T) ((-879 . -1077) T) ((-879 . -1132) T) ((-879 . -745) T) ((-879 . -21) T) ((-879 . -665) 123175) ((-879 . -23) T) ((-879 . -1121) T) ((-879 . -629) 123137) ((-879 . -1237) T) ((-879 . -102) T) ((-879 . -25) T) ((-879 . -133) T) ((-879 . -667) 123097) ((-879 . -632) 123032) ((-879 . -502) 123009) ((-879 . -38) 122979) ((-879 . -111) 122944) ((-879 . -1071) 122914) ((-879 . -1076) 122884) ((-879 . -659) 122854) ((-879 . -736) 122824) ((-878 . -1121) T) ((-878 . -629) 122806) ((-878 . -1237) T) ((-878 . -102) T) ((-877 . -856) T) ((-877 . -863) T) ((-877 . -860) T) ((-877 . -1121) T) ((-877 . -629) 122788) ((-877 . -1237) T) ((-877 . -102) T) ((-877 . -381) T) ((-877 . -630) 122710) ((-876 . -1121) T) ((-876 . -629) 122692) ((-876 . -1237) T) ((-876 . -102) T) ((-875 . -874) T) ((-875 . -176) T) ((-875 . -629) 122674) ((-871 . -860) T) ((-871 . -629) 122656) ((-871 . -1121) T) ((-871 . -102) T) ((-871 . -1237) T) ((-871 . -863) T) ((-868 . -865) 122640) ((-868 . -1058) 122536) ((-868 . -632) 122433) ((-868 . -424) 122417) ((-868 . -736) 122387) ((-868 . -659) 122357) ((-868 . -667) 122331) ((-868 . -665) 122290) ((-868 . -133) T) ((-868 . -25) T) ((-868 . -102) T) ((-868 . -1237) T) ((-868 . -629) 122272) ((-868 . -1121) T) ((-868 . -23) T) ((-868 . -21) T) ((-868 . -1076) 122256) ((-868 . -1071) 122240) ((-868 . -111) 122219) ((-868 . -1069) T) ((-868 . -1077) T) ((-868 . -1132) T) ((-868 . -745) T) ((-868 . -38) 122189) ((-867 . -865) 122173) ((-867 . -1058) 122069) ((-867 . -632) 121987) ((-867 . -424) 121971) ((-867 . -736) 121941) ((-867 . -659) 121911) ((-867 . -667) 121885) ((-867 . -665) 121844) ((-867 . -133) T) ((-867 . -25) T) ((-867 . -102) T) ((-867 . -1237) T) ((-867 . -629) 121826) ((-867 . -1121) T) ((-867 . -23) T) ((-867 . -21) T) ((-867 . -1076) 121810) ((-867 . -1071) 121794) ((-867 . -111) 121773) ((-867 . -1069) T) ((-867 . -1077) T) ((-867 . -1132) T) ((-867 . -745) T) ((-867 . -38) 121743) ((-861 . -863) T) ((-861 . -1237) T) ((-861 . -102) T) ((-861 . -502) 121727) ((-861 . -629) 121675) ((-861 . -632) 121659) ((-854 . -1121) T) ((-854 . -629) 121641) ((-854 . -1237) T) ((-854 . -102) T) ((-854 . -424) 121625) ((-854 . -632) 121493) ((-854 . -1058) 121389) ((-854 . -21) 121341) ((-854 . -665) 121258) ((-854 . -23) 121210) ((-854 . -25) 121162) ((-854 . -133) 121114) ((-854 . -859) 121093) ((-854 . -667) 121066) ((-854 . -1077) 121045) ((-854 . -1069) 121024) ((-854 . -818) 121003) ((-854 . -815) 120982) ((-854 . -863) 120961) ((-854 . -860) 120940) ((-854 . -813) 120919) ((-854 . -811) 120898) ((-854 . -1132) 120877) ((-854 . -745) 120856) ((-853 . -1121) T) ((-853 . -629) 120838) ((-853 . -1237) T) ((-853 . -102) T) ((-850 . -848) 120820) ((-850 . -102) T) ((-850 . -1237) T) ((-850 . -629) 120802) ((-850 . -1121) T) ((-846 . -1069) T) ((-846 . -1077) T) ((-846 . -1132) T) ((-846 . -745) T) ((-846 . -21) T) ((-846 . -665) 120747) ((-846 . -23) T) ((-846 . -1121) T) ((-846 . -629) 120729) ((-846 . -1237) T) ((-846 . -102) T) ((-846 . -25) T) ((-846 . -133) T) ((-846 . -667) 120689) ((-846 . -632) 120643) ((-846 . -1058) 120612) ((-846 . -298) 120591) ((-846 . -149) 120570) ((-846 . -147) 120549) ((-846 . -38) 120519) ((-846 . -111) 120484) ((-846 . -1071) 120454) ((-846 . -1076) 120424) ((-846 . -659) 120394) ((-846 . -736) 120364) ((-844 . -1121) T) ((-844 . -629) 120346) ((-844 . -1237) T) ((-844 . -102) T) ((-844 . -424) 120330) ((-844 . -632) 120198) ((-844 . -1058) 120094) ((-844 . -21) 120046) ((-844 . -665) 119963) ((-844 . -23) 119915) ((-844 . -25) 119867) ((-844 . -133) 119819) ((-844 . -859) 119798) ((-844 . -667) 119771) ((-844 . -1077) 119750) ((-844 . -1069) 119729) ((-844 . -818) 119708) ((-844 . -815) 119687) ((-844 . -863) 119666) ((-844 . -860) 119645) ((-844 . -813) 119624) ((-844 . -811) 119603) ((-844 . -1132) 119582) ((-844 . -745) 119561) ((-842 . -727) 119545) ((-842 . -632) 119500) ((-842 . -736) 119470) ((-842 . -659) 119440) ((-842 . -667) 119414) ((-842 . -665) 119373) ((-842 . -133) T) ((-842 . -25) T) ((-842 . -102) T) ((-842 . -1237) T) ((-842 . -629) 119355) ((-842 . -1121) T) ((-842 . -23) T) ((-842 . -21) T) ((-842 . -1076) 119339) ((-842 . -1071) 119323) ((-842 . -111) 119302) ((-842 . -1069) T) ((-842 . -1077) T) ((-842 . -1132) T) ((-842 . -745) T) ((-842 . -38) 119272) ((-842 . -240) 119251) ((-842 . -236) 119224) ((-842 . -239) 119203) ((-840 . -399) 119187) ((-840 . -632) 119171) ((-840 . -1058) 119155) ((-840 . -863) T) ((-840 . -860) T) ((-840 . -1132) T) ((-840 . -102) T) ((-840 . -1237) T) ((-840 . -629) 119137) ((-840 . -1121) T) ((-840 . -745) T) ((-840 . -858) T) ((-840 . -870) T) ((-839 . -277) 119121) ((-839 . -632) 119105) ((-839 . -1058) 119089) ((-839 . -863) T) ((-839 . -102) T) ((-839 . -1121) T) ((-839 . -629) 119071) ((-839 . -860) T) ((-839 . -236) 119058) ((-839 . -1237) T) ((-839 . -239) T) ((-838 . -111) 118993) ((-838 . -1071) 118944) ((-838 . -1076) 118895) ((-838 . -21) T) ((-838 . -665) 118831) ((-838 . -23) T) ((-838 . -1121) T) ((-838 . -629) 118800) ((-838 . -1237) T) ((-838 . -102) T) ((-838 . -25) T) ((-838 . -133) T) ((-838 . -667) 118751) ((-838 . -240) T) ((-838 . -632) 118660) ((-838 . -745) T) ((-838 . -1132) T) ((-838 . -1077) T) ((-838 . -1069) T) ((-838 . -236) 118647) ((-838 . -239) T) ((-838 . -502) 118631) ((-838 . -376) 118610) ((-838 . -1242) 118589) ((-838 . -939) 118568) ((-838 . -569) 118547) ((-838 . -175) 118526) ((-838 . -736) 118463) ((-838 . -659) 118400) ((-838 . -38) 118337) ((-838 . -464) 118316) ((-838 . -319) 118295) ((-838 . -302) 118274) ((-838 . -250) 118253) ((-837 . -262) 118192) ((-837 . -632) 117929) ((-837 . -1058) 117757) ((-837 . -630) NIL) ((-837 . -338) 117719) ((-837 . -424) 117703) ((-837 . -38) 117552) ((-837 . -111) 117374) ((-837 . -1071) 117217) ((-837 . -1076) 117060) ((-837 . -665) 116970) ((-837 . -667) 116859) ((-837 . -659) 116708) ((-837 . -736) 116557) ((-837 . -147) 116536) ((-837 . -149) 116515) ((-837 . -175) 116426) ((-837 . -569) 116357) ((-837 . -302) 116288) ((-837 . -47) 116250) ((-837 . -390) 116234) ((-837 . -657) 116182) ((-837 . -464) 116133) ((-837 . -526) 115998) ((-837 . -916) 115934) ((-837 . -910) 115830) ((-837 . -918) 115730) ((-837 . -900) NIL) ((-837 . -928) 115709) ((-837 . -1242) 115688) ((-837 . -968) 115635) ((-837 . -321) 115622) ((-837 . -240) 115601) ((-837 . -133) T) ((-837 . -25) T) ((-837 . -102) T) ((-837 . -629) 115583) ((-837 . -1121) T) ((-837 . -23) T) ((-837 . -21) T) ((-837 . -745) T) ((-837 . -1132) T) ((-837 . -1077) T) ((-837 . -1069) T) ((-837 . -236) 115528) ((-837 . -1237) T) ((-837 . -239) 115479) ((-837 . -274) 115463) ((-837 . -234) 115447) ((-836 . -245) 115426) ((-836 . -1295) 115396) ((-836 . -818) 115375) ((-836 . -815) 115354) ((-836 . -863) 115305) ((-836 . -860) 115256) ((-836 . -813) 115235) ((-836 . -814) 115214) ((-836 . -736) 115156) ((-836 . -659) 115078) ((-836 . -300) 115055) ((-836 . -298) 115032) ((-836 . -501) 115016) ((-836 . -526) 114949) ((-836 . -321) 114887) ((-836 . -34) T) ((-836 . -615) 114864) ((-836 . -1058) 114691) ((-836 . -632) 114489) ((-836 . -424) 114458) ((-836 . -657) 114364) ((-836 . -667) 114197) ((-836 . -390) 114166) ((-836 . -381) 114145) ((-836 . -240) 114097) ((-836 . -665) 113876) ((-836 . -745) 113854) ((-836 . -1132) 113832) ((-836 . -1077) 113810) ((-836 . -1069) 113788) ((-836 . -236) 113679) ((-836 . -239) 113576) ((-836 . -274) 113545) ((-836 . -910) 113412) ((-836 . -918) 113281) ((-836 . -916) 113213) ((-836 . -234) 113182) ((-836 . -629) 112875) ((-836 . -1076) 112796) ((-836 . -1071) 112697) ((-836 . -111) 112613) ((-836 . -133) 112484) ((-836 . -25) 112317) ((-836 . -102) 112049) ((-836 . -1237) T) ((-836 . -1121) 111801) ((-836 . -23) 111653) ((-836 . -21) 111564) ((-829 . -1121) T) ((-829 . -629) 111546) ((-829 . -1237) T) ((-829 . -102) T) ((-819 . -817) 111530) ((-819 . -863) 111509) ((-819 . -860) 111488) ((-819 . -1058) 111268) ((-819 . -632) 111114) ((-819 . -424) 111077) ((-819 . -298) 111035) ((-819 . -321) 111000) ((-819 . -526) 110912) ((-819 . -351) 110896) ((-819 . -381) 110875) ((-819 . -630) 110836) ((-819 . -149) 110815) ((-819 . -147) 110794) ((-819 . -736) 110778) ((-819 . -659) 110762) ((-819 . -667) 110736) ((-819 . -665) 110695) ((-819 . -133) T) ((-819 . -25) T) ((-819 . -102) T) ((-819 . -1237) T) ((-819 . -629) 110677) ((-819 . -1121) T) ((-819 . -23) T) ((-819 . -21) T) ((-819 . -1076) 110661) ((-819 . -1071) 110645) ((-819 . -111) 110624) ((-819 . -1069) T) ((-819 . -1077) T) ((-819 . -1132) T) ((-819 . -745) T) ((-819 . -38) 110608) ((-800 . -1263) 110592) ((-800 . -1172) 110570) ((-800 . -630) NIL) ((-800 . -321) 110557) ((-800 . -526) 110503) ((-800 . -338) 110480) ((-800 . -1058) 110339) ((-800 . -424) 110323) ((-800 . -38) 110152) ((-800 . -111) 109954) ((-800 . -1071) 109777) ((-800 . -1076) 109600) ((-800 . -665) 109510) ((-800 . -667) 109399) ((-800 . -659) 109228) ((-800 . -736) 109057) ((-800 . -632) 108805) ((-800 . -147) 108784) ((-800 . -149) 108763) ((-800 . -47) 108740) ((-800 . -390) 108724) ((-800 . -657) 108672) ((-800 . -916) 108615) ((-800 . -910) 108518) ((-800 . -918) 108425) ((-800 . -900) NIL) ((-800 . -928) 108404) ((-800 . -1242) 108383) ((-800 . -968) 108352) ((-800 . -939) 108331) ((-800 . -569) 108242) ((-800 . -302) 108153) ((-800 . -175) 108044) ((-800 . -464) 107975) ((-800 . -319) 107954) ((-800 . -298) 107881) ((-800 . -240) T) ((-800 . -133) T) ((-800 . -25) T) ((-800 . -102) T) ((-800 . -629) 107842) ((-800 . -1121) T) ((-800 . -23) T) ((-800 . -21) T) ((-800 . -745) T) ((-800 . -1132) T) ((-800 . -1077) T) ((-800 . -1069) T) ((-800 . -236) 107829) ((-800 . -1237) T) ((-800 . -239) T) ((-800 . -274) 107813) ((-800 . -234) 107797) ((-799 . -1085) 107764) ((-799 . -630) 107398) ((-799 . -321) 107385) ((-799 . -526) 107337) ((-799 . -338) 107309) ((-799 . -1058) 107166) ((-799 . -424) 107150) ((-799 . -38) 106999) ((-799 . -632) 106765) ((-799 . -667) 106654) ((-799 . -665) 106564) ((-799 . -745) T) ((-799 . -1132) T) ((-799 . -1077) T) ((-799 . -1069) T) ((-799 . -111) 106386) ((-799 . -1071) 106229) ((-799 . -1076) 106072) ((-799 . -21) T) ((-799 . -23) T) ((-799 . -1121) T) ((-799 . -629) 105986) ((-799 . -1237) T) ((-799 . -102) T) ((-799 . -25) T) ((-799 . -133) T) ((-799 . -659) 105835) ((-799 . -736) 105684) ((-799 . -147) 105663) ((-799 . -149) 105642) ((-799 . -175) 105553) ((-799 . -569) 105484) ((-799 . -302) 105415) ((-799 . -47) 105387) ((-799 . -390) 105371) ((-799 . -657) 105319) ((-799 . -464) 105270) ((-799 . -916) 105254) ((-799 . -910) 105236) ((-799 . -918) 105220) ((-799 . -900) 105079) ((-799 . -928) 105058) ((-799 . -1242) 105037) ((-799 . -968) 105004) ((-792 . -1121) T) ((-792 . -629) 104986) ((-792 . -1237) T) ((-792 . -102) T) ((-790 . -814) T) ((-790 . -133) T) ((-790 . -25) T) ((-790 . -102) T) ((-790 . -1237) T) ((-790 . -629) 104968) ((-790 . -1121) T) ((-790 . -23) T) ((-790 . -813) T) ((-790 . -860) T) ((-790 . -863) T) ((-790 . -815) T) ((-790 . -818) T) ((-790 . -745) T) ((-790 . -1132) T) ((-788 . -1121) T) ((-788 . -629) 104950) ((-788 . -1237) T) ((-788 . -102) T) ((-755 . -756) 104934) ((-755 . -1119) 104918) ((-755 . -242) 104902) ((-755 . -630) 104863) ((-755 . -153) 104847) ((-755 . -501) 104831) ((-755 . -1121) T) ((-755 . -526) 104764) ((-755 . -321) 104702) ((-755 . -629) 104684) ((-755 . -102) T) ((-755 . -1237) T) ((-755 . -34) T) ((-755 . -107) 104668) ((-755 . -714) 104652) ((-754 . -1069) T) ((-754 . -1077) T) ((-754 . -1132) T) ((-754 . -745) T) ((-754 . -21) T) ((-754 . -665) 104597) ((-754 . -23) T) ((-754 . -1121) T) ((-754 . -629) 104579) ((-754 . -1237) T) ((-754 . -102) T) ((-754 . -25) T) ((-754 . -133) T) ((-754 . -667) 104539) ((-754 . -632) 104495) ((-754 . -1058) 104466) ((-754 . -149) 104445) ((-754 . -147) 104424) ((-754 . -38) 104394) ((-754 . -111) 104359) ((-754 . -1071) 104329) ((-754 . -1076) 104299) ((-754 . -659) 104269) ((-754 . -736) 104239) ((-754 . -381) 104192) ((-750 . -968) 104145) ((-750 . -632) 103930) ((-750 . -1058) 103806) ((-750 . -1242) 103785) ((-750 . -928) 103764) ((-750 . -900) NIL) ((-750 . -918) 103741) ((-750 . -910) 103716) ((-750 . -916) 103693) ((-750 . -526) 103631) ((-750 . -464) 103582) ((-750 . -657) 103530) ((-750 . -667) 103419) ((-750 . -390) 103403) ((-750 . -47) 103368) ((-750 . -38) 103217) ((-750 . -659) 103066) ((-750 . -736) 102915) ((-750 . -302) 102846) ((-750 . -569) 102777) ((-750 . -111) 102599) ((-750 . -1071) 102442) ((-750 . -1076) 102285) ((-750 . -175) 102196) ((-750 . -149) 102175) ((-750 . -147) 102154) ((-750 . -665) 102064) ((-750 . -133) T) ((-750 . -25) T) ((-750 . -102) T) ((-750 . -1237) T) ((-750 . -629) 102046) ((-750 . -1121) T) ((-750 . -23) T) ((-750 . -21) T) ((-750 . -1069) T) ((-750 . -1077) T) ((-750 . -1132) T) ((-750 . -745) T) ((-750 . -424) 102030) ((-750 . -338) 101995) ((-750 . -321) 101982) ((-750 . -630) 101843) ((-737 . -485) T) ((-737 . -1132) T) ((-737 . -102) T) ((-737 . -1237) T) ((-737 . -629) 101825) ((-737 . -1121) T) ((-737 . -745) T) ((-734 . -1069) T) ((-734 . -1077) T) ((-734 . -1132) T) ((-734 . -745) T) ((-734 . -21) T) ((-734 . -665) 101797) ((-734 . -23) T) ((-734 . -1121) T) ((-734 . -629) 101779) ((-734 . -1237) T) ((-734 . -102) T) ((-734 . -25) T) ((-734 . -133) T) ((-734 . -667) 101766) ((-734 . -632) 101748) ((-733 . -1069) T) ((-733 . -1077) T) ((-733 . -1132) T) ((-733 . -745) T) ((-733 . -21) T) ((-733 . -665) 101693) ((-733 . -23) T) ((-733 . -1121) T) ((-733 . -629) 101675) ((-733 . -1237) T) ((-733 . -102) T) ((-733 . -25) T) ((-733 . -133) T) ((-733 . -667) 101635) ((-733 . -632) 101589) ((-733 . -1058) 101558) ((-733 . -298) 101537) ((-733 . -149) 101516) ((-733 . -147) 101495) ((-733 . -38) 101465) ((-733 . -111) 101430) ((-733 . -1071) 101400) ((-733 . -1076) 101370) ((-733 . -659) 101340) ((-733 . -736) 101310) ((-732 . -860) T) ((-732 . -629) 101245) ((-732 . -1121) T) ((-732 . -102) T) ((-732 . -1237) T) ((-732 . -863) T) ((-732 . -502) 101195) ((-732 . -632) 101145) ((-731 . -1263) 101129) ((-731 . -1172) 101107) ((-731 . -630) NIL) ((-731 . -321) 101094) ((-731 . -526) 101040) ((-731 . -338) 101017) ((-731 . -1058) 100897) ((-731 . -424) 100881) ((-731 . -38) 100710) ((-731 . -111) 100512) ((-731 . -1071) 100335) ((-731 . -1076) 100158) ((-731 . -665) 100068) ((-731 . -667) 99957) ((-731 . -659) 99786) ((-731 . -736) 99615) ((-731 . -632) 99371) ((-731 . -147) 99350) ((-731 . -149) 99329) ((-731 . -47) 99306) ((-731 . -390) 99290) ((-731 . -657) 99238) ((-731 . -916) 99181) ((-731 . -910) 99084) ((-731 . -918) 98991) ((-731 . -900) NIL) ((-731 . -928) 98970) ((-731 . -1242) 98949) ((-731 . -968) 98918) ((-731 . -939) 98897) ((-731 . -569) 98808) ((-731 . -302) 98719) ((-731 . -175) 98610) ((-731 . -464) 98541) ((-731 . -319) 98520) ((-731 . -298) 98447) ((-731 . -240) T) ((-731 . -133) T) ((-731 . -25) T) ((-731 . -102) T) ((-731 . -629) 98429) ((-731 . -1121) T) ((-731 . -23) T) ((-731 . -21) T) ((-731 . -745) T) ((-731 . -1132) T) ((-731 . -1077) T) ((-731 . -1069) T) ((-731 . -236) 98416) ((-731 . -1237) T) ((-731 . -239) T) ((-731 . -274) 98400) ((-731 . -234) 98384) ((-731 . -381) 98363) ((-730 . -376) T) ((-730 . -1242) T) ((-730 . -939) T) ((-730 . -569) T) ((-730 . -175) T) ((-730 . -632) 98313) ((-730 . -736) 98278) ((-730 . -659) 98243) ((-730 . -38) 98208) ((-730 . -464) T) ((-730 . -319) T) ((-730 . -667) 98173) ((-730 . -665) 98123) ((-730 . -745) T) ((-730 . -1132) T) ((-730 . -1077) T) ((-730 . -1069) T) ((-730 . -111) 98072) ((-730 . -1071) 98037) ((-730 . -1076) 98002) ((-730 . -21) T) ((-730 . -23) T) ((-730 . -1121) T) ((-730 . -629) 97984) ((-730 . -1237) T) ((-730 . -102) T) ((-730 . -25) T) ((-730 . -133) T) ((-730 . -302) T) ((-730 . -250) T) ((-729 . -1121) T) ((-729 . -629) 97966) ((-729 . -1237) T) ((-729 . -102) T) ((-720 . -401) T) ((-720 . -1058) 97948) ((-720 . -863) T) ((-720 . -860) T) ((-720 . -38) 97935) ((-720 . -632) 97907) ((-720 . -745) T) ((-720 . -1132) T) ((-720 . -1077) T) ((-720 . -1069) T) ((-720 . -111) 97892) ((-720 . -1071) 97879) ((-720 . -1076) 97866) ((-720 . -21) T) ((-720 . -665) 97838) ((-720 . -23) T) ((-720 . -1121) T) ((-720 . -629) 97820) ((-720 . -1237) T) ((-720 . -102) T) ((-720 . -25) T) ((-720 . -133) T) ((-720 . -667) 97792) ((-720 . -659) 97779) ((-720 . -736) 97766) ((-720 . -175) T) ((-720 . -302) T) ((-720 . -569) T) ((-720 . -557) T) ((-720 . -1242) T) ((-720 . -1172) T) ((-720 . -630) 97681) ((-720 . -1040) T) ((-720 . -900) 97663) ((-720 . -859) T) ((-720 . -818) T) ((-720 . -815) T) ((-720 . -813) T) ((-720 . -811) T) ((-720 . -841) T) ((-720 . -657) 97645) ((-720 . -939) T) ((-720 . -464) T) ((-720 . -319) T) ((-720 . -239) T) ((-720 . -236) 97632) ((-720 . -240) T) ((-720 . -145) T) ((-720 . -149) T) ((-718 . -416) T) ((-718 . -149) T) ((-718 . -632) 97567) ((-718 . -667) 97532) ((-718 . -665) 97482) ((-718 . -133) T) ((-718 . -25) T) ((-718 . -102) T) ((-718 . -1237) T) ((-718 . -629) 97464) ((-718 . -1121) T) ((-718 . -23) T) ((-718 . -21) T) ((-718 . -745) T) ((-718 . -1132) T) ((-718 . -1077) T) ((-718 . -1069) T) ((-718 . -630) 97409) ((-718 . -376) T) ((-718 . -1242) T) ((-718 . -939) T) ((-718 . -569) T) ((-718 . -175) T) ((-718 . -736) 97374) ((-718 . -659) 97339) ((-718 . -38) 97304) ((-718 . -464) T) ((-718 . -319) T) ((-718 . -111) 97253) ((-718 . -1071) 97218) ((-718 . -1076) 97183) ((-718 . -302) T) ((-718 . -250) T) ((-718 . -859) T) ((-718 . -818) T) ((-718 . -815) T) ((-718 . -863) T) ((-718 . -860) T) ((-718 . -813) T) ((-718 . -811) T) ((-718 . -900) 97165) ((-718 . -1022) T) ((-718 . -1040) T) ((-718 . -1058) 97110) ((-718 . -1080) T) ((-718 . -401) T) ((-713 . -401) T) ((-713 . -1058) 97055) ((-713 . -863) T) ((-713 . -860) T) ((-713 . -38) 97005) ((-713 . -632) 96940) ((-713 . -745) T) ((-713 . -1132) T) ((-713 . -1077) T) ((-713 . -1069) T) ((-713 . -111) 96867) ((-713 . -1071) 96817) ((-713 . -1076) 96767) ((-713 . -21) T) ((-713 . -665) 96702) ((-713 . -23) T) ((-713 . -1121) T) ((-713 . -629) 96684) ((-713 . -1237) T) ((-713 . -102) T) ((-713 . -25) T) ((-713 . -133) T) ((-713 . -667) 96634) ((-713 . -659) 96584) ((-713 . -736) 96534) ((-713 . -175) T) ((-713 . -302) T) ((-713 . -569) T) ((-713 . -168) 96516) ((-713 . -35) NIL) ((-713 . -95) NIL) ((-713 . -296) NIL) ((-713 . -505) NIL) ((-713 . -1226) NIL) ((-713 . -1223) NIL) ((-713 . -1022) NIL) ((-713 . -928) NIL) ((-713 . -630) 96424) ((-713 . -898) 96406) ((-713 . -381) NIL) ((-713 . -363) NIL) ((-713 . -1172) NIL) ((-713 . -414) NIL) ((-713 . -422) 96373) ((-713 . -383) 96340) ((-713 . -743) 96307) ((-713 . -424) 96289) ((-713 . -900) 96271) ((-713 . -412) 96253) ((-713 . -657) 96235) ((-713 . -390) 96217) ((-713 . -298) NIL) ((-713 . -321) NIL) ((-713 . -526) NIL) ((-713 . -351) 96199) ((-713 . -250) T) ((-713 . -1242) T) ((-713 . -376) T) ((-713 . -939) T) ((-713 . -464) T) ((-713 . -319) T) ((-713 . -240) NIL) ((-713 . -236) NIL) ((-713 . -239) NIL) ((-713 . -274) 96181) ((-713 . -910) NIL) ((-713 . -918) NIL) ((-713 . -916) NIL) ((-713 . -234) 96163) ((-713 . -149) T) ((-713 . -147) NIL) ((-710 . -1283) T) ((-710 . -1058) 96147) ((-710 . -632) 96131) ((-710 . -629) 96113) ((-708 . -705) 96071) ((-708 . -501) 96055) ((-708 . -1121) 96033) ((-708 . -526) 95966) ((-708 . -321) 95904) ((-708 . -629) 95836) ((-708 . -102) 95786) ((-708 . -1237) T) ((-708 . -34) T) ((-708 . -57) 95744) ((-708 . -630) 95705) ((-700 . -1103) T) ((-700 . -502) 95686) ((-700 . -629) 95636) ((-700 . -632) 95617) ((-700 . -1121) T) ((-700 . -1237) T) ((-700 . -102) T) ((-700 . -93) T) ((-696 . -860) T) ((-696 . -629) 95599) ((-696 . -1121) T) ((-696 . -102) T) ((-696 . -1237) T) ((-696 . -863) T) ((-696 . -1058) 95583) ((-696 . -632) 95567) ((-695 . -1103) T) ((-695 . -502) 95548) ((-695 . -629) 95514) ((-695 . -632) 95495) ((-695 . -1121) T) ((-695 . -1237) T) ((-695 . -102) T) ((-695 . -93) T) ((-694 . -501) 95479) ((-694 . -1121) 95457) ((-694 . -526) 95390) ((-694 . -321) 95328) ((-694 . -629) 95260) ((-694 . -102) 95210) ((-694 . -1237) T) ((-694 . -34) T) ((-691 . -860) T) ((-691 . -629) 95192) ((-691 . -1121) T) ((-691 . -102) T) ((-691 . -1237) T) ((-691 . -863) T) ((-691 . -1058) 95176) ((-691 . -632) 95160) ((-690 . -1103) T) ((-690 . -502) 95141) ((-690 . -629) 95107) ((-690 . -632) 95088) ((-690 . -1121) T) ((-690 . -1237) T) ((-690 . -102) T) ((-690 . -93) T) ((-689 . -1143) 95033) ((-689 . -501) 95017) ((-689 . -526) 94950) ((-689 . -321) 94888) ((-689 . -34) T) ((-689 . -1073) 94828) ((-689 . -1058) 94724) ((-689 . -632) 94642) ((-689 . -424) 94626) ((-689 . -657) 94574) ((-689 . -667) 94512) ((-689 . -390) 94496) ((-689 . -240) 94475) ((-689 . -236) 94420) ((-689 . -239) 94371) ((-689 . -274) 94355) ((-689 . -910) 94276) ((-689 . -918) 94199) ((-689 . -916) 94158) ((-689 . -234) 94142) ((-689 . -736) 94126) ((-689 . -659) 94110) ((-689 . -665) 94069) ((-689 . -133) T) ((-689 . -25) T) ((-689 . -102) T) ((-689 . -1237) T) ((-689 . -629) 94031) ((-689 . -1121) T) ((-689 . -23) T) ((-689 . -21) T) ((-689 . -1076) 94015) ((-689 . -1071) 93999) ((-689 . -111) 93978) ((-689 . -1069) T) ((-689 . -1077) T) ((-689 . -1132) T) ((-689 . -745) T) ((-689 . -38) 93938) ((-689 . -430) 93922) ((-689 . -763) 93906) ((-689 . -739) T) ((-689 . -780) T) ((-689 . -380) 93890) ((-689 . -298) 93867) ((-683 . -387) 93846) ((-683 . -736) 93830) ((-683 . -659) 93814) ((-683 . -667) 93798) ((-683 . -665) 93767) ((-683 . -133) T) ((-683 . -25) T) ((-683 . -102) T) ((-683 . -1237) T) ((-683 . -629) 93749) ((-683 . -1121) T) ((-683 . -23) T) ((-683 . -21) T) ((-683 . -1076) 93733) ((-683 . -1071) 93717) ((-683 . -111) 93696) ((-683 . -651) 93680) ((-683 . -397) 93652) ((-683 . -632) 93629) ((-683 . -1058) 93606) ((-675 . -677) 93590) ((-675 . -38) 93560) ((-675 . -632) 93478) ((-675 . -667) 93452) ((-675 . -665) 93411) ((-675 . -745) T) ((-675 . -1132) T) ((-675 . -1077) T) ((-675 . -1069) T) ((-675 . -111) 93390) ((-675 . -1071) 93374) ((-675 . -1076) 93358) ((-675 . -21) T) ((-675 . -23) T) ((-675 . -1121) T) ((-675 . -629) 93340) ((-675 . -102) T) ((-675 . -25) T) ((-675 . -133) T) ((-675 . -659) 93310) ((-675 . -736) 93280) ((-675 . -424) 93264) ((-675 . -1058) 93160) ((-675 . -865) 93144) ((-675 . -1237) T) ((-675 . -298) 93105) ((-674 . -677) 93089) ((-674 . -38) 93059) ((-674 . -632) 92977) ((-674 . -667) 92951) ((-674 . -665) 92910) ((-674 . -745) T) ((-674 . -1132) T) ((-674 . -1077) T) ((-674 . -1069) T) ((-674 . -111) 92889) ((-674 . -1071) 92873) ((-674 . -1076) 92857) ((-674 . -21) T) ((-674 . -23) T) ((-674 . -1121) T) ((-674 . -629) 92839) ((-674 . -102) T) ((-674 . -25) T) ((-674 . -133) T) ((-674 . -659) 92809) ((-674 . -736) 92779) ((-674 . -424) 92763) ((-674 . -1058) 92659) ((-674 . -865) 92643) ((-674 . -1237) T) ((-674 . -298) 92622) ((-673 . -677) 92606) ((-673 . -38) 92576) ((-673 . -632) 92494) ((-673 . -667) 92468) ((-673 . -665) 92427) ((-673 . -745) T) ((-673 . -1132) T) ((-673 . -1077) T) ((-673 . -1069) T) ((-673 . -111) 92406) ((-673 . -1071) 92390) ((-673 . -1076) 92374) ((-673 . -21) T) ((-673 . -23) T) ((-673 . -1121) T) ((-673 . -629) 92356) ((-673 . -102) T) ((-673 . -25) T) ((-673 . -133) T) ((-673 . -659) 92326) ((-673 . -736) 92296) ((-673 . -424) 92280) ((-673 . -1058) 92176) ((-673 . -865) 92160) ((-673 . -1237) T) ((-673 . -298) 92139) ((-671 . -736) 92123) ((-671 . -659) 92107) ((-671 . -667) 92091) ((-671 . -665) 92060) ((-671 . -133) T) ((-671 . -25) T) ((-671 . -102) T) ((-671 . -1237) T) ((-671 . -629) 92042) ((-671 . -1121) T) ((-671 . -23) T) ((-671 . -21) T) ((-671 . -1076) 92026) ((-671 . -1071) 92010) ((-671 . -111) 91989) ((-671 . -811) 91968) ((-671 . -813) 91947) ((-671 . -860) 91926) ((-671 . -863) 91905) ((-671 . -815) 91884) ((-671 . -818) 91863) ((-668 . -1121) T) ((-668 . -629) 91845) ((-668 . -1237) T) ((-668 . -102) T) ((-668 . -1058) 91829) ((-668 . -632) 91813) ((-666 . -714) 91797) ((-666 . -107) 91781) ((-666 . -34) T) ((-666 . -1237) T) ((-666 . -102) 91731) ((-666 . -629) 91663) ((-666 . -321) 91601) ((-666 . -526) 91534) ((-666 . -1121) 91512) ((-666 . -501) 91496) ((-666 . -153) 91480) ((-666 . -630) 91441) ((-666 . -242) 91425) ((-664 . -1103) T) ((-664 . -502) 91406) ((-664 . -629) 91359) ((-664 . -632) 91340) ((-664 . -1121) T) ((-664 . -1237) T) ((-664 . -102) T) ((-664 . -93) T) ((-660 . -685) 91324) ((-660 . -1276) 91308) ((-660 . -1030) 91292) ((-660 . -1170) 91276) ((-660 . -860) 91255) ((-660 . -863) 91234) ((-660 . -385) 91218) ((-660 . -670) 91202) ((-660 . -300) 91179) ((-660 . -298) 91131) ((-660 . -615) 91108) ((-660 . -630) 91069) ((-660 . -501) 91053) ((-660 . -1121) 91003) ((-660 . -526) 90936) 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. -102) T) ((-229 . -1237) T) ((-229 . -629) 17892) ((-229 . -1121) T) ((-229 . -23) T) ((-229 . -21) T) ((-229 . -745) T) ((-229 . -1132) T) ((-229 . -1077) T) ((-229 . -1069) T) ((-229 . -630) 17822) ((-229 . -376) T) ((-229 . -1242) T) ((-229 . -939) T) ((-229 . -569) T) ((-229 . -175) T) ((-229 . -736) 17787) ((-229 . -659) 17752) ((-229 . -38) 17717) ((-229 . -464) T) ((-229 . -319) T) ((-229 . -111) 17666) ((-229 . -1071) 17631) ((-229 . -1076) 17596) ((-229 . -302) T) ((-229 . -250) T) ((-229 . -859) T) ((-229 . -818) T) ((-229 . -815) T) ((-229 . -863) T) ((-229 . -860) T) ((-229 . -813) T) ((-229 . -811) T) ((-229 . -900) 17578) ((-229 . -1022) T) ((-229 . -1040) T) ((-229 . -1058) 17538) ((-229 . -1080) T) ((-229 . -240) T) ((-229 . -236) 17525) ((-229 . -239) T) ((-229 . -1223) T) ((-229 . -1226) T) ((-229 . -505) T) ((-229 . -296) T) ((-229 . -95) T) ((-229 . -35) T) ((-227 . -637) 17502) ((-227 . -632) 17464) ((-227 . -667) 17431) ((-227 . -665) 17383) ((-227 . -745) T) 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16689) ((-221 . -657) 16671) ((-221 . -390) 16653) ((-221 . -298) NIL) ((-221 . -321) NIL) ((-221 . -526) NIL) ((-221 . -351) 16635) ((-221 . -250) T) ((-221 . -111) 16562) ((-221 . -1071) 16512) ((-221 . -1076) 16462) ((-221 . -302) T) ((-221 . -736) 16412) ((-221 . -659) 16362) ((-221 . -667) 16312) ((-221 . -665) 16262) ((-221 . -38) 16212) ((-221 . -319) T) ((-221 . -464) T) ((-221 . -175) T) ((-221 . -569) T) ((-221 . -939) T) ((-221 . -1242) T) ((-221 . -376) T) ((-221 . -240) T) ((-221 . -236) 16199) ((-221 . -239) T) ((-221 . -274) 16181) ((-221 . -910) NIL) ((-221 . -918) NIL) ((-221 . -916) NIL) ((-221 . -234) 16163) ((-221 . -149) T) ((-221 . -147) NIL) ((-221 . -133) T) ((-221 . -25) T) ((-221 . -102) T) ((-221 . -1237) T) ((-221 . -629) 16104) ((-221 . -1121) T) ((-221 . -23) T) ((-221 . -21) T) ((-221 . -1069) T) ((-221 . -1077) T) ((-221 . -1132) T) ((-221 . -745) T) ((-218 . -856) T) ((-218 . -863) T) ((-218 . -860) T) ((-218 . -1121) T) ((-218 . -629) 16086) ((-218 . 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. -35) 14810) ((-171 . -95) 14788) ((-171 . -296) 14766) ((-171 . -505) 14744) ((-171 . -1226) 14722) ((-171 . -1223) 14700) ((-171 . -1022) 14651) ((-171 . -928) 14604) ((-171 . -630) 14370) ((-171 . -898) 14354) ((-171 . -381) 14305) ((-171 . -363) 14284) ((-171 . -1172) 14263) ((-171 . -414) 14242) ((-171 . -422) 14213) ((-171 . -38) 14041) ((-171 . -111) 13930) ((-171 . -1071) 13840) ((-171 . -1076) 13750) ((-171 . -659) 13578) ((-171 . -736) 13406) ((-171 . -383) 13377) ((-171 . -743) 13348) ((-171 . -1058) 13244) ((-171 . -632) 13022) ((-171 . -424) 13006) ((-171 . -900) 12931) ((-171 . -412) 12915) ((-171 . -657) 12863) ((-171 . -667) 12737) ((-171 . -665) 12632) ((-171 . -390) 12616) ((-171 . -298) 12574) ((-171 . -321) 12539) ((-171 . -526) 12451) ((-171 . -351) 12435) ((-171 . -250) 12386) ((-171 . -1242) 12291) ((-171 . -376) 12242) ((-171 . -939) 12173) ((-171 . -569) 12084) ((-171 . -302) 11995) ((-171 . -464) 11926) ((-171 . -319) 11857) ((-171 . -240) 11808) ((-171 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index d18e81a6..9ff0ef0d 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3524522242) -(4428 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3524556578) +(4427 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -187,9 +187,9 @@ |IntegrationResultFunctions2| |IntegrationResultToFunction| |InternalRepresentationForm| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| - |InternalRationalUnivariateRepresentationPackage| |IsAst| |IndexedString| - |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| - |InternalTypeForm| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| + |InternalRationalUnivariateRepresentationPackage| |IsAst| |InnerPolySum| + |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InternalTypeForm| + |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| |JoinAst| |AssociatedJordanAlgebra| |JVMBytecode| |JVMClassFileAccess| |JVMConstantTag| |JVMFieldAccess| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 2b14c8a9..900dd82f 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4383 +1,4380 @@ -(3097043 . 3524522254) -((-1935 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-1933 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-4218 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-1255 (-558)) |#2|) 44 T ELT)) (-2510 (($ $) 80 T ELT)) (-4272 ((|#2| (-1 |#2| |#2| |#2|) $ 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T) ((-23) . T) ((-25) . T) ((-38 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1224)) ((-95) |has| |#1| (-1224)) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -3957 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-633 (-419 (-558))) -3957 (|has| |#1| (-1059 (-419 (-558)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-630 (-877)) . T) ((-175) . T) ((-631 (-171 (-229))) |has| |#1| (-1041)) ((-631 (-171 (-391))) |has| |#1| (-1041)) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-631 (-905 (-391))) |has| |#1| (-631 (-905 (-391)))) ((-631 (-905 (-558))) |has| |#1| (-631 (-905 (-558)))) ((-631 (-1192 |#1|)) . T) ((-236 $) -3957 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -3957 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -3957 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1224)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -3957 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-414) |has| |#1| (-363)) ((-381) -3957 (|has| |#1| (-363)) (|has| |#1| (-381))) ((-363) |has| |#1| (-363)) ((-383 |#1| (-1192 |#1|)) . T) ((-422 |#1| (-1192 |#1|)) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-412 |#1|) . T) ((-424 |#1|) . T) ((-464) -3957 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-505) |has| |#1| (-1224)) ((-526 (-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-569) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-666 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 |#1|) . T) ((-660 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-658 (-558)) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-737 |#1|) . T) ((-737 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-744 |#1| (-1192 |#1|)) . T) ((-746) . T) ((-911 $ (-1198)) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-917 (-1198)) |has| |#1| (-917 (-1198))) ((-919 (-1198)) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-901 (-391)) |has| |#1| (-901 (-391))) ((-901 (-558)) |has| |#1| (-901 (-558))) ((-899 |#1|) . T) ((-929) -12 (|has| |#1| (-319)) (|has| |#1| (-929))) ((-940) -3957 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1023) -12 (|has| |#1| (-1023)) (|has| |#1| (-1224))) ((-1059 (-419 (-558))) |has| |#1| (-1059 (-419 (-558)))) ((-1059 (-558)) |has| |#1| (-1059 (-558))) ((-1059 |#1|) . T) ((-1072 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 (-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1173) |has| |#1| (-363)) ((-1224) |has| |#1| (-1224)) ((-1227) |has| |#1| (-1224)) ((-1238) . 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T) ((-23) . T) ((-25) . T) ((-38 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1223)) ((-95) |has| |#1| (-1223)) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -3956 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) -3956 (|has| |#1| (-1058 (-419 (-558)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-632 (-558)) . T) ((-632 |#1|) . T) ((-632 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-629 (-876)) . T) ((-175) . 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T) ((-250) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1223)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -3956 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-414) |has| |#1| (-363)) ((-381) -3956 (|has| |#1| (-363)) (|has| |#1| (-381))) ((-363) |has| |#1| (-363)) ((-383 |#1| (-1191 |#1|)) . T) ((-422 |#1| (-1191 |#1|)) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-412 |#1|) . T) ((-424 |#1|) . T) ((-464) -3956 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-505) |has| |#1| (-1223)) ((-526 (-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-569) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-665 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-665 (-558)) . T) ((-665 |#1|) . T) ((-665 $) . T) ((-667 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-667 (-558)) |has| |#1| (-657 (-558))) ((-667 |#1|) . T) ((-667 $) . T) ((-659 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-659 |#1|) . T) ((-659 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-657 (-558)) |has| |#1| (-657 (-558))) ((-657 |#1|) . T) ((-736 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-736 |#1|) . T) ((-736 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-743 |#1| (-1191 |#1|)) . T) ((-745) . T) ((-910 $ (-1197)) -3956 (|has| |#1| (-918 (-1197))) (|has| |#1| (-916 (-1197)))) ((-916 (-1197)) |has| |#1| (-916 (-1197))) ((-918 (-1197)) -3956 (|has| |#1| (-918 (-1197))) (|has| |#1| (-916 (-1197)))) ((-900 (-391)) |has| |#1| (-900 (-391))) ((-900 (-558)) |has| |#1| (-900 (-558))) ((-898 |#1|) . T) ((-928) -12 (|has| |#1| (-319)) (|has| |#1| (-928))) ((-939) -3956 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1022) -12 (|has| |#1| (-1022)) (|has| |#1| (-1223))) ((-1058 (-419 (-558))) |has| |#1| (-1058 (-419 (-558)))) ((-1058 (-558)) |has| |#1| (-1058 (-558))) ((-1058 |#1|) . T) ((-1071 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1071 |#1|) . T) ((-1071 $) . T) ((-1076 (-419 (-558))) -3956 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1076 |#1|) . T) ((-1076 $) . T) ((-1069) . T) ((-1077) . T) ((-1132) . T) ((-1121) . T) ((-1172) |has| |#1| (-363)) ((-1223) |has| |#1| (-1223)) ((-1226) |has| |#1| (-1223)) ((-1237) . 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T) ((-102) -3957 (|has| |#2| (-1122)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -3957 (|has| |#2| (-1070)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-633 (-419 (-558))) -12 (|has| |#2| (-1059 (-419 (-558)))) (|has| |#2| (-1122))) ((-633 (-558)) -3957 (|has| |#2| (-1070)) (-12 (|has| |#2| (-1059 (-558))) (|has| |#2| (-1122)))) ((-633 |#2|) |has| |#2| (-1122)) ((-630 (-877)) -3957 (|has| |#2| (-1122)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-630 (-877))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-630 (-1288 |#2|)) . T) ((-236 $) -3957 (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1070)))) ((-234 |#2|) |has| |#2| (-1070)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1070))) ((-239) -3957 (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1070)))) ((-274 |#2|) |has| |#2| (-1070)) ((-298 (-558) |#2|) . T) ((-300 (-558) |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1070)) ((-424 |#2|) |has| |#2| (-1122)) ((-501 |#2|) . T) ((-616 (-558) |#2|) . 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|%noBranch|) (IF (|has| |t#2| (-860)) (-6 (-860)) |%noBranch|) (IF (|has| |t#2| (-814)) (-6 (-814)) |%noBranch|) (IF (|has| |t#2| (-376)) (-6 (-1295 |t#2|)) |%noBranch|))) +(((-21) -3956 (|has| |#2| (-1069)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-23) -3956 (|has| |#2| (-1069)) (|has| |#2| (-814)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -3956 (|has| |#2| (-1069)) (|has| |#2| (-814)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3956 (|has| |#2| (-1121)) (|has| |#2| (-1069)) (|has| |#2| (-860)) (|has| |#2| (-814)) (|has| |#2| (-745)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3956 (|has| |#2| (-1069)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -3956 (|has| |#2| (-1069)) (|has| |#2| (-814)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-632 (-419 (-558))) -12 (|has| |#2| (-1058 (-419 (-558)))) (|has| |#2| (-1121))) ((-632 (-558)) -3956 (|has| |#2| (-1069)) (-12 (|has| |#2| (-1058 (-558))) (|has| |#2| (-1121)))) ((-632 |#2|) |has| |#2| (-1121)) ((-629 (-876)) -3956 (|has| |#2| (-1121)) (|has| |#2| (-1069)) (|has| |#2| (-860)) (|has| |#2| (-814)) (|has| |#2| (-745)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-629 (-876))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-629 (-1287 |#2|)) . T) ((-236 $) -3956 (-12 (|has| |#2| (-239)) (|has| |#2| (-1069))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1069)))) ((-234 |#2|) |has| |#2| (-1069)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1069))) ((-239) -3956 (-12 (|has| |#2| (-239)) (|has| |#2| (-1069))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1069)))) ((-274 |#2|) |has| |#2| (-1069)) ((-298 (-558) |#2|) . T) ((-300 (-558) |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1121))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1069)) ((-424 |#2|) |has| |#2| (-1121)) ((-501 |#2|) . T) ((-615 (-558) |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1121))) ((-665 (-558)) -3956 (|has| |#2| (-1069)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-665 |#2|) -3956 (|has| |#2| (-1069)) (|has| |#2| (-745)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-665 $) |has| |#2| (-1069)) ((-667 (-558)) -12 (|has| |#2| (-657 (-558))) (|has| |#2| (-1069))) ((-667 |#2|) -3956 (|has| |#2| (-1069)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-667 $) |has| |#2| (-1069)) ((-659 |#2|) -3956 (|has| |#2| (-745)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-657 (-558)) -12 (|has| |#2| (-657 (-558))) (|has| |#2| (-1069))) ((-657 |#2|) |has| |#2| (-1069)) ((-736 |#2|) -3956 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-745) |has| |#2| (-1069)) ((-813) |has| |#2| (-814)) ((-814) |has| |#2| (-814)) ((-815) |has| |#2| (-814)) ((-818) |has| |#2| (-814)) ((-860) -3956 (|has| |#2| (-860)) (|has| |#2| (-814))) ((-863) -3956 (|has| |#2| (-860)) (|has| |#2| (-814))) ((-910 $ (-1197)) -3956 (-12 (|has| |#2| (-918 (-1197))) (|has| |#2| (-1069))) (-12 (|has| |#2| (-916 (-1197))) (|has| |#2| (-1069)))) ((-916 (-1197)) -12 (|has| |#2| (-916 (-1197))) (|has| |#2| (-1069))) ((-918 (-1197)) -3956 (-12 (|has| |#2| (-918 (-1197))) (|has| |#2| (-1069))) (-12 (|has| |#2| (-916 (-1197))) (|has| |#2| (-1069)))) ((-1058 (-419 (-558))) -12 (|has| |#2| (-1058 (-419 (-558)))) (|has| |#2| (-1121))) ((-1058 (-558)) -12 (|has| |#2| (-1058 (-558))) (|has| |#2| (-1121))) ((-1058 |#2|) |has| |#2| (-1121)) ((-1071 |#2|) -3956 (|has| |#2| (-1069)) (|has| |#2| (-745)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1076 |#2|) -3956 (|has| |#2| (-1069)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1069) |has| |#2| (-1069)) ((-1077) |has| |#2| (-1069)) ((-1132) |has| |#2| (-1069)) ((-1121) -3956 (|has| |#2| (-1121)) (|has| |#2| (-1069)) (|has| |#2| (-860)) (|has| |#2| (-814)) (|has| |#2| (-745)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1237) . T) ((-1295 |#2|) |has| |#2| (-376))) +((-2966 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-3605 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-4136 (($ (-937)) 63 (|has| |#2| (-1069)) ELT)) (-2412 (((-1293) $ (-558) (-558)) NIL (|has| $ (-6 -4425)) ELT)) (-2872 (($ $ $) 69 (|has| |#2| (-814)) ELT)) (-1425 (((-3 $ #1="failed") $ $) 54 (|has| |#2| (-133)) ELT)) (-3537 (((-790)) NIL (|has| |#2| (-381)) ELT)) (-4217 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4425)) ELT)) (-4153 (($) NIL T CONST)) (-3574 (((-3 (-558) #1#) $) NIL (-12 (|has| |#2| (-1058 (-558))) (|has| |#2| (-1121))) ELT) (((-3 (-419 (-558)) #1#) $) NIL (-12 (|has| |#2| (-1058 (-419 (-558)))) (|has| |#2| (-1121))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1121)) ELT)) (-3573 (((-558) $) NIL (-12 (|has| |#2| (-1058 (-558))) (|has| |#2| (-1121))) ELT) (((-419 (-558)) $) NIL (-12 (|has| |#2| (-1058 (-419 (-558)))) (|has| |#2| (-1121))) ELT) ((|#2| $) 29 (|has| |#2| (-1121)) ELT)) (-2492 (((-708 (-558)) (-708 $)) NIL (-12 (|has| |#2| 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 (-419 (-558))) -3957 (|has| |#1| (-1059 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 |#2|) . T) ((-633 |#3|) . T) ((-633 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-630 (-877)) . 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T) ((-569) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-666 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-668 (-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-658 (-558)) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-746) . T) ((-911 $ (-1198)) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-911 $ |#3|) . T) ((-917 (-1198)) |has| |#1| (-917 (-1198))) ((-917 |#3|) . T) ((-919 (-1198)) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-919 |#3|) . T) ((-901 (-391)) -12 (|has| |#1| (-901 (-391))) (|has| |#3| (-901 (-391)))) ((-901 (-558)) -12 (|has| |#1| (-901 (-558))) (|has| |#3| (-901 (-558)))) ((-969 |#1| |#4| |#3|) . T) ((-929) |has| |#1| (-929)) ((-1059 (-419 (-558))) |has| |#1| (-1059 (-419 (-558)))) ((-1059 (-558)) |has| |#1| (-1059 (-558))) ((-1059 |#1|) . T) ((-1059 |#2|) . T) ((-1059 |#3|) . T) ((-1072 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1072 |#1|) . T) ((-1072 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1077 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1077 |#1|) . T) ((-1077 $) -3957 (|has| |#1| (-929)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) -3956 (|has| |#1| (-1058 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-632 (-558)) . T) ((-632 |#1|) . T) ((-632 |#2|) . T) ((-632 |#3|) . T) ((-632 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-629 (-876)) . T) ((-175) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-630 (-547)) -12 (|has| |#1| (-630 (-547))) (|has| |#3| (-630 (-547)))) ((-630 (-904 (-391))) -12 (|has| |#1| (-630 (-904 (-391)))) (|has| |#3| (-630 (-904 (-391))))) ((-630 (-904 (-558))) -12 (|has| |#1| (-630 (-904 (-558)))) (|has| |#3| (-630 (-904 (-558))))) ((-236 $) -3956 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -3956 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-424 |#1|) . T) ((-464) -3956 (|has| |#1| (-928)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-240)) ((-526 |#2| $) |has| |#1| (-240)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-569) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-665 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-665 (-558)) . T) ((-665 |#1|) . T) ((-665 $) . T) ((-667 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-667 (-558)) |has| |#1| (-657 (-558))) ((-667 |#1|) . T) ((-667 $) . T) ((-659 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-659 |#1|) |has| |#1| (-175)) ((-659 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-657 (-558)) |has| |#1| (-657 (-558))) ((-657 |#1|) . T) ((-736 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-736 |#1|) |has| |#1| (-175)) ((-736 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-745) . T) ((-910 $ (-1197)) -3956 (|has| |#1| (-918 (-1197))) (|has| |#1| (-916 (-1197)))) ((-910 $ |#3|) . T) ((-916 (-1197)) |has| |#1| (-916 (-1197))) ((-916 |#3|) . T) ((-918 (-1197)) -3956 (|has| |#1| (-918 (-1197))) (|has| |#1| (-916 (-1197)))) ((-918 |#3|) . T) ((-900 (-391)) -12 (|has| |#1| (-900 (-391))) (|has| |#3| (-900 (-391)))) ((-900 (-558)) -12 (|has| |#1| (-900 (-558))) (|has| |#3| (-900 (-558)))) ((-968 |#1| |#4| |#3|) . T) ((-928) |has| |#1| (-928)) ((-1058 (-419 (-558))) |has| |#1| (-1058 (-419 (-558)))) ((-1058 (-558)) |has| |#1| (-1058 (-558))) ((-1058 |#1|) . T) ((-1058 |#2|) . T) ((-1058 |#3|) . T) ((-1071 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1071 |#1|) . T) ((-1071 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1076 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1076 |#1|) . T) ((-1076 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1069) . T) ((-1077) . T) ((-1132) . T) ((-1121) . T) ((-1237) . 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T) ((-23) . T) ((-47 |#1| (-558)) . T) ((-25) . T) ((-38 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-633 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 (-1198)) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-1198)))) ((-633 |#1|) |has| |#1| (-175)) ((-633 |#2|) . T) ((-633 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-630 (-877)) . T) ((-175) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-631 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-631 (-547)) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-547)))) ((-631 (-905 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-905 (-391))))) ((-631 (-905 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-905 (-558))))) ((-236 $) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-239) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 (-558) |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1133)) ((-302) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-412 |#2|) |has| |#1| (-376)) ((-464) |has| |#1| (-376)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-526 (-1198) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1198) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-666 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 |#2|) |has| |#1| (-376)) ((-666 $) . T) ((-668 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-668 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-660 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-660 |#1|) |has| |#1| (-175)) ((-660 |#2|) |has| |#1| (-376)) ((-660 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-658 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-658 |#2|) |has| |#1| (-376)) ((-737 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-737 |#1|) |has| |#1| (-175)) ((-737 |#2|) |has| |#1| (-376)) ((-737 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-746) . T) ((-812) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-860) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-861) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-861))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-864) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-861))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-911 $ (-1198)) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-917 (-1198)) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-919 (-1198)) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-901 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-901 (-391)))) ((-901 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-901 (-558)))) ((-899 |#2|) |has| |#1| (-376)) ((-929) -12 (|has| |#1| (-376)) (|has| |#2| (-929))) ((-994 |#1| (-558) (-1103)) . T) ((-940) |has| |#1| (-376)) ((-1012 |#2|) |has| |#1| (-376)) ((-1023) |has| |#1| (-38 (-419 (-558)))) ((-1041) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-1059 (-419 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-558)))) ((-1059 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-558)))) ((-1059 (-1198)) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-1198)))) ((-1059 |#2|) . T) ((-1072 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1072 |#1|) . T) ((-1072 |#2|) |has| |#1| (-376)) ((-1072 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1077 (-419 (-558))) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1077 |#1|) . T) ((-1077 |#2|) |has| |#1| (-376)) ((-1077 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1173) -12 (|has| |#1| (-376)) (|has| |#2| (-1173))) ((-1224) |has| |#1| (-38 (-419 (-558)))) ((-1227) |has| |#1| (-38 (-419 (-558)))) ((-1238) . T) ((-1243) |has| |#1| (-376)) ((-1250 |#1|) . T) ((-1267 |#1| (-558)) . 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T) ((-1072 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1077 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1077 |#1|) . T) ((-1077 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1224) |has| |#1| (-38 (-419 (-558)))) ((-1227) |has| |#1| (-38 (-419 (-558)))) ((-1238) . T) ((-1267 |#1| (-791)) . 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NIL NIL NIL) (-1174 2626223 2626597 2626745 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1173 2625719 2625964 2625994 "STEP" 2626088 STEP (NIL) -9 NIL 2626159 NIL) (-1172 2618915 2625637 2625714 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1171 2613095 2617706 2617749 "STAGG" 2618181 STAGG (NIL T) -9 NIL 2618360 NIL) (-1170 2611470 2612220 2613090 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1169 2609613 2611297 2611389 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1168 2608930 2609443 2609473 "SRING" 2609478 SRING (NIL) -9 NIL 2609498 NIL) (-1167 2601459 2607441 2607897 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2595200 2596647 2598160 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2587584 2592529 2592559 "SRAGG" 2593862 SRAGG (NIL) -9 NIL 2594470 NIL) (-1164 2586879 2587200 2587579 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1163 2580972 2586197 2586621 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2575154 2578345 2579072 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2571553 2572384 2573030 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2570528 2570833 2570863 "SPFCAT" 2571307 SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2569465 2569717 2569981 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2560112 2562428 2562458 "SPADXPT" 2567134 SPADXPT (NIL) -9 NIL 2569298 NIL) (-1157 2559914 2559960 2560029 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2557528 2559878 2559909 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1155 2549129 2551232 2551275 "SPACEC" 2555648 SPACEC (NIL T) -9 NIL 2557464 NIL) (-1154 2546943 2549075 2549124 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2545870 2546061 2546352 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2544268 2544601 2545013 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2543533 2543767 2544028 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2539713 2540673 2541668 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2536071 2536770 2537499 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2529817 2535420 2535517 "SNTSCAT" 2535522 SNTSCAT (NIL T T T T) -9 NIL 2535592 NIL) (-1147 2523685 2528450 2528841 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2517499 2523603 2523680 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2515931 2516262 2516660 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2507560 2512496 2512599 "SMATCAT" 2513953 SMATCAT (NIL NIL T T T) -9 NIL 2514503 NIL) (-1143 2505400 2506384 2507555 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1142 2502980 2504608 2504651 "SKAGG" 2504912 SKAGG (NIL T) -9 NIL 2505047 NIL) (-1141 2498822 2502630 2502800 "SINT" NIL SINT (NIL) -8 NIL NIL 2502952) (-1140 2498632 2498676 2498742 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2497707 2497939 2498207 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1138 2496707 2496869 2497146 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1137 2496049 2496392 2496516 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1136 2495392 2495702 2495842 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1135 2493503 2493995 2494501 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2486976 2493422 2493498 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2486487 2486727 2486757 "SGROUP" 2486850 SGROUP (NIL) -9 NIL 2486912 NIL) (-1132 2486377 2486409 2486482 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1131 2483797 2484567 2485290 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1130 2477641 2483244 2483341 "SFRTCAT" 2483346 SFRTCAT (NIL T T T T) -9 NIL 2483385 NIL) (-1129 2471977 2473097 2474233 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2466066 2467245 2468429 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2465727 2465834 2465945 "SFORT" NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2464687 2465601 2465722 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2460276 2461183 2461278 "SEXCAT" 2463900 SEXCAT (NIL T T T T T) -9 NIL 2464460 NIL) (-1124 2459237 2460203 2460271 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1123 2457622 2458211 2458514 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1122 2457152 2457340 2457370 "SETCAT" 2457487 SETCAT (NIL) -9 NIL 2457572 NIL) (-1121 2456984 2457048 2457147 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1120 2453198 2455445 2455488 "SETAGG" 2456358 SETAGG (NIL T) -9 NIL 2456698 NIL) (-1119 2452804 2452956 2453193 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1118 2449740 2452751 2452799 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1117 2449202 2449515 2449616 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1116 2448329 2448695 2448756 "SEGXCAT" 2449042 SEGXCAT (NIL T T) -9 NIL 2449162 NIL) (-1115 2447254 2447522 2447565 "SEGCAT" 2448087 SEGCAT (NIL T) -9 NIL 2448308 NIL) (-1114 2446934 2446999 2447112 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1113 2445997 2446470 2446678 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2445571 2445853 2445930 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1111 2444936 2445072 2445276 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1110 2443999 2444749 2444931 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1109 2443245 2443947 2443994 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2434770 2443110 2443240 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2433624 2433914 2434233 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2432916 2433130 2433322 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-1105 2432257 2432415 2432594 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2431836 2432070 2432100 "SASTCAT" 2432105 SASTCAT (NIL) -9 NIL 2432118 NIL) (-1103 2431293 2431725 2431801 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-1102 2430893 2430934 2431107 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2430521 2430562 2430721 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1100 2423634 2430436 2430516 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1099 2422271 2422603 2423004 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2421014 2421380 2421685 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2420632 2420856 2420939 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1096 2418066 2418704 2419162 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1095 2417899 2417933 2418004 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2417382 2417688 2417782 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2412953 2413826 2414746 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2401659 2407262 2407359 "RSETCAT" 2411478 RSETCAT (NIL T T T T) -9 NIL 2412575 NIL) (-1091 2400183 2400830 2401654 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1090 2393892 2395346 2396866 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2391761 2392324 2392398 "RRCC" 2393484 RRCC (NIL T T) -9 NIL 2393828 NIL) (-1088 2391277 2391479 2391756 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-1087 2390739 2391052 2391153 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-1086 2363064 2373764 2373831 "RPOLCAT" 2384497 RPOLCAT (NIL T T T) -9 NIL 2387657 NIL) (-1085 2357133 2359969 2363059 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-1084 2348172 2355804 2356286 "ROUTINE" NIL ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2344380 2347916 2348056 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-1082 2342689 2343435 2343695 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2338379 2341144 2341174 "RNS" 2341443 RNS (NIL) -9 NIL 2341699 NIL) (-1080 2337285 2337770 2338304 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-1079 2336395 2336799 2337001 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1078 2335688 2336192 2336222 "RNG" 2336227 RNG (NIL) -9 NIL 2336248 NIL) (-1077 2334983 2335461 2335504 "RMODULE" 2335509 RMODULE (NIL T) -9 NIL 2335536 NIL) (-1076 2333906 2334012 2334348 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2330762 2333490 2333787 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2323372 2325849 2325964 "RMATCAT" 2329323 RMATCAT (NIL NIL NIL T T T) -9 NIL 2330305 NIL) (-1073 2322877 2323060 2323367 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-1072 2322450 2322664 2322707 "RLINSET" 2322769 RLINSET (NIL T) -9 NIL 2322813 NIL) (-1071 2322092 2322173 2322301 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2321016 2321690 2321720 "RING" 2321776 RING (NIL) -9 NIL 2321868 NIL) (-1069 2320858 2320914 2321011 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-1068 2319905 2320172 2320430 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-1067 2310833 2319525 2319731 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2310091 2310575 2310616 "RGBCSPC" 2310674 RGBCSPC (NIL T) -9 NIL 2310726 NIL) (-1065 2309157 2309616 2309657 "RGBCMDL" 2309889 RGBCMDL (NIL T) -9 NIL 2310003 NIL) (-1064 2308866 2308935 2309038 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1063 2308626 2308667 2308764 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1062 2307037 2307467 2307849 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-1061 2304613 2305281 2305951 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-1060 2304158 2304256 2304419 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2303776 2303874 2303917 "RETRACT" 2304050 RETRACT (NIL T) -9 NIL 2304137 NIL) (-1058 2303653 2303684 2303771 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-1057 2303249 2303523 2303593 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-1056 2295825 2303007 2303134 "RESULT" NIL RESULT (NIL) -8 NIL NIL NIL) (-1055 2294359 2295191 2295390 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2294046 2294107 2294205 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2293786 2293827 2293934 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2293518 2293559 2293670 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-1051 2288538 2289995 2291218 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-1050 2285608 2286366 2287177 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-1049 2283568 2284190 2284792 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-1048 2276097 2282079 2282535 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2275021 2275460 2275710 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2274502 2274617 2274784 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2270112 2273887 2274114 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2269339 2269538 2269753 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2266621 2267459 2268343 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1042 2263193 2264229 2265290 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1041 2263027 2263080 2263110 "REAL" 2263115 REAL (NIL) -9 NIL 2263150 NIL) (-1040 2262510 2262816 2262910 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2261987 2262065 2262272 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2261215 2261407 2261620 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2260096 2260393 2260763 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2258348 2258820 2259358 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2257265 2257542 2257932 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2256084 2256394 2256817 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2249467 2252933 2252963 "RCFIELD" 2254258 RCFIELD (NIL) -9 NIL 2254989 NIL) (-1032 2248088 2248698 2249392 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-1031 2244251 2246161 2246204 "RCAGG" 2247288 RCAGG (NIL T) -9 NIL 2247753 NIL) (-1030 2243973 2244084 2244246 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-1029 2243406 2243536 2243701 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2243019 2243098 2243219 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2242427 2242577 2242729 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2242206 2242256 2242329 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2234675 2241314 2241625 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2224370 2234540 2234670 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2223999 2224092 2224122 "RADCAT" 2224282 RADCAT (NIL) -9 NIL NIL NIL) (-1022 2223834 2223894 2223994 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-1021 2221916 2223661 2223753 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2221590 2221639 2221770 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2213887 2217925 2217967 "QUATCAT" 2218758 QUATCAT (NIL T) -9 NIL 2219524 NIL) (-1018 2211130 2212413 2213791 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-1017 2207012 2211077 2211125 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-1016 2204379 2206060 2206103 "QUAGG" 2206484 QUAGG (NIL T) -9 NIL 2206659 NIL) (-1015 2203975 2204249 2204319 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2203005 2203607 2203772 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2202679 2202728 2202859 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1012 2192303 2198437 2198479 "QFCAT" 2199147 QFCAT (NIL T) -9 NIL 2200148 NIL) (-1011 2189196 2190632 2192207 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-1010 2188737 2188871 2189003 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2182826 2184005 2185189 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2182237 2182419 2182655 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1007 2180036 2180570 2180998 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1006 2178930 2179172 2179491 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2177278 2177476 2177832 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2173005 2174221 2174264 "PTRANFN" 2176175 PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2171631 2171976 2172300 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2171317 2171380 2171491 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2165344 2170103 2170146 "PTCAT" 2170446 PTCAT (NIL T) -9 NIL 2170599 NIL) (-1000 2165034 2165075 2165201 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2163913 2164229 2164563 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2152712 2155287 2157611 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2145553 2148470 2148566 "PSETCAT" 2151587 PSETCAT (NIL T T T T) -9 NIL 2152401 NIL) (-996 2143985 2144727 2145548 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-995 2143304 2143499 2143527 "PSCURVE" 2143795 PSCURVE (NIL) -9 NIL 2143962 NIL) (-994 2138950 2140717 2140782 "PSCAT" 2141626 PSCAT (NIL T T T) -9 NIL 2141866 NIL) (-993 2138263 2138545 2138945 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-992 2136684 2137575 2137838 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-991 2136171 2136477 2136569 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-990 2127191 2129613 2131801 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2124922 2126513 2126553 "PRQAGG" 2126736 PRQAGG (NIL T) -9 NIL 2126838 NIL) (-988 2124101 2124550 2124578 "PROPLOG" 2124717 PROPLOG (NIL) -9 NIL 2124832 NIL) (-987 2123776 2123839 2123962 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-986 2123212 2123351 2123523 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-985 2121457 2122223 2122520 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2121010 2121141 2121269 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-983 2115599 2119950 2120770 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2115428 2115466 2115525 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-981 2114864 2115005 2115157 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-980 2113332 2113751 2114217 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-979 2113049 2113110 2113138 "PRIMCAT" 2113262 PRIMCAT (NIL) -9 NIL NIL NIL) (-978 2112220 2112416 2112644 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-977 2108068 2112170 2112215 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2107767 2107829 2107940 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-975 2104948 2107414 2107648 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-974 2104399 2104556 2104584 "PPCURVE" 2104789 PPCURVE (NIL) -9 NIL 2104925 NIL) (-973 2104009 2104257 2104340 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-972 2101765 2102186 2102778 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2101206 2101270 2101504 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-970 2097916 2098402 2099014 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-969 2083491 2089576 2089641 "POLYCAT" 2093155 POLYCAT (NIL T T T) -9 NIL 2095033 NIL) (-968 2078998 2081146 2083486 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-967 2078653 2078727 2078847 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-966 2078342 2078405 2078514 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-965 2071746 2078073 2078233 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-964 2070633 2070896 2071172 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2069230 2069543 2069874 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2064354 2069178 2069225 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2062842 2063253 2063628 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2061590 2061899 2062298 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2061261 2061345 2061462 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2060838 2060913 2061088 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2060318 2060416 2060578 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-956 2059784 2059906 2060062 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-955 2058676 2058894 2059272 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2058287 2058372 2058524 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2057836 2057918 2058100 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2057528 2057609 2057722 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2057039 2057114 2057323 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2056378 2056508 2056713 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2055740 2055874 2056037 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-948 2055044 2055226 2055407 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-947 2054767 2054841 2054935 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2051322 2052516 2053437 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-945 2050406 2050607 2050842 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-944 2045955 2047345 2048493 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-943 2025864 2030755 2035606 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2025604 2025657 2025760 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-941 2025045 2025179 2025359 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-940 2023129 2024295 2024323 "PID" 2024520 PID (NIL) -9 NIL 2024647 NIL) (-939 2022917 2022960 2023035 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-938 2022096 2022764 2022851 "PI" NIL PI (NIL) -8 NIL NIL 2022891) (-937 2021548 2021699 2021875 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2017876 2018834 2019739 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-935 2016240 2016529 2016895 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2015682 2015797 2015958 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2012278 2014551 2014904 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2010884 2011164 2011489 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2009646 2009901 2010250 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2008349 2008577 2008931 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2005433 2006939 2006967 "PFECAT" 2007560 PFECAT (NIL) -9 NIL 2007937 NIL) (-928 2005056 2005221 2005428 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-927 2003880 2004162 2004463 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-926 2002062 2002449 2002879 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-925 1998082 2001988 2002057 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-924 1993973 1995126 1995996 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-923 1991885 1992997 1993038 "PERMCAT" 1993438 PERMCAT (NIL T) -9 NIL 1993736 NIL) (-922 1991579 1991626 1991750 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-921 1987999 1989705 1990352 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-920 1985445 1987753 1987875 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 1984326 1984589 1984630 "PDSPC" 1985163 PDSPC (NIL T) -9 NIL 1985408 NIL) (-918 1983693 1983959 1984321 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-917 1982407 1983343 1983384 "PDRING" 1983389 PDRING (NIL T) -9 NIL 1983417 NIL) (-916 1981150 1981912 1981966 "PDMOD" 1981971 PDMOD (NIL T T) -9 NIL 1982075 NIL) (-915 1978965 1979791 1980459 "PDEPROB" NIL PDEPROB (NIL) -8 NIL NIL NIL) (-914 1977009 1977549 1978104 "PDEPACK" NIL PDEPACK (NIL) -7 NIL NIL NIL) (-913 1976102 1976314 1976563 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 1973619 1974510 1974538 "PDECAT" 1975325 PDECAT (NIL) -9 NIL 1976038 NIL) (-911 1973236 1973303 1973357 "PDDOM" 1973522 PDDOM (NIL T T) -9 NIL 1973602 NIL) (-910 1973088 1973124 1973231 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-909 1972872 1972911 1973001 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 1971183 1971944 1972241 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 1970872 1970935 1971044 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-906 1968992 1969428 1969885 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-905 1962572 1964419 1965720 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 1962203 1962276 1962408 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-903 1959908 1960589 1961068 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-902 1958094 1958529 1958936 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 1957548 1957799 1957840 "PATMAB" 1957947 PATMAB (NIL T) -9 NIL 1958030 NIL) (-900 1956189 1956597 1956855 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 1955727 1955858 1955899 "PATAB" 1955904 PATAB (NIL T) -9 NIL 1956076 NIL) (-898 1954270 1954707 1955130 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-897 1953948 1954023 1954125 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 1953637 1953700 1953809 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 1953442 1953488 1953555 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-894 1953120 1953195 1953297 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 1952809 1952872 1952981 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 1952500 1952570 1952667 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 1952189 1952252 1952361 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 1951340 1951724 1951906 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-889 1950947 1951045 1951164 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 1949848 1950276 1950504 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-887 1948507 1949167 1949527 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 1941633 1947910 1948105 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 1934090 1941130 1941315 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 1930889 1932750 1932790 "PADICCT" 1933371 PADICCT (NIL NIL) -9 NIL 1933653 NIL) (-883 1928935 1930839 1930884 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-882 1928097 1928307 1928573 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 1927439 1927582 1927786 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 1925875 1926843 1927123 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 1925397 1925658 1925755 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-878 1924449 1925134 1925306 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 1914865 1917738 1919938 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-876 1914254 1914569 1914696 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-875 1913531 1913726 1913754 "OUTBCON" 1914072 OUTBCON (NIL) -9 NIL 1914238 NIL) (-874 1913239 1913369 1913526 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-873 1912620 1912765 1912926 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-872 1911985 1912418 1912507 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-871 1911404 1911826 1911854 "OSGROUP" 1911859 OSGROUP (NIL) -9 NIL 1911881 NIL) (-870 1910368 1910629 1910914 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 1907690 1910242 1910363 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 1904883 1907439 1907566 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 1902894 1903422 1903983 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 1896272 1898760 1898801 "OREPCAT" 1901149 OREPCAT (NIL T) -9 NIL 1902253 NIL) (-865 1894297 1895231 1896267 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-864 1893489 1893767 1893795 "ORDTYPE" 1894104 ORDTYPE (NIL) -9 NIL 1894267 NIL) (-863 1893013 1893229 1893484 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-862 1892467 1892850 1893008 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-861 1891965 1892335 1892363 "ORDSET" 1892368 ORDSET (NIL) -9 NIL 1892390 NIL) (-860 1890616 1891587 1891615 "ORDRING" 1891620 ORDRING (NIL) -9 NIL 1891649 NIL) (-859 1889867 1890432 1890460 "ORDMON" 1890465 ORDMON (NIL) -9 NIL 1890486 NIL) (-858 1889162 1889327 1889522 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-857 1888377 1888892 1888920 "ORDFIN" 1888985 ORDFIN (NIL) -9 NIL 1889059 NIL) (-856 1887771 1887910 1888096 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-855 1884516 1886733 1887142 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1881831 1882801 1883615 "OPTPROB" NIL OPTPROB (NIL) -8 NIL NIL NIL) (-853 1879257 1879956 1880660 "OPTPACK" NIL OPTPACK (NIL) -7 NIL NIL NIL) (-852 1876870 1877696 1877724 "OPTCAT" 1878543 OPTCAT (NIL) -9 NIL 1879193 NIL) (-851 1876273 1876632 1876737 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-850 1876081 1876126 1876192 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-849 1875387 1875667 1875708 "OPERCAT" 1875920 OPERCAT (NIL T) -9 NIL 1876017 NIL) (-848 1875197 1875265 1875382 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-847 1872596 1873979 1874483 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-846 1872017 1872144 1872318 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-845 1868988 1871150 1871519 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1865613 1868428 1868468 "OMSAGG" 1868529 OMSAGG (NIL T) -9 NIL 1868593 NIL) (-843 1864081 1865281 1865450 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 1862359 1863551 1863579 "OINTDOM" 1863584 OINTDOM (NIL) -9 NIL 1863605 NIL) (-841 1859778 1861359 1861689 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 1859025 1859728 1859773 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 1856281 1858865 1859020 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 1847858 1856150 1856276 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 1841301 1847748 1847853 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 1840273 1840510 1840783 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 1837907 1838577 1839281 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 1833662 1834622 1835647 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 1833170 1833258 1833452 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 1830605 1831187 1831862 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 1827992 1828500 1829097 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 1826353 1826997 1827483 "ODEPROB" NIL ODEPROB (NIL) -8 NIL NIL NIL) (-829 1823340 1823879 1824526 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 1822691 1822799 1823059 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 1819637 1820488 1821352 "ODEPACK" NIL ODEPACK (NIL) -7 NIL NIL NIL) (-826 1818791 1818916 1819138 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 1814283 1815744 1817191 "ODEIFTBL" NIL ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 1810540 1811342 1812262 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 1809978 1810073 1810296 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 1808041 1808750 1808778 "ODECAT" 1809383 ODECAT (NIL) -9 NIL 1809914 NIL) (-821 1807722 1807771 1807898 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 1804339 1807517 1807639 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-819 1803532 1804132 1804160 "OCAMON" 1804165 OCAMON (NIL) -9 NIL 1804186 NIL) (-818 1797803 1800568 1800608 "OC" 1801705 OC (NIL T) -9 NIL 1802563 NIL) (-817 1795803 1796731 1797709 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-816 1795223 1795648 1795676 "OASGP" 1795681 OASGP (NIL) -9 NIL 1795701 NIL) (-815 1794319 1794946 1794974 "OAMONS" 1795014 OAMONS (NIL) -9 NIL 1795057 NIL) (-814 1793495 1794054 1794082 "OAMON" 1794140 OAMON (NIL) -9 NIL 1794192 NIL) (-813 1793389 1793422 1793490 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-812 1792170 1792923 1792951 "OAGROUP" 1793098 OAGROUP (NIL) -9 NIL 1793191 NIL) (-811 1791959 1792047 1792165 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-810 1791699 1791755 1791843 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-809 1786734 1788306 1789842 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-808 1783429 1784463 1785498 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-807 1780710 1781650 1781678 "NUMINT" 1782601 NUMINT (NIL) -9 NIL 1783365 NIL) (-806 1779820 1780053 1780271 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-805 1768660 1771699 1774149 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-804 1762506 1768109 1768204 "NTSCAT" 1768209 NTSCAT (NIL T T T T) -9 NIL 1768248 NIL) (-803 1761847 1762026 1762219 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-802 1761536 1761599 1761708 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1749189 1759140 1759952 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-800 1738207 1749051 1749184 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-799 1736927 1737252 1737609 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-798 1735763 1736027 1736385 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-797 1734930 1735063 1735279 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-796 1733233 1733553 1733962 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-795 1732946 1732980 1733104 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-794 1732765 1732800 1732869 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1732538 1732731 1732760 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-792 1732097 1732165 1732344 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-791 1730405 1731460 1731715 "NNI" NIL NNI (NIL) -8 NIL NIL 1732062) (-790 1729133 1729470 1729834 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-789 1726193 1727248 1728147 "NIPROB" NIL NIPROB (NIL) -8 NIL NIL NIL) (-788 1725170 1725422 1725724 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-787 1724254 1724820 1724861 "NETCLT" 1725033 NETCLT (NIL T) -9 NIL 1725115 NIL) (-786 1723158 1723425 1723706 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-785 1722957 1723000 1723075 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-784 1721488 1721876 1722296 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-783 1720158 1721098 1721126 "NASRING" 1721236 NASRING (NIL) -9 NIL 1721316 NIL) (-782 1720003 1720059 1720153 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-781 1718970 1719621 1719649 "NARNG" 1719766 NARNG (NIL) -9 NIL 1719857 NIL) (-780 1718746 1718831 1718965 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-779 1717798 1718047 1718282 "NAGSP" NIL NAGSP (NIL) -7 NIL NIL NIL) (-778 1710495 1712407 1714080 "NAGS" NIL NAGS (NIL) -7 NIL NIL NIL) (-777 1709330 1709662 1709993 "NAGF07" NIL NAGF07 (NIL) -7 NIL NIL NIL) (-776 1705089 1706446 1707753 "NAGF04" NIL NAGF04 (NIL) -7 NIL NIL NIL) (-775 1699574 1701284 1702917 "NAGF02" NIL NAGF02 (NIL) -7 NIL NIL NIL) (-774 1695835 1696995 1698112 "NAGF01" NIL NAGF01 (NIL) -7 NIL NIL NIL) (-773 1690980 1692594 1694179 "NAGE04" NIL NAGE04 (NIL) -7 NIL NIL NIL) (-772 1684151 1686380 1688510 "NAGE02" NIL NAGE02 (NIL) -7 NIL NIL NIL) (-771 1680988 1681995 1682959 "NAGE01" NIL NAGE01 (NIL) -7 NIL NIL NIL) (-770 1679303 1679855 1680413 "NAGD03" NIL NAGD03 (NIL) -7 NIL NIL NIL) (-769 1672933 1674915 1676869 "NAGD02" NIL NAGD02 (NIL) -7 NIL NIL NIL) (-768 1668092 1669589 1671029 "NAGD01" NIL NAGD01 (NIL) -7 NIL NIL NIL) (-767 1665046 1665940 1666777 "NAGC06" NIL NAGC06 (NIL) -7 NIL NIL NIL) (-766 1663829 1664179 1664535 "NAGC05" NIL NAGC05 (NIL) -7 NIL NIL NIL) (-765 1663317 1663448 1663592 "NAGC02" NIL NAGC02 (NIL) -7 NIL NIL NIL) (-764 1662118 1662845 1662885 "NAALG" 1662964 NAALG (NIL T) -9 NIL 1663025 NIL) (-763 1661988 1662023 1662113 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-762 1656964 1658150 1659337 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-761 1656359 1656446 1656630 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-760 1648414 1652852 1652905 "MTSCAT" 1653975 MTSCAT (NIL T T) -9 NIL 1654490 NIL) (-759 1648180 1648240 1648332 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-758 1648006 1648045 1648105 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-757 1644862 1647567 1647608 "MSETAGG" 1647613 MSETAGG (NIL T) -9 NIL 1647647 NIL) (-756 1640977 1643904 1644224 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-755 1637291 1639056 1639801 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-754 1636924 1636997 1637128 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-753 1636577 1636618 1636762 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-752 1634442 1634779 1635210 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-751 1627882 1634340 1634437 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-750 1627407 1627448 1627656 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-749 1626964 1627013 1627197 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1626232 1626325 1626546 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1624849 1625210 1625600 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-746 1623994 1624377 1624405 "MONOID" 1624624 MONOID (NIL) -9 NIL 1624771 NIL) (-745 1623659 1623808 1623989 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-744 1612553 1619391 1619450 "MONOGEN" 1620124 MONOGEN (NIL T T) -9 NIL 1620580 NIL) (-743 1610565 1611451 1612434 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-742 1609282 1609830 1609858 "MONADWU" 1610250 MONADWU (NIL) -9 NIL 1610488 NIL) (-741 1608828 1609029 1609277 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-740 1608113 1608417 1608445 "MONAD" 1608652 MONAD (NIL) -9 NIL 1608764 NIL) (-739 1607880 1607976 1608108 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-738 1606266 1607040 1607319 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-737 1605434 1605934 1605974 "MODULE" 1605979 MODULE (NIL T) -9 NIL 1606018 NIL) (-736 1605113 1605239 1605429 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-735 1602882 1603709 1604024 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-734 1600094 1601458 1601979 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-733 1598717 1599298 1599575 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-732 1587927 1597371 1597785 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-731 1584938 1586927 1587196 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1584019 1584389 1584579 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-729 1583588 1583637 1583816 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-728 1581481 1582420 1582461 "MLO" 1582884 MLO (NIL T) -9 NIL 1583126 NIL) (-727 1579362 1579889 1580484 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-726 1578830 1578926 1579080 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-725 1578500 1578576 1578699 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-724 1577712 1577898 1578126 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-723 1577205 1577321 1577477 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-722 1576577 1576691 1576876 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-721 1572717 1576247 1576383 "MINT" NIL MINT (NIL) -8 NIL NIL NIL) (-720 1571744 1572017 1572294 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-719 1566912 1570664 1571069 "MFLOAT" NIL MFLOAT (NIL) -8 NIL NIL NIL) (-718 1566345 1566433 1566604 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-717 1563503 1564382 1565261 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-716 1562170 1562518 1562871 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-715 1558817 1561301 1561342 "MDAGG" 1561597 MDAGG (NIL T) -9 NIL 1561740 NIL) (-714 1546789 1558297 1558504 "MCMPLX" NIL MCMPLX (NIL) -8 NIL NIL NIL) (-713 1546059 1546223 1546424 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-712 1544177 1544489 1544869 "MCALCFN" NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-711 1543248 1543536 1543769 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-710 1541335 1541912 1542474 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-709 1537084 1540922 1541170 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-708 1533431 1534202 1534936 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-707 1532176 1532345 1532676 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1521623 1525230 1525307 "MATCAT" 1530342 MATCAT (NIL T T T) -9 NIL 1531814 NIL) (-705 1518895 1520205 1521618 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-704 1517296 1517656 1518040 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-703 1516429 1516626 1516848 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-702 1515180 1515506 1515833 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-701 1514338 1514743 1514920 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-700 1514007 1514071 1514194 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-699 1513655 1513728 1513842 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-698 1513190 1513305 1513447 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-697 1511385 1512162 1512466 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-696 1510875 1511180 1511271 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-695 1507660 1509542 1510003 "M3D" NIL M3D (NIL T) -8 NIL NIL NIL) (-694 1501131 1505968 1506009 "LZSTAGG" 1506791 LZSTAGG (NIL T) -9 NIL 1507086 NIL) (-693 1498220 1499669 1501126 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-692 1495590 1496566 1497053 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-691 1495167 1495449 1495524 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-690 1487358 1495028 1495162 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-689 1486721 1486866 1487094 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-688 1484202 1484901 1485614 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1482311 1482635 1483084 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-686 1475438 1481398 1481439 "LSAGG" 1481501 LSAGG (NIL T) -9 NIL 1481579 NIL) (-685 1473110 1474220 1475433 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-684 1470617 1472459 1472708 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-683 1470284 1470375 1470498 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-682 1469967 1470046 1470074 "LOGIC" 1470185 LOGIC (NIL) -9 NIL 1470267 NIL) (-681 1469862 1469891 1469962 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-680 1469181 1469339 1469532 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1467958 1468207 1468560 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1463841 1466586 1466627 "LODOCAT" 1467065 LODOCAT (NIL T) -9 NIL 1467276 NIL) (-677 1463633 1463709 1463836 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-676 1460687 1463510 1463628 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1457839 1460637 1460682 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1454979 1457768 1457834 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1454029 1454204 1454507 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1452183 1453291 1453544 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1447263 1450346 1450387 "LNAGG" 1451249 LNAGG (NIL T) -9 NIL 1451684 NIL) (-670 1446648 1446916 1447258 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-669 1443213 1444158 1444797 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-668 1442512 1442990 1443031 "LMODULE" 1443036 LMODULE (NIL T) -9 NIL 1443062 NIL) (-667 1439671 1442247 1442370 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-666 1439247 1439461 1439502 "LLINSET" 1439563 LLINSET (NIL T) -9 NIL 1439607 NIL) (-665 1438919 1439182 1439242 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-664 1438518 1438598 1438737 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1436969 1437317 1437716 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1436140 1436336 1436564 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-661 1429116 1435394 1435649 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-660 1428699 1428935 1428976 "LINSET" 1428981 LINSET (NIL T) -9 NIL 1429015 NIL) (-659 1427628 1428322 1428489 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-658 1425927 1426655 1426696 "LINEXP" 1427186 LINEXP (NIL T) -9 NIL 1427459 NIL) (-657 1424632 1425536 1425717 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-656 1423451 1423724 1424028 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-655 1422657 1423253 1423363 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-654 1420207 1420929 1421679 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-653 1418833 1419130 1419522 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-652 1417661 1418236 1418276 "LIECAT" 1418416 LIECAT (NIL T) -9 NIL 1418567 NIL) (-651 1417535 1417568 1417656 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-650 1411771 1417225 1417453 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-649 1404213 1411447 1411603 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-648 1400665 1401614 1402549 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-647 1399289 1400197 1400225 "LFCAT" 1400432 LFCAT (NIL) -9 NIL 1400571 NIL) (-646 1397506 1397840 1398190 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-645 1395002 1395674 1396362 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-644 1392010 1392992 1393495 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-643 1391498 1391803 1391895 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-642 1390202 1390527 1390928 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-641 1389459 1389545 1389774 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-640 1384509 1388024 1388562 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-639 1384132 1384182 1384343 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-638 1382980 1383696 1383737 "LALG" 1383799 LALG (NIL T) -9 NIL 1383858 NIL) (-637 1382762 1382839 1382975 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-636 1380668 1382030 1382281 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-635 1380497 1380527 1380568 "KVTFROM" 1380630 KVTFROM (NIL T) -9 NIL NIL NIL) (-634 1379419 1380029 1380214 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-633 1379248 1379278 1379319 "KRCFROM" 1379381 KRCFROM (NIL T) -9 NIL NIL NIL) (-632 1378344 1378541 1378838 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-631 1378173 1378203 1378244 "KONVERT" 1378306 KONVERT (NIL T) -9 NIL NIL NIL) (-630 1378002 1378032 1378073 "KOERCE" 1378135 KOERCE (NIL T) -9 NIL NIL NIL) (-629 1377572 1377665 1377797 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1375603 1376509 1376886 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-627 1368943 1373838 1373892 "KDAGG" 1374269 KDAGG (NIL T T) -9 NIL 1374475 NIL) (-626 1368591 1368733 1368938 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-625 1361534 1368374 1368529 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-624 1361181 1361466 1361529 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-623 1360146 1360650 1360899 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-622 1359267 1359721 1359926 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-621 1358128 1358623 1358923 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-620 1357405 1357809 1357970 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-619 1357112 1357351 1357400 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-618 1351347 1356802 1357030 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1350761 1351097 1351218 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-616 1346907 1348938 1348992 "IXAGG" 1349921 IXAGG (NIL T T) -9 NIL 1350380 NIL) (-615 1346111 1346483 1346902 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-614 1341328 1346047 1346106 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1340286 1340564 1340830 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1338936 1339143 1339438 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1337887 1338109 1338392 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1337562 1337625 1337748 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1336821 1337196 1337370 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-608 1334842 1336086 1336364 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1324388 1330109 1331272 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1323633 1323785 1324021 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1318606 1323587 1323628 "ISTRING" NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1318094 1318399 1318491 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-603 1317378 1317471 1317687 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1316510 1316735 1316975 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-601 1314917 1315298 1315727 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1314702 1314746 1314822 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1313546 1313845 1314142 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1312816 1313170 1313321 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-597 1312015 1312146 1312360 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1310170 1310667 1311211 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1307272 1308514 1309206 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-594 1307097 1307137 1307197 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1303145 1307023 1307092 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1301203 1303083 1303140 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1300571 1300873 1301003 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1300021 1300312 1300444 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-589 1299099 1299725 1299852 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-588 1298509 1299003 1299031 "IOBCON" 1299036 IOBCON (NIL) -9 NIL 1299057 NIL) (-587 1298078 1298142 1298325 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1290110 1292485 1294814 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1287218 1288002 1288867 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1286895 1286992 1287109 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-583 1284387 1286831 1286890 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1282494 1283023 1283591 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1281989 1282104 1282246 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1280368 1280774 1281237 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1278142 1278736 1279348 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1275509 1276119 1276840 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1271645 1272683 1273732 "INTPACK" NIL INTPACK (NIL) -7 NIL NIL NIL) (-576 1271049 1271207 1271415 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1270568 1270654 1270842 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1268773 1269294 1269751 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-573 1261841 1263494 1265224 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1251431 1254844 1258229 "INTFTBL" NIL INTFTBL (NIL) -8 NIL NIL NIL) (-571 1250797 1250959 1251132 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1248664 1249128 1249673 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1246861 1247756 1247784 "INTDOM" 1248085 INTDOM (NIL) -9 NIL 1248292 NIL) (-568 1246410 1246614 1246856 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-567 1242278 1244699 1244753 "INTCAT" 1245552 INTCAT (NIL T) -9 NIL 1245873 NIL) (-566 1241840 1241961 1242089 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-565 1240676 1240848 1241155 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1240249 1240345 1240502 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1233382 1240104 1240244 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1232673 1233235 1233300 "INT8" NIL INT8 (NIL) -8 NIL NIL 1233334) (-561 1231963 1232525 1232590 "INT64" NIL INT64 (NIL) -8 NIL NIL 1232624) (-560 1231253 1231815 1231880 "INT32" NIL INT32 (NIL) -8 NIL NIL 1231914) (-559 1230543 1231105 1231170 "INT16" NIL INT16 (NIL) -8 NIL NIL 1231204) (-558 1227049 1230462 1230538 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-557 1221160 1224597 1224625 "INS" 1225559 INS (NIL) -9 NIL 1226224 NIL) (-556 1219230 1220148 1221087 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-555 1218285 1218508 1218784 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1217499 1217640 1217837 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1216489 1216630 1216867 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1215641 1215805 1216065 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1214921 1215036 1215224 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1213660 1213929 1214253 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1212940 1213081 1213264 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1212603 1212675 1212773 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1209677 1211175 1211690 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-546 1209276 1209383 1209497 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-545 1208431 1209077 1209178 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-544 1207281 1207549 1207870 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1206344 1207211 1207276 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1205969 1206049 1206166 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1204877 1205424 1205630 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-540 1200969 1202025 1202969 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1199823 1200146 1200174 "INBCON" 1200687 INBCON (NIL) -9 NIL 1200953 NIL) (-538 1199277 1199542 1199818 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-537 1198767 1199072 1199163 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-536 1198220 1198532 1198638 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-535 1194301 1198111 1198215 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1193137 1193276 1193592 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1191561 1191828 1192165 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1185491 1191498 1191556 "ILIST" NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1183293 1185373 1185486 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1178171 1183224 1183288 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1177548 1177884 1178000 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-528 1172317 1176983 1177171 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1171375 1172239 1172312 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1170947 1171024 1171078 "IEVALAB" 1171285 IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1170702 1170782 1170942 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-524 1169766 1170622 1170697 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1168899 1169686 1169761 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1168298 1168832 1168894 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1166778 1167305 1167357 "IDPC" 1167869 IDPC (NIL T T) -9 NIL 1168150 NIL) (-520 1166140 1166700 1166773 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1165385 1166062 1166135 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1165075 1165291 1165351 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-517 1162137 1163021 1163916 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1155736 1157024 1158071 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1154994 1155124 1155324 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1154096 1154601 1154748 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-513 1152473 1152804 1153197 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1147783 1152174 1152287 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1145041 1145665 1146360 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1143267 1143747 1144280 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1141017 1143159 1143262 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1136856 1140955 1141012 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1130371 1135729 1136210 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-506 1129939 1130002 1130175 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1129431 1129580 1129608 "HYPCAT" 1129815 HYPCAT (NIL) -9 NIL NIL NIL) (-504 1129087 1129240 1129426 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-503 1128697 1128945 1129028 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1128530 1128579 1128620 "HOMOTOP" 1128625 HOMOTOP (NIL T) -9 NIL 1128658 NIL) (-501 1125074 1126462 1126503 "HOAGG" 1127484 HOAGG (NIL T) -9 NIL 1128213 NIL) (-500 1124066 1124543 1125069 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-499 1117300 1123789 1123939 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-498 1116235 1116493 1116756 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1115197 1116100 1116230 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1113377 1115030 1115118 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1112688 1113043 1113177 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-494 1106175 1112621 1112683 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1099355 1105909 1106061 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1098805 1098963 1099127 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-491 1091981 1098696 1098800 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1091469 1091774 1091866 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-489 1089071 1091253 1091435 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-488 1084423 1088953 1089066 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1077602 1084320 1084418 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1069582 1076967 1077223 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1068613 1069126 1069154 "GROUP" 1069357 GROUP (NIL) -9 NIL 1069491 NIL) (-484 1068156 1068357 1068608 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-483 1066828 1067167 1067554 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1065656 1066016 1066067 "GRMOD" 1066596 GRMOD (NIL T T) -9 NIL 1066764 NIL) (-481 1065475 1065523 1065651 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-480 1061595 1062809 1063809 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1060293 1060626 1060950 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-478 1059846 1059974 1060115 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-477 1058923 1059425 1059476 "GRALG" 1059629 GRALG (NIL T T) -9 NIL 1059722 NIL) (-476 1058658 1058755 1058918 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-475 1055350 1058336 1058514 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1054761 1054824 1055082 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1050632 1051500 1052026 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1049807 1050009 1050247 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1044795 1045722 1046742 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1044543 1044600 1044689 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1044025 1044114 1044279 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1043534 1043575 1043788 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1042332 1042616 1042921 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1035649 1042020 1042182 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1025443 1030439 1031543 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1023570 1024618 1024646 "GCDDOM" 1024901 GCDDOM (NIL) -9 NIL 1025058 NIL) (-463 1023193 1023350 1023565 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-462 1013974 1016448 1018840 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1012100 1012428 1012849 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1011041 1011230 1011497 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1009912 1010119 1010423 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1009372 1009515 1009664 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1007974 1008322 1008636 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1006507 1006829 1007153 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1004109 1004465 1004872 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 997325 998999 1000590 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 994611 995371 995399 "FVFUN" 996555 FVFUN (NIL) -9 NIL 997275 NIL) (-452 993841 994059 994087 "FVC" 994378 FVC (NIL) -9 NIL 994561 NIL) (-451 993490 993714 993782 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-450 993111 993335 993416 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 991971 992595 992798 "FTEM" NIL FTEM (NIL) -8 NIL NIL NIL) (-448 990056 990745 991208 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-447 988638 988947 989342 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 987269 987636 987968 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-445 986568 986692 986880 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 985542 985808 986155 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 983189 983723 984209 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 982770 982830 983000 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 981129 981984 982287 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 980273 980407 980631 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 979444 979605 979832 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 975419 978388 978429 "FSAGG" 978799 FSAGG (NIL T) -9 NIL 979058 NIL) (-437 973765 974528 975324 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-436 971707 972005 972553 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 970748 970931 971233 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 970425 970474 970603 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 950580 960087 960128 "FS" 964012 FS (NIL T) -9 NIL 966301 NIL) (-432 942782 946290 950280 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-431 942316 942443 942595 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 936859 940005 940045 "FRNAALG" 941365 FRNAALG (NIL T) -9 NIL 941963 NIL) (-429 933600 934851 936109 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-428 933281 933330 933457 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 931756 932318 932614 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 931034 931127 931418 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 928848 929618 929936 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 927939 928388 928429 "FRETRCT" 928434 FRETRCT (NIL T) -9 NIL 928610 NIL) (-423 927312 927590 927934 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-422 924133 925596 925655 "FRAMALG" 926537 FRAMALG (NIL T T) -9 NIL 926829 NIL) (-421 922729 923280 923910 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-420 922422 922485 922592 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 916099 922226 922417 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 915792 915855 915962 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 908143 912667 913998 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-416 901979 905435 905463 "FPS" 906582 FPS (NIL) -9 NIL 907139 NIL) (-415 901536 901669 901833 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-414 898417 900406 900434 "FPC" 900659 FPC (NIL) -9 NIL 900801 NIL) (-413 898263 898315 898412 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-412 897021 897751 897792 "FPATMAB" 897797 FPATMAB (NIL T) -9 NIL 897949 NIL) (-411 895448 896047 896394 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 891347 891947 892629 "FORTRAN" NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 888921 889585 889613 "FORTFN" 890673 FORTFN (NIL) -9 NIL 891297 NIL) (-408 888673 888735 888763 "FORTCAT" 888822 FORTCAT (NIL) -9 NIL 888884 NIL) (-407 886878 887408 887947 "FORT" NIL FORT (NIL) -7 NIL NIL NIL) (-406 886453 886511 886684 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 885686 885886 886079 "FOP" NIL FOP (NIL) -7 NIL NIL NIL) (-404 884217 885084 885258 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 882831 883342 883370 "FNCAT" 883830 FNCAT (NIL) -9 NIL 884090 NIL) (-402 882282 882798 882826 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-401 880608 881781 881809 "FMTC" 881814 FMTC (NIL) -9 NIL 881850 NIL) (-400 879187 880557 880603 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 875776 877142 877183 "FMONCAT" 878400 FMONCAT (NIL T) -9 NIL 879005 NIL) (-398 873098 873846 873874 "FMFUN" 875018 FMFUN (NIL) -9 NIL 875726 NIL) (-397 869971 871023 871077 "FMCAT" 872272 FMCAT (NIL T T) -9 NIL 872767 NIL) (-396 869204 869421 869449 "FMC" 869739 FMC (NIL) -9 NIL 869921 NIL) (-395 867929 869025 869125 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 867051 867775 867924 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-393 865238 865690 866184 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 863173 863709 864287 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 856608 861510 862124 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-390 855126 856200 856241 "FLINEXP" 856246 FLINEXP (NIL T) -9 NIL 856339 NIL) (-389 854534 854793 855121 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-388 853740 853902 854126 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 850658 851710 851762 "FLALG" 852989 FLALG (NIL T T) -9 NIL 853456 NIL) (-386 849829 849990 850217 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 843195 847235 847276 "FLAGG" 848538 FLAGG (NIL T) -9 NIL 849190 NIL) (-384 842289 842700 843190 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-383 838927 840134 840193 "FINRALG" 841321 FINRALG (NIL T T) -9 NIL 841829 NIL) (-382 838318 838583 838922 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-381 837624 837923 837951 "FINITE" 838147 FINITE (NIL) -9 NIL 838254 NIL) (-380 829575 832154 832194 "FINAALG" 835861 FINAALG (NIL T) -9 NIL 837314 NIL) (-379 825800 827059 828196 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-378 824360 824782 824836 "FILECAT" 825520 FILECAT (NIL T T) -9 NIL 825736 NIL) (-377 823708 824185 824288 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-376 821026 822851 822879 "FIELD" 822919 FIELD (NIL) -9 NIL 822999 NIL) (-375 820047 820510 821021 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-374 818046 818996 819343 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 817286 817468 817688 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 812591 817224 817281 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 812253 812320 812455 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 811793 811835 812044 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 808467 809346 810125 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 803786 808399 808462 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 798500 803275 803465 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 793016 797781 798039 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 787258 792467 792678 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 786281 786491 786806 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 781789 784441 784469 "FFIELDC" 785089 FFIELDC (NIL) -9 NIL 785465 NIL) (-362 780864 781303 781784 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-361 780479 780537 780661 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 778623 779146 779663 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-359 773752 778422 778523 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 768885 773541 773648 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 763586 768676 768784 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 763040 763089 763324 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 741502 752543 752629 "FFCAT" 757794 FFCAT (NIL T T T) -9 NIL 759245 NIL) (-354 737728 738960 740272 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-353 732606 737659 737723 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 722496 726758 727946 "FEXPR" NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 721424 721893 721934 "FEVALAB" 722018 FEVALAB (NIL T) -9 NIL 722279 NIL) (-350 720829 721081 721419 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-349 717691 718576 718691 "FDIVCAT" 720259 FDIVCAT (NIL T T T T) -9 NIL 720696 NIL) (-348 717483 717516 717686 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-347 716790 716883 717160 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 715303 716274 716477 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 714393 714780 714982 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-344 713318 713607 713896 "FCPAK1" NIL FCPAK1 (NIL) -7 NIL NIL NIL) (-343 712430 712927 713068 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 699262 703098 706636 "FC" NIL FC (NIL) -8 NIL NIL NIL) (-341 690886 695496 695536 "FAXF" 697338 FAXF (NIL T) -9 NIL 698030 NIL) (-340 688796 689603 690421 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-339 683622 688315 688491 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 678107 680482 680535 "FAMR" 681558 FAMR (NIL T T) -9 NIL 682018 NIL) (-337 677303 677669 678102 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-336 676352 677245 677298 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 673982 674834 674887 "FAMONC" 675828 FAMONC (NIL T T) -9 NIL 676214 NIL) (-334 672562 673840 673977 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 670634 670995 671398 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 669911 670108 670330 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 661813 669358 669557 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 659832 660402 660988 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 656704 657356 658086 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 651840 652547 653353 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 651529 651592 651701 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 636330 650574 651003 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 626889 635645 635936 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 626380 626684 626775 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-323 626153 626346 626375 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-322 625842 625910 626023 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 625359 625501 625542 "EVALAB" 625712 EVALAB (NIL T) -9 NIL 625816 NIL) (-320 624987 625133 625354 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-319 622102 623643 623671 "EUCDOM" 624226 EUCDOM (NIL) -9 NIL 624576 NIL) (-318 621027 621521 622097 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-317 620716 620779 620888 "ESTOOLS2" NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 620509 620557 620637 "ESTOOLS1" NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 610556 613537 616287 "ESTOOLS" NIL ESTOOLS (NIL) -7 NIL NIL NIL) (-314 610333 610371 610453 "ESCONT1" NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 607401 608228 609008 "ESCONT" NIL ESCONT (NIL) -7 NIL NIL NIL) (-312 607126 607182 607282 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 606814 606878 606987 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 600513 602443 602471 "ES" 605239 ES (NIL) -9 NIL 606649 NIL) (-309 596979 598534 600349 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-308 596327 596480 596656 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-307 589509 596231 596322 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 589198 589261 589370 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 582897 585940 587377 "EQ" NIL -3956 (NIL T) -8 NIL NIL NIL) (-304 579200 580296 581389 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-303 578026 578377 578683 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-302 576986 577660 577688 "ENTIRER" 577693 ENTIRER (NIL) -9 NIL 577739 NIL) (-301 573675 575416 575765 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 572779 572990 573044 "ELTAGG" 573424 ELTAGG (NIL T T) -9 NIL 573635 NIL) (-299 572559 572633 572774 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-298 572317 572352 572406 "ELTAB" 572490 ELTAB (NIL T T) -9 NIL 572542 NIL) (-297 571568 571738 571937 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 571292 571366 571394 "ELEMFUN" 571499 ELEMFUN (NIL) -9 NIL NIL NIL) (-295 571192 571219 571287 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-294 565714 569231 569272 "ELAGG" 570212 ELAGG (NIL T) -9 NIL 570675 NIL) (-293 564504 565046 565709 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-292 563922 564089 564245 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-291 562826 563148 563430 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-290 556190 558188 559017 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-289 550168 552164 552975 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-288 547973 548379 548851 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 538896 540815 542363 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-286 538003 538510 538659 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-285 537133 537970 537998 "E04UCFA" NIL E04UCFA (NIL) -8 NIL NIL NIL) (-284 536263 537100 537128 "E04NAFA" NIL E04NAFA (NIL) -8 NIL NIL NIL) (-283 535393 536230 536258 "E04MBFA" NIL E04MBFA (NIL) -8 NIL NIL NIL) (-282 534523 535360 535388 "E04JAFA" NIL E04JAFA (NIL) -8 NIL NIL NIL) (-281 533655 534490 534518 "E04GCFA" NIL E04GCFA (NIL) -8 NIL NIL NIL) (-280 532787 533622 533650 "E04FDFA" NIL E04FDFA (NIL) -8 NIL NIL NIL) (-279 531917 532754 532782 "E04DGFA" NIL E04DGFA (NIL) -8 NIL NIL NIL) (-278 527338 528786 530150 "E04AGNT" NIL E04AGNT (NIL) -7 NIL NIL NIL) (-277 525958 526639 526679 "DVARCAT" 527020 DVARCAT (NIL T) -9 NIL 527183 NIL) (-276 525373 525639 525953 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-275 517480 525239 525368 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 515830 516621 516662 "DSEXT" 517025 DSEXT (NIL T) -9 NIL 517319 NIL) (-273 514635 515159 515825 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-272 514359 514424 514522 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 510495 511717 512854 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-270 506126 507488 508556 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-269 504801 505162 505548 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-268 504487 504546 504664 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 503459 503758 504049 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-266 503042 503117 503268 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 495455 497567 499682 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 490972 491991 493070 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 487554 489637 489678 "DQAGG" 490307 DQAGG (NIL T) -9 NIL 490581 NIL) (-262 474080 481677 481760 "DPOLCAT" 483612 DPOLCAT (NIL T T T T) -9 NIL 484157 NIL) (-261 470485 472134 474075 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-260 463460 470382 470480 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 456344 463288 463455 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 455935 456197 456286 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 455344 455797 455877 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-256 454627 454955 455106 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-255 447807 454361 454513 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 445583 446873 446914 "DMEXT" 446919 DMEXT (NIL T) -9 NIL 447095 NIL) (-253 445239 445301 445445 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-252 438522 444724 444914 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 435172 437347 437388 "DLAGG" 437938 DLAGG (NIL T) -9 NIL 438168 NIL) (-250 433597 434411 434439 "DIVRING" 434531 DIVRING (NIL) -9 NIL 434614 NIL) (-249 433048 433292 433592 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-248 431476 431893 432299 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-247 430513 430734 430999 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 424020 430445 430508 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 412293 418720 418773 "DIRPCAT" 419031 DIRPCAT (NIL NIL T) -9 NIL 419906 NIL) (-244 410307 411075 411956 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-243 409754 409920 410106 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-242 406279 408638 408679 "DIOPS" 409113 DIOPS (NIL T) -9 NIL 409342 NIL) (-241 405939 406083 406274 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-240 404846 405618 405646 "DIFRING" 405651 DIFRING (NIL) -9 NIL 405673 NIL) (-239 404494 404592 404620 "DIFFSPC" 404739 DIFFSPC (NIL) -9 NIL 404814 NIL) (-238 404235 404337 404489 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-237 403171 403769 403810 "DIFFMOD" 403815 DIFFMOD (NIL T) -9 NIL 403913 NIL) (-236 402867 402924 402965 "DIFFDOM" 403086 DIFFDOM (NIL T) -9 NIL 403154 NIL) (-235 402748 402778 402862 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-234 400487 401951 401992 "DIFEXT" 401997 DIFEXT (NIL T) -9 NIL 402150 NIL) (-233 397632 399991 400032 "DIAGG" 400037 DIAGG (NIL T) -9 NIL 400057 NIL) (-232 397182 397375 397627 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-231 392376 396372 396649 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 388834 389887 390897 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-229 383429 387986 388314 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-228 381974 382272 382654 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 379134 380329 380729 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 376840 378965 379054 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 376220 376365 376548 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 373533 374257 375058 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 371635 372094 372658 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 371014 371350 371465 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-221 364248 370737 370887 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-220 362162 362674 363180 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 361801 361850 362001 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 361053 361622 361713 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 359071 359517 359878 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 358360 358652 358798 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 357426 358327 358355 "D03FAFA" NIL D03FAFA (NIL) -8 NIL NIL NIL) (-214 356493 357393 357421 "D03EEFA" NIL D03EEFA (NIL) -8 NIL NIL NIL) (-213 354888 355378 355867 "D03AGNT" NIL D03AGNT (NIL) -7 NIL NIL NIL) (-212 354137 354855 354883 "D02EJFA" NIL D02EJFA (NIL) -8 NIL NIL NIL) (-211 353386 354104 354132 "D02CJFA" NIL D02CJFA (NIL) -8 NIL NIL NIL) (-210 352635 353353 353381 "D02BHFA" NIL D02BHFA (NIL) -8 NIL NIL NIL) (-209 351884 352602 352630 "D02BBFA" NIL D02BBFA (NIL) -8 NIL NIL NIL) (-208 346601 348256 349862 "D02AGNT" NIL D02AGNT (NIL) -7 NIL NIL NIL) (-207 344881 345420 345964 "D01WGTS" NIL D01WGTS (NIL) -7 NIL NIL NIL) (-206 343896 344848 344876 "D01TRNS" NIL D01TRNS (NIL) -8 NIL NIL NIL) (-205 342912 343863 343891 "D01GBFA" NIL D01GBFA (NIL) -8 NIL NIL NIL) (-204 341928 342879 342907 "D01FCFA" NIL D01FCFA (NIL) -8 NIL NIL NIL) (-203 340944 341895 341923 "D01ASFA" NIL D01ASFA (NIL) -8 NIL NIL NIL) (-202 339960 340911 340939 "D01AQFA" NIL D01AQFA (NIL) -8 NIL NIL NIL) (-201 338976 339927 339955 "D01APFA" NIL D01APFA (NIL) -8 NIL NIL NIL) (-200 337992 338943 338971 "D01ANFA" NIL D01ANFA (NIL) -8 NIL NIL NIL) (-199 337008 337959 337987 "D01AMFA" NIL D01AMFA (NIL) -8 NIL NIL NIL) (-198 336024 336975 337003 "D01ALFA" NIL D01ALFA (NIL) -8 NIL NIL NIL) (-197 335040 335991 336019 "D01AKFA" NIL D01AKFA (NIL) -8 NIL NIL NIL) (-196 334056 335007 335035 "D01AJFA" NIL D01AJFA (NIL) -8 NIL NIL NIL) (-195 328820 330445 332006 "D01AGNT" NIL D01AGNT (NIL) -7 NIL NIL NIL) (-194 328271 328417 328569 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 325633 326426 327153 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-192 325072 325218 325389 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 323131 323443 323812 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 322685 322943 323044 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-189 321890 322278 322306 "CTORCAT" 322488 CTORCAT (NIL) -9 NIL 322601 NIL) (-188 321591 321726 321885 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-187 321081 321341 321449 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 320492 320928 321001 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-185 319951 320068 320221 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 316336 317095 317853 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 315823 316129 316221 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-182 315042 315251 315479 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 314546 314651 314855 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 314299 314333 314439 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 311222 311984 312703 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 310732 310877 311019 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-177 306680 309195 309687 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 306554 306581 306609 "CONDUIT" 306646 CONDUIT (NIL) -9 NIL NIL NIL) (-175 305508 306182 306210 "COMRING" 306215 COMRING (NIL) -9 NIL 306267 NIL) (-174 304654 305030 305214 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-173 304350 304391 304519 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 304043 304106 304213 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 292851 303993 304038 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292312 292451 292611 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-169 292065 292106 292204 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 273356 285657 285697 "COMPCAT" 286701 COMPCAT (NIL T) -9 NIL 288049 NIL) (-167 265896 269410 273000 "COMPCAT-" NIL COMPCAT- 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T) ((-23) . T) ((-47 |#1| (-558)) . T) ((-25) . T) ((-38 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-632 (-558)) . T) ((-632 |#1|) |has| |#1| (-175)) ((-632 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-629 (-876)) . 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T) ((-659 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-659 |#1|) |has| |#1| (-175)) ((-659 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-736 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-736 |#1|) |has| |#1| (-175)) ((-736 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-745) . T) ((-910 $ (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-916 (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-918 (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-993 |#1| (-558) (-1102)) . T) ((-939) |has| |#1| (-376)) ((-1022) |has| |#1| (-38 (-419 (-558)))) ((-1071 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1071 |#1|) . T) ((-1071 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1076 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1076 |#1|) . T) ((-1076 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1069) . T) ((-1077) . T) ((-1132) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-558)))) ((-1226) |has| |#1| (-38 (-419 (-558)))) ((-1237) . T) ((-1242) |has| |#1| (-376)) ((-1266 |#1| (-558)) . 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T) ((-23) . T) ((-47 |#1| (-558)) . T) ((-25) . T) ((-38 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -3956 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -3956 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-632 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-632 (-558)) . T) ((-632 (-1197)) -12 (|has| |#1| (-376)) (|has| |#2| (-1058 (-1197)))) ((-632 |#1|) |has| |#1| (-175)) ((-632 |#2|) . T) ((-632 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-629 (-876)) . T) ((-175) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-630 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1040))) ((-630 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1040))) ((-630 (-547)) -12 (|has| |#1| (-376)) (|has| |#2| (-630 (-547)))) ((-630 (-904 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-630 (-904 (-391))))) ((-630 (-904 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-630 (-904 (-558))))) ((-236 $) -3956 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -3956 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-239) -3956 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 (-558) |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1132)) ((-302) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-412 |#2|) |has| |#1| (-376)) ((-464) |has| |#1| (-376)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-526 (-1197) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1197) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-665 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-665 (-558)) . T) ((-665 |#1|) . T) ((-665 |#2|) |has| |#1| (-376)) ((-665 $) . T) ((-667 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-667 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-657 (-558)))) ((-667 |#1|) . T) ((-667 |#2|) |has| |#1| (-376)) ((-667 $) . T) ((-659 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-659 |#1|) |has| |#1| (-175)) ((-659 |#2|) |has| |#1| (-376)) ((-659 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-657 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-657 (-558)))) ((-657 |#2|) |has| |#1| (-376)) ((-736 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-736 |#1|) |has| |#1| (-175)) ((-736 |#2|) |has| |#1| (-376)) ((-736 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-745) . T) ((-811) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-815) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-841) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-859) -12 (|has| |#1| (-376)) (|has| |#2| (-841))) ((-860) -3956 (-12 (|has| |#1| (-376)) (|has| |#2| (-860))) (-12 (|has| |#1| (-376)) (|has| |#2| (-841)))) ((-863) -3956 (-12 (|has| |#1| (-376)) (|has| |#2| (-860))) (-12 (|has| |#1| (-376)) (|has| |#2| (-841)))) ((-910 $ (-1197)) -3956 (-12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-918 (-1197)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-916 (-1197))))) ((-916 (-1197)) -3956 (-12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-916 (-1197))))) ((-918 (-1197)) -3956 (-12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-918 (-1197)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-916 (-1197))))) ((-900 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-900 (-391)))) ((-900 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-900 (-558)))) ((-898 |#2|) |has| |#1| (-376)) ((-928) -12 (|has| |#1| (-376)) (|has| |#2| (-928))) ((-993 |#1| (-558) (-1102)) . T) ((-939) |has| |#1| (-376)) ((-1011 |#2|) |has| |#1| (-376)) ((-1022) |has| |#1| (-38 (-419 (-558)))) ((-1040) -12 (|has| |#1| (-376)) (|has| |#2| (-1040))) ((-1058 (-419 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-1058 (-558)))) ((-1058 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-1058 (-558)))) ((-1058 (-1197)) -12 (|has| |#1| (-376)) (|has| |#2| (-1058 (-1197)))) ((-1058 |#2|) . T) ((-1071 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1071 |#1|) . T) ((-1071 |#2|) |has| |#1| (-376)) ((-1071 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1076 (-419 (-558))) -3956 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1076 |#1|) . T) ((-1076 |#2|) |has| |#1| (-376)) ((-1076 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1069) . T) ((-1077) . T) ((-1132) . T) ((-1121) . T) ((-1172) -12 (|has| |#1| (-376)) (|has| |#2| (-1172))) ((-1223) |has| |#1| (-38 (-419 (-558)))) ((-1226) |has| |#1| (-38 (-419 (-558)))) ((-1237) . T) ((-1242) |has| |#1| (-376)) ((-1249 |#1|) . T) ((-1266 |#1| (-558)) . 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T) ((-23) . T) ((-47 |#1| (-790)) . T) ((-25) . T) ((-38 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) -3956 (|has| |#1| (-1058 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-632 (-558)) . T) ((-632 (-1102)) . T) ((-632 |#1|) . T) ((-632 $) -3956 (|has| |#1| (-928)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-629 (-876)) . 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-632 (-558)) . T) ((-632 |#1|) |has| |#1| (-175)) ((-632 $) |has| |#1| (-569)) ((-629 (-876)) . T) ((-175) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-240) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-298 |#2| |#1|) . T) ((-298 $ $) |has| |#2| (-1132)) ((-302) |has| |#1| (-569)) ((-569) |has| |#1| (-569)) ((-665 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-665 (-558)) . T) ((-665 |#1|) . T) ((-665 $) . 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T) ((-23) . T) ((-47 |#1| (-790)) . T) ((-25) . T) ((-38 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 (-419 (-558)) (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-632 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-632 (-558)) . T) ((-632 |#1|) |has| |#1| (-175)) ((-632 $) |has| |#1| (-569)) ((-629 (-876)) . T) ((-175) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-790) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-790) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-790) |#1|))) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 (-790) |#1|) . T) ((-298 $ $) |has| (-790) (-1132)) ((-302) |has| |#1| (-569)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-569) |has| |#1| (-569)) ((-665 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-665 (-558)) . T) ((-665 |#1|) . T) ((-665 $) . T) ((-667 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-667 |#1|) . T) ((-667 $) . T) ((-659 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-659 |#1|) |has| |#1| (-175)) ((-659 $) |has| |#1| (-569)) ((-736 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-736 |#1|) |has| |#1| (-175)) ((-736 $) |has| |#1| (-569)) ((-745) . T) ((-910 $ (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-790) |#1|)))) ((-916 (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-790) |#1|)))) ((-918 (-1197)) -12 (|has| |#1| (-916 (-1197))) (|has| |#1| (-15 * (|#1| (-790) |#1|)))) ((-993 |#1| (-790) (-1102)) . T) ((-1022) |has| |#1| (-38 (-419 (-558)))) ((-1071 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1071 |#1|) . T) ((-1071 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1076 (-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-1076 |#1|) . T) ((-1076 $) -3956 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1069) . T) ((-1077) . T) ((-1132) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-558)))) ((-1226) |has| |#1| (-38 (-419 (-558)))) ((-1237) . T) ((-1266 |#1| (-790)) . 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(-1264 2919106 2919155 2919288 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1263 2903166 2912117 2912160 "UPOLYC" 2914261 UPOLYC (NIL T) -9 NIL 2915482 NIL) (-1262 2897186 2900053 2903161 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1261 2896618 2896743 2896907 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1260 2896252 2896339 2896478 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1259 2895065 2895332 2895636 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1258 2894394 2894524 2894710 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1257 2893982 2894057 2894206 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1256 2884746 2893746 2893875 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1255 2884108 2884245 2884450 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1254 2882703 2883554 2883831 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1253 2881929 2882127 2882353 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1252 2868731 2881852 2881924 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1251 2848470 2861717 2861779 "ULSCCAT" 2862417 ULSCCAT (NIL T T) -9 NIL 2862706 NIL) (-1250 2847802 2848089 2848465 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1249 2836162 2843251 2843294 "ULSCAT" 2844157 ULSCAT (NIL T) -9 NIL 2844888 NIL) (-1248 2835671 2835756 2835935 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1247 2817738 2835167 2835409 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1246 2816765 2817465 2817579 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2817690) (-1245 2815791 2816491 2816605 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2816716) (-1244 2814817 2815517 2815631 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2815742) (-1243 2813843 2814543 2814657 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2814768) (-1242 2811922 2813089 2813119 "UFD" 2813331 UFD (NIL) -9 NIL 2813445 NIL) (-1241 2811764 2811822 2811917 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1240 2811016 2811223 2811439 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1239 2809218 2809677 2810148 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1238 2808939 2809182 2809213 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1237 2808872 2808877 2808907 "TYPE" 2808912 TYPE (NIL) -9 NIL NIL NIL) (-1236 2808031 2808251 2808491 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1235 2807206 2807640 2807875 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1234 2805360 2805933 2806472 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1233 2804380 2804621 2804862 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1232 2792631 2797139 2797236 "TSETCAT" 2802505 TSETCAT (NIL T T T T) -9 NIL 2804036 NIL) (-1231 2788925 2790762 2792626 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1230 2783366 2788145 2788428 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2778703 2779716 2780645 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1228 2778200 2778275 2778438 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1227 2776263 2776554 2776911 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1226 2775747 2775896 2775926 "TRIGCAT" 2776139 TRIGCAT (NIL) -9 NIL NIL NIL) (-1225 2775498 2775601 2775742 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1224 2772470 2774602 2774883 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1223 2771576 2772272 2772302 "TRANFUN" 2772337 TRANFUN (NIL) -9 NIL 2772403 NIL) (-1222 2771040 2771291 2771571 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1221 2770877 2770915 2770976 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1220 2770330 2770461 2770613 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1219 2769065 2769726 2769963 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1218 2768877 2768914 2768986 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1217 2767088 2767737 2768166 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1216 2766792 2766867 2766957 "TEMUTL" NIL TEMUTL (NIL) -7 NIL NIL NIL) (-1215 2765163 2765503 2765828 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1214 2756357 2763007 2763063 "TBAGG" 2763463 TBAGG (NIL T T) -9 NIL 2763674 NIL) (-1213 2752928 2754600 2756352 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1212 2752405 2752530 2752675 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1211 2751911 2752235 2752325 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1210 2751408 2751525 2751663 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1209 2744588 2751310 2751403 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1208 2740332 2741630 2742878 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1207 2739701 2739860 2740041 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1206 2736855 2737608 2738391 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1205 2736626 2736819 2736850 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1204 2735573 2736265 2736391 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2736577) (-1203 2734830 2735385 2735464 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2735524) (-1202 2731628 2732796 2733506 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1201 2729318 2729998 2730630 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1200 2725396 2726442 2727419 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1199 2722540 2725049 2725279 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1198 2722133 2722220 2722343 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1197 2718746 2720228 2721049 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1196 2713917 2715672 2717392 "SWITCH" NIL SWITCH (NIL) -8 NIL NIL NIL) (-1195 2706921 2713109 2713403 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2698651 2706509 2706773 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2697930 2698069 2698286 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1192 2697610 2697675 2697788 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1191 2688332 2697319 2697445 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2687057 2687355 2687711 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1189 2686459 2686537 2686729 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1188 2668561 2685955 2686197 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2668157 2668431 2668501 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1186 2667490 2667774 2667914 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1185 2662041 2663308 2664267 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1184 2661573 2661673 2661837 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1183 2656684 2657966 2659113 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1182 2651142 2652613 2653924 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1181 2644021 2646085 2647877 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1180 2636944 2643933 2644016 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1179 2631606 2636660 2636773 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1178 2631193 2631276 2631420 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1177 2630344 2630545 2630780 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1176 2630084 2630142 2630235 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1175 2622776 2628279 2628890 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1174 2621952 2622157 2622388 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1173 2621193 2621567 2621715 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1172 2620689 2620934 2620964 "STEP" 2621058 STEP (NIL) -9 NIL 2621129 NIL) (-1171 2613885 2620607 2620684 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1170 2608065 2612676 2612719 "STAGG" 2613151 STAGG (NIL T) -9 NIL 2613330 NIL) (-1169 2606440 2607190 2608060 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1168 2604583 2606267 2606359 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1167 2603900 2604413 2604443 "SRING" 2604448 SRING (NIL) -9 NIL 2604468 NIL) (-1166 2596429 2602411 2602867 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1165 2590170 2591617 2593130 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1164 2582554 2587499 2587529 "SRAGG" 2588832 SRAGG (NIL) -9 NIL 2589440 NIL) (-1163 2581849 2582170 2582549 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1162 2575942 2581167 2581591 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1161 2570124 2573315 2574042 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1160 2566523 2567354 2568000 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1159 2565498 2565803 2565833 "SPFCAT" 2566277 SPFCAT (NIL) -9 NIL NIL NIL) (-1158 2564435 2564687 2564951 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1157 2555082 2557398 2557428 "SPADXPT" 2562104 SPADXPT (NIL) -9 NIL 2564268 NIL) (-1156 2554884 2554930 2554999 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1155 2552498 2554848 2554879 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1154 2544099 2546202 2546245 "SPACEC" 2550618 SPACEC (NIL T) -9 NIL 2552434 NIL) (-1153 2541913 2544045 2544094 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1152 2540840 2541031 2541322 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1151 2539238 2539571 2539983 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1150 2538503 2538737 2538998 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1149 2534683 2535643 2536638 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1148 2531041 2531740 2532469 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1147 2524787 2530390 2530487 "SNTSCAT" 2530492 SNTSCAT (NIL T T T T) -9 NIL 2530562 NIL) (-1146 2518655 2523420 2523811 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1145 2512469 2518573 2518650 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1144 2510901 2511232 2511630 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1143 2502530 2507466 2507569 "SMATCAT" 2508923 SMATCAT (NIL NIL T T T) -9 NIL 2509473 NIL) (-1142 2500370 2501354 2502525 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1141 2497950 2499578 2499621 "SKAGG" 2499882 SKAGG (NIL T) -9 NIL 2500017 NIL) (-1140 2493792 2497600 2497770 "SINT" NIL SINT (NIL) -8 NIL NIL 2497922) (-1139 2493602 2493646 2493712 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1138 2492677 2492909 2493177 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1137 2491677 2491839 2492116 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1136 2491019 2491362 2491486 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1135 2490362 2490672 2490812 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1134 2488473 2488965 2489471 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1133 2481946 2488392 2488468 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1132 2481457 2481697 2481727 "SGROUP" 2481820 SGROUP (NIL) -9 NIL 2481882 NIL) (-1131 2481347 2481379 2481452 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1130 2478767 2479537 2480260 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1129 2472611 2478214 2478311 "SFRTCAT" 2478316 SFRTCAT (NIL T T T T) -9 NIL 2478355 NIL) (-1128 2466947 2468067 2469203 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1127 2461036 2462215 2463399 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1126 2460697 2460804 2460915 "SFORT" NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1125 2459657 2460571 2460692 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1124 2455246 2456153 2456248 "SEXCAT" 2458870 SEXCAT (NIL T T T T T) -9 NIL 2459430 NIL) (-1123 2454207 2455173 2455241 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1122 2452592 2453181 2453484 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1121 2452122 2452310 2452340 "SETCAT" 2452457 SETCAT (NIL) -9 NIL 2452542 NIL) (-1120 2451954 2452018 2452117 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1119 2448168 2450415 2450458 "SETAGG" 2451328 SETAGG (NIL T) -9 NIL 2451668 NIL) (-1118 2447774 2447926 2448163 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1117 2444710 2447721 2447769 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1116 2444172 2444485 2444586 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1115 2443299 2443665 2443726 "SEGXCAT" 2444012 SEGXCAT (NIL T T) -9 NIL 2444132 NIL) (-1114 2442224 2442492 2442535 "SEGCAT" 2443057 SEGCAT (NIL T) -9 NIL 2443278 NIL) (-1113 2441904 2441969 2442082 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1112 2440967 2441440 2441648 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1111 2440541 2440823 2440900 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1110 2439906 2440042 2440246 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1109 2438969 2439719 2439901 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1108 2438215 2438917 2438964 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1107 2429740 2438080 2438210 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1106 2428594 2428884 2429203 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1105 2427886 2428100 2428292 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-1104 2427227 2427385 2427564 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1103 2426806 2427040 2427070 "SASTCAT" 2427075 SASTCAT (NIL) -9 NIL 2427088 NIL) (-1102 2426263 2426695 2426771 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-1101 2425863 2425904 2426077 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1100 2425491 2425532 2425691 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1099 2418604 2425406 2425486 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2417241 2417573 2417974 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1097 2415984 2416350 2416655 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1096 2415602 2415826 2415909 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1095 2413036 2413674 2414132 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2412869 2412903 2412974 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-1093 2412352 2412658 2412752 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-1092 2407923 2408796 2409716 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1091 2396629 2402232 2402329 "RSETCAT" 2406448 RSETCAT (NIL T T T T) -9 NIL 2407545 NIL) (-1090 2395153 2395800 2396624 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1089 2388862 2390316 2391836 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1088 2386731 2387294 2387368 "RRCC" 2388454 RRCC (NIL T T) -9 NIL 2388798 NIL) (-1087 2386247 2386449 2386726 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-1086 2385709 2386022 2386123 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-1085 2358034 2368734 2368801 "RPOLCAT" 2379467 RPOLCAT (NIL T T T) -9 NIL 2382627 NIL) (-1084 2352103 2354939 2358029 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-1083 2343142 2350774 2351256 "ROUTINE" NIL ROUTINE (NIL) -8 NIL NIL NIL) (-1082 2339350 2342886 2343026 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-1081 2337659 2338405 2338665 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1080 2333349 2336114 2336144 "RNS" 2336413 RNS (NIL) -9 NIL 2336669 NIL) (-1079 2332255 2332740 2333274 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-1078 2331365 2331769 2331971 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1077 2330658 2331162 2331192 "RNG" 2331197 RNG (NIL) -9 NIL 2331218 NIL) (-1076 2329953 2330431 2330474 "RMODULE" 2330479 RMODULE (NIL T) -9 NIL 2330506 NIL) (-1075 2328876 2328982 2329318 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1074 2325732 2328460 2328757 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1073 2318342 2320819 2320934 "RMATCAT" 2324293 RMATCAT (NIL NIL NIL T T T) -9 NIL 2325275 NIL) (-1072 2317847 2318030 2318337 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-1071 2317420 2317634 2317677 "RLINSET" 2317739 RLINSET (NIL T) -9 NIL 2317783 NIL) (-1070 2317062 2317143 2317271 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1069 2315986 2316660 2316690 "RING" 2316746 RING (NIL) -9 NIL 2316838 NIL) (-1068 2315828 2315884 2315981 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-1067 2314875 2315142 2315400 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-1066 2305803 2314495 2314701 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1065 2305061 2305545 2305586 "RGBCSPC" 2305644 RGBCSPC (NIL T) -9 NIL 2305696 NIL) (-1064 2304127 2304586 2304627 "RGBCMDL" 2304859 RGBCMDL (NIL T) -9 NIL 2304973 NIL) (-1063 2303836 2303905 2304008 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1062 2303596 2303637 2303734 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1061 2302007 2302437 2302819 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-1060 2299583 2300251 2300921 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-1059 2299128 2299226 2299389 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1058 2298746 2298844 2298887 "RETRACT" 2299020 RETRACT (NIL T) -9 NIL 2299107 NIL) (-1057 2298623 2298654 2298741 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-1056 2298219 2298493 2298563 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-1055 2290795 2297977 2298104 "RESULT" NIL RESULT (NIL) -8 NIL NIL NIL) (-1054 2289329 2290161 2290360 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1053 2289016 2289077 2289175 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1052 2288756 2288797 2288904 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1051 2288488 2288529 2288640 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-1050 2283508 2284965 2286188 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-1049 2280578 2281336 2282147 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-1048 2278538 2279160 2279762 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-1047 2271067 2277049 2277505 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1046 2269991 2270430 2270680 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-1045 2269472 2269587 2269754 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1044 2265082 2268857 2269084 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1043 2264309 2264508 2264723 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-1042 2261591 2262429 2263313 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1041 2258163 2259199 2260260 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1040 2257997 2258050 2258080 "REAL" 2258085 REAL (NIL) -9 NIL 2258120 NIL) (-1039 2257480 2257786 2257880 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-1038 2256957 2257035 2257242 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1037 2256185 2256377 2256590 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-1036 2255066 2255363 2255733 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1035 2253318 2253790 2254328 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1034 2252235 2252512 2252902 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1033 2251054 2251364 2251787 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1032 2244437 2247903 2247933 "RCFIELD" 2249228 RCFIELD (NIL) -9 NIL 2249959 NIL) (-1031 2243058 2243668 2244362 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-1030 2239221 2241131 2241174 "RCAGG" 2242258 RCAGG (NIL T) -9 NIL 2242723 NIL) (-1029 2238943 2239054 2239216 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-1028 2238376 2238506 2238671 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-1027 2237989 2238068 2238189 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1026 2237397 2237547 2237699 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-1025 2237176 2237226 2237299 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-1024 2229645 2236284 2236595 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1023 2219340 2229510 2229640 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1022 2218969 2219062 2219092 "RADCAT" 2219252 RADCAT (NIL) -9 NIL NIL NIL) (-1021 2218804 2218864 2218964 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-1020 2216886 2218631 2218723 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1019 2216560 2216609 2216740 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1018 2208857 2212895 2212937 "QUATCAT" 2213728 QUATCAT (NIL T) -9 NIL 2214494 NIL) (-1017 2206100 2207383 2208761 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-1016 2201982 2206047 2206095 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-1015 2199349 2201030 2201073 "QUAGG" 2201454 QUAGG (NIL T) -9 NIL 2201629 NIL) (-1014 2198945 2199219 2199289 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-1013 2197975 2198577 2198742 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1012 2197649 2197698 2197829 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1011 2187273 2193407 2193449 "QFCAT" 2194117 QFCAT (NIL T) -9 NIL 2195118 NIL) (-1010 2184166 2185602 2187177 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-1009 2183707 2183841 2183973 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-1008 2177796 2178975 2180159 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1007 2177207 2177389 2177625 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1006 2175006 2175540 2175968 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2173900 2174142 2174461 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1004 2172248 2172446 2172802 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1003 2167975 2169191 2169234 "PTRANFN" 2171145 PTRANFN (NIL T) -9 NIL NIL NIL) (-1002 2166601 2166946 2167270 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1001 2166287 2166350 2166461 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1000 2160314 2165073 2165116 "PTCAT" 2165416 PTCAT (NIL T) -9 NIL 2165569 NIL) (-999 2160007 2160048 2160172 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-998 2158886 2159202 2159536 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-997 2147685 2150260 2152584 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-996 2140526 2143443 2143539 "PSETCAT" 2146560 PSETCAT (NIL T T T T) -9 NIL 2147374 NIL) (-995 2138958 2139700 2140521 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-994 2138277 2138472 2138500 "PSCURVE" 2138768 PSCURVE (NIL) -9 NIL 2138935 NIL) (-993 2133923 2135690 2135755 "PSCAT" 2136599 PSCAT (NIL T T T) -9 NIL 2136839 NIL) (-992 2133236 2133518 2133918 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-991 2131657 2132548 2132811 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-990 2131144 2131450 2131542 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-989 2122164 2124586 2126774 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-988 2119895 2121486 2121526 "PRQAGG" 2121709 PRQAGG (NIL T) -9 NIL 2121811 NIL) (-987 2119074 2119523 2119551 "PROPLOG" 2119690 PROPLOG (NIL) -9 NIL 2119805 NIL) (-986 2118749 2118812 2118935 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-985 2118185 2118324 2118496 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-984 2116430 2117196 2117493 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-983 2115983 2116114 2116242 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-982 2110572 2114923 2115743 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-981 2110401 2110439 2110498 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-980 2109837 2109978 2110130 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-979 2108305 2108724 2109190 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-978 2108022 2108083 2108111 "PRIMCAT" 2108235 PRIMCAT (NIL) -9 NIL NIL NIL) (-977 2107193 2107389 2107617 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-976 2103041 2107143 2107188 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-975 2102740 2102802 2102913 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-974 2099921 2102387 2102621 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-973 2099372 2099529 2099557 "PPCURVE" 2099762 PPCURVE (NIL) -9 NIL 2099898 NIL) (-972 2098982 2099230 2099313 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-971 2096738 2097159 2097751 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-970 2096179 2096243 2096477 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-969 2092889 2093375 2093987 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-968 2078464 2084549 2084614 "POLYCAT" 2088128 POLYCAT (NIL T T T) -9 NIL 2090006 NIL) (-967 2073971 2076119 2078459 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-966 2073626 2073700 2073820 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-965 2073315 2073378 2073487 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-964 2066719 2073046 2073206 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-963 2065606 2065869 2066145 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-962 2064203 2064516 2064847 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-961 2059327 2064151 2064198 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-960 2057815 2058226 2058601 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-959 2056563 2056872 2057271 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-958 2056234 2056318 2056435 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-957 2055811 2055886 2056061 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-956 2055291 2055389 2055551 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-955 2054757 2054879 2055035 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2053649 2053867 2054245 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-953 2053260 2053345 2053497 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-952 2052809 2052891 2053073 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-951 2052501 2052582 2052695 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-950 2052012 2052087 2052296 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-949 2051351 2051481 2051686 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-948 2050713 2050847 2051010 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-947 2050017 2050199 2050380 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-946 2049740 2049814 2049908 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-945 2046295 2047489 2048410 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-944 2045379 2045580 2045815 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-943 2040928 2042318 2043466 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-942 2020837 2025728 2030579 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-941 2020577 2020630 2020733 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-940 2020018 2020152 2020332 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2018102 2019268 2019296 "PID" 2019493 PID (NIL) -9 NIL 2019620 NIL) (-938 2017890 2017933 2018008 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-937 2017069 2017737 2017824 "PI" NIL PI (NIL) -8 NIL NIL 2017864) (-936 2016521 2016672 2016848 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-935 2012849 2013807 2014712 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-934 2011213 2011502 2011868 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-933 2010655 2010770 2010931 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-932 2007251 2009524 2009877 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-931 2005857 2006137 2006462 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-930 2004619 2004874 2005223 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-929 2003322 2003550 2003904 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-928 2000406 2001912 2001940 "PFECAT" 2002533 PFECAT (NIL) -9 NIL 2002910 NIL) (-927 2000029 2000194 2000401 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-926 1998853 1999135 1999436 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-925 1997035 1997422 1997852 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-924 1993055 1996961 1997030 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-923 1988946 1990099 1990969 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-922 1986858 1987970 1988011 "PERMCAT" 1988411 PERMCAT (NIL T) -9 NIL 1988709 NIL) (-921 1986552 1986599 1986723 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-920 1982972 1984678 1985325 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-919 1980418 1982726 1982848 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-918 1979299 1979562 1979603 "PDSPC" 1980136 PDSPC (NIL T) -9 NIL 1980381 NIL) (-917 1978666 1978932 1979294 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-916 1977380 1978316 1978357 "PDRING" 1978362 PDRING (NIL T) -9 NIL 1978390 NIL) (-915 1976123 1976885 1976939 "PDMOD" 1976944 PDMOD (NIL T T) -9 NIL 1977048 NIL) (-914 1973938 1974764 1975432 "PDEPROB" NIL PDEPROB (NIL) -8 NIL NIL NIL) (-913 1971982 1972522 1973077 "PDEPACK" NIL PDEPACK (NIL) -7 NIL NIL NIL) (-912 1971075 1971287 1971536 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-911 1968592 1969483 1969511 "PDECAT" 1970298 PDECAT (NIL) -9 NIL 1971011 NIL) (-910 1968209 1968276 1968330 "PDDOM" 1968495 PDDOM (NIL T T) -9 NIL 1968575 NIL) (-909 1968061 1968097 1968204 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-908 1967845 1967884 1967974 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-907 1966156 1966917 1967214 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-906 1965845 1965908 1966017 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-905 1963965 1964401 1964858 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-904 1957545 1959392 1960693 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-903 1957176 1957249 1957381 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-902 1954881 1955562 1956041 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 1953067 1953502 1953909 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-900 1952521 1952772 1952813 "PATMAB" 1952920 PATMAB (NIL T) -9 NIL 1953003 NIL) (-899 1951162 1951570 1951828 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-898 1950700 1950831 1950872 "PATAB" 1950877 PATAB (NIL T) -9 NIL 1951049 NIL) (-897 1949243 1949680 1950103 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-896 1948921 1948996 1949098 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-895 1948610 1948673 1948782 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-894 1948415 1948461 1948528 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-893 1948093 1948168 1948270 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-892 1947782 1947845 1947954 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-891 1947473 1947543 1947640 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-890 1947162 1947225 1947334 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-889 1946313 1946697 1946879 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-888 1945920 1946018 1946137 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-887 1944821 1945249 1945477 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-886 1943480 1944140 1944500 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-885 1936606 1942883 1943078 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-884 1929063 1936103 1936288 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-883 1925862 1927723 1927763 "PADICCT" 1928344 PADICCT (NIL NIL) -9 NIL 1928626 NIL) (-882 1923908 1925812 1925857 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 1923070 1923280 1923546 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-880 1922412 1922555 1922759 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-879 1920848 1921816 1922096 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-878 1920370 1920631 1920728 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-877 1919422 1920107 1920279 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-876 1909838 1912711 1914911 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-875 1909227 1909542 1909669 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-874 1908504 1908699 1908727 "OUTBCON" 1909045 OUTBCON (NIL) -9 NIL 1909211 NIL) (-873 1908212 1908342 1908499 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-872 1907593 1907738 1907899 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-871 1906958 1907391 1907480 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-870 1906377 1906799 1906827 "OSGROUP" 1906832 OSGROUP (NIL) -9 NIL 1906854 NIL) (-869 1905341 1905602 1905887 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-868 1902663 1905215 1905336 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-867 1899856 1902412 1902539 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-866 1897867 1898395 1898956 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-865 1891245 1893733 1893774 "OREPCAT" 1896122 OREPCAT (NIL T) -9 NIL 1897226 NIL) (-864 1889270 1890204 1891240 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-863 1888462 1888740 1888768 "ORDTYPE" 1889077 ORDTYPE (NIL) -9 NIL 1889240 NIL) (-862 1887986 1888202 1888457 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-861 1887440 1887823 1887981 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-860 1886938 1887308 1887336 "ORDSET" 1887341 ORDSET (NIL) -9 NIL 1887363 NIL) (-859 1885589 1886560 1886588 "ORDRING" 1886593 ORDRING (NIL) -9 NIL 1886622 NIL) (-858 1884840 1885405 1885433 "ORDMON" 1885438 ORDMON (NIL) -9 NIL 1885459 NIL) (-857 1884135 1884300 1884495 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1883350 1883865 1883893 "ORDFIN" 1883958 ORDFIN (NIL) -9 NIL 1884032 NIL) (-855 1882744 1882883 1883069 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-854 1879489 1881706 1882115 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-853 1876804 1877774 1878588 "OPTPROB" NIL OPTPROB (NIL) -8 NIL NIL NIL) (-852 1874230 1874929 1875633 "OPTPACK" NIL OPTPACK (NIL) -7 NIL NIL NIL) (-851 1871843 1872669 1872697 "OPTCAT" 1873516 OPTCAT (NIL) -9 NIL 1874166 NIL) (-850 1871246 1871605 1871710 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-849 1871054 1871099 1871165 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-848 1870360 1870640 1870681 "OPERCAT" 1870893 OPERCAT (NIL T) -9 NIL 1870990 NIL) (-847 1870170 1870238 1870355 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-846 1867569 1868952 1869456 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-845 1866990 1867117 1867291 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-844 1863961 1866123 1866492 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-843 1860586 1863401 1863441 "OMSAGG" 1863502 OMSAGG (NIL T) -9 NIL 1863566 NIL) (-842 1859054 1860254 1860423 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-841 1857332 1858524 1858552 "OINTDOM" 1858557 OINTDOM (NIL) -9 NIL 1858578 NIL) (-840 1854751 1856332 1856662 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-839 1853998 1854701 1854746 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-838 1851254 1853838 1853993 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-837 1842831 1851123 1851249 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-836 1836274 1842721 1842826 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-835 1835246 1835483 1835756 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-834 1832880 1833550 1834254 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-833 1828635 1829595 1830620 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-832 1828143 1828231 1828425 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-831 1825578 1826160 1826835 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-830 1822965 1823473 1824070 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-829 1821326 1821970 1822456 "ODEPROB" NIL ODEPROB (NIL) -8 NIL NIL NIL) (-828 1818313 1818852 1819499 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-827 1817664 1817772 1818032 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-826 1814610 1815461 1816325 "ODEPACK" NIL ODEPACK (NIL) -7 NIL NIL NIL) (-825 1813764 1813889 1814111 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-824 1809256 1810717 1812164 "ODEIFTBL" NIL ODEIFTBL (NIL) -8 NIL NIL NIL) (-823 1805513 1806315 1807235 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-822 1804951 1805046 1805269 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-821 1803014 1803723 1803751 "ODECAT" 1804356 ODECAT (NIL) -9 NIL 1804887 NIL) (-820 1802695 1802744 1802871 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-819 1799312 1802490 1802612 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-818 1798505 1799105 1799133 "OCAMON" 1799138 OCAMON (NIL) -9 NIL 1799159 NIL) (-817 1792776 1795541 1795581 "OC" 1796678 OC (NIL T) -9 NIL 1797536 NIL) (-816 1790776 1791704 1792682 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-815 1790196 1790621 1790649 "OASGP" 1790654 OASGP (NIL) -9 NIL 1790674 NIL) (-814 1789292 1789919 1789947 "OAMONS" 1789987 OAMONS (NIL) -9 NIL 1790030 NIL) (-813 1788468 1789027 1789055 "OAMON" 1789113 OAMON (NIL) -9 NIL 1789165 NIL) (-812 1788362 1788395 1788463 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-811 1787143 1787896 1787924 "OAGROUP" 1788071 OAGROUP (NIL) -9 NIL 1788164 NIL) (-810 1786932 1787020 1787138 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-809 1786672 1786728 1786816 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-808 1781707 1783279 1784815 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-807 1778402 1779436 1780471 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-806 1775683 1776623 1776651 "NUMINT" 1777574 NUMINT (NIL) -9 NIL 1778338 NIL) (-805 1774793 1775026 1775244 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-804 1763633 1766672 1769122 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-803 1757479 1763082 1763177 "NTSCAT" 1763182 NTSCAT (NIL T T T T) -9 NIL 1763221 NIL) (-802 1756820 1756999 1757192 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-801 1756509 1756572 1756681 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-800 1744162 1754113 1754925 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-799 1733180 1744024 1744157 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-798 1731900 1732225 1732582 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-797 1730736 1731000 1731358 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-796 1729903 1730036 1730252 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-795 1728206 1728526 1728935 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-794 1727919 1727953 1728077 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-793 1727738 1727773 1727842 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-792 1727511 1727704 1727733 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-791 1727070 1727138 1727317 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-790 1725378 1726433 1726688 "NNI" NIL NNI (NIL) -8 NIL NIL 1727035) (-789 1724106 1724443 1724807 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-788 1721166 1722221 1723120 "NIPROB" NIL NIPROB (NIL) -8 NIL NIL NIL) (-787 1720143 1720395 1720697 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-786 1719227 1719793 1719834 "NETCLT" 1720006 NETCLT (NIL T) -9 NIL 1720088 NIL) (-785 1718131 1718398 1718679 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-784 1717930 1717973 1718048 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-783 1716461 1716849 1717269 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-782 1715131 1716071 1716099 "NASRING" 1716209 NASRING (NIL) -9 NIL 1716289 NIL) (-781 1714976 1715032 1715126 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-780 1713943 1714594 1714622 "NARNG" 1714739 NARNG (NIL) -9 NIL 1714830 NIL) (-779 1713719 1713804 1713938 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-778 1712771 1713020 1713255 "NAGSP" NIL NAGSP (NIL) -7 NIL NIL NIL) (-777 1705468 1707380 1709053 "NAGS" NIL NAGS (NIL) -7 NIL NIL NIL) (-776 1704303 1704635 1704966 "NAGF07" NIL NAGF07 (NIL) -7 NIL NIL NIL) (-775 1700062 1701419 1702726 "NAGF04" NIL NAGF04 (NIL) -7 NIL NIL NIL) (-774 1694547 1696257 1697890 "NAGF02" NIL NAGF02 (NIL) -7 NIL NIL NIL) (-773 1690808 1691968 1693085 "NAGF01" NIL NAGF01 (NIL) -7 NIL NIL NIL) (-772 1685953 1687567 1689152 "NAGE04" NIL NAGE04 (NIL) -7 NIL NIL NIL) (-771 1679124 1681353 1683483 "NAGE02" NIL NAGE02 (NIL) -7 NIL NIL NIL) (-770 1675961 1676968 1677932 "NAGE01" NIL NAGE01 (NIL) -7 NIL NIL NIL) (-769 1674276 1674828 1675386 "NAGD03" NIL NAGD03 (NIL) -7 NIL NIL NIL) (-768 1667906 1669888 1671842 "NAGD02" NIL NAGD02 (NIL) -7 NIL NIL NIL) (-767 1663065 1664562 1666002 "NAGD01" NIL NAGD01 (NIL) -7 NIL NIL NIL) (-766 1660019 1660913 1661750 "NAGC06" NIL NAGC06 (NIL) -7 NIL NIL NIL) (-765 1658802 1659152 1659508 "NAGC05" NIL NAGC05 (NIL) -7 NIL NIL NIL) (-764 1658290 1658421 1658565 "NAGC02" NIL NAGC02 (NIL) -7 NIL NIL NIL) (-763 1657091 1657818 1657858 "NAALG" 1657937 NAALG (NIL T) -9 NIL 1657998 NIL) (-762 1656961 1656996 1657086 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-761 1651937 1653123 1654310 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-760 1651332 1651419 1651603 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-759 1643387 1647825 1647878 "MTSCAT" 1648948 MTSCAT (NIL T T) -9 NIL 1649463 NIL) (-758 1643153 1643213 1643305 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-757 1642979 1643018 1643078 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-756 1639835 1642540 1642581 "MSETAGG" 1642586 MSETAGG (NIL T) -9 NIL 1642620 NIL) (-755 1635950 1638877 1639197 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-754 1632264 1634029 1634774 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-753 1631897 1631970 1632101 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-752 1631550 1631591 1631735 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-751 1629415 1629752 1630183 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-750 1622855 1629313 1629410 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-749 1622380 1622421 1622629 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-748 1621937 1621986 1622170 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1621205 1621298 1621519 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-746 1619822 1620183 1620573 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-745 1618967 1619350 1619378 "MONOID" 1619597 MONOID (NIL) -9 NIL 1619744 NIL) (-744 1618632 1618781 1618962 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-743 1607526 1614364 1614423 "MONOGEN" 1615097 MONOGEN (NIL T T) -9 NIL 1615553 NIL) (-742 1605538 1606424 1607407 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-741 1604255 1604803 1604831 "MONADWU" 1605223 MONADWU (NIL) -9 NIL 1605461 NIL) (-740 1603801 1604002 1604250 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-739 1603086 1603390 1603418 "MONAD" 1603625 MONAD (NIL) -9 NIL 1603737 NIL) (-738 1602853 1602949 1603081 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-737 1601239 1602013 1602292 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-736 1600407 1600907 1600947 "MODULE" 1600952 MODULE (NIL T) -9 NIL 1600991 NIL) (-735 1600086 1600212 1600402 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-734 1597855 1598682 1598997 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-733 1595067 1596431 1596952 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-732 1593690 1594271 1594548 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-731 1582900 1592344 1592758 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-730 1579911 1581900 1582169 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-729 1578992 1579362 1579552 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-728 1578561 1578610 1578789 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-727 1576454 1577393 1577434 "MLO" 1577857 MLO (NIL T) -9 NIL 1578099 NIL) (-726 1574335 1574862 1575457 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-725 1573803 1573899 1574053 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-724 1573473 1573549 1573672 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-723 1572685 1572871 1573099 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-722 1572178 1572294 1572450 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-721 1571550 1571664 1571849 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-720 1567690 1571220 1571356 "MINT" NIL MINT (NIL) -8 NIL NIL NIL) (-719 1566717 1566990 1567267 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-718 1561885 1565637 1566042 "MFLOAT" NIL MFLOAT (NIL) -8 NIL NIL NIL) (-717 1561318 1561406 1561577 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-716 1558476 1559355 1560234 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-715 1557143 1557491 1557844 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-714 1553790 1556274 1556315 "MDAGG" 1556570 MDAGG (NIL T) -9 NIL 1556713 NIL) (-713 1541762 1553270 1553477 "MCMPLX" NIL MCMPLX (NIL) -8 NIL NIL NIL) (-712 1541032 1541196 1541397 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-711 1539150 1539462 1539842 "MCALCFN" NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-710 1538221 1538509 1538742 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-709 1536308 1536885 1537447 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-708 1532057 1535895 1536143 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-707 1528404 1529175 1529909 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-706 1527149 1527318 1527649 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-705 1516596 1520203 1520280 "MATCAT" 1525315 MATCAT (NIL T T T) -9 NIL 1526787 NIL) (-704 1513868 1515178 1516591 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-703 1512269 1512629 1513013 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-702 1511402 1511599 1511821 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-701 1510153 1510479 1510806 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-700 1509311 1509716 1509893 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-699 1508980 1509044 1509167 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-698 1508628 1508701 1508815 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-697 1508163 1508278 1508420 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-696 1506358 1507135 1507439 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-695 1505848 1506153 1506244 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-694 1502633 1504515 1504976 "M3D" NIL M3D (NIL T) -8 NIL NIL NIL) (-693 1496104 1500941 1500982 "LZSTAGG" 1501764 LZSTAGG (NIL T) -9 NIL 1502059 NIL) (-692 1493193 1494642 1496099 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-691 1490563 1491539 1492026 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-690 1490140 1490422 1490497 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-689 1482331 1490001 1490135 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-688 1481694 1481839 1482067 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-687 1479175 1479874 1480587 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-686 1477284 1477608 1478057 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-685 1470411 1476371 1476412 "LSAGG" 1476474 LSAGG (NIL T) -9 NIL 1476552 NIL) (-684 1468083 1469193 1470406 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-683 1465590 1467432 1467681 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-682 1465257 1465348 1465471 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-681 1464940 1465019 1465047 "LOGIC" 1465158 LOGIC (NIL) -9 NIL 1465240 NIL) (-680 1464835 1464864 1464935 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-679 1464154 1464312 1464505 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-678 1462931 1463180 1463533 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-677 1458814 1461559 1461600 "LODOCAT" 1462038 LODOCAT (NIL T) -9 NIL 1462249 NIL) (-676 1458606 1458682 1458809 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-675 1455660 1458483 1458601 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-674 1452812 1455610 1455655 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-673 1449952 1452741 1452807 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-672 1449002 1449177 1449480 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-671 1447156 1448264 1448517 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-670 1442236 1445319 1445360 "LNAGG" 1446222 LNAGG (NIL T) -9 NIL 1446657 NIL) (-669 1441621 1441889 1442231 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-668 1438186 1439131 1439770 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-667 1437485 1437963 1438004 "LMODULE" 1438009 LMODULE (NIL T) -9 NIL 1438035 NIL) (-666 1434644 1437220 1437343 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-665 1434220 1434434 1434475 "LLINSET" 1434536 LLINSET (NIL T) -9 NIL 1434580 NIL) (-664 1433892 1434155 1434215 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-663 1433491 1433571 1433710 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-662 1431942 1432290 1432689 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-661 1431113 1431309 1431537 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-660 1424089 1430367 1430622 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-659 1423672 1423908 1423949 "LINSET" 1423954 LINSET (NIL T) -9 NIL 1423988 NIL) (-658 1422601 1423295 1423462 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-657 1420900 1421628 1421669 "LINEXP" 1422159 LINEXP (NIL T) -9 NIL 1422432 NIL) (-656 1419605 1420509 1420690 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-655 1418424 1418697 1419001 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-654 1417630 1418226 1418336 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-653 1415180 1415902 1416652 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-652 1413806 1414103 1414495 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-651 1412634 1413209 1413249 "LIECAT" 1413389 LIECAT (NIL T) -9 NIL 1413540 NIL) (-650 1412508 1412541 1412629 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-649 1406744 1412198 1412426 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-648 1399186 1406420 1406576 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-647 1395638 1396587 1397522 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-646 1394262 1395170 1395198 "LFCAT" 1395405 LFCAT (NIL) -9 NIL 1395544 NIL) (-645 1392479 1392813 1393163 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-644 1389975 1390647 1391335 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-643 1386983 1387965 1388468 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-642 1386471 1386776 1386868 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-641 1385175 1385500 1385901 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-640 1384432 1384518 1384747 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-639 1379482 1382997 1383535 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-638 1379105 1379155 1379316 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-637 1377953 1378669 1378710 "LALG" 1378772 LALG (NIL T) -9 NIL 1378831 NIL) (-636 1377735 1377812 1377948 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-635 1375641 1377003 1377254 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-634 1375470 1375500 1375541 "KVTFROM" 1375603 KVTFROM (NIL T) -9 NIL NIL NIL) (-633 1374392 1375002 1375187 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-632 1374221 1374251 1374292 "KRCFROM" 1374354 KRCFROM (NIL T) -9 NIL NIL NIL) (-631 1373317 1373514 1373811 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-630 1373146 1373176 1373217 "KONVERT" 1373279 KONVERT (NIL T) -9 NIL NIL NIL) (-629 1372975 1373005 1373046 "KOERCE" 1373108 KOERCE (NIL T) -9 NIL NIL NIL) (-628 1372545 1372638 1372770 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-627 1370576 1371482 1371859 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-626 1363916 1368811 1368865 "KDAGG" 1369242 KDAGG (NIL T T) -9 NIL 1369448 NIL) (-625 1363564 1363706 1363911 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-624 1356507 1363347 1363502 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-623 1356154 1356439 1356502 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-622 1355119 1355623 1355872 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-621 1354240 1354694 1354899 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-620 1353101 1353596 1353896 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-619 1352378 1352782 1352943 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-618 1352085 1352324 1352373 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-617 1346320 1351775 1352003 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-616 1345734 1346070 1346191 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-615 1341880 1343911 1343965 "IXAGG" 1344894 IXAGG (NIL T T) -9 NIL 1345353 NIL) (-614 1341084 1341456 1341875 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-613 1336301 1341020 1341079 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-612 1335259 1335537 1335803 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-611 1333909 1334116 1334411 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-610 1332860 1333082 1333365 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-609 1332535 1332598 1332721 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-608 1331794 1332169 1332343 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-607 1329815 1331059 1331337 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-606 1319361 1325082 1326245 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-605 1318606 1318758 1318994 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-604 1318094 1318399 1318491 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-603 1317378 1317471 1317687 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1316510 1316735 1316975 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-601 1314917 1315298 1315727 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1314702 1314746 1314822 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1313546 1313845 1314142 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1312816 1313170 1313321 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-597 1312015 1312146 1312360 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1310170 1310667 1311211 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1307272 1308514 1309206 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-594 1307097 1307137 1307197 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1303145 1307023 1307092 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1301203 1303083 1303140 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1300571 1300873 1301003 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1300021 1300312 1300444 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-589 1299099 1299725 1299852 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-588 1298509 1299003 1299031 "IOBCON" 1299036 IOBCON (NIL) -9 NIL 1299057 NIL) (-587 1298078 1298142 1298325 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1290110 1292485 1294814 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1287218 1288002 1288867 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1286895 1286992 1287109 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-583 1284387 1286831 1286890 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1282494 1283023 1283591 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1281989 1282104 1282246 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1280368 1280774 1281237 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1278142 1278736 1279348 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1275509 1276119 1276840 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1271645 1272683 1273732 "INTPACK" NIL INTPACK (NIL) -7 NIL NIL NIL) (-576 1271049 1271207 1271415 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1270568 1270654 1270842 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1268773 1269294 1269751 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-573 1261841 1263494 1265224 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1251431 1254844 1258229 "INTFTBL" NIL INTFTBL (NIL) -8 NIL NIL NIL) (-571 1250797 1250959 1251132 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1248664 1249128 1249673 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1246861 1247756 1247784 "INTDOM" 1248085 INTDOM (NIL) -9 NIL 1248292 NIL) (-568 1246410 1246614 1246856 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-567 1242278 1244699 1244753 "INTCAT" 1245552 INTCAT (NIL T) -9 NIL 1245873 NIL) (-566 1241840 1241961 1242089 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-565 1240676 1240848 1241155 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1240249 1240345 1240502 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1233382 1240104 1240244 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1232673 1233235 1233300 "INT8" NIL INT8 (NIL) -8 NIL NIL 1233334) (-561 1231963 1232525 1232590 "INT64" NIL INT64 (NIL) -8 NIL NIL 1232624) (-560 1231253 1231815 1231880 "INT32" NIL INT32 (NIL) -8 NIL NIL 1231914) (-559 1230543 1231105 1231170 "INT16" NIL INT16 (NIL) -8 NIL NIL 1231204) (-558 1227049 1230462 1230538 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-557 1221160 1224597 1224625 "INS" 1225559 INS (NIL) -9 NIL 1226224 NIL) (-556 1219230 1220148 1221087 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-555 1218285 1218508 1218784 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1217499 1217640 1217837 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1216489 1216630 1216867 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1215641 1215805 1216065 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1214921 1215036 1215224 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1213660 1213929 1214253 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1212940 1213081 1213264 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1212603 1212675 1212773 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1209677 1211175 1211690 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-546 1209276 1209383 1209497 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-545 1208431 1209077 1209178 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-544 1207281 1207549 1207870 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1206344 1207211 1207276 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1205969 1206049 1206166 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1204877 1205424 1205630 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-540 1200969 1202025 1202969 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1199823 1200146 1200174 "INBCON" 1200687 INBCON (NIL) -9 NIL 1200953 NIL) (-538 1199277 1199542 1199818 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-537 1198767 1199072 1199163 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-536 1198220 1198532 1198638 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-535 1194301 1198111 1198215 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1193137 1193276 1193592 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1191561 1191828 1192165 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1185491 1191498 1191556 "ILIST" NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1183293 1185373 1185486 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1178171 1183224 1183288 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1177548 1177884 1178000 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-528 1172317 1176983 1177171 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1171375 1172239 1172312 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1170947 1171024 1171078 "IEVALAB" 1171285 IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1170702 1170782 1170942 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-524 1169766 1170622 1170697 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1168899 1169686 1169761 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1168298 1168832 1168894 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1166778 1167305 1167357 "IDPC" 1167869 IDPC (NIL T T) -9 NIL 1168150 NIL) (-520 1166140 1166700 1166773 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1165385 1166062 1166135 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1165075 1165291 1165351 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-517 1162137 1163021 1163916 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1155736 1157024 1158071 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1154994 1155124 1155324 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1154096 1154601 1154748 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-513 1152473 1152804 1153197 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1147783 1152174 1152287 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1145041 1145665 1146360 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1143267 1143747 1144280 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1141017 1143159 1143262 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1136856 1140955 1141012 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1130371 1135729 1136210 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-506 1129939 1130002 1130175 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1129431 1129580 1129608 "HYPCAT" 1129815 HYPCAT (NIL) -9 NIL NIL NIL) (-504 1129087 1129240 1129426 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-503 1128697 1128945 1129028 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1128530 1128579 1128620 "HOMOTOP" 1128625 HOMOTOP (NIL T) -9 NIL 1128658 NIL) (-501 1125074 1126462 1126503 "HOAGG" 1127484 HOAGG (NIL T) -9 NIL 1128213 NIL) (-500 1124066 1124543 1125069 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-499 1117300 1123789 1123939 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-498 1116235 1116493 1116756 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1115197 1116100 1116230 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1113377 1115030 1115118 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1112688 1113043 1113177 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-494 1106175 1112621 1112683 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1099355 1105909 1106061 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1098805 1098963 1099127 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-491 1091981 1098696 1098800 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1091469 1091774 1091866 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-489 1089071 1091253 1091435 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-488 1084423 1088953 1089066 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1077602 1084320 1084418 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1069582 1076967 1077223 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1068613 1069126 1069154 "GROUP" 1069357 GROUP (NIL) -9 NIL 1069491 NIL) (-484 1068156 1068357 1068608 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-483 1066828 1067167 1067554 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1065656 1066016 1066067 "GRMOD" 1066596 GRMOD (NIL T T) -9 NIL 1066764 NIL) (-481 1065475 1065523 1065651 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-480 1061595 1062809 1063809 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1060293 1060626 1060950 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-478 1059846 1059974 1060115 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-477 1058923 1059425 1059476 "GRALG" 1059629 GRALG (NIL T T) -9 NIL 1059722 NIL) (-476 1058658 1058755 1058918 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-475 1055350 1058336 1058514 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1054761 1054824 1055082 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1050632 1051500 1052026 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1049807 1050009 1050247 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1044795 1045722 1046742 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1044543 1044600 1044689 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1044025 1044114 1044279 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1043534 1043575 1043788 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1042332 1042616 1042921 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1035649 1042020 1042182 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1025443 1030439 1031543 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1023570 1024618 1024646 "GCDDOM" 1024901 GCDDOM (NIL) -9 NIL 1025058 NIL) (-463 1023193 1023350 1023565 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-462 1013974 1016448 1018840 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1012100 1012428 1012849 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1011041 1011230 1011497 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1009912 1010119 1010423 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1009372 1009515 1009664 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1007974 1008322 1008636 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1006507 1006829 1007153 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1004109 1004465 1004872 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 997325 998999 1000590 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 994611 995371 995399 "FVFUN" 996555 FVFUN (NIL) -9 NIL 997275 NIL) (-452 993841 994059 994087 "FVC" 994378 FVC (NIL) -9 NIL 994561 NIL) (-451 993490 993714 993782 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-450 993111 993335 993416 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 991971 992595 992798 "FTEM" NIL FTEM (NIL) -8 NIL NIL NIL) (-448 990056 990745 991208 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-447 988638 988947 989342 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 987269 987636 987968 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-445 986568 986692 986880 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 985542 985808 986155 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 983189 983723 984209 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 982770 982830 983000 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 981129 981984 982287 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 980273 980407 980631 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 979444 979605 979832 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 975419 978388 978429 "FSAGG" 978799 FSAGG (NIL T) -9 NIL 979058 NIL) (-437 973765 974528 975324 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-436 971707 972005 972553 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 970748 970931 971233 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 970425 970474 970603 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 950580 960087 960128 "FS" 964012 FS (NIL T) -9 NIL 966301 NIL) (-432 942782 946290 950280 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-431 942316 942443 942595 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 936859 940005 940045 "FRNAALG" 941365 FRNAALG (NIL T) -9 NIL 941963 NIL) (-429 933600 934851 936109 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-428 933281 933330 933457 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 931756 932318 932614 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 931034 931127 931418 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 928848 929618 929936 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 927939 928388 928429 "FRETRCT" 928434 FRETRCT (NIL T) -9 NIL 928610 NIL) (-423 927312 927590 927934 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-422 924133 925596 925655 "FRAMALG" 926537 FRAMALG (NIL T T) -9 NIL 926829 NIL) (-421 922729 923280 923910 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-420 922422 922485 922592 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 916099 922226 922417 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 915792 915855 915962 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 908143 912667 913998 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-416 901979 905435 905463 "FPS" 906582 FPS (NIL) -9 NIL 907139 NIL) (-415 901536 901669 901833 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-414 898417 900406 900434 "FPC" 900659 FPC (NIL) -9 NIL 900801 NIL) (-413 898263 898315 898412 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-412 897021 897751 897792 "FPATMAB" 897797 FPATMAB (NIL T) -9 NIL 897949 NIL) (-411 895448 896047 896394 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 891347 891947 892629 "FORTRAN" NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 888921 889585 889613 "FORTFN" 890673 FORTFN (NIL) -9 NIL 891297 NIL) (-408 888673 888735 888763 "FORTCAT" 888822 FORTCAT (NIL) -9 NIL 888884 NIL) (-407 886878 887408 887947 "FORT" NIL FORT (NIL) -7 NIL NIL NIL) (-406 886453 886511 886684 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 885686 885886 886079 "FOP" NIL FOP (NIL) -7 NIL NIL NIL) (-404 884217 885084 885258 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 882831 883342 883370 "FNCAT" 883830 FNCAT (NIL) -9 NIL 884090 NIL) (-402 882282 882798 882826 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-401 880608 881781 881809 "FMTC" 881814 FMTC (NIL) -9 NIL 881850 NIL) (-400 879187 880557 880603 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 875776 877142 877183 "FMONCAT" 878400 FMONCAT (NIL T) -9 NIL 879005 NIL) (-398 873098 873846 873874 "FMFUN" 875018 FMFUN (NIL) -9 NIL 875726 NIL) (-397 869971 871023 871077 "FMCAT" 872272 FMCAT (NIL T T) -9 NIL 872767 NIL) (-396 869204 869421 869449 "FMC" 869739 FMC (NIL) -9 NIL 869921 NIL) (-395 867929 869025 869125 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 867051 867775 867924 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-393 865238 865690 866184 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 863173 863709 864287 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 856608 861510 862124 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-390 855126 856200 856241 "FLINEXP" 856246 FLINEXP (NIL T) -9 NIL 856339 NIL) (-389 854534 854793 855121 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-388 853740 853902 854126 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 850658 851710 851762 "FLALG" 852989 FLALG (NIL T T) -9 NIL 853456 NIL) (-386 849829 849990 850217 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 843195 847235 847276 "FLAGG" 848538 FLAGG (NIL T) -9 NIL 849190 NIL) (-384 842289 842700 843190 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-383 838927 840134 840193 "FINRALG" 841321 FINRALG (NIL T T) -9 NIL 841829 NIL) (-382 838318 838583 838922 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-381 837624 837923 837951 "FINITE" 838147 FINITE (NIL) -9 NIL 838254 NIL) (-380 829575 832154 832194 "FINAALG" 835861 FINAALG (NIL T) -9 NIL 837314 NIL) (-379 825800 827059 828196 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-378 824360 824782 824836 "FILECAT" 825520 FILECAT (NIL T T) -9 NIL 825736 NIL) (-377 823708 824185 824288 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-376 821026 822851 822879 "FIELD" 822919 FIELD (NIL) -9 NIL 822999 NIL) (-375 820047 820510 821021 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-374 818046 818996 819343 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 817286 817468 817688 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 812591 817224 817281 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 812253 812320 812455 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 811793 811835 812044 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 808467 809346 810125 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 803786 808399 808462 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 798500 803275 803465 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 793016 797781 798039 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 787258 792467 792678 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 786281 786491 786806 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 781789 784441 784469 "FFIELDC" 785089 FFIELDC (NIL) -9 NIL 785465 NIL) (-362 780864 781303 781784 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-361 780479 780537 780661 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 778623 779146 779663 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-359 773752 778422 778523 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 768885 773541 773648 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 763586 768676 768784 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 763040 763089 763324 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 741502 752543 752629 "FFCAT" 757794 FFCAT (NIL T T T) -9 NIL 759245 NIL) (-354 737728 738960 740272 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-353 732606 737659 737723 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 722496 726758 727946 "FEXPR" NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 721424 721893 721934 "FEVALAB" 722018 FEVALAB (NIL T) -9 NIL 722279 NIL) (-350 720829 721081 721419 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-349 717691 718576 718691 "FDIVCAT" 720259 FDIVCAT (NIL T T T T) -9 NIL 720696 NIL) (-348 717483 717516 717686 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-347 716790 716883 717160 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 715303 716274 716477 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 714393 714780 714982 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-344 713318 713607 713896 "FCPAK1" NIL FCPAK1 (NIL) -7 NIL NIL NIL) (-343 712430 712927 713068 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 699262 703098 706636 "FC" NIL FC (NIL) -8 NIL NIL NIL) (-341 690886 695496 695536 "FAXF" 697338 FAXF (NIL T) -9 NIL 698030 NIL) (-340 688796 689603 690421 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-339 683622 688315 688491 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 678107 680482 680535 "FAMR" 681558 FAMR (NIL T T) -9 NIL 682018 NIL) (-337 677303 677669 678102 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-336 676352 677245 677298 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 673982 674834 674887 "FAMONC" 675828 FAMONC (NIL T T) -9 NIL 676214 NIL) (-334 672562 673840 673977 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 670634 670995 671398 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 669911 670108 670330 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 661813 669358 669557 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 659832 660402 660988 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 656704 657356 658086 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 651840 652547 653353 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 651529 651592 651701 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 636330 650574 651003 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 626889 635645 635936 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 626380 626684 626775 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-323 626153 626346 626375 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-322 625842 625910 626023 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 625359 625501 625542 "EVALAB" 625712 EVALAB (NIL T) -9 NIL 625816 NIL) (-320 624987 625133 625354 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-319 622102 623643 623671 "EUCDOM" 624226 EUCDOM (NIL) -9 NIL 624576 NIL) (-318 621027 621521 622097 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-317 620716 620779 620888 "ESTOOLS2" NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 620509 620557 620637 "ESTOOLS1" NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 610556 613537 616287 "ESTOOLS" NIL ESTOOLS (NIL) -7 NIL NIL NIL) (-314 610333 610371 610453 "ESCONT1" NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 607401 608228 609008 "ESCONT" NIL ESCONT (NIL) -7 NIL NIL NIL) (-312 607126 607182 607282 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 606814 606878 606987 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 600513 602443 602471 "ES" 605239 ES (NIL) -9 NIL 606649 NIL) (-309 596979 598534 600349 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-308 596327 596480 596656 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-307 589509 596231 596322 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 589198 589261 589370 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 582897 585940 587377 "EQ" NIL -3955 (NIL T) -8 NIL NIL NIL) (-304 579200 580296 581389 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-303 578026 578377 578683 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-302 576986 577660 577688 "ENTIRER" 577693 ENTIRER (NIL) -9 NIL 577739 NIL) (-301 573675 575416 575765 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 572779 572990 573044 "ELTAGG" 573424 ELTAGG (NIL T T) -9 NIL 573635 NIL) (-299 572559 572633 572774 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-298 572317 572352 572406 "ELTAB" 572490 ELTAB (NIL T T) -9 NIL 572542 NIL) (-297 571568 571738 571937 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 571292 571366 571394 "ELEMFUN" 571499 ELEMFUN (NIL) -9 NIL NIL NIL) (-295 571192 571219 571287 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-294 565714 569231 569272 "ELAGG" 570212 ELAGG (NIL T) -9 NIL 570675 NIL) (-293 564504 565046 565709 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-292 563922 564089 564245 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-291 562826 563148 563430 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-290 556190 558188 559017 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-289 550168 552164 552975 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-288 547973 548379 548851 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 538896 540815 542363 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-286 538003 538510 538659 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-285 537133 537970 537998 "E04UCFA" NIL E04UCFA (NIL) -8 NIL NIL NIL) (-284 536263 537100 537128 "E04NAFA" NIL E04NAFA (NIL) -8 NIL NIL NIL) (-283 535393 536230 536258 "E04MBFA" NIL E04MBFA (NIL) -8 NIL NIL NIL) (-282 534523 535360 535388 "E04JAFA" NIL E04JAFA (NIL) -8 NIL NIL NIL) (-281 533655 534490 534518 "E04GCFA" NIL E04GCFA (NIL) -8 NIL NIL NIL) (-280 532787 533622 533650 "E04FDFA" NIL E04FDFA (NIL) -8 NIL NIL NIL) (-279 531917 532754 532782 "E04DGFA" NIL E04DGFA (NIL) -8 NIL NIL NIL) (-278 527338 528786 530150 "E04AGNT" NIL E04AGNT (NIL) -7 NIL NIL NIL) (-277 525958 526639 526679 "DVARCAT" 527020 DVARCAT (NIL T) -9 NIL 527183 NIL) (-276 525373 525639 525953 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-275 517480 525239 525368 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 515830 516621 516662 "DSEXT" 517025 DSEXT (NIL T) -9 NIL 517319 NIL) (-273 514635 515159 515825 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-272 514359 514424 514522 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 510495 511717 512854 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-270 506126 507488 508556 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-269 504801 505162 505548 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-268 504487 504546 504664 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 503459 503758 504049 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-266 503042 503117 503268 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 495455 497567 499682 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 490972 491991 493070 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 487554 489637 489678 "DQAGG" 490307 DQAGG (NIL T) -9 NIL 490581 NIL) (-262 474080 481677 481760 "DPOLCAT" 483612 DPOLCAT (NIL T T T T) -9 NIL 484157 NIL) (-261 470485 472134 474075 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-260 463460 470382 470480 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 456344 463288 463455 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 455935 456197 456286 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 455344 455797 455877 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-256 454627 454955 455106 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-255 447807 454361 454513 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 445583 446873 446914 "DMEXT" 446919 DMEXT (NIL T) -9 NIL 447095 NIL) (-253 445239 445301 445445 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-252 438522 444724 444914 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 435172 437347 437388 "DLAGG" 437938 DLAGG (NIL T) -9 NIL 438168 NIL) (-250 433597 434411 434439 "DIVRING" 434531 DIVRING (NIL) -9 NIL 434614 NIL) (-249 433048 433292 433592 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-248 431476 431893 432299 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-247 430513 430734 430999 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 424020 430445 430508 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 412293 418720 418773 "DIRPCAT" 419031 DIRPCAT (NIL NIL T) -9 NIL 419906 NIL) (-244 410307 411075 411956 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-243 409754 409920 410106 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-242 406279 408638 408679 "DIOPS" 409113 DIOPS (NIL T) -9 NIL 409342 NIL) (-241 405939 406083 406274 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-240 404846 405618 405646 "DIFRING" 405651 DIFRING (NIL) -9 NIL 405673 NIL) (-239 404494 404592 404620 "DIFFSPC" 404739 DIFFSPC (NIL) -9 NIL 404814 NIL) (-238 404235 404337 404489 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-237 403171 403769 403810 "DIFFMOD" 403815 DIFFMOD (NIL T) -9 NIL 403913 NIL) (-236 402867 402924 402965 "DIFFDOM" 403086 DIFFDOM (NIL T) -9 NIL 403154 NIL) (-235 402748 402778 402862 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-234 400487 401951 401992 "DIFEXT" 401997 DIFEXT (NIL T) -9 NIL 402150 NIL) (-233 397632 399991 400032 "DIAGG" 400037 DIAGG (NIL T) -9 NIL 400057 NIL) (-232 397182 397375 397627 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-231 392376 396372 396649 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 388834 389887 390897 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-229 383429 387986 388314 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-228 381974 382272 382654 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 379134 380329 380729 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 376840 378965 379054 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 376220 376365 376548 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 373533 374257 375058 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 371635 372094 372658 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 371014 371350 371465 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-221 364248 370737 370887 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-220 362162 362674 363180 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 361801 361850 362001 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 361053 361622 361713 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 359071 359517 359878 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 358360 358652 358798 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 357426 358327 358355 "D03FAFA" NIL D03FAFA (NIL) -8 NIL NIL NIL) (-214 356493 357393 357421 "D03EEFA" NIL D03EEFA (NIL) -8 NIL NIL NIL) (-213 354888 355378 355867 "D03AGNT" NIL D03AGNT (NIL) -7 NIL NIL NIL) (-212 354137 354855 354883 "D02EJFA" NIL D02EJFA (NIL) -8 NIL NIL NIL) (-211 353386 354104 354132 "D02CJFA" NIL D02CJFA (NIL) -8 NIL NIL NIL) (-210 352635 353353 353381 "D02BHFA" NIL D02BHFA (NIL) -8 NIL NIL NIL) (-209 351884 352602 352630 "D02BBFA" NIL D02BBFA (NIL) -8 NIL NIL NIL) (-208 346601 348256 349862 "D02AGNT" NIL D02AGNT (NIL) -7 NIL NIL NIL) (-207 344881 345420 345964 "D01WGTS" NIL D01WGTS (NIL) -7 NIL NIL NIL) (-206 343896 344848 344876 "D01TRNS" NIL D01TRNS (NIL) -8 NIL NIL NIL) (-205 342912 343863 343891 "D01GBFA" NIL D01GBFA (NIL) -8 NIL NIL NIL) (-204 341928 342879 342907 "D01FCFA" NIL D01FCFA (NIL) -8 NIL NIL NIL) (-203 340944 341895 341923 "D01ASFA" NIL D01ASFA (NIL) -8 NIL NIL NIL) (-202 339960 340911 340939 "D01AQFA" NIL D01AQFA (NIL) -8 NIL NIL NIL) (-201 338976 339927 339955 "D01APFA" NIL D01APFA (NIL) -8 NIL NIL NIL) (-200 337992 338943 338971 "D01ANFA" NIL D01ANFA (NIL) -8 NIL NIL NIL) (-199 337008 337959 337987 "D01AMFA" NIL D01AMFA (NIL) -8 NIL NIL NIL) (-198 336024 336975 337003 "D01ALFA" NIL D01ALFA (NIL) -8 NIL NIL NIL) (-197 335040 335991 336019 "D01AKFA" NIL D01AKFA (NIL) -8 NIL NIL NIL) (-196 334056 335007 335035 "D01AJFA" NIL D01AJFA (NIL) -8 NIL NIL NIL) (-195 328820 330445 332006 "D01AGNT" NIL D01AGNT (NIL) -7 NIL NIL NIL) (-194 328271 328417 328569 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 325633 326426 327153 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-192 325072 325218 325389 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 323131 323443 323812 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 322685 322943 323044 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-189 321890 322278 322306 "CTORCAT" 322488 CTORCAT (NIL) -9 NIL 322601 NIL) (-188 321591 321726 321885 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-187 321081 321341 321449 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 320492 320928 321001 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-185 319951 320068 320221 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 316336 317095 317853 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 315823 316129 316221 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-182 315042 315251 315479 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 314546 314651 314855 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 314299 314333 314439 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 311222 311984 312703 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 310732 310877 311019 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-177 306680 309195 309687 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 306554 306581 306609 "CONDUIT" 306646 CONDUIT (NIL) -9 NIL NIL NIL) (-175 305508 306182 306210 "COMRING" 306215 COMRING (NIL) -9 NIL 306267 NIL) (-174 304654 305030 305214 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-173 304350 304391 304519 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 304043 304106 304213 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 292851 303993 304038 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292312 292451 292611 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-169 292065 292106 292204 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 273356 285657 285697 "COMPCAT" 286701 COMPCAT (NIL T) -9 NIL 288049 NIL) (-167 265896 269410 273000 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-166 265653 265687 265790 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 265480 265520 265579 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-164 265057 265339 265414 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-163 264631 264875 264962 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-162 263826 264074 264102 "COMBOPC" 264440 COMBOPC (NIL) -9 NIL 264615 NIL) (-161 262890 263142 263384 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 259811 260499 261126 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 258688 259142 259377 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-158 258176 258481 258573 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-157 257863 257916 258041 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 257330 257642 257741 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-155 253850 254920 256000 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-154 252198 253124 253364 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 248291 250316 250357 "CLAGG" 251286 CLAGG (NIL T) -9 NIL 251822 NIL) (-152 247168 247703 248286 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-151 246797 246888 247028 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 244734 245241 245789 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 243774 244448 244476 "CHARZ" 244481 CHARZ (NIL) -9 NIL 244496 NIL) (-148 243568 243614 243692 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 242486 243192 243220 "CHARNZ" 243281 CHARNZ (NIL) -9 NIL 243330 NIL) (-146 239939 241049 241578 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-145 239647 239726 239754 "CFCAT" 239865 CFCAT (NIL) -9 NIL NIL NIL) (-144 238986 239115 239298 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 234957 238399 238679 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-142 234335 234522 234699 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-141 233858 234282 234330 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-140 233327 233639 233737 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-139 232815 233120 233212 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-138 232064 232224 232445 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 227649 228909 229653 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 226023 227036 227293 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-135 225600 225882 225957 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-134 225042 225298 225326 "CACHSET" 225458 CACHSET (NIL) -9 NIL 225536 NIL) (-133 224432 224820 224848 "CABMON" 224898 CABMON (NIL) -9 NIL 224954 NIL) (-132 223959 224226 224336 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-131 219152 223616 223788 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-130 218114 218826 218961 "BYTE" NIL BYTE (NIL) -8 NIL NIL 219124) (-129 215566 217880 217987 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 212974 215304 215426 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 210194 212416 212457 "BTCAT" 212525 BTCAT (NIL T) -9 NIL 212602 NIL) (-126 209942 210040 210189 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-125 204915 209158 209186 "BTAGG" 209300 BTAGG (NIL) -9 NIL 209410 NIL) (-124 204543 204704 204910 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-123 201578 204004 204219 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 200830 200986 201170 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 197337 199528 199569 "BRAGG" 200218 BRAGG (NIL T) -9 NIL 200476 NIL) (-120 196279 196779 197332 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-119 188736 195776 195961 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 186782 188686 188731 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 186510 186546 186660 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 184703 185149 185612 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 180611 182041 182939 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-114 179475 180373 180497 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-113 179068 179225 179253 "BOOLE" 179364 BOOLE (NIL) -9 NIL 179445 NIL) (-112 178970 178997 179063 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-111 178139 178639 178693 "BMODULE" 178698 BMODULE (NIL T T) -9 NIL 178763 NIL) (-110 173627 177990 178063 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-109 173144 173287 173427 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-108 166380 172868 173017 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-107 164098 165607 165648 "BGAGG" 165908 BGAGG (NIL T) -9 NIL 166045 NIL) (-106 163964 164002 164093 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-105 163172 163533 163738 "BFUNCT" NIL BFUNCT (NIL) -8 NIL NIL NIL) (-104 162012 162213 162501 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158623 161161 161491 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158206 158302 158330 "BASTYPE" 158507 BASTYPE (NIL) -9 NIL 158606 NIL) (-101 157967 158066 158201 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-100 157478 157566 157718 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156369 157048 157234 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156095 156100 156126 "ATTREG" 156131 ATTREG (NIL) -9 NIL NIL NIL) (-97 154591 155126 155478 "ATTRBUT" NIL ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154193 154467 154533 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-95 153693 153842 153868 "ATRIG" 154069 ATRIG (NIL) -9 NIL NIL NIL) (-94 153548 153601 153688 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-93 153126 153360 153386 "ASTCAT" 153391 ASTCAT (NIL) -9 NIL 153421 NIL) (-92 152925 153002 153121 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-91 151070 152758 152846 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149877 150190 150555 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148916 149629 149753 "ASP9" NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 147809 148632 148774 "ASP80" NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 147545 147765 147804 "ASP8" NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 146500 147309 147427 "ASP78" NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 145469 146266 146383 "ASP77" NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 144395 145207 145338 "ASP74" NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 143310 144131 144263 "ASP73" NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 142223 143046 143178 "ASP7" NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 141310 142118 142218 "ASP6" NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 140258 141074 141192 "ASP55" NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 139209 140020 140139 "ASP50" NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138290 138989 139099 "ASP49" NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 137099 137940 138108 "ASP42" NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 135903 136745 136915 "ASP41" NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134984 135683 135793 "ASP4" NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 133935 134748 134866 "ASP35" NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133672 133891 133930 "ASP34" NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133436 133521 133597 "ASP33" NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132345 133172 133304 "ASP31" NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 132082 132301 132340 "ASP30" NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131844 131931 132007 "ASP29" NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131581 131800 131839 "ASP28" NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131318 131537 131576 "ASP27" NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130396 131096 131207 "ASP24" NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129468 130279 130391 "ASP20" NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128413 129230 129349 "ASP19" NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 128177 128262 128338 "ASP12" NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 127056 127889 128033 "ASP10" NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 126137 126836 126946 "ASP1" NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 123923 126041 126132 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 123114 123305 123526 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 118671 122845 122959 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 112827 114873 114948 "ARR2CAT" 117578 ARR2CAT (NIL T T T) -9 NIL 118336 NIL) (-56 111190 111967 112822 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 110548 110924 111049 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 109470 109640 109939 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 109169 109223 109342 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 108549 108696 108853 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 107951 108244 108364 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 105560 106664 106991 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 105082 105345 105441 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 98718 104057 104511 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 94294 95903 95954 "AMR" 96702 AMR (NIL T T) -9 NIL 97302 NIL) (-46 93645 93926 94289 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77150 93579 93640 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73566 76826 76995 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70576 71236 71843 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69955 70068 70252 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 66354 66985 67579 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55838 66047 66197 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55152 55307 55486 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53941 54679 54717 "ALGEBRA" 54722 ALGEBRA (NIL T) -9 NIL 54763 NIL) (-37 53727 53804 53936 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34130 51007 51059 "ALAGG" 51195 ALAGG (NIL T T) -9 NIL 51356 NIL) (-35 33630 33779 33805 "AHYP" 34006 AHYP (NIL) -9 NIL NIL NIL) (-34 32932 33115 33141 "AGG" 33424 AGG (NIL) -9 NIL 33613 NIL) (-33 32725 32812 32927 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30843 31312 31717 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30335 30640 30730 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29705 30000 30156 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17213 26525 26563 "ACFS" 27170 ACFS (NIL T) -9 NIL 27409 NIL) (-28 15836 16446 17208 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11459 13782 13808 "ACF" 14687 ACF (NIL) -9 NIL 15100 NIL) (-26 10555 10961 11454 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10065 10308 10334 "ABELSG" 10426 ABELSG (NIL) -9 NIL 10491 NIL) (-24 9963 9994 10060 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9232 9579 9605 "ABELMON" 9775 ABELMON (NIL) -9 NIL 9887 NIL) (-22 8981 9089 9227 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8231 8687 8713 "ABELGRP" 8785 ABELGRP (NIL) -9 NIL 8860 NIL) (-20 7845 8010 8226 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3064 7104 7143 "A1AGG" 7148 A1AGG (NIL T) -9 NIL 7188 NIL) (-18 30 1497 3059 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 3a983c3a..a05f0234 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,407 +1,407 @@ -(719468 . 3524522244) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1288 *4)) (-4 *4 (-13 (-1070) (-658 (-558)))) - (-5 *2 (-1288 (-419 (-558)))) (-5 *1 (-1317 *4))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-1288 *4)) (-4 *4 (-13 (-1070) (-658 (-558)))) - (-5 *2 (-1288 (-558))) (-5 *1 (-1317 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1288 *4)) (-4 *4 (-13 (-1070) (-658 (-558)))) (-5 *2 (-114)) - (-5 *1 (-1317 *4))))) -(((*1 *2 *3) - (-12 (-4 *5 (-13 (-631 *2) (-175))) (-5 *2 (-905 *4)) (-5 *1 (-173 *4 *5 *3)) - (-4 *4 (-1122)) (-4 *3 (-168 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-661 (-1110 (-855 (-391))))) - (-5 *2 (-661 (-1110 (-855 (-229))))) (-5 *1 (-315)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1288 *3)) (-4 *3 (-175)) (-4 *1 (-422 *3 *4)) - (-4 *4 (-1264 *3)))) - 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(-4 *7 (-1122))))) + (|partial| -12 (-5 *4 (-627 *3)) (-5 *5 (-419 (-1191 *3))) + (-4 *3 (-13 (-433 *6) (-27) (-1223))) + (-4 *6 (-13 (-464) (-1058 (-558)) (-149) (-657 (-558)))) + (-5 *2 (-2 (|:| -2350 *3) (|:| |coeff| *3))) (-5 *1 (-573 *6 *3 *7)) + (-4 *7 (-1121))))) (((*1 *2 *3 *4 *4 *3 *5) - (-12 (-5 *4 (-628 *3)) (-5 *5 (-1192 *3)) - (-4 *3 (-13 (-433 *6) (-27) (-1224))) - (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3)) - (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1122)))) + (-12 (-5 *4 (-627 *3)) (-5 *5 (-1191 *3)) + (-4 *3 (-13 (-433 *6) (-27) (-1223))) + (-4 *6 (-13 (-464) (-1058 (-558)) (-149) (-657 (-558)))) (-5 *2 (-595 *3)) + (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1121)))) ((*1 *2 *3 *4 *4 *4 *3 *5) - (-12 (-5 *4 (-628 *3)) (-5 *5 (-419 (-1192 *3))) - (-4 *3 (-13 (-433 *6) (-27) (-1224))) - (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3)) - (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1122))))) + (-12 (-5 *4 (-627 *3)) (-5 *5 (-419 (-1191 *3))) + (-4 *3 (-13 (-433 *6) (-27) (-1223))) + (-4 *6 (-13 (-464) (-1058 (-558)) (-149) (-657 (-558)))) (-5 *2 (-595 *3)) + (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1121))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) - (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-229))) + (|:| -1637 (-1109 (-854 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -12217,9 +12217,9 @@ (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1176 (-229))) + (-3 (|:| |str| (-1175 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1638 + (|:| -1637 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12229,8 +12229,8 @@ (((*1 *2 *3) (|partial| -12 (-5 *3 - (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) - (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-229))) + (|:| -1637 (-1109 (-854 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -12243,9 +12243,9 @@ (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1176 (-229))) + (-3 (|:| |str| (-1175 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1638 + (|:| -1637 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12255,13 +12255,13 @@ (((*1 *1 *2) (-12 (-5 *2 - (-661 + (-660 (-2 - (|:| -4290 - (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) - (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) + (|:| -4289 + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-229))) + (|:| -1637 (-1109 (-854 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (|:| -2286 + (|:| -2285 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -12274,10 +12274,10 @@ (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1176 (-229))) + (-3 (|:| |str| (-1175 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1638 + (|:| -1637 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -12285,68 +12285,68 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-572))))) -(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-572))))) +(((*1 *2) (-12 (-5 *2 (-1293)) (-5 *1 (-572))))) (((*1 *1) (-5 *1 (-572)))) (((*1 *2 *2) (|partial| -12 (-5 *1 (-571 *2)) (-4 *2 (-557))))) (((*1 *2 *3) (-12 (-5 *2 (-417 *3)) (-5 *1 (-571 *3)) (-4 *3 (-557))))) (((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1198)) (-5 *6 (-661 (-628 *3))) (-5 *5 (-628 *3)) - (-4 *3 (-13 (-27) (-1224) (-433 *7))) - (-4 *7 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558)))) - (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-570 *7 *3))))) + (|partial| -12 (-5 *4 (-1197)) (-5 *6 (-660 (-627 *3))) (-5 *5 (-627 *3)) + (-4 *3 (-13 (-27) (-1223) (-433 *7))) + (-4 *7 (-13 (-464) (-149) (-1058 (-558)) (-657 (-558)))) + (-5 *2 (-2 (|:| -2350 *3) (|:| |coeff| *3))) (-5 *1 (-570 *7 *3))))) (((*1 *2 *3 *4) - 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(|partial| -12 (-5 *4 (-1198)) - (-4 *5 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558)))) - (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-570 *5 *3)) - (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) + (|partial| -12 (-5 *4 (-1197)) + (-4 *5 (-13 (-464) (-149) (-1058 (-558)) (-657 (-558)))) + (-5 *2 (-2 (|:| -2350 *3) (|:| |coeff| *3))) (-5 *1 (-570 *5 *3)) + (-4 *3 (-13 (-27) (-1223) (-433 *5)))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1980 *1) (|:| -4412 *1) (|:| |associate| *1))) + (-12 (-5 *2 (-2 (|:| -1979 *1) (|:| -4411 *1) (|:| |associate| *1))) (-4 *1 (-569))))) (((*1 *1 *1) (-4 *1 (-569)))) (((*1 *2 *1 *1) (-12 (-4 *1 (-569)) (-5 *2 (-114))))) (((*1 *2 *1) (-12 (-4 *1 (-569)) (-5 *2 (-114))))) (((*1 *1 *2) - (-12 (-5 *2 (-419 (-558))) (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1224))))) - ((*1 *1 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224))))) - ((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) -(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) + (-12 (-5 *2 (-419 (-558))) (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1223))))) + ((*1 *1 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1223))))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1223)))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1223)))))) +(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1223)))))) (((*1 *2 *1 *3) - 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(-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1264 *6)) (-4 *6 (-13 (-27) (-433 *5))) - (-4 *5 (-13 (-569) (-1059 (-558)))) (-4 *8 (-1264 (-419 *7))) + (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1263 *6)) (-4 *6 (-13 (-27) (-433 *5))) + (-4 *5 (-13 (-569) (-1058 (-558)))) (-4 *8 (-1263 (-419 *7))) (-5 *2 (-595 *3)) (-5 *1 (-565 *5 *6 *7 *8 *3)) (-4 *3 (-355 *6 *7 *8))))) (((*1 *2 *3 *4 *4 *5) - (-12 (-5 *4 (-628 *3)) (-5 *5 (-1 (-1192 *3) (-1192 *3))) + (-12 (-5 *4 (-627 *3)) (-5 *5 (-1 (-1191 *3) (-1191 *3))) (-4 *3 (-13 (-27) (-433 *6))) (-4 *6 (-569)) (-5 *2 (-595 *3)) (-5 *1 (-564 *6 *3))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-557)) (-5 *2 (-114))))) @@ -12361,426 +12361,426 @@ (((*1 *1 *1 *1 *1) (-4 *1 (-557)))) (((*1 *1 *1 *1) (-4 *1 (-557)))) (((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *4 (-1 (-3 (-558) #1="failed") *5)) (-4 *5 (-1070)) - (-5 *2 (-558)) (-5 *1 (-555 *5 *3)) (-4 *3 (-1264 *5)))) + (|partial| -12 (-5 *4 (-1 (-3 (-558) #1="failed") *5)) (-4 *5 (-1069)) + (-5 *2 (-558)) (-5 *1 (-555 *5 *3)) (-4 *3 (-1263 *5)))) ((*1 *2 *3 *4 *2 *5) - 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\ No newline at end of file |