diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-08-10 02:33:46 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-08-10 02:33:46 +0000 |
| commit | 0a0661e0c50e9c3e160d54b8e0a5b891d419e2bc (patch) | |
| tree | 42ef806af61677a355623104e7ef3d35ecbbaedb | |
| parent | f1a4ca4eb786bfb440fd537d06a25264b0596369 (diff) | |
| download | open-axiom-0a0661e0c50e9c3e160d54b8e0a5b891d419e2bc.tar.gz | |
* interp/setvart.boot: Remoe OpenMath description.
* interp/setvars.boot (setOutputOpenMath): Remove.
(describeOutputOpenMath): Likewise.
* algebra/Makefile.in (axiom_algebra_layer_14): Don't include OMSERVER.
* algebra/float.spad.pamphlet (Float): Remove OpenMath exports.
* algebra/fraction.spad.pamphlet (Fraction): Likewise.
* algebra/gaussian.spad.pamphlet (Complex): Likewise.
* algebra/integer.spad.pamphlet (Integer): Likewise.
* algebra/list.spad.pamphlet (List): Likewise.
* algebra/sf.spad.pamphlet (DoubleFloat): Likewise.
* algebra/si.spad.pamphlet (SingleInteger): Likewise.
* algebra/string.spad.pamphlet (String): Likewise.
* algebra/symbol.spad.pamphlet (Symbol): Likewise.
| -rw-r--r-- | src/ChangeLog | 16 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 2 | ||||
| -rw-r--r-- | src/algebra/float.spad.pamphlet | 46 | ||||
| -rw-r--r-- | src/algebra/fraction.spad.pamphlet | 50 | ||||
| -rw-r--r-- | src/algebra/gaussian.spad.pamphlet | 47 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 45 | ||||
| -rw-r--r-- | src/algebra/list.spad.pamphlet | 50 | ||||
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 38 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 47 | ||||
| -rw-r--r-- | src/algebra/string.spad.pamphlet | 38 | ||||
| -rw-r--r-- | src/algebra/symbol.spad.pamphlet | 43 | ||||
| -rw-r--r-- | src/interp/setvars.boot | 109 | ||||
| -rw-r--r-- | src/interp/setvart.boot | 47 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2346 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 7469 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1978 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10386 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32298 |
18 files changed, 26186 insertions, 28869 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 2512483d..d1101fc5 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,19 @@ +2011-08-09 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * interp/setvart.boot: Remoe OpenMath description. + * interp/setvars.boot (setOutputOpenMath): Remove. + (describeOutputOpenMath): Likewise. + * algebra/Makefile.in (axiom_algebra_layer_14): Don't include OMSERVER. + * algebra/float.spad.pamphlet (Float): Remove OpenMath exports. + * algebra/fraction.spad.pamphlet (Fraction): Likewise. + * algebra/gaussian.spad.pamphlet (Complex): Likewise. + * algebra/integer.spad.pamphlet (Integer): Likewise. + * algebra/list.spad.pamphlet (List): Likewise. + * algebra/sf.spad.pamphlet (DoubleFloat): Likewise. + * algebra/si.spad.pamphlet (SingleInteger): Likewise. + * algebra/string.spad.pamphlet (String): Likewise. + * algebra/symbol.spad.pamphlet (Symbol): Likewise. + 2011-08-08 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/define.boot (NRTgetLookupFunction): Take an environment diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index f116a4d8..0f52ada6 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -1225,7 +1225,7 @@ axiom_algebra_layer_14 = \ MPC2 MPC3 MPOLY MPRFF \ MRATFAC MULTSQFR NORMRETR NPCOEF \ NSUP NTPOLFN ODP ODEPRIM \ - ODEPRRIC OMPKG OMSERVER PADEPAC \ + ODEPRRIC OMPKG PADEPAC \ PADICRAT PADICRC PCOMP PDECOMP \ PF PFBR PFBRU PFOTOOLS \ PFRPAC PGCD PINTERPA PLEQN \ diff --git a/src/algebra/float.spad.pamphlet b/src/algebra/float.spad.pamphlet index 917d4490..ffafb040 100644 --- a/src/algebra/float.spad.pamphlet +++ b/src/algebra/float.spad.pamphlet @@ -119,7 +119,7 @@ N ==> NonNegativeInteger Float(): - Join(FloatingPointSystem, DifferentialRing, ConvertibleTo String, OpenMath,_ + Join(FloatingPointSystem, DifferentialRing, ConvertibleTo String,_ CoercibleTo DoubleFloat, TranscendentalFunctionCategory, _ ConvertibleTo InputForm,ConvertibleFrom SF) with / : (%, I) -> % @@ -210,50 +210,6 @@ Float(): cosSeries: % -> % -- cos(x) by taylor series |x| < 1/2 piRamanujan: () -> % -- pi using Ramanujans series - writeOMFloat(dev: OpenMathDevice, x: %): Void == - OMputApp(dev) - OMputSymbol(dev, "bigfloat1", "bigfloat") - OMputInteger(dev, mantissa x) - OMputInteger(dev, 2) - OMputInteger(dev, exponent x) - OMputEndApp(dev) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMFloat(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMFloat(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMFloat(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMFloat(dev, x) - if wholeObj then - OMputEndObject(dev) - shift2(x,y) == sign(x)*shift(sign(x)*x,y) asin x == diff --git a/src/algebra/fraction.spad.pamphlet b/src/algebra/fraction.spad.pamphlet index 21162627..6fecb082 100644 --- a/src/algebra/fraction.spad.pamphlet +++ b/src/algebra/fraction.spad.pamphlet @@ -311,7 +311,6 @@ QuotientFieldCategoryFunctions2(A, B, R, S): Exports == Impl where ++ If S is also a GcdDomain, then gcd's between numerator and ++ denominator will be cancelled during all operations. Fraction(S: IntegralDomain): QuotientFieldCategory S with - if S has IntegerNumberSystem and S has OpenMath then OpenMath if S has canonical and S has GcdDomain and S has canonicalUnitNormal then canonical ++ \spad{canonical} means that equal elements are in fact identical. @@ -353,55 +352,6 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with negative? x => -floor(-x) 1 + wholePart x - if S has OpenMath then - -- TODO: somwhere this file does something which redefines the division - -- operator. Doh! - - writeOMFrac(dev: OpenMathDevice, x: %): Void == - OMputApp(dev) - OMputSymbol(dev, "nums1", "rational") - OMwrite(dev, x.num, false) - OMwrite(dev, x.den, false) - OMputEndApp(dev) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := _ - OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMFrac(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := _ - OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMFrac(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMFrac(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMFrac(dev, x) - if wholeObj then - OMputEndObject(dev) - if S has GcdDomain then cancelGcd: % -> S normalize: % -> % diff --git a/src/algebra/gaussian.spad.pamphlet b/src/algebra/gaussian.spad.pamphlet index 44e9b918..c87d880a 100644 --- a/src/algebra/gaussian.spad.pamphlet +++ b/src/algebra/gaussian.spad.pamphlet @@ -547,55 +547,10 @@ ComplexPatternMatch(R, S, CS) : C == T where ++ \spadtype {Complex(R)} creates the domain of elements of the form ++ \spad{a + b * i} where \spad{a} and b come from the ring R, ++ and i is a new element such that \spad{i**2 = -1}. -Complex(R:CommutativeRing): ComplexCategory(R) with - if R has OpenMath then OpenMath +Complex(R:CommutativeRing): ComplexCategory(R) == add Rep := Record(real:R, imag:R) - if R has OpenMath then - writeOMComplex(dev: OpenMathDevice, x: %): Void == - OMputApp(dev) - OMputSymbol(dev, "complex1", "complex__cartesian") - OMwrite(dev, real x) - OMwrite(dev, imag x) - OMputEndApp(dev) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMComplex(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMComplex(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMComplex(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMComplex(dev, x) - if wholeObj then - OMputEndObject(dev) - 0 == [0, 0] 1 == [1, 0] zero? x == zero?(x.real) and zero?(x.imag) diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index cc3fbff5..9052e19d 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -70,7 +70,7 @@ IntegerSolveLinearPolynomialEquation(): C ==T ++ Description: \spadtype{Integer} provides the domain of arbitrary precision ++ integers. -Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with +Integer: Join(IntegerNumberSystem, ConvertibleTo String) with canonical ++ mathematical equality is data structure equality. canonicalsClosed @@ -110,49 +110,6 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with x,y: % n: NonNegativeInteger - writeOMInt(dev: OpenMathDevice, x: %): Void == - if negative? x then - OMputApp(dev) - OMputSymbol(dev, "arith1", "unary__minus") - OMputInteger(dev, (-x) pretend Integer) - OMputEndApp(dev) - else - OMputInteger(dev, x pretend Integer) - - OMwrite(x: %): String == - s: String := "" - sp: String := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp, OMencodingXML()) - OMputObject(dev) - writeOMInt(dev, x) - OMputEndObject(dev) - OMclose(dev) - OM_-STRINGPTRTOSTRING(sp)$Lisp - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp: String := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMInt(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - OM_-STRINGPTRTOSTRING(sp)$Lisp - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMInt(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMInt(dev, x) - if wholeObj then - OMputEndObject(dev) - zero? x == x = %icst0 one? x == x = %icst1 0 == %icst0 diff --git a/src/algebra/list.spad.pamphlet b/src/algebra/list.spad.pamphlet index bb770203..1d5a8522 100644 --- a/src/algebra/list.spad.pamphlet +++ b/src/algebra/list.spad.pamphlet @@ -269,7 +269,6 @@ List(S:Type): Exports == Implementation where ++ 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. - if S has OpenMath then OpenMath Implementation ==> IndexedList(S, LISTMININDEX) add @@ -283,55 +282,6 @@ List(S:Type): Exports == Implementation where cons(s, l) == %pair(s,l) append(l:%, t:%) == %lconcat(l,t) - if S has OpenMath then - writeOMList(dev: OpenMathDevice, x: %): Void == - OMputApp(dev) - OMputSymbol(dev, "list1", "list") - -- The following didn't compile because the compiler isn't - -- convinced that `xval' is a S. Duhhh! MCD. - --for xval in x repeat - -- OMwrite(dev, xval, false) - while not null x repeat - OMwrite(dev,first x,false) - x := rest x - OMputEndApp(dev) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMList(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMList(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMList(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMList(dev, x) - if wholeObj then - OMputEndObject(dev) - if S has SetCategory then setUnion(l1:%,l2:%) == removeDuplicates concat(l1,l2) diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index a6ed7e59..e15fdddd 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -250,7 +250,7 @@ FloatingPointSystem(): Category == RealNumberSystem() with ++ \spadtype{Float} is that it is much more expensive than small floats when the latter can be used. -- I've put some timing comparisons in the notes for the Float -- domain about the difference in speed between the two domains. -DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, +DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, TranscendentalFunctionCategory, ConvertibleTo InputForm) with / : (%, Integer) -> % ++ x / i computes the division from x by an integer i. @@ -330,42 +330,6 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, manexp: % -> MER - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - OMputFloat(dev, convert x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - OMputFloat(dev, convert x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - OMputFloat(dev, convert x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - OMputFloat(dev, convert x) - if wholeObj then - OMputEndObject(dev) - base() == %fbase() mantissa x == manexp(x).MANTISSA exponent x == manexp(x).EXPONENT diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index f8296439..7b58a44f 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -183,7 +183,7 @@ IntegerNumberSystem(): Category == -- QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD -SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) with +SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic) with canonical ++ \spad{canonical} means that mathematical equality is implied by data structure equality. canonicalsClosed @@ -237,51 +237,6 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w import %bitior: (%,%) -> % from Foreign Builtin import %bitxor: (%,%) -> % from Foreign Builtin - writeOMSingleInt(dev: OpenMathDevice, x: %): Void == - if negative? x then - OMputApp(dev) - OMputSymbol(dev, "arith1", "unary_minus") - OMputInteger(dev, convert(-x)) - OMputEndApp(dev) - else - OMputInteger(dev, convert(x)) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMSingleInt(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMSingleInt(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMSingleInt(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMSingleInt(dev, x) - if wholeObj then - OMputEndObject(dev) - reducedSystem(m: Matrix %) == m pretend Matrix(Integer) coerce(x):OutputForm == rep(x)::OutputForm convert(x:%):Integer == rep x diff --git a/src/algebra/string.spad.pamphlet b/src/algebra/string.spad.pamphlet index 2271f92b..6ad08dc3 100644 --- a/src/algebra/string.spad.pamphlet +++ b/src/algebra/string.spad.pamphlet @@ -493,7 +493,7 @@ the coercion. MINSTRINGINDEX ==> 1 -- as of 3/14/90. String(): Public == Private where - Public == Join(StringAggregate(), OpenMath) with + Public == StringAggregate with string: Integer -> % ++ \spad{string i} returns the decimal representation of ++ \spad{i} in a string @@ -505,42 +505,6 @@ String(): Public == Private where string(n: Integer) == %i2s n string(f: DoubleFloat) == %f2s(f)$Foreign(Builtin) - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - OMputString(dev, x pretend String) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - OMputString(dev, x pretend String) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - OMputString(dev, x pretend String) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - OMputString(dev, x pretend String) - if wholeObj then - OMputEndObject(dev) - @ \section{License} diff --git a/src/algebra/symbol.spad.pamphlet b/src/algebra/symbol.spad.pamphlet index 67539450..7f80ecdb 100644 --- a/src/algebra/symbol.spad.pamphlet +++ b/src/algebra/symbol.spad.pamphlet @@ -22,7 +22,7 @@ Symbol(): Exports == Implementation where L ==> List OutputForm Scripts ==> Record(sub:L,sup:L,presup:L,presub:L,args:L) - Exports ==> Join(OrderedSet, ConvertibleTo InputForm, OpenMath, + Exports ==> Join(OrderedSet, ConvertibleTo InputForm, ConvertibleTo Symbol,CoercibleFrom String, ConvertibleTo Pattern Integer, ConvertibleTo Pattern Float, PatternMatchable Integer, PatternMatchable Float) with @@ -82,47 +82,6 @@ Symbol(): Exports == Implementation where ALPHAS:String:="ABCDEFGHIJKLMNOPQRSTUVWXYZ" alphas:String:="abcdefghijklmnopqrstuvwxyz" - writeOMSym(dev: OpenMathDevice, x: %): Void == - scripted? x => - error "Cannot convert a scripted symbol to OpenMath" - OMputVariable(dev, x pretend Symbol) - - OMwrite(x: %): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - OMputObject(dev) - writeOMSym(dev, x) - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(x: %, wholeObj: Boolean): String == - s: String := "" - sp := OM_-STRINGTOSTRINGPTR(s)$Lisp - dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML()) - if wholeObj then - OMputObject(dev) - writeOMSym(dev, x) - if wholeObj then - OMputEndObject(dev) - OMclose(dev) - s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String - s - - OMwrite(dev: OpenMathDevice, x: %): Void == - OMputObject(dev) - writeOMSym(dev, x) - OMputEndObject(dev) - - OMwrite(dev: OpenMathDevice, x: %, wholeObj: Boolean): Void == - if wholeObj then - OMputObject(dev) - writeOMSym(dev, x) - if wholeObj then - OMputEndObject(dev) - hd:String := "*" lhd := #hd ord0 := ord char("0")$Character diff --git a/src/interp/setvars.boot b/src/interp/setvars.boot index 2cea7a29..ab05dbed 100644 --- a/src/interp/setvars.boot +++ b/src/interp/setvars.boot @@ -1355,115 +1355,6 @@ describeSetOutputMathml() == '"The current setting is: ",'%b,setOutputMathml "%display%",'%d] --- See the subsection output openmath in setvart.boot --- --- ------------------ The openmath Option ------------------------ - --- Description: create output in OpenMath style - --- )set output tex is used to tell AXIOM to turn TeX-style output --- printing on and off, and where to place the output. By default, --- the destination for the output is the screen but printing is --- turned off. - --- Syntax: )set output tex <arg> --- where arg can be one of --- on turn TeX printing on --- off turn TeX printing off (default state) --- console send TeX output to screen (default state) --- fp<.fe> send TeX output to file with file prefix fp --- and file extension .fe. If not given, --- .fe defaults to .som. - --- If you wish to send the output to a file, you must issue --- this command twice: once with on and once with the file name. --- For example, to send TeX output to the file polymer.som, --- issue the two commands - --- )set output tex on --- )set output tex polymer - --- The output is placed in the directory from which you invoked --- AXIOM or the one you set with the )cd system command. --- The current setting is: Off:CONSOLE - - -setOutputOpenMath arg == - arg = "%initialize%" => - $openMathOutputStream := - DEFIOSTREAM('((MODE . OUTPUT) (DEVICE . CONSOLE)),255,0) - $openMathOutputFile := '"CONSOLE" - $openMathFormat := nil - - arg = "%display%" => - if $openMathFormat then label := '"On:" else label := '"Off:" - strconc(label,$openMathOutputFile) - - (null arg) or (arg = "%describe%") or (first arg = '_?) => - describeSetOutputOpenMath() - - -- try to figure out what the argument is - - if arg is [fn] and - fn in '(Y N YE YES NO O ON OF OFF CONSOLE y n ye yes no o on of off console) - then 'ok - else arg := [fn,'som] - - arg is [fn] => - UPCASE(fn) in '(Y N YE O OF) => - sayKeyedMsg("S2IV0002",'(OpenMath openmath)) - UPCASE(fn) in '(NO OFF) => $openMathFormat := nil - UPCASE(fn) in '(YES ON) => $openMathFormat := true - UPCASE(fn) = 'CONSOLE => - SHUT $openMathOutputStream - $openMathOutputStream := - DEFIOSTREAM('((MODE . OUTPUT) (DEVICE . CONSOLE)),255,0) - $openMathOutputFile := '"CONSOLE" - - (arg is [fn,ft]) or (arg is [fn,ft,fm]) => -- aha, a file - if (ptype := pathnameType fn) then - fn := strconc(pathnameDirectory fn,pathnameName fn) - ft := ptype - if null fm then fm := 'A - filename := $FILEP(fn,ft,fm) - null filename => - sayKeyedMsg("S2IV0003",[fn,ft,fm]) - (testStream := MAKE_-OUTSTREAM(filename,255,0)) => - SHUT $openMathOutputStream - $openMathOutputStream := testStream - $openMathOutputFile := object2String filename - sayKeyedMsg("S2IV0004",['"OpenMath",$openMathOutputFile]) - sayKeyedMsg("S2IV0003",[fn,ft,fm]) - - sayKeyedMsg("S2IV0005",nil) - describeSetOutputOpenMath() - - -describeSetOutputOpenMath() == - sayBrightly ['%b,'")set output openmath",'%d,_ - '"is used to tell AXIOM to turn OpenMath output",'%l,_ - '"printing on and off, and where to place the output. By default, the",'%l,_ - '"destination for the output is the screen but printing is turned off.",'%l,_ - '%l,_ - '"Syntax: )set output openmath <arg>",'%l,_ - '" where arg can be one of",'%l,_ - '" on turn OpenMath printing on",'%l,_ - '" off turn OpenMath printing off (default state)",'%l,_ - '" console send OpenMath output to screen (default state)",'%l,_ - '" fp<.fe> send OpenMath output to file with file prefix fp and file",'%l,_ - '" extension .fe. If not given, .fe defaults to .som.",'%l, - '%l,_ - '"If you wish to send the output to a file, you must issue this command",'%l,_ - '"twice: once with",'%b,'"on",'%d,'"and once with the file name. For example, to send",'%l,_ - '"OpenMath output to the file",'%b,'"polymer.som,",'%d,'"issue the two commands",'%l,_ - '%l,_ - '" )set output openmath on",'%l,_ - '" )set output openmath polymer",'%l,_ - '%l,_ - '"The output is placed in the directory from which you invoked AXIOM or",'%l,_ - '"the one you set with the )cd system command.",'%l,_ - '"The current setting is: ",'%b,setOutputOpenMath "%display%",'%d] - -- See the section tex in setvart.boot -- -- ----------------------- The tex Option ------------------------ diff --git a/src/interp/setvart.boot b/src/interp/setvart.boot index c19f8688..ab3fb77c 100644 --- a/src/interp/setvart.boot +++ b/src/interp/setvart.boot @@ -1341,53 +1341,6 @@ $setOptions := '( (10 245) 77) --- ----------------------- The openmath Option ------------------------ --- --- Description: create output in OpenMath style --- --- )set output tex is used to tell AXIOM to turn OpenMath output --- printing on and off, and where to place the output. By default, --- the destination for the output is the screen but printing is --- turned off. --- --- Syntax: )set output tex <arg> --- where arg can be one of --- on turn OpenMath printing on --- off turn OpenMath printing off (default state) --- console send OpenMath output to screen (default state) --- fp<.fe> send OpenMath output to file with file prefix fp --- and file extension .fe. If not given, --- .fe defaults to .sopen. --- --- If you wish to send the output to a file, you must issue --- this command twice: once with on and once with the file name. --- For example, to send OpenMath output to the file polymer.sopen, --- issue the two commands --- --- )set output openmath on --- )set output openmath polymer --- --- The output is placed in the directory from which you invoked --- AXIOM or the one you set with the )cd system command. --- The current setting is: Off:CONSOLE - (openmath - "create output in OpenMath style" - interpreter - FUNCTION - setOutputOpenMath - (("create output in OpenMath format" - LITERALS - $openMathFormat - (off on) - off) - (break $openMathFormat) - ("where TeX output goes (enter {\em console} or a pathname)" - FILENAME - $openMathOutputFile - chkOutputFileName - "console")) - NIL) - -- --------------------- The scripts Option ---------------------- -- -- Description: show subscripts,... linearly diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 8097d65b..f40ffcf2 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2291520 . 3521495070) +(2287954 . 3521929246) (-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."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . 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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4503 . T) (-4501 . T) (-4500 . T) ((-4508 "*") . T) (-4499 . T) (-4504 . T) (-4498 . T)) +((-4499 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4495 . T) (-4500 . T) (-4494 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1801) +(-32 R -3572) ((|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 -1068) (QUOTE (-558))))) +((|HasCategory| |#1| (|%list| (QUOTE -1067) (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 -4506))) +((|HasAttribute| |#1| (QUOTE -4502))) (-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}."))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . 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"))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . 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 -1801 UP UPUP -3264) +(-40 -3572 UP UPUP -3090) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4499 |has| (-419 |#2|) (-376)) (-4504 |has| (-419 |#2|) (-376)) (-4498 |has| (-419 |#2|) (-376)) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4089 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4089 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4089 (-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)))) (-4089 (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-363))))) (-4089 (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4089 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (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|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))))) -(-41 R -1801) +((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4034 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-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)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (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 -927) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) +(-41 R -3572) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-319)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4503 |has| |#1| (-569)) (-4501 . T) (-4500 . T)) +((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . 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."))) -((-4506 . T) (-4507 . T)) -((-4089 (-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|))))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-870))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|))))))) +((-4502 . T) (-4503 . T)) +((-4034 (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869)))) (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (|%list| (QUOTE -1068) (QUOTE (-558))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (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}."))) -((-4503 . T)) +((-4499 . 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 -1801) +(-54 |Base| R -3572) ((|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"))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . 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}"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -1898) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4047) ((|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 -1898) +(-62 -4047) ((|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 -1898) +(-63 -4047) ((|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 -1898) +(-64 -4047) ((|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 -1898) +(-65 -4047) ((|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 -1898) +(-66 -4047) ((|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 -1898) +(-67 -4047) ((|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 -1898) +(-68 -4047) ((|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 -1898) +(-69 -4047) ((|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 -1898) +(-70 -4047) ((|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 -1898) +(-71 -4047) ((|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 -1898) +(-72 -4047) ((|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 -1898) +(-73 -4047) ((|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 -1898) +(-74 -4047) ((|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 -1898) +(-75 -4047) ((|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 -1898) +(-78 -4047) ((|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 -1898) +(-79 -4047) ((|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 -1898) +(-80 -4047) ((|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 -1898) +(-81 -4047) ((|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 -1898) +(-82 -4047) ((|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 -1898) +(-83 -4047) ((|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 -1898) +(-84 -4047) ((|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 -1898) +(-85 -4047) ((|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 -1898) +(-86 -4047) ((|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 -1898) +(-87 -4047) ((|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 -1898) +(-88 -4047) ((|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 -1898) +(-89 -4047) ((|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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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\"."))) -((-4506 . T)) +((-4502 . 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."))) -((-4506 . T) ((-4508 "*") . T) (-4507 . T) (-4503 . T) (-4501 . T) (-4500 . T) (-4499 . T) (-4504 . T) (-4498 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4494 . T) (-4502 . T) (-4505 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4493 . T)) +((-4502 . T) ((-4504 "*") . T) (-4503 . T) (-4499 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4500 . T) (-4494 . T) (-4493 . T) (-4492 . T) (-4491 . T) (-4490 . T) (-4498 . T) (-4501 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4489 . 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}."))) -((-4503 . T)) +((-4499 . 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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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 (-4508 "*")))) +((|HasAttribute| |#1| (QUOTE (-4504 "*")))) (-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"))) -((-4506 . T)) +((-4502 . 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."))) -((-4507 . T)) +((-4503 . 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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-558) (QUOTE (-938))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1050))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870))) (-4089 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870)))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1182))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1207)) (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 (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-938)))) (|HasCategory| (-558) (QUOTE (-147))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (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 (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|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}"))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| (-114) (QUOTE (-1131))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-870))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-114) (QUOTE (-1131))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-114) (QUOTE (-102)))) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-885)))) (|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}"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . 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 -1801 UP) +(-117 -3572 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}."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-938))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1050))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-870))) (-4089 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-870)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1207)) (|%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 (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-118 |#1|) (QUOTE (-937))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1049))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-869))) (-4034 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-869)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1181))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%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 (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-937)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4507))) +((|HasAttribute| |#1| (QUOTE -4503))) (-121 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-125) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL (-126 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . T)) NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1131))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4089 (-12 (|HasCategory| (-130) (QUOTE (-1131))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-130) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1131)))) (|HasCategory| (-130) (QUOTE (-870))) (-4089 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1131))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1131))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4034 (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-130) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-130) (QUOTE (-869))) (-4034 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4508 "*") . T)) +(((-4504 "*") . T)) NIL -(-137 |minix| -4398 R) +(-137 |minix| -3097 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| -4398 S T$) +(-138 |minix| -3097 S T$) ((|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}."))) -((-4506 . T) (-4496 . T) (-4507 . T)) -((-4089 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4502 . T) (-4492 . T) (-4503 . T)) +((-4034 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|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."))) -((-4503 . T)) +((-4499 . 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."))) -((-4503 . T)) +((-4499 . T)) NIL -(-150 -1801 UP UPUP) +(-150 -3572 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 (-1131))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasAttribute| |#1| (QUOTE -4502))) (-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."))) -((-4501 . T) (-4500 . T) (-4503 . T)) +((-4497 . T) (-4496 . T) (-4499 . 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 -1801) +(-160 R -3572) ((|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 (-938))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4502)) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569)))) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4498)) (|HasAttribute| |#2| (QUOTE -4501)) (|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})"))) -((-4499 -4089 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4502 |has| |#1| (-6 -4502)) (-4505 |has| |#1| (-6 -4505)) (-3607 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 -4034 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4501 |has| |#1| (-6 -4501)) (-1498 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}."))) -((-4499 -4089 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4502 |has| |#1| (-6 -4502)) (-4505 |has| |#1| (-6 -4505)) (-3607 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4089 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-938))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-938))))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasAttribute| |#1| (QUOTE -4502)) (|HasAttribute| |#1| (QUOTE -4505)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207))))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4495 -4034 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4501 |has| |#1| (-6 -4501)) (-1498 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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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."))) -(((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}."))) -(((-4508 "*") . T) (-4499 . T) (-4504 . T) (-4498 . T) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") . T) (-4495 . T) (-4500 . T) (-4494 . T) (-4496 . T) (-4497 . T) (-4499 . 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|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -655,7 +655,7 @@ NIL (-181 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-974 |#2|) (|%list| (QUOTE -910) (|devaluate| |#1|)))) +((|HasCategory| (-973 |#2|) (|%list| (QUOTE -909) (|devaluate| |#1|)))) (-182 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -1801) +(-191 R -3572) ((|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 @@ -804,28 +804,28 @@ 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 -1801 UP UPUP R) +(-219 -3572 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 -1801 FP) +(-220 -3572 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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-558) (QUOTE (-938))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1050))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870))) (-4089 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870)))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1182))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1207)) (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 (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-938)))) (|HasCategory| (-558) (QUOTE (-147))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (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 (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|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 -1801) -((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +(-223 R -3572) +((|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 (-224 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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 (-225 R1 R2) @@ -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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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}."))) -((-4503 . T)) +((-4499 . T)) NIL -(-228 R -1801) +(-228 R -3572) ((|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}."))) -((-3595 . T) (-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}"))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4508 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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."))) -((-4507 . T)) +((-4503 . 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 \\%."))) -((-4503 . T)) +((-4499 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -878,7 +878,7 @@ NIL NIL (-237 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL (-238 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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"))) -((-4503 . T)) +((-4499 . 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 -4506))) +((|HasAttribute| |#1| (QUOTE -4502))) (-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}."))) -((-4507 . T)) +((-4503 . 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 -4398 R) +(-244 S -3097 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 (-870))) (|HasAttribute| |#3| (QUOTE -4503)) (|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 (-1079))) (|HasCategory| |#3| (QUOTE (-1131)))) -(-245 -4398 R) +((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-869))) (|HasAttribute| |#3| (QUOTE -4499)) (|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 (-1078))) (|HasCategory| |#3| (QUOTE (-1130)))) +(-245 -3097 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"))) -((-4500 |has| |#2| (-1079)) (-4501 |has| |#2| (-1079)) (-4503 |has| |#2| (-6 -4503)) (-4506 . T)) +((-4496 |has| |#2| (-1078)) (-4497 |has| |#2| (-1078)) (-4499 |has| |#2| (-6 -4499)) (-4502 . T)) NIL -(-246 -4398 R) +(-246 -3097 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."))) -((-4500 |has| |#2| (-1079)) (-4501 |has| |#2| (-1079)) (-4503 |has| |#2| (-6 -4503)) (-4506 . 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(QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) +(-247 -3097 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}."))) -((-4499 . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) (-4496 . T) (-4497 . T) (-4499 . 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}"))) -((-4507 . T) (-4506 . 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T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) 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(QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-869))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-869))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1078)))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-869))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-869))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1078)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1078))))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1078)))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasAttribute| |#3| (QUOTE -4499)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1078))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1078)))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1206))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . 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}."))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . 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 -928) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|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"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . 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T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#3| (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|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 -1801) +(-287 R -3572) ((|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 -1801) +(-288 R -3572) ((|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 (-870))) (|HasCategory| |#2| (QUOTE (-1131)))) +((|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130)))) (-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}."))) -((-4507 . T)) +((-4503 . 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 -4507))) +((|HasAttribute| |#1| (QUOTE -4503))) (-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| -2774 -4003 |exactQuo|) +(-301 S R |Mod| -2255 -4015 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-302) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4499 . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-303) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4503 -4089 (|has| |#1| (-1079)) (|has| |#1| (-485))) (-4500 |has| |#1| (-1079)) (-4501 |has| |#1| (-1079))) -((|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1079)))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1079)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1079)))) (-4089 (|HasCategory| |#1| (|%list| 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(-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1141)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-310))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485)))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746)))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-746)))) (-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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#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 -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1079)))) +((|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1078)))) (-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 -1801 S) +(-311 -3572 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 -1801) +(-312 E -3572) ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-320 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -1801) +(-322 -3572) ((|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}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1050))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-870))) (-4089 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-870)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1182))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -526) (QUOTE (-1207)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))) (-4089 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-938))) (|HasCategory| $ (QUOTE (-147)))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1049))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-869))) (-4034 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-869)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1181))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-147))))) (-326 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4503 -4089 (-12 (|has| |#1| (-569)) (-4089 (|has| |#1| (-1079)) (|has| |#1| (-485)))) (|has| |#1| (-1079)) (|has| |#1| (-485))) (-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) ((-4508 "*") |has| |#1| (-569)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-569)) (-4498 |has| |#1| (-569))) -((-4089 (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE 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(|%list| (QUOTE -658) (QUOTE (-558))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-21)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1141)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-25)))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1078)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (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 -1801) +(-329 R -3572) ((|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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|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 -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|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 -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) (-332 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}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."))) -((-4501 . T) (-4500 . T)) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| (-558) (QUOTE (-814)))) +((-4497 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-814)))) (-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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1282,19 +1282,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) (-338 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . 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."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1801) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -3572) ((|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 -1801) +(-341 -3572) ((|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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 -1801 UP UPUP R) +(-346 -3572 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 -1801 UP UPUP R) +(-348 S -3572 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 -1801 UP UPUP R) +(-349 -3572 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|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) (-351 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|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.}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#3| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1068) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (|%list| (QUOTE -1068) (QUOTE (-558))))) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| (-934 |#1|) (QUOTE (-147))) (|HasCategory| (-934 |#1|) (QUOTE (-381)))) (|HasCategory| (-934 |#1|) (QUOTE (-149))) (|HasCategory| (-934 |#1|) (QUOTE (-381))) (|HasCategory| (-934 |#1|) (QUOTE (-147)))) -(-354 S -1801 UP UPUP) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#1|) (QUOTE (-147)))) +(-354 S -3572 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 -1801 UP UPUP) +(-355 -3572 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."))) -((-4499 |has| (-419 |#2|) (-376)) (-4504 |has| (-419 |#2|) (-376)) (-4498 |has| (-419 |#2|) (-376)) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| (-934 |#1|) (QUOTE (-147))) (|HasCategory| (-934 |#1|) (QUOTE (-381)))) (|HasCategory| (-934 |#1|) (QUOTE (-149))) (|HasCategory| (-934 |#1|) (QUOTE (-381))) (|HasCategory| (-934 |#1|) (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-364 R UP -1801) +(-364 R UP -3572) ((|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| (-934 |#1|) (QUOTE (-147))) (|HasCategory| (-934 |#1|) (QUOTE (-381)))) (|HasCategory| (-934 |#1|) (QUOTE (-149))) (|HasCategory| (-934 |#1|) (QUOTE (-381))) (|HasCategory| (-934 |#1|) (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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 -1801 GF) +(-370 -3572 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 -1801 FP FPP) +(-371 -3572 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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4503 . T)) +((-4499 . T)) NIL (-375 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1434,7 +1434,7 @@ NIL NIL (-376) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4503 |has| |#1| (-569)) (-4501 . T) (-4500 . T)) +((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . T)) NIL (-381) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL (-384 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131)))) +((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130)))) (-385 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4506 . T)) +((-4502 . T)) NIL (-386 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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) (-4501 . T) (-4500 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . 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."))) @@ -1494,7 +1494,7 @@ 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}."))) -((-4489 . T) (-4497 . T) (-3595 . T) (-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4485 . T) (-4493 . T) (-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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."))) -((-4501 . T) (-4500 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-4497 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-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}"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . 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}."))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . 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 (-870)))) +((|HasCategory| |#1| (QUOTE (-869)))) (-401) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . 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 -1801 UP UPUP R) +(-406 -3572 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 -1898 |returnType| -1415 |symbols|) +(-410 -4047 |returnType| -1545 |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 -1801 UP) +(-411 -3572 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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4489)) (|HasAttribute| |#1| (QUOTE -4497))) +((|HasAttribute| |#1| (QUOTE -4485)) (|HasAttribute| |#1| (QUOTE -4493))) (-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\"."))) -((-3595 . T) (-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1252))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (|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 -928) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((|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."))) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1251))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1251)))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|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 -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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."))) -((-4493 -12 (|has| |#1| (-6 -4504)) (|has| |#1| (-464)) (|has| |#1| (-6 -4493))) (-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-870)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843))))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4493)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +((-4489 -12 (|has| |#1| (-6 -4500)) (|has| |#1| (-464)) (|has| |#1| (-6 -4489))) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1181))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|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 -4489)) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464)))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL (-423 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558))))) +((|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-424 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-425 R -1801 UP A) +(-425 R -3572 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4503 . T)) +((-4499 . 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 -1801 UP A |ibasis|) +(-427 R -3572 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -1068) (|devaluate| |#2|)))) +((|HasCategory| |#4| (|%list| (QUOTE -1067) (|devaluate| |#2|)))) (-428 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1650,7 +1650,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-430 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4503 |has| |#1| (-569)) (-4501 . T) (-4500 . T)) +((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . 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 -1068) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1142))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) +((|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (|%list| (QUOTE -631) (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}."))) -((-4503 -4089 (|has| |#1| (-1079)) (|has| |#1| (-485))) (-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) ((-4508 "*") |has| |#1| (-569)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-569)) (-4498 |has| |#1| (-569))) +((-4499 -4034 (|has| |#1| (-1078)) (|has| |#1| (-485))) (-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) ((-4504 "*") |has| |#1| (-569)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-569)) (-4494 |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 (-870))) (|HasCategory| |#2| (QUOTE (-381)))) +((|HasCategory| |#2| (QUOTE (-869))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4506 . T) (-4496 . T) (-4507 . T)) +((-4502 . T) (-4492 . T) (-4503 . T)) NIL (-439 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -1801) +(-440 R -3572) ((|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"))) -((-4493 -12 (|has| |#1| (-6 -4493)) (|has| |#2| (-6 -4493))) (-4500 . T) (-4501 . T) (-4503 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#2| (QUOTE -4493)))) -(-442 R -1801) +((-4489 -12 (|has| |#1| (-6 -4489)) (|has| |#2| (-6 -4489))) (-4496 . T) (-4497 . T) (-4499 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4489)) (|HasAttribute| |#2| (QUOTE -4489)))) +(-442 R -3572) ((|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 -1801) +(-443 R -3572) ((|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 -1801) +(-444 R -3572) ((|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 -1801) +(-445 R -3572) ((|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 @@ -1716,12 +1716,12 @@ 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 -1801 UP) +(-447 R -3572 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 -1068) (QUOTE (-48))))) +((|HasCategory| |#2| (|%list| (QUOTE -1067) (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| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|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| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) +((|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 NIL (-449) @@ -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 -1801) +(-455 R UP -3572) ((|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}."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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"))) -((-4503 |has| (-419 (-974 |#1|)) (-569)) (-4501 . T) (-4500 . T)) -((|HasCategory| (-419 (-974 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-974 |#1|)) (QUOTE (-569)))) +((-4499 |has| (-419 (-973 |#1|)) (-569)) (-4497 . T) (-4496 . T)) +((|HasCategory| (-419 (-973 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-973 |#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"))) -(((-4508 "*") |has| |#2| (-175)) (-4499 |has| |#2| (-569)) (-4504 |has| |#2| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (-4089 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4089 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-887 |#1|) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-887 |#1|) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-887 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-887 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-887 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-886 |#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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,8 +1830,8 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -1801 R) +(-483 |lv| -3572 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4503 . T)) +((-4499 . T)) NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|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 -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|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 -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) (-487 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131)))) +((-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-488 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (-492) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre'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. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-493 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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T)) +((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (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 (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|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 -4506)) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) +((|HasAttribute| |#1| (QUOTE -4502)) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,34 +1952,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -1801 UP |AlExt| |AlPol|) +(-506 -3572 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (|%list| (QUOTE -1068) (QUOTE (-558))))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (QUOTE (-558))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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 -1801) +(-511 R UP -3572) ((|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}."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| (-114) (QUOTE (-1131))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-870))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-114) (QUOTE (-1131))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-114) (QUOTE (-102)))) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-885)))) (|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 -1801 |Expon| |VarSet| |DPoly|) +(-516 -3572 |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 (-1207))))) +((|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-1206))))) (-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 (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-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 (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL @@ -2019,15 +2019,15 @@ NIL (-522 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-523 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-524 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-525 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|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 @@ -2042,36 +2042,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-814)))) (-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}"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((-4089 (|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)))) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((-4034 (|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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|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 -4507))) +((|HasAttribute| |#3| (QUOTE -4503))) (-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 -4507))) +((|HasAttribute| |#7| (QUOTE -4503))) (-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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4508 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|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| (-791) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131))))) -(-544 K -1801 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-791) (QUOTE (-1130))))) +(-544 K -3572 |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 -1801 |Par|) +(-550 K -3572 |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 @@ -2149,7 +2149,7 @@ NIL NIL NIL (-555 R UP) -((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) +((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL (-556 S) @@ -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."))) -((-4504 . T) (-4505 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-558) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \\spad{nothing}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4488 . T) (-4494 . T) (-4498 . T) (-4493 . T) (-4504 . T) (-4505 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4484 . T) (-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102)))) -(-564 R -1801) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) +(-564 R -3572) ((|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 -1801 UP UPUP R) +(-565 R0 -3572 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."))) -((-3595 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4277 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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."))) @@ -2206,10 +2206,10 @@ 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."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-570 R -1801) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}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|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) +(-570 R -3572) +((|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 (-571 I) @@ -2217,22 +2217,22 @@ NIL NIL NIL (-572) -((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) +((|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 -1801 L) -((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) +(-573 R -3572 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|)))) (-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 -1801 UP UPUP R) +(-575 -3572 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 -1801 UP) +(-576 -3572 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 -1801 L) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'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}."))) +(-578 R -3572 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 -1801) +(-579 R -3572) ((|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 -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1169)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-647))))) -(-580 -1801 UP) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1168)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-647))))) +(-580 -3572 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 -1801) +(-582 -3572) ((|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."))) -((-3595 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4277 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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 -1801) +(-585 R -3572) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) -(-586 -1801 UP) -((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) +(-586 -3572 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 -1801) +(-587 R -3572) ((|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."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . 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 -1801) +(-595 -3572) ((|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}."))) -((-4501 . T) (-4500 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-1207))))) -(-596 E -1801) +((-4497 . T) (-4496 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-1206))))) +(-596 E -3572) ((|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 -1801) +(-597 R -3572) ((|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 @@ -2350,19 +2350,19 @@ NIL NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4089 (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-870))) (-4089 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4034 (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-146) (QUOTE (-869))) (-4034 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-606 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|) ((|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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4089 (|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 -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|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 -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) (-608 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4508 "*") |has| |#1| (-569)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-569)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) ((|HasCategory| |#1| (QUOTE (-569)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2376,7 +2376,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-612 R -1801 FG) +(-612 R -3572 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 @@ -2386,12 +2386,12 @@ NIL NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-615 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 -4507)) (|HasCategory| |#2| (QUOTE (-870))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#3| (QUOTE (-1131)))) +((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-869))) (|HasAttribute| |#1| (QUOTE -4502)) (|HasCategory| |#3| (QUOTE (-1130)))) (-616 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2402,8 +2402,8 @@ NIL NIL (-618 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4503 -4089 (-2093 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4501 . T) (-4500 . T)) -((-4089 (|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|)))) (-4089 (-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|)))) +((-4499 -4034 (-3038 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4497 . T) (-4496 . T)) +((-4034 (|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|)))) (-4034 (-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) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2430,20 +2430,20 @@ NIL NIL (-625 |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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1188))) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) (-626 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|) ((|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}."))) -((-4507 . T)) +((-4503 . T)) NIL (-628 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 -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) +((|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-629 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 @@ -2456,7 +2456,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-632 -1801 UP) +(-632 -3572 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2474,24 +2474,24 @@ NIL NIL (-636 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}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-869)))) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-868)))) (-637 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) ((|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."))) -((-4503 . T)) +((-4499 . T)) NIL -(-639 R -1801) +(-639 R -3572) ((|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) ((|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"))) -((-4501 . T) (-4500 . T) ((-4508 "*") . T) (-4499 . T) (-4503 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) +((-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4495 . T) (-4499 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-641 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 @@ -2506,13 +2506,13 @@ NIL NIL (-644 |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}}."))) -((-4503 . T)) +((-4499 . T)) NIL (-645 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 -1801) +(-646 R -3572) ((|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 @@ -2520,32 +2520,32 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-648 |lv| -1801) +(-648 |lv| -3572) ((|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) ((|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."))) -((-4507 . 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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)."))) -((-4503 -4089 (-2093 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4501 . T) (-4500 . 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T)) +((-4034 (|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|)))) (-4034 (-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) ((|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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-652 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-4501 . T) (-4500 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . T)) NIL (-653 R FE) -((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) +((|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) -((|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|))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|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}."))) +((|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|) @@ -2555,18 +2555,18 @@ NIL (-656 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 -((-2083 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-3036 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-657 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}."))) -((-4501 . T) (-4500 . T)) -((-12 (|HasCategory| (-655 |#2|) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131))))) +((-4497 . T) (-4496 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-655 |#2|) (QUOTE (-1130))))) (-658 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) ((|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}."))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL (-660 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."))) @@ -2574,8 +2574,8 @@ NIL NIL (-661 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."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-662 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 @@ -2598,8 +2598,8 @@ NIL NIL (-667 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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-668 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 @@ -2611,40 +2611,40 @@ NIL (-670 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 -4507))) +((|HasAttribute| |#1| (QUOTE -4503))) (-671 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) ((|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}."))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-812)))) -(-673 R -1801 L) +(-673 R -3572 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 -1972) +(-674 A -2896) ((|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}}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) (-675 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}}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) (-676 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) (-677 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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) ((|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}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-679 -1801 UP) +(-679 -3572 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)))) @@ -2666,7 +2666,7 @@ NIL NIL (-684 |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) (-4501 . T) (-4500 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . T)) ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) (-685 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}."))) @@ -2674,14 +2674,14 @@ NIL NIL (-686 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}."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-687 -1801 |Row| |Col| M) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-687 -3572 |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 -1801) -((|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|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-688 -3572) +((|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) @@ -2690,8 +2690,8 @@ NIL NIL (-690 |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."))) -((-4503 . T) (-4506 . T) (-4500 . T) (-4501 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4508 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (-4089 (-12 (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-4089 (|HasAttribute| |#2| (QUOTE (-4508 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((-4499 . T) (-4502 . T) (-4496 . T) (-4497 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4504 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|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 -925) (QUOTE (-1206)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-4034 (|HasAttribute| |#2| (QUOTE (-4504 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-691) ((|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 @@ -2711,7 +2711,7 @@ NIL (-695 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 -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-696) ((|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 @@ -2751,10 +2751,10 @@ NIL (-705 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 (-4508 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) +((|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) (-706 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"))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . T)) NIL (-707 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}."))) @@ -2766,8 +2766,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569)))) (-709 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."))) -((-4506 . T) (-4507 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4508 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4502 . T) (-4503 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-710 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 @@ -2776,7 +2776,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `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 -1801 FLAF FLAS) +(-712 S -3572 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}."))) 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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}."))) -((-4507 . T)) +((-4503 . T)) NIL (-716 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) -((|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|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) +((|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 -1801 PG) +(-718 OV E -3572 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) ((|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}"))) -((-3595 . T) (-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-720 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."))) @@ -2814,7 +2814,7 @@ NIL NIL (-721) ((|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}"))) -((-4505 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4501 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-722 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"))) @@ -2832,7 +2832,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-726 S -1907 I) +(-726 S -3147 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 @@ -2842,7 +2842,7 @@ NIL NIL (-728 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)}.}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL (-729 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}."))) @@ -2852,25 +2852,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-731 R |Mod| -2774 -4003 |exactQuo|) +(-731 R |Mod| -2255 -4015 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-732 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4502 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . 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(|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) (-4503 . T)) +((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-735 R |Mod| -2774 -4003 |exactQuo|) +(-735 R |Mod| -2255 -4015 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4503 . T)) +((-4499 . T)) NIL (-736 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2878,11 +2878,11 @@ NIL NIL (-737 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL -(-738 -1801) +(-738 -3572) ((|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]]}."))) -((-4503 . T)) +((-4499 . T)) NIL (-739 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."))) @@ -2906,7 +2906,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) (-744 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."))) -((-4499 |has| |#1| (-376)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-745 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."))) @@ -2916,7 +2916,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-747 -1801 UP) +(-747 -3572 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 @@ -2934,8 +2934,8 @@ NIL NIL (-751 |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."))) -(((-4508 "*") |has| |#2| (-175)) (-4499 |has| |#2| (-569)) (-4504 |has| |#2| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . 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T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-886 |#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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-752 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2950,15 +2950,15 @@ NIL NIL (-755 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) (-4503 . 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 (-870)))) +((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . 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 (-869)))) (-756 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}."))) -((-4506 . T) (-4496 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4502 . T) (-4492 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-757 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4496 . T) (-4507 . T)) +((-4492 . T) (-4503 . T)) NIL (-758) ((|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."))) @@ -2970,7 +2970,7 @@ NIL NIL (-760 |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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4501 . T) (-4500 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL (-761 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"))) @@ -2986,7 +2986,7 @@ NIL NIL (-764 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}."))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL (-765) ((|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}."))) @@ -3068,11 +3068,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-785 -1801) +(-785 -3572) ((|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 -1801) +(-786 P -3572) ((|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 @@ -3080,7 +3080,7 @@ NIL NIL NIL NIL -(-788 UP -1801) +(-788 UP -3572) ((|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 @@ -3094,9 +3094,9 @@ NIL NIL (-791) ((|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."))) -(((-4508 "*") . T)) +(((-4504 "*") . T)) NIL -(-792 R -1801) +(-792 R -3572) ((|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 @@ -3116,7 +3116,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of 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 -1801 |ExtF| |SUEx| |ExtP| |n|) +(-797 -3572 |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 @@ -3130,12 +3130,12 @@ NIL NIL (-800 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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . 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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)}"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4502 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1111) (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1181))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-802 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 @@ -3146,12 +3146,12 @@ NIL ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-804 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.}"))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL (-805 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 (-870)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-175)))) +((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-175)))) (-806) ((|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 @@ -3199,10 +3199,10 @@ NIL (-817 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-381)))) +((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-381)))) (-818 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL (-819) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -3210,9 +3210,9 @@ NIL NIL (-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4089 (|HasCategory| (-1026 |#1|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (|HasCategory| (-1026 |#1|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1026 |#1|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1026 |#1|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) -(-821 -4089 R OS S) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4034 (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1089))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) +(-821 -4034 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 @@ -3220,19 +3220,19 @@ NIL ((|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 -1801 L) +(-823 R -3572 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 -1801) -((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) +(-824 R -3572) +((|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) ((|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 -1801) +(-826 R -3572) ((|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 @@ -3240,11 +3240,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE'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 -1801 UP UPUP R) +(-828 -3572 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 -1801 UP L LQ) +(-829 -3572 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 @@ -3252,41 +3252,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-831 -1801 UP L LQ) +(-831 -3572 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 -1801 UP) -((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) +(-832 -3572 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 -1801 L UP A LO) +(-833 -3572 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 -1801 UP) +(-834 -3572 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 -1801 LO) +(-835 -3572 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-836 -1801 LODO) +(-836 -3572 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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T)) -((-4089 (-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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T)) -((|HasCategory| |#1| (QUOTE (-938))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-840 (-1206)) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-840 (-1206)) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-840 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-840 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-840 (-1206)) (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-839 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4508 "*") |has| |#2| (-376)) (-4499 |has| |#2| (-376)) (-4504 |has| |#2| (-376)) (-4498 |has| |#2| (-376)) (-4503 . T) (-4501 . T) (-4500 . T)) +(((-4504 "*") |has| |#2| (-376)) (-4495 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4494 |has| |#2| (-376)) (-4499 . T) (-4497 . T) (-4496 . T)) ((|HasCategory| |#2| (QUOTE (-376)))) (-840 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}))."))) @@ -3295,10 +3295,10 @@ NIL (-841 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 (-870)))) +((|HasCategory| |#1| (QUOTE (-869)))) (-842) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL (-843) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath XML encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3330,7 +3330,7 @@ NIL NIL (-850 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) (-851) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the CDs supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) @@ -3338,1907 +3338,1903 @@ NIL NIL (-852 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4506 . T) (-4496 . T) (-4507 . T)) -NIL -(-853) -((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) +((-4502 . T) (-4492 . T) (-4503 . T)) NIL -NIL -(-854 R) +(-853 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."))) -((-4503 |has| |#1| (-869))) -((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-21))) (-4089 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4089 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) -(-855 R S) +((-4499 |has| |#1| (-868))) +((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-21))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-868)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) +(-854 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 -(-856 R) +(-855 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) (-4503 . T)) +((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-857 A S) +(-856 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 -(-858 S) +(-857 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-859) +(-858) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-860) +(-859) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 -(-861) +(-860) ((|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 -(-862) +(-861) ((|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 -(-863) +(-862) ((|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 -(-864 R) +(-863 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4503 |has| |#1| (-869))) -((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-21))) (-4089 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4089 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) -(-865 R S) +((-4499 |has| |#1| (-868))) +((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-21))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-868)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) +(-864 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-866) +(-865) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -4398 S) +(-866 -3097 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-868) +(-867) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-869) +(-868) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-4503 . T)) +((-4499 . T)) NIL -(-870) +(-869) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-871 T$ |f|) +(-870 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 (-886))))) -(-872 S) +((|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) +(-871 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-873) +(-872) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-874 S R) +(-873 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) -(-875 R) +(-874 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-876 R C) +(-875 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)))) -(-877 R |sigma| -2404) +(-876 R |sigma| -3739) ((|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."))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) -(-878 |x| R |sigma| -2404) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) +(-877 |x| R |sigma| -3739) ((|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}."))) -((-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) -(-879 R) +((-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) +(-878 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)))))) -(-880) +(-879) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-881) +(-880) ((|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 -(-882) +(-881) ((|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 -(-883 S) +(-882 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 -(-884) +(-883) ((|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 -(-885) +(-884) ((|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 -(-886) +(-885) ((|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 -(-887 |VariableList|) +(-886 |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 -(-888) +(-887) ((|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 -(-889 R |vl| |wl| |wtlevel|) +(-888 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)"))) -((-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) (-4503 . T)) +((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) -(-890 R PS UP) +(-889 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 -(-891 R |x| |pt|) +(-890 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 -(-892 |p|) +(-891 |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)."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-893 |p|) +(-892 |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}."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-894 |p|) +(-893 |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)."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-892 |#1|) (QUOTE (-938))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-892 |#1|) (QUOTE (-147))) (|HasCategory| (-892 |#1|) (QUOTE (-149))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-892 |#1|) (QUOTE (-1050))) (|HasCategory| (-892 |#1|) (QUOTE (-842))) (|HasCategory| (-892 |#1|) (QUOTE (-870))) (-4089 (|HasCategory| (-892 |#1|) (QUOTE (-842))) (|HasCategory| (-892 |#1|) (QUOTE (-870)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-892 |#1|) (QUOTE (-1182))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-892 |#1|) (QUOTE (-239))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-892 |#1|) (QUOTE (-240))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -526) (QUOTE (-1207)) (|%list| (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| (-892 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -892) (|devaluate| |#1|)) (|%list| (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| (-892 |#1|) (QUOTE (-319))) (|HasCategory| (-892 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-892 |#1|) (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-892 |#1|) (QUOTE (-938)))) (|HasCategory| (-892 |#1|) (QUOTE (-147))))) -(-895 |p| PADIC) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-891 |#1|) (QUOTE (-937))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-149))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-891 |#1|) (QUOTE (-1049))) (|HasCategory| (-891 |#1|) (QUOTE (-842))) (|HasCategory| (-891 |#1|) (QUOTE (-869))) (-4034 (|HasCategory| (-891 |#1|) (QUOTE (-842))) (|HasCategory| (-891 |#1|) (QUOTE (-869)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (QUOTE (-1181))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (QUOTE (-239))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (QUOTE (-240))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -891) (|devaluate| |#1|)) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (QUOTE (-319))) (|HasCategory| (-891 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-937)))) (|HasCategory| (-891 |#1|) (QUOTE (-147))))) +(-894 |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)}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-870))) (-4089 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-870)))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1207)) (|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| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-896 S T$) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1206)) (|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 (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(-895 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 (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))))) -(-897) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))))) +(-896) ((|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 -(-898) +(-897) ((|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 -(-899) +(-898) ((|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 -(-900 CF1 CF2) +(-899 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-901 |ComponentFunction|) +(-900 |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 -(-902 CF1 CF2) +(-901 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-903 |ComponentFunction|) +(-902 |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 -(-904) +(-903) ((|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 -(-905 CF1 CF2) +(-904 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-906 |ComponentFunction|) +(-905 |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 -(-907) +(-906) ((|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 -(-908 R) +(-907 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 -(-909 R S L) +(-908 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 -(-910 S) +(-909 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 -(-911 |Base| |Subject| |Pat|) +(-910 |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 (-2083 (|HasCategory| |#2| (QUOTE (-1079)))) (-2083 (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (-2083 (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207))))) -(-912 R S) +((-12 (-3036 (|HasCategory| |#2| (QUOTE (-1078)))) (-3036 (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (-3036 (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206))))) +(-911 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 -(-913 R A B) +(-912 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 -(-914 R) +(-913 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 -(-915 R -1907) +(-914 R -3147) ((|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 -(-916 R S) +(-915 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 -(-917 |VarSet|) +(-916 |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 -(-918 UP R) +(-917 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-919 A T$ S) +(-918 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 -(-920 T$ S) +(-919 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 -(-921) +(-920) ((|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 -(-922 UP -1801) +(-921 UP -3572) ((|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 -(-923) +(-922) ((|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 -(-924) +(-923) ((|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 -(-925 R S) +(-924 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL -(-926 S) +(-925 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4503 . T)) +((-4499 . T)) NIL -(-927 A S) +(-926 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 -(-928 S) +(-927 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 -(-929 S) +(-928 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 (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-930 S) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-929 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4503 . T)) -((-4089 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-870)))) -(-931 |n| R) +((-4499 . T)) +((-4034 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-869)))) +(-930 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 -(-932 S) +(-931 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."))) -((-4503 . T)) +((-4499 . T)) NIL -(-933 S) +(-932 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 -(-934 |p|) +(-933 |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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) -(-935 R E |VarSet| S) +(-934 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 -(-936 R S) +(-935 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 -(-937 S) +(-936 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)))) -(-938) +(-937) ((|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}."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-939 R0 -1801 UP UPUP R) +(-938 R0 -3572 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 -(-940 UP UPUP R) +(-939 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 -(-941 UP UPUP) +(-940 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 -(-942 R) +(-941 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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-943 R) +(-942 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 -(-944 E OV R P) +(-943 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 -(-945) +(-944) ((|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 -(-946 -1801) +(-945 -3572) ((|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 -(-947) +(-946) ((|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}."))) -(((-4508 "*") . T)) +(((-4504 "*") . T)) NIL -(-948 R) +(-947 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 -(-949) +(-948) ((|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)}"))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-950 |xx| -1801) +(-949 |xx| -3572) ((|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 -(-951 -1801 P) +(-950 -3572 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-952 R |Var| |Expon| GR) +(-951 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 -(-953) +(-952) ((|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 -(-954 S) +(-953 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 -(-955) +(-954) ((|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 -(-956) +(-955) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-957) +(-956) ((|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 -(-958 R -1801) +(-957 R -3572) ((|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 -(-959 S A B) +(-958 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 -(-960 S R -1801) +(-959 S R -3572) ((|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 -(-961 I) +(-960 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 -(-962 S E) +(-961 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 -(-963 S R L) +(-962 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 -(-964 S E V R P) +(-963 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 -910) (|devaluate| |#1|)))) -(-965 -1907) +((|HasCategory| |#3| (|%list| (QUOTE -909) (|devaluate| |#1|)))) +(-964 -3147) ((|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 -(-966 R -1801 -1907) +(-965 R -3572 -3147) ((|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 -(-967 S R Q) +(-966 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 -(-968 S) +(-967 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 -(-969 S R P) +(-968 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 -(-970) +(-969) ((|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 -(-971 R) +(-970 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-972 |lv| R) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-971 |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 -(-973 |TheField| |ThePols|) +(-972 |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 (-869)))) -(-974 R) +((|HasCategory| |#1| (QUOTE (-868)))) +(-973 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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . 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T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1206) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1206) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1206) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1206) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1206) (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-974 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|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 -(-976 |x| R) +(-975 |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 -(-977 S R E |VarSet|) +(-976 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 (-938))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) -(-978 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-937))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) +(-977 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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL -(-979 E V R P -1801) +(-978 E V R P -3572) ((|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 -(-980 E |Vars| R P S) +(-979 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 -(-981 E V R P -1801) +(-980 E V R P -3572) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) -(-982) +(-981) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-983) +(-982) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-984 R E) +(-983 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4504))) -(-985 R L) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4500))) +(-984 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 -(-986 S) +(-985 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"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-987 A B) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-986 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 -(-988) +(-987) ((|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 -(-989 -1801) +(-988 -3572) ((|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 -(-990 I) +(-989 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 -(-991) +(-990) ((|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 -(-992 A B) +(-991 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"))) -((-4503 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-870))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-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)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-4089 (-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)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-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 (-870))) (|HasCategory| |#2| (QUOTE (-870))))) -(-993) +((-4499 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-869))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-4034 (-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)))) (-4034 (-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)))) (-4034 (-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)))) (-4034 (-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 (-869))) (|HasCategory| |#2| (QUOTE (-869))))) +(-992) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-994 T$) +(-993 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-995 T$) +(-994 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-996 S T$) +(-995 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-997) +(-996) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-998 S) +(-997 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . T)) NIL -(-999 R |polR|) +(-998 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)))) -(-1000) +(-999) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1001) +(-1000) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 -(-1002 S |Coef| |Expon| |Var|) +(-1001 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 -(-1003 |Coef| |Expon| |Var|) +(-1002 |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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1004) +(-1003) ((|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 -(-1005 S R E |VarSet| P) +(-1004 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)))) -(-1006 R E |VarSet| P) +(-1005 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."))) -((-4506 . T)) +((-4502 . T)) NIL -(-1007 R E V P) +(-1006 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)))) -(-1008 K) +(-1007 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 -(-1009 |VarSet| E RC P) +(-1008 |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 -(-1010 R) +(-1009 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}."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1011 R1 R2) +(-1010 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-1012 R) +(-1011 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 -(-1013 K) +(-1012 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 -(-1014 R E OV PPR) +(-1013 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 -(-1015 K R UP -1801) +(-1014 K R UP -3572) ((|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 -(-1016 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|) "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|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +(-1015 R |Var| |Expon| |Dpoly|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\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))))) -(-1017 |vl| |nv|) +(-1016 |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 -(-1018 R E V P TS) +(-1017 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 -(-1019) +(-1018) ((|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 -(-1020 A S) +(-1019 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 (-938))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1182)))) -(-1021 S) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1181)))) +(-1020 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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1022 A B R S) +(-1021 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 -(-1023 |n| K) +(-1022 |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 -(-1024) +(-1023) ((|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 -(-1025 S) +(-1024 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."))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . T)) NIL -(-1026 R) +(-1025 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.}"))) -((-4499 |has| |#1| (-302)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1207)) (|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 -928) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-557)))) -(-1027 S R) +((-4495 |has| |#1| (-302)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|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 -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1089))) (|HasCategory| |#1| (QUOTE (-557)))) +(-1026 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 (-1090))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-302)))) -(-1028 R) +((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-302)))) +(-1027 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4499 |has| |#1| (-302)) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 |has| |#1| (-302)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1029 QR R QS S) +(-1028 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-1030 S) +(-1029 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1031 S) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1030 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1032) +(-1031) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1033 -1801 UP UPUP |radicnd| |n|) +(-1032 -3572 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4499 |has| (-419 |#2|) (-376)) (-4504 |has| (-419 |#2|) (-376)) (-4498 |has| (-419 |#2|) (-376)) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4089 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4089 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4089 (-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)))) (-4089 (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-363))))) (-4089 (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4089 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1068) (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|) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))))) -(-1034 |bb|) +((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4034 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-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)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (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 -927) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) +(-1033 |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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-558) (QUOTE (-938))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1050))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870))) (-4089 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-870)))) (|HasCategory| (-558) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1182))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1207)) (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 (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-938)))) (|HasCategory| (-558) (QUOTE (-147))))) -(-1035) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (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 (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|HasCategory| (-558) (QUOTE (-147))))) +(-1034) ((|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 -(-1036) +(-1035) ((|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 -(-1037 RP) +(-1036 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 -(-1038 S) +(-1037 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 -(-1039 A S) +(-1038 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 -4507)) (|HasCategory| |#2| (QUOTE (-1131)))) -(-1040 S) +((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-1130)))) +(-1039 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 -(-1041 S) +(-1040 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 -(-1042) +(-1041) ((|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}}"))) -((-4499 . T) (-4504 . T) (-4498 . T) (-4501 . T) (-4500 . T) ((-4508 "*") . T) (-4503 . T)) +((-4495 . T) (-4500 . T) (-4494 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4499 . T)) NIL -(-1043 R -1801) +(-1042 R -3572) ((|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 -(-1044 R -1801) +(-1043 R -3572) ((|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 -(-1045 -1801 UP) +(-1044 -3572 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 -(-1046 -1801 UP) +(-1045 -3572 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 -(-1047 S) +(-1046 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 -(-1048 F1 UP UPUP R F2) +(-1047 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 -(-1049) +(-1048) ((|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 -(-1050) +(-1049) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1051 |Pol|) +(-1050 |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 -(-1052 |Pol|) +(-1051 |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 -(-1053) +(-1052) ((|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 -(-1054 |TheField|) +(-1053 |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"))) -((-4499 . T) (-4504 . T) (-4498 . T) (-4501 . T) (-4500 . T) ((-4508 "*") . T) (-4503 . T)) -((-4089 (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1068) (QUOTE (-558))))) -(-1055 -1801 L) +((-4495 . T) (-4500 . T) (-4494 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4499 . T)) +((-4034 (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (QUOTE (-558))))) +(-1054 -3572 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 -(-1056 S) +(-1055 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 (-1131)))) -(-1057 R E V P) +((|HasCategory| |#1| (QUOTE (-1130)))) +(-1056 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."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1058) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1057) ((|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 -(-1059 R) +(-1058 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 (-4508 "*")))) -(-1060 R) +((|HasAttribute| |#1| (QUOTE (-4504 "*")))) +(-1059 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)))) -(-1061 S) +(-1060 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1062 S) +(-1061 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-1063 S) +(-1062 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 -(-1064 -1801 |Expon| |VarSet| |FPol| |LFPol|) +(-1063 -3572 |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"))) -(((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1065) +(-1064) ((|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.}"))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2065) (QUOTE (-51))))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-51) (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-51) (QUOTE (-1131))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1131))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-870))) (|HasCategory| (-51) (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102)))) -(-1066) +((-4502 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1206))) (|%list| (QUOTE |:|) (QUOTE -2294) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130))) (|HasCategory| (-1206) (QUOTE (-869))) (|HasCategory| (-51) (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) +(-1065) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1067 A S) +(-1066 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 -(-1068 S) +(-1067 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 -(-1069 Q R) +(-1068 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 -(-1070 R) +(-1069 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 -(-1071) +(-1070) ((|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 -(-1072 UP) +(-1071 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 -(-1073 R) +(-1072 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 -(-1074 T$) +(-1073 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| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-1075 T$) +(-1074 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 -(-1076 R |ls|) +(-1075 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}."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| (-800 |#1| (-887 |#2|)) (QUOTE (-1131))) (|HasCategory| (-800 |#1| (-887 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -800) (|devaluate| |#1|) (|%list| (QUOTE -887) (|devaluate| |#2|)))))) (|HasCategory| (-800 |#1| (-887 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-800 |#1| (-887 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-887 |#2|) (QUOTE (-381))) (|HasCategory| (-800 |#1| (-887 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-800 |#1| (-887 |#2|)) (QUOTE (-102)))) -(-1077) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-1130))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -800) (|devaluate| |#1|) (|%list| (QUOTE -886) (|devaluate| |#2|)))))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-886 |#2|) (QUOTE (-381))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-102)))) +(-1076) ((|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 -(-1078 S) +(-1077 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 -(-1079) +(-1078) ((|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."))) -((-4503 . T)) +((-4499 . T)) NIL -(-1080 |xx| -1801) +(-1079 |xx| -3572) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1081 S) +(-1080 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 -(-1082 S |m| |n| R |Row| |Col|) +(-1081 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)))) -(-1083 |m| |n| R |Row| |Col|) +(-1082 |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"))) -((-4506 . T) (-4501 . T) (-4500 . T)) +((-4502 . T) (-4497 . T) (-4496 . T)) NIL -(-1084 |m| |n| R) +(-1083 |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}."))) -((-4506 . T) (-4501 . T) (-4500 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-4089 (-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 (-1131))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-886))))) -(-1085 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4502 . T) (-4497 . T) (-4496 . T)) +((|HasCategory| |#3| (QUOTE (-175))) (-4034 (-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 (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-885))))) +(-1084 |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 -(-1086 R) +(-1085 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 -(-1087) +(-1086) ((|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 -(-1088 S T$) +(-1087 S T$) ((|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 (-1131)))) -(-1089 S) +((|HasCategory| |#1| (QUOTE (-1130)))) +(-1088 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1090) +(-1089) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1091 |TheField| |ThePolDom|) +(-1090 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1092) +(-1091) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4494 . T) (-4498 . T) (-4493 . T) (-4504 . T) (-4505 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1093) +(-1092) ((|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}"))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2065) (QUOTE (-51))))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-51) (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-51) (QUOTE (-1131))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1131))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-870))) (|HasCategory| (-51) (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1207)) (|:| -2065 (-51))) (QUOTE (-102)))) -(-1094 S R E V) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1206))) (|%list| (QUOTE |:|) (QUOTE -2294) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130))) (|HasCategory| (-1206) (QUOTE (-869))) (|HasCategory| (-51) (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) +(-1093 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1021) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-1207))))) -(-1095 R E V) +((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1020) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-1206))))) +(-1094 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL -(-1096) +(-1095) ((|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 -(-1097 S |TheField| |ThePols|) +(-1096 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 -(-1098 |TheField| |ThePols|) +(-1097 |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 -(-1099 R E V P TS) +(-1098 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 -(-1100 S R E V P) +(-1099 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 -(-1101 R E V P) +(-1100 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}."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1102 R E V P TS) +(-1101 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 -(-1103) +(-1102) ((|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 -(-1104) +(-1103) ((|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 -(-1105 |Base| R -1801) +(-1104 |Base| R -3572) ((|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 -(-1106 |f|) +(-1105 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1107 |Base| R -1801) +(-1106 |Base| R -3572) ((|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 -(-1108 R |ls|) +(-1107 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 -(-1109 R UP M) +(-1108 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."))) -((-4499 |has| |#1| (-376)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4089 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207))))) (-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 -926) (QUOTE (-1207)))))) -(-1110 UP SAE UPA) +((-4495 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206))))) (-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 -925) (QUOTE (-1206)))))) +(-1109 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 -(-1111 UP SAE UPA) +(-1110 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 -(-1112) +(-1111) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1113) +(-1112) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1114 S) +(-1113 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 -(-1115) +(-1114) ((|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 -(-1116 R) +(-1115 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 -(-1117 R) +(-1116 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"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1118 (-1207)) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1118 (-1207)) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-1118 (-1207)) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-1118 (-1207)) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-1118 (-1207)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-1118 S) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1117 (-1206)) (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-1117 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 -(-1119 S) +(-1118 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1131)))) -(-1120 R S) +((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-1130)))) +(-1119 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 (-869)))) -(-1121) +((|HasCategory| |#1| (QUOTE (-868)))) +(-1120) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1122 S) +(-1121 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1119 |#1|) (QUOTE (-1131)))) -(-1123 R S) +((|HasCategory| (-1118 |#1|) (QUOTE (-1130)))) +(-1122 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1124 S) +(-1123 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 -(-1125 S L) +(-1124 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 -(-1126) +(-1125) ((|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 -(-1127 S) +(-1126 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)}}"))) -((-4506 . T) (-4496 . T) (-4507 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-1128 A S) +((-4502 . T) (-4492 . T) (-4503 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-1127 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1129 S) +(-1128 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4496 . T)) +((-4492 . T)) NIL -(-1130 S) +(-1129 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 -(-1131) +(-1130) ((|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 -(-1132 |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| $ "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| $ "failed") $ (|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."))) +(-1131 |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 -(-1133) +(-1132) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1134 |Str| |Sym| |Int| |Flt| |Expr|) +(-1133 |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|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1135 |Str| |Sym| |Int| |Flt| |Expr|) +(-1134 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1136 R FS) +(-1135 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 -(-1137 R E V P TS) +(-1136 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 -(-1138 R E V P TS) +(-1137 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 -(-1139 R E V P) +(-1138 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.}"))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1140) +(-1139) ((|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 -(-1141 S) +(-1140 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1142) +(-1141) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 -(-1143 |dimtot| |dim1| S) +(-1142 |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}."))) -((-4500 |has| |#3| (-1079)) (-4501 |has| |#3| (-1079)) (-4503 |has| |#3| (-6 -4503)) (-4506 . 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(QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) +(-1143 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)))) -(-1145) +(-1144) ((|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 -(-1146) +(-1145) ((|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 -(-1147 R -1801) -((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1146 R -3572) +((|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 -(-1148 R) -((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1147 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 -(-1149) +(-1148) ((|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 -(-1150) +(-1149) ((|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."))) -((-4494 . T) (-4498 . T) (-4493 . T) (-4504 . T) (-4505 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1151 S) +(-1150 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4506 . T) (-4507 . T)) +((-4502 . T) (-4503 . T)) NIL -(-1152 S |ndim| R |Row| |Col|) +(-1151 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-4508 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) -(-1153 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4504 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) +(-1152 |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."))) -((-4506 . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4502 . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1154 R |Row| |Col| M) +(-1153 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 -(-1155 R |VarSet|) +(-1154 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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-938))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147))))) -(-1156 |Coef| |Var| SMP) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-1155 |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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1157 R E V P) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) +(-1156 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}"))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1158 UP -1801) +(-1157 UP -3572) ((|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 -(-1159 R) +(-1158 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 -(-1160 R) +(-1159 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 -(-1161 R) +(-1160 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 -(-1162 S A) +(-1161 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 (-870)))) -(-1163 R) +((|HasCategory| |#1| (QUOTE (-869)))) +(-1162 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 -(-1164 R) +(-1163 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 -(-1165) +(-1164) ((|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 -(-1166) +(-1165) ((|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 -(-1167) +(-1166) ((|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 -(-1168) +(-1167) ((|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 -(-1169) +(-1168) ((|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 -(-1170 V C) +(-1169 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 -(-1171 V C) +(-1170 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."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-1170 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1131)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1131))) (-4089 (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1131)))) (-4089 (|HasCategory| (-1170 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-886)))) (-12 (|HasCategory| (-1170 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1131))))) (|HasCategory| (-1170 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-102)))) -(-1172 |ndim| R) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130))) (-4034 (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-102)))) +(-1171 |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}."))) -((-4503 . T) (-4495 |has| |#2| (-6 (-4508 "*"))) (-4506 . T) (-4500 . T) (-4501 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4508 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (QUOTE (-558)))) (-4089 (-12 (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (-4089 (|HasAttribute| |#2| (QUOTE (-4508 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) -(-1173 S) +((-4499 . T) (-4491 |has| |#2| (-6 (-4504 "*"))) (-4502 . T) (-4496 . T) (-4497 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|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 -925) (QUOTE (-1206)))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-376))) (-4034 (|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +(-1172 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1174) +(-1173) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1175 R E V P TS) +(-1174 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 -(-1176 R E V P) +(-1175 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."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1177) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1176) ((|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 -(-1178 S) +(-1177 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}."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1179 A S) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1178 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 -(-1180 S) +(-1179 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 -(-1181 |Key| |Ent| |dent|) +(-1180 |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."))) -((-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131)))) -(-1182) +((-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) +(-1181) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \\spad{nothing}.}")) (|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 -(-1183) +(-1182) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1184 |Coef|) +(-1183 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1185 S) +(-1184 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4507 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1186 S) +((-4503 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1185 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 -(-1187 A B) +(-1186 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 -(-1188 A B C) +(-1187 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 -(-1189) +(-1188) ((|string| (($ (|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"))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4089 (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-870))) (-4089 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) -(-1190 |Entry|) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4034 (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-146) (QUOTE (-869))) (-4034 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +(-1189 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#1|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 (-1189)) (|:| -2065 |#1|)) (QUOTE (-102)))) -(-1191 A) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1188))) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) +(-1190 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)))))) -(-1192 |Coef|) +(-1191 |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 -(-1193 |Coef|) +(-1192 |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 -(-1194 R UP) +(-1193 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)))) -(-1195 |n| R) +(-1194 |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 -(-1203 E OV R P) +(-1202 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 -(-1204 |Coef| |var| |cen|) +(-1203 |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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|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 -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) -(-1205 |Coef| |var| |cen|) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|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 -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1204 |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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4089 (|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 -926) (QUOTE (-1207)))) (|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 (-1142))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) -(-1206) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|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 -925) (QUOTE (-1206)))) (|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 (-1141))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1205) ((|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 -(-1207) +(-1206) ((|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 -(-1208 R) +(-1207 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 -(-1209 R) +(-1208 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-6 -4504)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4089 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-1001) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4504))) -(-1210) -((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-1000) (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4500))) +(-1209) +((|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 -(-1211) +(-1210) ((|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 -(-1212) +(-1211) ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1213 N) +(-1212 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1214 N) +(-1213 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 -(-1215) +(-1214) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1216 R) +(-1215 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 -(-1217) +(-1216) ((|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 -(-1218 S) +(-1217 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 -(-1219 |Key| |Entry|) +(-1218 |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}"))) -((-4506 . T) (-4507 . T)) -((-12 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4312) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2065) (|devaluate| |#2|)))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1131))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886))))) (-4089 (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -4312 |#1|) (|:| -2065 |#2|)) (QUOTE (-102)))) -(-1220 S) +((-4502 . T) (-4503 . T)) +((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) +(-1219 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 -(-1221 S) +(-1220 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 -(-1222 R) +(-1221 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 -(-1223 S |Key| |Entry|) +(-1222 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 -(-1224 |Key| |Entry|) +(-1223 |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})}."))) -((-4507 . T)) +((-4503 . T)) NIL -(-1225 |Key| |Entry|) +(-1224 |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 -(-1226) +(-1225) ((|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 -(-1227) +(-1226) ((|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 -(-1228 S) +(-1227 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 -(-1229) +(-1228) ((|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 -(-1230 R) +(-1229 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 -(-1231) +(-1230) ((|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 -(-1232 S) +(-1231 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1233) +(-1232) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1234 S) +(-1233 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1235 S) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1234 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1236) +(-1235) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -1801) +(-1236 R -3572) ((|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 -(-1238 R |Row| |Col| M) +(-1237 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 -(-1239 R -1801) +(-1238 R -3572) ((|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 -914) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -910) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (|devaluate| |#1|))))) -(-1240 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -909) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (|devaluate| |#1|))))) +(-1239 |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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1241 S R E V P) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) +(-1240 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)))) -(-1242 R E V P) +(-1241 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1243 |Curve|) +(-1242 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 -(-1244) +(-1243) ((|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 -(-1245 S) +(-1244 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 (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) -(-1246 -1801) +((|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) +(-1245 -3572) ((|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 -(-1247) +(-1246) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1248) +(-1247) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1249 S) +(-1248 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 (-870)))) -(-1250) +((|HasCategory| |#1| (QUOTE (-869)))) +(-1249) ((|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 -(-1251 S) +(-1250 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1252) +(-1251) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1253) +(-1252) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1254) +(-1253) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1255) +(-1254) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1256) +(-1255) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1257 |Coef| |var| |cen|) +(-1256 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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(((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . 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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)))) -(-1261 |Coef| UTS) +(-1260 |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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(|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL -((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1131)))) -(-1265 R S) +((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-1130)))) +(-1264 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|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 (-869)))) -(-1266 |x| R) +((|HasCategory| |#1| (QUOTE (-868)))) +(-1265 |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}"))) -(((-4508 "*") |has| |#2| (-175)) (-4499 |has| |#2| (-569)) (-4502 |has| |#2| (-376)) (-4504 |has| |#2| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4089 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -910) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -910) (QUOTE (-558))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-391)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -914) (QUOTE (-558)))))) (-12 (|HasCategory| (-1112) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%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 -1068) (QUOTE (-558)))) (-4089 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4089 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-4089 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-1267 |x| R |y| S) +(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4498 |has| |#2| (-376)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1111) (|%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 -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) +(-1266 |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 -(-1268 R Q UP) +(-1267 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 -(-1269 R UP) +(-1268 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 -(-1270 R UP) +(-1269 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 -(-1271 R U) +(-1270 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 -(-1272 S R) +(-1271 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 (-1182)))) -(-1273 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 (-1181)))) +(-1272 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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4502 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4501 . T) (-4500 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL -(-1274 R PR S PS) +(-1273 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 -(-1275 S |Coef| |Expon|) +(-1274 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 -926) (QUOTE (-1207)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1142))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3451) (|%list| (|devaluate| |#2|) (QUOTE (-1207)))))) -(-1276 |Coef| |Expon|) +((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1141))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#2|) (QUOTE (-1206)))))) +(-1275 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1277 RC P) -((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) +(-1276 RC P) +((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1278 |Coef| |var| |cen|) +(-1277 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|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 -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) -(-1279 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|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 -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1278 |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 -(-1280 |Coef|) +(-1279 |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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1281 S |Coef| ULS) +(-1280 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 -(-1282 |Coef| ULS) +(-1281 |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)}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1283 |Coef| ULS) +(-1282 |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)}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4504 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -926) (QUOTE (-1207)))) (|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 (-1142))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4089 (|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 -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) -(-1284 R FE |var| |cen|) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|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 (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|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 -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) +(-1283 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))}."))) -(((-4508 "*") |has| (-1278 |#2| |#3| |#4|) (-175)) (-4499 |has| (-1278 |#2| |#3| |#4|) (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) -((|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-4089 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1068) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1068) (QUOTE (-558)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-569)))) -(-1285 A S) +(((-4504 "*") |has| (-1277 |#2| |#3| |#4|) (-175)) (-4495 |has| (-1277 |#2| |#3| |#4|) (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-175))) (-4034 (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) +(-1284 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4507))) -(-1286 S) +((|HasAttribute| |#1| (QUOTE -4503))) +(-1285 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1287 |Coef| |var| |cen|) +(-1286 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . 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T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4089 (|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 -926) (QUOTE (-1207)))) (|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 (-1142))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -3451) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4089 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#1|))))))) -(-1288 |Coef1| |Coef2| UTS1 UTS2) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|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 -925) (QUOTE (-1206)))) (|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 (-1141))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|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 -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1287 |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 -(-1289 S |Coef|) +(-1288 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 (-988))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%list| (QUOTE -4086) (|%list| (|%list| (QUOTE -661) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -1779) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) -(-1290 |Coef|) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-987))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasSignature| |#2| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) +(-1289 |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."))) -(((-4508 "*") |has| |#1| (-175)) (-4499 |has| |#1| (-569)) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1291 |Coef| UTS) +(-1290 |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 -(-1292 -1801 UP L UTS) +(-1291 -3572 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)))) -(-1293) +(-1292) ((|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 -(-1294 |sym|) +(-1293 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1295 S R) +(-1294 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 (-1032))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1296 R) +((|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1295 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4507 . T) (-4506 . T)) +((-4503 . T) (-4502 . T)) NIL -(-1297 R) +(-1296 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4507 . T) (-4506 . T)) -((-4089 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4089 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4089 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-870))) (-4089 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-558) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-1298 A B) +((-4503 . T) (-4502 . T)) +((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-1297 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 -(-1299) +(-1298) ((|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 -(-1300) +(-1299) ((|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 -(-1301) +(-1300) ((|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 -(-1302) +(-1301) ((|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 -(-1303) +(-1302) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1304 A S) +(-1303 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1305 S) +(-1304 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}."))) -((-4501 . T) (-4500 . T)) +((-4497 . T) (-4496 . T)) NIL -(-1306 R) +(-1305 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 -(-1307 K R UP -1801) +(-1306 K R UP -3572) ((|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 -(-1308) +(-1307) ((|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 -(-1309) +(-1308) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1310 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1309 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)"))) -((-4501 |has| |#1| (-175)) (-4500 |has| |#1| (-175)) (-4503 . T)) +((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) -(-1311 R E V P) +(-1310 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}."))) -((-4507 . T) (-4506 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1312 R) +((-4503 . T) (-4502 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1311 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)"))) -((-4500 . T) (-4501 . T) (-4503 . T)) +((-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1313 |vl| R) +(-1312 |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."))) -((-4503 . T) (-4499 |has| |#2| (-6 -4499)) (-4501 . T) (-4500 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4499))) -(-1314 R |VarSet| XPOLY) +((-4499 . T) (-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4495))) +(-1313 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 -(-1315 S -1801) +(-1314 S -3572) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1316 -1801) +(-1315 -3572) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4498 . T) (-4504 . T) (-4499 . T) ((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL -(-1317 |vl| R) +(-1316 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4499 |has| |#2| (-6 -4499)) (-4501 . T) (-4500 . T) (-4503 . T)) +((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL -(-1318 |VarSet| R) +(-1317 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) -((-4499 |has| |#2| (-6 -4499)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -737) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4499))) -(-1319 R) +((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -737) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4495))) +(-1318 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."))) -((-4499 |has| |#1| (-6 -4499)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4499))) -(-1320 |vl| R) +((-4495 |has| |#1| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4495))) +(-1319 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4499 |has| |#2| (-6 -4499)) (-4501 . T) (-4500 . T) (-4503 . T)) +((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) NIL -(-1321 R E) +(-1320 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4503 . T) (-4504 |has| |#1| (-6 -4504)) (-4499 |has| |#1| (-6 -4499)) (-4501 . T) (-4500 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4499))) -(-1322 |VarSet| R) +((-4499 . T) (-4500 |has| |#1| (-6 -4500)) (-4495 |has| |#1| (-6 -4495)) (-4497 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4499)) (|HasAttribute| |#1| (QUOTE -4500)) (|HasAttribute| |#1| (QUOTE -4495))) +(-1321 |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."))) -((-4499 |has| |#2| (-6 -4499)) (-4501 . T) (-4500 . T) (-4503 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4499))) -(-1323) +((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4495))) +(-1322) ((|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 -(-1324 A) +(-1323 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 -(-1325 R |ls| |ls2|) +(-1324 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 -(-1326 R) +(-1325 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 -(-1327 |p|) +(-1326 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4508 "*") . T) (-4500 . T) (-4501 . T) (-4503 . T)) +(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) NIL NIL NIL @@ -5256,4 +5252,4 @@ NIL NIL NIL NIL -((-3 NIL 2291500 2291505 2291510 2291515) (-2 NIL 2291480 2291485 2291490 2291495) (-1 NIL 2291460 2291465 2291470 2291475) (0 NIL 2291440 2291445 2291450 2291455) (-1327 "ZMOD.spad" 2291249 2291262 2291378 2291435) (-1326 "ZLINDEP.spad" 2290347 2290358 2291239 2291244) (-1325 "ZDSOLVE.spad" 2280307 2280329 2290337 2290342) (-1324 "YSTREAM.spad" 2279802 2279813 2280297 2280302) (-1323 "YDIAGRAM.spad" 2279436 2279445 2279792 2279797) (-1322 "XRPOLY.spad" 2278656 2278676 2279292 2279361) (-1321 "XPR.spad" 2276451 2276464 2278374 2278473) (-1320 "XPOLYC.spad" 2275770 2275786 2276377 2276446) (-1319 "XPOLY.spad" 2275325 2275336 2275626 2275695) (-1318 "XPBWPOLY.spad" 2273764 2273784 2275099 2275168) (-1317 "XFALG.spad" 2270812 2270828 2273690 2273759) (-1316 "XF.spad" 2269275 2269290 2270714 2270807) (-1315 "XF.spad" 2267718 2267735 2269159 2269164) (-1314 "XEXPPKG.spad" 2266977 2267003 2267708 2267713) (-1313 "XDPOLY.spad" 2266591 2266607 2266833 2266902) (-1312 "XALG.spad" 2266259 2266270 2266547 2266586) (-1311 "WUTSET.spad" 2262229 2262246 2265860 2265887) (-1310 "WP.spad" 2261436 2261480 2262087 2262154) (-1309 "WHILEAST.spad" 2261234 2261243 2261426 2261431) (-1308 "WHEREAST.spad" 2260905 2260914 2261224 2261229) (-1307 "WFFINTBS.spad" 2258568 2258590 2260895 2260900) (-1306 "WEIER.spad" 2256790 2256801 2258558 2258563) (-1305 "VSPACE.spad" 2256463 2256474 2256758 2256785) (-1304 "VSPACE.spad" 2256156 2256169 2256453 2256458) (-1303 "VOID.spad" 2255833 2255842 2256146 2256151) (-1302 "VIEWDEF.spad" 2251034 2251043 2255823 2255828) (-1301 "VIEW3D.spad" 2234995 2235004 2251024 2251029) (-1300 "VIEW2D.spad" 2222894 2222903 2234985 2234990) (-1299 "VIEW.spad" 2220614 2220623 2222884 2222889) (-1298 "VECTOR2.spad" 2219253 2219266 2220604 2220609) (-1297 "VECTOR.spad" 2217753 2217764 2218004 2218031) (-1296 "VECTCAT.spad" 2215665 2215676 2217721 2217748) (-1295 "VECTCAT.spad" 2213384 2213397 2215442 2215447) (-1294 "VARIABLE.spad" 2213164 2213179 2213374 2213379) (-1293 "UTYPE.spad" 2212808 2212817 2213154 2213159) (-1292 "UTSODETL.spad" 2212103 2212127 2212764 2212769) (-1291 "UTSODE.spad" 2210319 2210339 2212093 2212098) (-1290 "UTSCAT.spad" 2207798 2207814 2210217 2210314) (-1289 "UTSCAT.spad" 2204897 2204915 2207318 2207323) (-1288 "UTS2.spad" 2204492 2204527 2204887 2204892) (-1287 "UTS.spad" 2199370 2199398 2202890 2202987) (-1286 "URAGG.spad" 2194091 2194102 2199360 2199365) (-1285 "URAGG.spad" 2188776 2188789 2194047 2194052) (-1284 "UPXSSING.spad" 2186394 2186420 2187830 2187963) (-1283 "UPXSCONS.spad" 2184072 2184092 2184445 2184594) (-1282 "UPXSCCA.spad" 2182643 2182663 2183918 2184067) (-1281 "UPXSCCA.spad" 2181356 2181378 2182633 2182638) (-1280 "UPXSCAT.spad" 2179945 2179961 2181202 2181351) (-1279 "UPXS2.spad" 2179488 2179541 2179935 2179940) (-1278 "UPXS.spad" 2176703 2176731 2177539 2177688) (-1277 "UPSQFREE.spad" 2175117 2175131 2176693 2176698) (-1276 "UPSCAT.spad" 2172912 2172936 2175015 2175112) (-1275 "UPSCAT.spad" 2170392 2170418 2172497 2172502) (-1274 "UPOLYC2.spad" 2169863 2169882 2170382 2170387) (-1273 "UPOLYC.spad" 2164943 2164954 2169705 2169858) (-1272 "UPOLYC.spad" 2159909 2159922 2164673 2164678) (-1271 "UPMP.spad" 2158841 2158854 2159899 2159904) (-1270 "UPDIVP.spad" 2158406 2158420 2158831 2158836) (-1269 "UPDECOMP.spad" 2156667 2156681 2158396 2158401) (-1268 "UPCDEN.spad" 2155884 2155900 2156657 2156662) (-1267 "UP2.spad" 2155248 2155269 2155874 2155879) (-1266 "UP.spad" 2152276 2152291 2152663 2152816) (-1265 "UNISEG2.spad" 2151773 2151786 2152232 2152237) (-1264 "UNISEG.spad" 2151126 2151137 2151692 2151697) (-1263 "UNIFACT.spad" 2150229 2150241 2151116 2151121) (-1262 "ULSCONS.spad" 2141141 2141161 2141511 2141660) (-1261 "ULSCCAT.spad" 2138878 2138898 2140987 2141136) (-1260 "ULSCCAT.spad" 2136723 2136745 2138834 2138839) (-1259 "ULSCAT.spad" 2134963 2134979 2136569 2136718) (-1258 "ULS2.spad" 2134477 2134530 2134953 2134958) (-1257 "ULS.spad" 2124048 2124076 2124993 2125422) (-1256 "UINT8.spad" 2123925 2123934 2124038 2124043) (-1255 "UINT64.spad" 2123801 2123810 2123915 2123920) (-1254 "UINT32.spad" 2123677 2123686 2123791 2123796) (-1253 "UINT16.spad" 2123553 2123562 2123667 2123672) (-1252 "UFD.spad" 2122618 2122627 2123479 2123548) (-1251 "UFD.spad" 2121745 2121756 2122608 2122613) (-1250 "UDVO.spad" 2120626 2120635 2121735 2121740) (-1249 "UDPO.spad" 2118207 2118218 2120582 2120587) (-1248 "TYPEAST.spad" 2118126 2118135 2118197 2118202) (-1247 "TYPE.spad" 2118058 2118067 2118116 2118121) (-1246 "TWOFACT.spad" 2116710 2116725 2118048 2118053) (-1245 "TUPLE.spad" 2116201 2116212 2116606 2116611) (-1244 "TUBETOOL.spad" 2113068 2113077 2116191 2116196) (-1243 "TUBE.spad" 2111715 2111732 2113058 2113063) (-1242 "TSETCAT.spad" 2099786 2099803 2111683 2111710) (-1241 "TSETCAT.spad" 2087843 2087862 2099742 2099747) (-1240 "TS.spad" 2086436 2086452 2087402 2087499) (-1239 "TRMANIP.spad" 2080800 2080817 2086124 2086129) (-1238 "TRIMAT.spad" 2079763 2079788 2080790 2080795) (-1237 "TRIGMNIP.spad" 2078290 2078307 2079753 2079758) (-1236 "TRIGCAT.spad" 2077802 2077811 2078280 2078285) (-1235 "TRIGCAT.spad" 2077312 2077323 2077792 2077797) (-1234 "TREE.spad" 2075758 2075769 2076790 2076817) (-1233 "TRANFUN.spad" 2075597 2075606 2075748 2075753) (-1232 "TRANFUN.spad" 2075434 2075445 2075587 2075592) (-1231 "TOPSP.spad" 2075108 2075117 2075424 2075429) (-1230 "TOOLSIGN.spad" 2074771 2074782 2075098 2075103) (-1229 "TEXTFILE.spad" 2073332 2073341 2074761 2074766) (-1228 "TEX1.spad" 2072888 2072899 2073322 2073327) (-1227 "TEX.spad" 2070082 2070091 2072878 2072883) (-1226 "TEMUTL.spad" 2069637 2069646 2070072 2070077) (-1225 "TBCMPPK.spad" 2067738 2067761 2069627 2069632) (-1224 "TBAGG.spad" 2066796 2066819 2067718 2067733) (-1223 "TBAGG.spad" 2065862 2065887 2066786 2066791) (-1222 "TANEXP.spad" 2065270 2065281 2065852 2065857) (-1221 "TALGOP.spad" 2064994 2065005 2065260 2065265) (-1220 "TABLEAU.spad" 2064475 2064486 2064984 2064989) (-1219 "TABLE.spad" 2062408 2062431 2062678 2062705) (-1218 "TABLBUMP.spad" 2059187 2059198 2062398 2062403) (-1217 "SYSTEM.spad" 2058415 2058424 2059177 2059182) (-1216 "SYSSOLP.spad" 2055898 2055909 2058405 2058410) (-1215 "SYSPTR.spad" 2055797 2055806 2055888 2055893) (-1214 "SYSNNI.spad" 2055020 2055031 2055787 2055792) (-1213 "SYSINT.spad" 2054424 2054435 2055010 2055015) (-1212 "SYNTAX.spad" 2050758 2050767 2054414 2054419) (-1211 "SYMTAB.spad" 2048826 2048835 2050748 2050753) (-1210 "SYMS.spad" 2044849 2044858 2048816 2048821) (-1209 "SYMPOLY.spad" 2043828 2043839 2043910 2044037) (-1208 "SYMFUNC.spad" 2043329 2043340 2043818 2043823) (-1207 "SYMBOL.spad" 2040824 2040833 2043319 2043324) (-1206 "SWITCH.spad" 2037595 2037604 2040814 2040819) (-1205 "SUTS.spad" 2034574 2034602 2035993 2036090) (-1204 "SUPXS.spad" 2031776 2031804 2032625 2032774) (-1203 "SUPFRACF.spad" 2030881 2030899 2031766 2031771) (-1202 "SUP2.spad" 2030273 2030286 2030871 2030876) (-1201 "SUP.spad" 2026915 2026926 2027688 2027841) (-1200 "SUMRF.spad" 2025889 2025900 2026905 2026910) (-1199 "SUMFS.spad" 2025518 2025535 2025879 2025884) (-1198 "SULS.spad" 2015076 2015104 2016034 2016463) (-1197 "SUCHTAST.spad" 2014845 2014854 2015066 2015071) (-1196 "SUCH.spad" 2014535 2014550 2014835 2014840) (-1195 "SUBSPACE.spad" 2006666 2006681 2014525 2014530) (-1194 "SUBRESP.spad" 2005836 2005850 2006622 2006627) (-1193 "STTFNC.spad" 2002304 2002320 2005826 2005831) (-1192 "STTF.spad" 1998403 1998419 2002294 2002299) (-1191 "STTAYLOR.spad" 1991048 1991059 1998278 1998283) (-1190 "STRTBL.spad" 1989063 1989080 1989212 1989239) (-1189 "STRING.spad" 1987829 1987838 1988050 1988077) (-1188 "STREAM3.spad" 1987402 1987417 1987819 1987824) (-1187 "STREAM2.spad" 1986530 1986543 1987392 1987397) (-1186 "STREAM1.spad" 1986236 1986247 1986520 1986525) (-1185 "STREAM.spad" 1983022 1983033 1985629 1985644) (-1184 "STINPROD.spad" 1981958 1981974 1983012 1983017) (-1183 "STEPAST.spad" 1981192 1981201 1981948 1981953) (-1182 "STEP.spad" 1980401 1980410 1981182 1981187) (-1181 "STBL.spad" 1978449 1978477 1978616 1978631) (-1180 "STAGG.spad" 1977148 1977159 1978439 1978444) (-1179 "STAGG.spad" 1975845 1975858 1977138 1977143) (-1178 "STACK.spad" 1975073 1975084 1975323 1975350) (-1177 "SRING.spad" 1974833 1974842 1975063 1975068) (-1176 "SREGSET.spad" 1972532 1972549 1974434 1974461) (-1175 "SRDCMPK.spad" 1971109 1971129 1972522 1972527) (-1174 "SRAGG.spad" 1966292 1966301 1971077 1971104) (-1173 "SRAGG.spad" 1961495 1961506 1966282 1966287) (-1172 "SQMATRIX.spad" 1958990 1959008 1959906 1959993) (-1171 "SPLTREE.spad" 1953456 1953469 1958252 1958279) (-1170 "SPLNODE.spad" 1950076 1950089 1953446 1953451) (-1169 "SPFCAT.spad" 1948885 1948894 1950066 1950071) (-1168 "SPECOUT.spad" 1947437 1947446 1948875 1948880) (-1167 "SPADXPT.spad" 1939528 1939537 1947427 1947432) (-1166 "spad-parser.spad" 1938993 1939002 1939518 1939523) (-1165 "SPADAST.spad" 1938694 1938703 1938983 1938988) (-1164 "SPACEC.spad" 1922909 1922920 1938684 1938689) (-1163 "SPACE3.spad" 1922685 1922696 1922899 1922904) (-1162 "SORTPAK.spad" 1922234 1922247 1922641 1922646) (-1161 "SOLVETRA.spad" 1919997 1920008 1922224 1922229) (-1160 "SOLVESER.spad" 1918453 1918464 1919987 1919992) (-1159 "SOLVERAD.spad" 1914479 1914490 1918443 1918448) (-1158 "SOLVEFOR.spad" 1912941 1912959 1914469 1914474) (-1157 "SNTSCAT.spad" 1912541 1912558 1912909 1912936) (-1156 "SMTS.spad" 1910823 1910849 1912100 1912197) (-1155 "SMP.spad" 1908226 1908246 1908616 1908743) (-1154 "SMITH.spad" 1907071 1907096 1908216 1908221) (-1153 "SMATCAT.spad" 1905189 1905219 1907015 1907066) (-1152 "SMATCAT.spad" 1903239 1903271 1905067 1905072) (-1151 "SKAGG.spad" 1902208 1902219 1903207 1903234) (-1150 "SINT.spad" 1901148 1901157 1902074 1902203) (-1149 "SIMPAN.spad" 1900876 1900885 1901138 1901143) (-1148 "SIGNRF.spad" 1899994 1900005 1900866 1900871) (-1147 "SIGNEF.spad" 1899273 1899290 1899984 1899989) (-1146 "SIGAST.spad" 1898690 1898699 1899263 1899268) (-1145 "SIG.spad" 1898052 1898061 1898680 1898685) (-1144 "SHP.spad" 1895996 1896011 1898008 1898013) (-1143 "SHDP.spad" 1883351 1883378 1883868 1883967) (-1142 "SGROUP.spad" 1882959 1882968 1883341 1883346) (-1141 "SGROUP.spad" 1882565 1882576 1882949 1882954) (-1140 "SGCF.spad" 1875704 1875713 1882555 1882560) (-1139 "SFRTCAT.spad" 1874650 1874667 1875672 1875699) (-1138 "SFRGCD.spad" 1873713 1873733 1874640 1874645) (-1137 "SFQCMPK.spad" 1868526 1868546 1873703 1873708) (-1136 "SFORT.spad" 1867965 1867979 1868516 1868521) (-1135 "SEXOF.spad" 1867808 1867848 1867955 1867960) (-1134 "SEXCAT.spad" 1865636 1865676 1867798 1867803) (-1133 "SEX.spad" 1865528 1865537 1865626 1865631) (-1132 "SETMN.spad" 1863986 1864003 1865518 1865523) (-1131 "SETCAT.spad" 1863471 1863480 1863976 1863981) (-1130 "SETCAT.spad" 1862954 1862965 1863461 1863466) (-1129 "SETAGG.spad" 1859503 1859514 1862934 1862949) (-1128 "SETAGG.spad" 1856060 1856073 1859493 1859498) (-1127 "SET.spad" 1854333 1854344 1855430 1855469) (-1126 "SEQAST.spad" 1854036 1854045 1854323 1854328) (-1125 "SEGXCAT.spad" 1853192 1853205 1854026 1854031) (-1124 "SEGCAT.spad" 1852117 1852128 1853182 1853187) (-1123 "SEGBIND2.spad" 1851815 1851828 1852107 1852112) (-1122 "SEGBIND.spad" 1851573 1851584 1851762 1851767) (-1121 "SEGAST.spad" 1851303 1851312 1851563 1851568) (-1120 "SEG2.spad" 1850738 1850751 1851259 1851264) (-1119 "SEG.spad" 1850551 1850562 1850657 1850662) (-1118 "SDVAR.spad" 1849827 1849838 1850541 1850546) (-1117 "SDPOL.spad" 1847082 1847093 1847373 1847500) (-1116 "SCPKG.spad" 1845171 1845182 1847072 1847077) (-1115 "SCOPE.spad" 1844348 1844357 1845161 1845166) (-1114 "SCACHE.spad" 1843044 1843055 1844338 1844343) (-1113 "SASTCAT.spad" 1842953 1842962 1843034 1843039) (-1112 "SAOS.spad" 1842825 1842834 1842943 1842948) (-1111 "SAERFFC.spad" 1842538 1842558 1842815 1842820) (-1110 "SAEFACT.spad" 1842239 1842259 1842528 1842533) (-1109 "SAE.spad" 1839673 1839689 1840284 1840419) (-1108 "RURPK.spad" 1837332 1837348 1839663 1839668) (-1107 "RULESET.spad" 1836785 1836809 1837322 1837327) (-1106 "RULECOLD.spad" 1836637 1836650 1836775 1836780) (-1105 "RULE.spad" 1834885 1834909 1836627 1836632) (-1104 "RTVALUE.spad" 1834620 1834629 1834875 1834880) (-1103 "RSTRCAST.spad" 1834337 1834346 1834610 1834615) (-1102 "RSETGCD.spad" 1830779 1830799 1834327 1834332) (-1101 "RSETCAT.spad" 1820747 1820764 1830747 1830774) (-1100 "RSETCAT.spad" 1810735 1810754 1820737 1820742) (-1099 "RSDCMPK.spad" 1809235 1809255 1810725 1810730) (-1098 "RRCC.spad" 1807619 1807649 1809225 1809230) (-1097 "RRCC.spad" 1806001 1806033 1807609 1807614) (-1096 "RPTAST.spad" 1805703 1805712 1805991 1805996) (-1095 "RPOLCAT.spad" 1785207 1785222 1805571 1805698) (-1094 "RPOLCAT.spad" 1764406 1764423 1784772 1784777) (-1093 "ROUTINE.spad" 1759807 1759816 1762555 1762582) (-1092 "ROMAN.spad" 1759135 1759144 1759673 1759802) (-1091 "ROIRC.spad" 1758215 1758247 1759125 1759130) (-1090 "RNS.spad" 1757191 1757200 1758117 1758210) (-1089 "RNS.spad" 1756253 1756264 1757181 1757186) (-1088 "RNGBIND.spad" 1755413 1755427 1756208 1756213) (-1087 "RNG.spad" 1755148 1755157 1755403 1755408) (-1086 "RMODULE.spad" 1754929 1754940 1755138 1755143) (-1085 "RMCAT2.spad" 1754349 1754406 1754919 1754924) (-1084 "RMATRIX.spad" 1753119 1753138 1753462 1753501) (-1083 "RMATCAT.spad" 1748698 1748729 1753075 1753114) (-1082 "RMATCAT.spad" 1744167 1744200 1748546 1748551) (-1081 "RLINSET.spad" 1743871 1743882 1744157 1744162) (-1080 "RINTERP.spad" 1743759 1743779 1743861 1743866) (-1079 "RING.spad" 1743229 1743238 1743739 1743754) (-1078 "RING.spad" 1742707 1742718 1743219 1743224) (-1077 "RIDIST.spad" 1742099 1742108 1742697 1742702) (-1076 "RGCHAIN.spad" 1740620 1740636 1741514 1741541) (-1075 "RGBCSPC.spad" 1740409 1740421 1740610 1740615) (-1074 "RGBCMDL.spad" 1739971 1739983 1740399 1740404) (-1073 "RFFACTOR.spad" 1739433 1739444 1739961 1739966) (-1072 "RFFACT.spad" 1739168 1739180 1739423 1739428) (-1071 "RFDIST.spad" 1738164 1738173 1739158 1739163) (-1070 "RF.spad" 1735838 1735849 1738154 1738159) (-1069 "RETSOL.spad" 1735257 1735270 1735828 1735833) (-1068 "RETRACT.spad" 1734685 1734696 1735247 1735252) (-1067 "RETRACT.spad" 1734111 1734124 1734675 1734680) (-1066 "RETAST.spad" 1733923 1733932 1734101 1734106) (-1065 "RESULT.spad" 1731485 1731494 1732072 1732099) (-1064 "RESRING.spad" 1730832 1730879 1731423 1731480) (-1063 "RESLATC.spad" 1730156 1730167 1730822 1730827) (-1062 "REPSQ.spad" 1729887 1729898 1730146 1730151) (-1061 "REPDB.spad" 1729594 1729605 1729877 1729882) (-1060 "REP2.spad" 1719308 1719319 1729436 1729441) (-1059 "REP1.spad" 1713528 1713539 1719258 1719263) (-1058 "REP.spad" 1711082 1711091 1713518 1713523) (-1057 "REGSET.spad" 1708874 1708891 1710683 1710710) (-1056 "REF.spad" 1708209 1708220 1708829 1708834) (-1055 "REDORDER.spad" 1707415 1707432 1708199 1708204) (-1054 "RECLOS.spad" 1706174 1706194 1706878 1706971) (-1053 "REALSOLV.spad" 1705314 1705323 1706164 1706169) (-1052 "REAL0Q.spad" 1702612 1702627 1705304 1705309) (-1051 "REAL0.spad" 1699456 1699471 1702602 1702607) (-1050 "REAL.spad" 1699328 1699337 1699446 1699451) (-1049 "RDUCEAST.spad" 1699049 1699058 1699318 1699323) (-1048 "RDIV.spad" 1698704 1698729 1699039 1699044) (-1047 "RDIST.spad" 1698271 1698282 1698694 1698699) (-1046 "RDETRS.spad" 1697135 1697153 1698261 1698266) (-1045 "RDETR.spad" 1695274 1695292 1697125 1697130) (-1044 "RDEEFS.spad" 1694373 1694390 1695264 1695269) (-1043 "RDEEF.spad" 1693383 1693400 1694363 1694368) (-1042 "RCFIELD.spad" 1690601 1690610 1693285 1693378) (-1041 "RCFIELD.spad" 1687905 1687916 1690591 1690596) (-1040 "RCAGG.spad" 1685841 1685852 1687895 1687900) (-1039 "RCAGG.spad" 1683704 1683717 1685760 1685765) (-1038 "RATRET.spad" 1683064 1683075 1683694 1683699) (-1037 "RATFACT.spad" 1682756 1682768 1683054 1683059) (-1036 "RANDSRC.spad" 1682075 1682084 1682746 1682751) (-1035 "RADUTIL.spad" 1681831 1681840 1682065 1682070) (-1034 "RADIX.spad" 1678610 1678624 1680156 1680249) (-1033 "RADFF.spad" 1676313 1676350 1676432 1676588) (-1032 "RADCAT.spad" 1675908 1675917 1676303 1676308) (-1031 "RADCAT.spad" 1675501 1675512 1675898 1675903) (-1030 "QUEUE.spad" 1674720 1674731 1674979 1675006) (-1029 "QUATCT2.spad" 1674340 1674359 1674710 1674715) (-1028 "QUATCAT.spad" 1672510 1672521 1674270 1674335) (-1027 "QUATCAT.spad" 1670428 1670441 1672190 1672195) (-1026 "QUAT.spad" 1668880 1668891 1669223 1669288) (-1025 "QUAGG.spad" 1667713 1667724 1668848 1668875) (-1024 "QQUTAST.spad" 1667481 1667490 1667703 1667708) (-1023 "QFORM.spad" 1667099 1667114 1667471 1667476) (-1022 "QFCAT2.spad" 1666791 1666808 1667089 1667094) (-1021 "QFCAT.spad" 1665493 1665504 1666693 1666786) (-1020 "QFCAT.spad" 1663777 1663790 1664979 1664984) (-1019 "QEQUAT.spad" 1663335 1663344 1663767 1663772) (-1018 "QCMPACK.spad" 1658249 1658269 1663325 1663330) (-1017 "QALGSET2.spad" 1656244 1656263 1658239 1658244) (-1016 "QALGSET.spad" 1652346 1652379 1656158 1656163) (-1015 "PWFFINTB.spad" 1649761 1649783 1652336 1652341) (-1014 "PUSHVAR.spad" 1649099 1649119 1649751 1649756) (-1013 "PTRANFN.spad" 1645234 1645245 1649089 1649094) (-1012 "PTPACK.spad" 1642321 1642332 1645224 1645229) (-1011 "PTFUNC2.spad" 1642143 1642158 1642311 1642316) (-1010 "PTCAT.spad" 1641397 1641408 1642111 1642138) (-1009 "PSQFR.spad" 1640711 1640736 1641387 1641392) (-1008 "PSEUDLIN.spad" 1639596 1639607 1640701 1640706) (-1007 "PSETPK.spad" 1626300 1626317 1639474 1639479) (-1006 "PSETCAT.spad" 1620699 1620723 1626280 1626295) (-1005 "PSETCAT.spad" 1615072 1615098 1620655 1620660) (-1004 "PSCURVE.spad" 1614070 1614079 1615062 1615067) (-1003 "PSCAT.spad" 1612852 1612882 1613968 1614065) (-1002 "PSCAT.spad" 1611724 1611756 1612842 1612847) (-1001 "PRTITION.spad" 1610421 1610430 1611714 1611719) (-1000 "PRTDAST.spad" 1610139 1610148 1610411 1610416) (-999 "PRS.spad" 1599757 1599774 1610095 1610100) (-998 "PRQAGG.spad" 1599192 1599202 1599725 1599752) (-997 "PROPLOG.spad" 1598796 1598804 1599182 1599187) (-996 "PROPFUN2.spad" 1598419 1598432 1598786 1598791) (-995 "PROPFUN1.spad" 1597825 1597836 1598409 1598414) (-994 "PROPFRML.spad" 1596393 1596404 1597815 1597820) (-993 "PROPERTY.spad" 1595889 1595897 1596383 1596388) (-992 "PRODUCT.spad" 1593571 1593583 1593855 1593910) (-991 "PRINT.spad" 1593323 1593331 1593561 1593566) (-990 "PRIMES.spad" 1591584 1591594 1593313 1593318) (-989 "PRIMELT.spad" 1589705 1589719 1591574 1591579) (-988 "PRIMCAT.spad" 1589348 1589356 1589695 1589700) (-987 "PRIMARR2.spad" 1588115 1588127 1589338 1589343) (-986 "PRIMARR.spad" 1586954 1586964 1587124 1587151) (-985 "PREASSOC.spad" 1586336 1586348 1586944 1586949) (-984 "PR.spad" 1584701 1584713 1585400 1585527) (-983 "PPCURVE.spad" 1583838 1583846 1584691 1584696) (-982 "PORTNUM.spad" 1583629 1583637 1583828 1583833) (-981 "POLYROOT.spad" 1582478 1582500 1583585 1583590) (-980 "POLYLIFT.spad" 1581743 1581766 1582468 1582473) (-979 "POLYCATQ.spad" 1579869 1579891 1581733 1581738) (-978 "POLYCAT.spad" 1573371 1573392 1579737 1579864) (-977 "POLYCAT.spad" 1566169 1566192 1572537 1572542) (-976 "POLY2UP.spad" 1565621 1565635 1566159 1566164) (-975 "POLY2.spad" 1565218 1565230 1565611 1565616) (-974 "POLY.spad" 1562481 1562491 1562996 1563123) (-973 "POLUTIL.spad" 1561446 1561475 1562437 1562442) (-972 "POLTOPOL.spad" 1560194 1560209 1561436 1561441) (-971 "POINT.spad" 1558858 1558868 1558945 1558972) (-970 "PNTHEORY.spad" 1555560 1555568 1558848 1558853) (-969 "PMTOOLS.spad" 1554335 1554349 1555550 1555555) (-968 "PMSYM.spad" 1553884 1553894 1554325 1554330) (-967 "PMQFCAT.spad" 1553475 1553489 1553874 1553879) (-966 "PMPREDFS.spad" 1552937 1552959 1553465 1553470) (-965 "PMPRED.spad" 1552424 1552438 1552927 1552932) (-964 "PMPLCAT.spad" 1551501 1551519 1552353 1552358) (-963 "PMLSAGG.spad" 1551086 1551100 1551491 1551496) (-962 "PMKERNEL.spad" 1550665 1550677 1551076 1551081) (-961 "PMINS.spad" 1550245 1550255 1550655 1550660) (-960 "PMFS.spad" 1549822 1549840 1550235 1550240) (-959 "PMDOWN.spad" 1549112 1549126 1549812 1549817) (-958 "PMASSFS.spad" 1548087 1548103 1549102 1549107) (-957 "PMASS.spad" 1547105 1547113 1548077 1548082) (-956 "PLOTTOOL.spad" 1546885 1546893 1547095 1547100) (-955 "PLOT3D.spad" 1543349 1543357 1546875 1546880) (-954 "PLOT1.spad" 1542522 1542532 1543339 1543344) (-953 "PLOT.spad" 1537445 1537453 1542512 1542517) (-952 "PLEQN.spad" 1524847 1524874 1537435 1537440) (-951 "PINTERPA.spad" 1524631 1524647 1524837 1524842) (-950 "PINTERP.spad" 1524253 1524272 1524621 1524626) (-949 "PID.spad" 1523227 1523235 1524179 1524248) (-948 "PICOERCE.spad" 1522884 1522894 1523217 1523222) (-947 "PI.spad" 1522501 1522509 1522858 1522879) (-946 "PGROEB.spad" 1521110 1521124 1522491 1522496) (-945 "PGE.spad" 1512783 1512791 1521100 1521105) (-944 "PGCD.spad" 1511737 1511754 1512773 1512778) (-943 "PFRPAC.spad" 1510886 1510896 1511727 1511732) (-942 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488662) (-334 "FAGROUP.spad" 486627 486637 486883 486910) (-333 "FACUTIL.spad" 484839 484856 486617 486622) (-332 "FACTFUNC.spad" 484041 484051 484829 484834) (-331 "EXPUPXS.spad" 480793 480816 482092 482241) (-330 "EXPRTUBE.spad" 478081 478089 480783 480788) (-329 "EXPRODE.spad" 475249 475265 478071 478076) (-328 "EXPR2UPS.spad" 471371 471384 475239 475244) (-327 "EXPR2.spad" 471076 471088 471361 471366) (-326 "EXPR.spad" 466161 466171 466875 467170) (-325 "EXPEXPAN.spad" 462905 462930 463537 463630) (-324 "EXITAST.spad" 462641 462649 462895 462900) (-323 "EXIT.spad" 462312 462320 462631 462636) (-322 "EVALCYC.spad" 461772 461786 462302 462307) (-321 "EVALAB.spad" 461352 461362 461762 461767) (-320 "EVALAB.spad" 460930 460942 461342 461347) (-319 "EUCDOM.spad" 458520 458528 460856 460925) (-318 "EUCDOM.spad" 456172 456182 458510 458515) (-317 "ESTOOLS2.spad" 455767 455781 456162 456167) (-316 "ESTOOLS1.spad" 455444 455455 455757 455762) (-315 "ESTOOLS.spad" 447322 447330 455434 455439) (-314 "ESCONT1.spad" 447063 447075 447312 447317) (-313 "ESCONT.spad" 443856 443864 447053 447058) (-312 "ES2.spad" 443369 443385 443846 443851) (-311 "ES1.spad" 442939 442955 443359 443364) (-310 "ES.spad" 435810 435818 442929 442934) (-309 "ES.spad" 428584 428594 435705 435710) (-308 "ERROR.spad" 425911 425919 428574 428579) (-307 "EQTBL.spad" 423905 423927 424114 424141) (-306 "EQ2.spad" 423623 423635 423895 423900) (-305 "EQ.spad" 418399 418409 421194 421306) (-304 "EP.spad" 414725 414735 418389 418394) (-303 "ENV.spad" 413403 413411 414715 414720) (-302 "ENTIRER.spad" 413071 413079 413347 413398) (-301 "EMR.spad" 412359 412400 412997 413066) (-300 "ELTAGG.spad" 410613 410632 412349 412354) (-299 "ELTAGG.spad" 408831 408852 410569 410574) (-298 "ELTAB.spad" 408306 408319 408821 408826) (-297 "ELFUTS.spad" 407741 407760 408296 408301) (-296 "ELEMFUN.spad" 407430 407438 407731 407736) (-295 "ELEMFUN.spad" 407117 407127 407420 407425) (-294 "ELAGG.spad" 405088 405098 407097 407112) (-293 "ELAGG.spad" 402996 403008 405007 405012) (-292 "ELABOR.spad" 402342 402350 402986 402991) (-291 "ELABEXPR.spad" 401274 401282 402332 402337) (-290 "EFUPXS.spad" 398050 398080 401230 401235) (-289 "EFULS.spad" 394886 394909 398006 398011) (-288 "EFSTRUC.spad" 392901 392917 394876 394881) (-287 "EF.spad" 387677 387693 392891 392896) (-286 "EAB.spad" 385977 385985 387667 387672) (-285 "E04UCFA.spad" 385513 385521 385967 385972) (-284 "E04NAFA.spad" 385090 385098 385503 385508) (-283 "E04MBFA.spad" 384670 384678 385080 385085) (-282 "E04JAFA.spad" 384206 384214 384660 384665) (-281 "E04GCFA.spad" 383742 383750 384196 384201) (-280 "E04FDFA.spad" 383278 383286 383732 383737) (-279 "E04DGFA.spad" 382814 382822 383268 383273) (-278 "E04AGNT.spad" 378688 378696 382804 382809) (-277 "DVARCAT.spad" 375578 375588 378678 378683) (-276 "DVARCAT.spad" 372466 372478 375568 375573) (-275 "DSMP.spad" 369762 369776 370067 370194) (-274 "DSEXT.spad" 369064 369074 369752 369757) (-273 "DSEXT.spad" 368270 368282 368960 368965) (-272 "DROPT1.spad" 367935 367945 368260 368265) (-271 "DROPT0.spad" 362800 362808 367925 367930) (-270 "DROPT.spad" 356759 356767 362790 362795) (-269 "DRAWPT.spad" 354932 354940 356749 356754) (-268 "DRAWHACK.spad" 354240 354250 354922 354927) (-267 "DRAWCX.spad" 351718 351726 354230 354235) (-266 "DRAWCURV.spad" 351265 351280 351708 351713) (-265 "DRAWCFUN.spad" 340797 340805 351255 351260) (-264 "DRAW.spad" 333673 333686 340787 340792) (-263 "DQAGG.spad" 331851 331861 333641 333668) (-262 "DPOLCAT.spad" 327208 327224 331719 331846) (-261 "DPOLCAT.spad" 322651 322669 327164 327169) (-260 "DPMO.spad" 314174 314190 314312 314525) (-259 "DPMM.spad" 305710 305728 305835 306048) (-258 "DOMTMPLT.spad" 305481 305489 305700 305705) (-257 "DOMCTOR.spad" 305236 305244 305471 305476) (-256 "DOMAIN.spad" 304347 304355 305226 305231) (-255 "DMP.spad" 301535 301550 302105 302232) (-254 "DMEXT.spad" 301402 301412 301503 301530) (-253 "DLP.spad" 300762 300772 301392 301397) (-252 "DLIST.spad" 299167 299177 299771 299798) (-251 "DLAGG.spad" 297584 297594 299157 299162) (-250 "DIVRING.spad" 297126 297134 297528 297579) (-249 "DIVRING.spad" 296712 296722 297116 297121) (-248 "DISPLAY.spad" 294902 294910 296702 296707) (-247 "DIRPROD2.spad" 293720 293738 294892 294897) (-246 "DIRPROD.spad" 280952 280968 281592 281691) (-245 "DIRPCAT.spad" 280145 280161 280848 280947) (-244 "DIRPCAT.spad" 278965 278983 279670 279675) (-243 "DIOSP.spad" 277790 277798 278955 278960) (-242 "DIOPS.spad" 276786 276796 277770 277785) (-241 "DIOPS.spad" 275756 275768 276742 276747) (-240 "DIFRING.spad" 275594 275602 275736 275751) (-239 "DIFFSPC.spad" 275173 275181 275584 275589) (-238 "DIFFSPC.spad" 274750 274760 275163 275168) (-237 "DIFFMOD.spad" 274239 274249 274718 274745) (-236 "DIFFDOM.spad" 273404 273415 274229 274234) (-235 "DIFFDOM.spad" 272567 272580 273394 273399) (-234 "DIFEXT.spad" 272386 272396 272547 272562) (-233 "DIAGG.spad" 272016 272026 272366 272381) (-232 "DIAGG.spad" 271654 271666 272006 272011) (-231 "DHMATRIX.spad" 269837 269847 270982 271009) (-230 "DFSFUN.spad" 263477 263485 269827 269832) (-229 "DFLOAT.spad" 260084 260092 263367 263472) (-228 "DFINTTLS.spad" 258315 258331 260074 260079) (-227 "DERHAM.spad" 256229 256261 258295 258310) (-226 "DEQUEUE.spad" 255424 255434 255707 255734) (-225 "DEGRED.spad" 255041 255055 255414 255419) (-224 "DEFINTRF.spad" 252578 252588 255031 255036) (-223 "DEFINTEF.spad" 251088 251104 252568 252573) (-222 "DEFAST.spad" 250472 250480 251078 251083) (-221 "DECIMAL.spad" 248436 248444 248797 248890) (-220 "DDFACT.spad" 246257 246274 248426 248431) (-219 "DBLRESP.spad" 245857 245881 246247 246252) (-218 "DBASIS.spad" 245483 245498 245847 245852) (-217 "DBASE.spad" 244147 244157 245473 245478) (-216 "DATAARY.spad" 243633 243646 244137 244142) (-215 "D03FAFA.spad" 243461 243469 243623 243628) (-214 "D03EEFA.spad" 243281 243289 243451 243456) (-213 "D03AGNT.spad" 242367 242375 243271 243276) (-212 "D02EJFA.spad" 241829 241837 242357 242362) (-211 "D02CJFA.spad" 241307 241315 241819 241824) (-210 "D02BHFA.spad" 240797 240805 241297 241302) (-209 "D02BBFA.spad" 240287 240295 240787 240792) (-208 "D02AGNT.spad" 235157 235165 240277 240282) (-207 "D01WGTS.spad" 233476 233484 235147 235152) (-206 "D01TRNS.spad" 233453 233461 233466 233471) (-205 "D01GBFA.spad" 232975 232983 233443 233448) (-204 "D01FCFA.spad" 232497 232505 232965 232970) (-203 "D01ASFA.spad" 231965 231973 232487 232492) (-202 "D01AQFA.spad" 231419 231427 231955 231960) (-201 "D01APFA.spad" 230859 230867 231409 231414) (-200 "D01ANFA.spad" 230353 230361 230849 230854) (-199 "D01AMFA.spad" 229863 229871 230343 230348) (-198 "D01ALFA.spad" 229403 229411 229853 229858) (-197 "D01AKFA.spad" 228929 228937 229393 229398) (-196 "D01AJFA.spad" 228452 228460 228919 228924) (-195 "D01AGNT.spad" 224519 224527 228442 228447) (-194 "CYCLOTOM.spad" 224025 224033 224509 224514) (-193 "CYCLES.spad" 220817 220825 224015 224020) (-192 "CVMP.spad" 220234 220244 220807 220812) (-191 "CTRIGMNP.spad" 218734 218750 220224 220229) (-190 "CTORKIND.spad" 218337 218345 218724 218729) (-189 "CTORCAT.spad" 217578 217586 218327 218332) (-188 "CTORCAT.spad" 216817 216827 217568 217573) (-187 "CTORCALL.spad" 216406 216416 216807 216812) (-186 "CTOR.spad" 216097 216105 216396 216401) (-185 "CSTTOOLS.spad" 215342 215355 216087 216092) (-184 "CRFP.spad" 209114 209127 215332 215337) (-183 "CRCEAST.spad" 208834 208842 209104 209109) (-182 "CRAPACK.spad" 207901 207911 208824 208829) (-181 "CPMATCH.spad" 207402 207417 207823 207828) (-180 "CPIMA.spad" 207107 207126 207392 207397) (-179 "COORDSYS.spad" 202116 202126 207097 207102) (-178 "CONTOUR.spad" 201543 201551 202106 202111) (-177 "CONTFRAC.spad" 197293 197303 201445 201538) (-176 "CONDUIT.spad" 197051 197059 197283 197288) (-175 "COMRING.spad" 196725 196733 196989 197046) (-174 "COMPPROP.spad" 196243 196251 196715 196720) (-173 "COMPLPAT.spad" 196010 196025 196233 196238) (-172 "COMPLEX2.spad" 195725 195737 196000 196005) (-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 2287934 2287939 2287944 2287949) (-2 NIL 2287914 2287919 2287924 2287929) (-1 NIL 2287894 2287899 2287904 2287909) (0 NIL 2287874 2287879 2287884 2287889) (-1326 "ZMOD.spad" 2287683 2287696 2287812 2287869) (-1325 "ZLINDEP.spad" 2286781 2286792 2287673 2287678) (-1324 "ZDSOLVE.spad" 2276741 2276763 2286771 2286776) (-1323 "YSTREAM.spad" 2276236 2276247 2276731 2276736) (-1322 "YDIAGRAM.spad" 2275870 2275879 2276226 2276231) (-1321 "XRPOLY.spad" 2275090 2275110 2275726 2275795) (-1320 "XPR.spad" 2272885 2272898 2274808 2274907) (-1319 "XPOLYC.spad" 2272204 2272220 2272811 2272880) (-1318 "XPOLY.spad" 2271759 2271770 2272060 2272129) (-1317 "XPBWPOLY.spad" 2270198 2270218 2271533 2271602) (-1316 "XFALG.spad" 2267246 2267262 2270124 2270193) (-1315 "XF.spad" 2265709 2265724 2267148 2267241) (-1314 "XF.spad" 2264152 2264169 2265593 2265598) (-1313 "XEXPPKG.spad" 2263411 2263437 2264142 2264147) (-1312 "XDPOLY.spad" 2263025 2263041 2263267 2263336) (-1311 "XALG.spad" 2262693 2262704 2262981 2263020) (-1310 "WUTSET.spad" 2258663 2258680 2262294 2262321) (-1309 "WP.spad" 2257870 2257914 2258521 2258588) (-1308 "WHILEAST.spad" 2257668 2257677 2257860 2257865) (-1307 "WHEREAST.spad" 2257339 2257348 2257658 2257663) (-1306 "WFFINTBS.spad" 2255002 2255024 2257329 2257334) (-1305 "WEIER.spad" 2253224 2253235 2254992 2254997) (-1304 "VSPACE.spad" 2252897 2252908 2253192 2253219) (-1303 "VSPACE.spad" 2252590 2252603 2252887 2252892) (-1302 "VOID.spad" 2252267 2252276 2252580 2252585) (-1301 "VIEWDEF.spad" 2247468 2247477 2252257 2252262) (-1300 "VIEW3D.spad" 2231429 2231438 2247458 2247463) (-1299 "VIEW2D.spad" 2219328 2219337 2231419 2231424) (-1298 "VIEW.spad" 2217048 2217057 2219318 2219323) (-1297 "VECTOR2.spad" 2215687 2215700 2217038 2217043) (-1296 "VECTOR.spad" 2214187 2214198 2214438 2214465) (-1295 "VECTCAT.spad" 2212099 2212110 2214155 2214182) (-1294 "VECTCAT.spad" 2209818 2209831 2211876 2211881) (-1293 "VARIABLE.spad" 2209598 2209613 2209808 2209813) (-1292 "UTYPE.spad" 2209242 2209251 2209588 2209593) (-1291 "UTSODETL.spad" 2208537 2208561 2209198 2209203) (-1290 "UTSODE.spad" 2206753 2206773 2208527 2208532) (-1289 "UTSCAT.spad" 2204232 2204248 2206651 2206748) (-1288 "UTSCAT.spad" 2201331 2201349 2203752 2203757) (-1287 "UTS2.spad" 2200926 2200961 2201321 2201326) (-1286 "UTS.spad" 2195804 2195832 2199324 2199421) (-1285 "URAGG.spad" 2190525 2190536 2195794 2195799) (-1284 "URAGG.spad" 2185210 2185223 2190481 2190486) (-1283 "UPXSSING.spad" 2182828 2182854 2184264 2184397) (-1282 "UPXSCONS.spad" 2180506 2180526 2180879 2181028) (-1281 "UPXSCCA.spad" 2179077 2179097 2180352 2180501) (-1280 "UPXSCCA.spad" 2177790 2177812 2179067 2179072) (-1279 "UPXSCAT.spad" 2176379 2176395 2177636 2177785) (-1278 "UPXS2.spad" 2175922 2175975 2176369 2176374) (-1277 "UPXS.spad" 2173137 2173165 2173973 2174122) (-1276 "UPSQFREE.spad" 2171552 2171566 2173127 2173132) (-1275 "UPSCAT.spad" 2169347 2169371 2171450 2171547) (-1274 "UPSCAT.spad" 2166827 2166853 2168932 2168937) (-1273 "UPOLYC2.spad" 2166298 2166317 2166817 2166822) (-1272 "UPOLYC.spad" 2161378 2161389 2166140 2166293) (-1271 "UPOLYC.spad" 2156344 2156357 2161108 2161113) (-1270 "UPMP.spad" 2155276 2155289 2156334 2156339) (-1269 "UPDIVP.spad" 2154841 2154855 2155266 2155271) (-1268 "UPDECOMP.spad" 2153102 2153116 2154831 2154836) (-1267 "UPCDEN.spad" 2152319 2152335 2153092 2153097) (-1266 "UP2.spad" 2151683 2151704 2152309 2152314) (-1265 "UP.spad" 2148711 2148726 2149098 2149251) (-1264 "UNISEG2.spad" 2148208 2148221 2148667 2148672) (-1263 "UNISEG.spad" 2147561 2147572 2148127 2148132) (-1262 "UNIFACT.spad" 2146664 2146676 2147551 2147556) (-1261 "ULSCONS.spad" 2137576 2137596 2137946 2138095) (-1260 "ULSCCAT.spad" 2135313 2135333 2137422 2137571) (-1259 "ULSCCAT.spad" 2133158 2133180 2135269 2135274) (-1258 "ULSCAT.spad" 2131398 2131414 2133004 2133153) (-1257 "ULS2.spad" 2130912 2130965 2131388 2131393) (-1256 "ULS.spad" 2120483 2120511 2121428 2121857) (-1255 "UINT8.spad" 2120360 2120369 2120473 2120478) (-1254 "UINT64.spad" 2120236 2120245 2120350 2120355) (-1253 "UINT32.spad" 2120112 2120121 2120226 2120231) (-1252 "UINT16.spad" 2119988 2119997 2120102 2120107) (-1251 "UFD.spad" 2119053 2119062 2119914 2119983) (-1250 "UFD.spad" 2118180 2118191 2119043 2119048) (-1249 "UDVO.spad" 2117061 2117070 2118170 2118175) (-1248 "UDPO.spad" 2114642 2114653 2117017 2117022) (-1247 "TYPEAST.spad" 2114561 2114570 2114632 2114637) (-1246 "TYPE.spad" 2114493 2114502 2114551 2114556) (-1245 "TWOFACT.spad" 2113145 2113160 2114483 2114488) (-1244 "TUPLE.spad" 2112636 2112647 2113041 2113046) (-1243 "TUBETOOL.spad" 2109503 2109512 2112626 2112631) (-1242 "TUBE.spad" 2108150 2108167 2109493 2109498) (-1241 "TSETCAT.spad" 2096221 2096238 2108118 2108145) (-1240 "TSETCAT.spad" 2084278 2084297 2096177 2096182) (-1239 "TS.spad" 2082871 2082887 2083837 2083934) (-1238 "TRMANIP.spad" 2077235 2077252 2082559 2082564) (-1237 "TRIMAT.spad" 2076198 2076223 2077225 2077230) (-1236 "TRIGMNIP.spad" 2074725 2074742 2076188 2076193) (-1235 "TRIGCAT.spad" 2074237 2074246 2074715 2074720) (-1234 "TRIGCAT.spad" 2073747 2073758 2074227 2074232) (-1233 "TREE.spad" 2072193 2072204 2073225 2073252) (-1232 "TRANFUN.spad" 2072032 2072041 2072183 2072188) (-1231 "TRANFUN.spad" 2071869 2071880 2072022 2072027) (-1230 "TOPSP.spad" 2071543 2071552 2071859 2071864) (-1229 "TOOLSIGN.spad" 2071206 2071217 2071533 2071538) (-1228 "TEXTFILE.spad" 2069767 2069776 2071196 2071201) (-1227 "TEX1.spad" 2069323 2069334 2069757 2069762) (-1226 "TEX.spad" 2066517 2066526 2069313 2069318) (-1225 "TEMUTL.spad" 2066072 2066081 2066507 2066512) (-1224 "TBCMPPK.spad" 2064173 2064196 2066062 2066067) (-1223 "TBAGG.spad" 2063231 2063254 2064153 2064168) (-1222 "TBAGG.spad" 2062297 2062322 2063221 2063226) (-1221 "TANEXP.spad" 2061705 2061716 2062287 2062292) (-1220 "TALGOP.spad" 2061429 2061440 2061695 2061700) (-1219 "TABLEAU.spad" 2060910 2060921 2061419 2061424) (-1218 "TABLE.spad" 2058843 2058866 2059113 2059140) (-1217 "TABLBUMP.spad" 2055622 2055633 2058833 2058838) (-1216 "SYSTEM.spad" 2054850 2054859 2055612 2055617) (-1215 "SYSSOLP.spad" 2052333 2052344 2054840 2054845) (-1214 "SYSPTR.spad" 2052232 2052241 2052323 2052328) (-1213 "SYSNNI.spad" 2051455 2051466 2052222 2052227) (-1212 "SYSINT.spad" 2050859 2050870 2051445 2051450) (-1211 "SYNTAX.spad" 2047193 2047202 2050849 2050854) (-1210 "SYMTAB.spad" 2045261 2045270 2047183 2047188) (-1209 "SYMS.spad" 2041290 2041299 2045251 2045256) (-1208 "SYMPOLY.spad" 2040269 2040280 2040351 2040478) (-1207 "SYMFUNC.spad" 2039770 2039781 2040259 2040264) (-1206 "SYMBOL.spad" 2037265 2037274 2039760 2039765) (-1205 "SWITCH.spad" 2034036 2034045 2037255 2037260) (-1204 "SUTS.spad" 2031015 2031043 2032434 2032531) (-1203 "SUPXS.spad" 2028217 2028245 2029066 2029215) (-1202 "SUPFRACF.spad" 2027322 2027340 2028207 2028212) (-1201 "SUP2.spad" 2026714 2026727 2027312 2027317) (-1200 "SUP.spad" 2023356 2023367 2024129 2024282) (-1199 "SUMRF.spad" 2022330 2022341 2023346 2023351) (-1198 "SUMFS.spad" 2021959 2021976 2022320 2022325) (-1197 "SULS.spad" 2011517 2011545 2012475 2012904) (-1196 "SUCHTAST.spad" 2011286 2011295 2011507 2011512) (-1195 "SUCH.spad" 2010976 2010991 2011276 2011281) (-1194 "SUBSPACE.spad" 2003107 2003122 2010966 2010971) (-1193 "SUBRESP.spad" 2002277 2002291 2003063 2003068) (-1192 "STTFNC.spad" 1998745 1998761 2002267 2002272) (-1191 "STTF.spad" 1994844 1994860 1998735 1998740) (-1190 "STTAYLOR.spad" 1987489 1987500 1994719 1994724) (-1189 "STRTBL.spad" 1985504 1985521 1985653 1985680) (-1188 "STRING.spad" 1984270 1984279 1984491 1984518) (-1187 "STREAM3.spad" 1983843 1983858 1984260 1984265) (-1186 "STREAM2.spad" 1982971 1982984 1983833 1983838) (-1185 "STREAM1.spad" 1982677 1982688 1982961 1982966) (-1184 "STREAM.spad" 1979463 1979474 1982070 1982085) (-1183 "STINPROD.spad" 1978399 1978415 1979453 1979458) (-1182 "STEPAST.spad" 1977633 1977642 1978389 1978394) (-1181 "STEP.spad" 1976842 1976851 1977623 1977628) (-1180 "STBL.spad" 1974890 1974918 1975057 1975072) (-1179 "STAGG.spad" 1973589 1973600 1974880 1974885) (-1178 "STAGG.spad" 1972286 1972299 1973579 1973584) (-1177 "STACK.spad" 1971514 1971525 1971764 1971791) (-1176 "SRING.spad" 1971274 1971283 1971504 1971509) (-1175 "SREGSET.spad" 1968973 1968990 1970875 1970902) (-1174 "SRDCMPK.spad" 1967550 1967570 1968963 1968968) (-1173 "SRAGG.spad" 1962733 1962742 1967518 1967545) (-1172 "SRAGG.spad" 1957936 1957947 1962723 1962728) (-1171 "SQMATRIX.spad" 1955431 1955449 1956347 1956434) (-1170 "SPLTREE.spad" 1949897 1949910 1954693 1954720) (-1169 "SPLNODE.spad" 1946517 1946530 1949887 1949892) (-1168 "SPFCAT.spad" 1945326 1945335 1946507 1946512) (-1167 "SPECOUT.spad" 1943878 1943887 1945316 1945321) (-1166 "SPADXPT.spad" 1935969 1935978 1943868 1943873) (-1165 "spad-parser.spad" 1935434 1935443 1935959 1935964) (-1164 "SPADAST.spad" 1935135 1935144 1935424 1935429) (-1163 "SPACEC.spad" 1919350 1919361 1935125 1935130) (-1162 "SPACE3.spad" 1919126 1919137 1919340 1919345) (-1161 "SORTPAK.spad" 1918675 1918688 1919082 1919087) (-1160 "SOLVETRA.spad" 1916438 1916449 1918665 1918670) (-1159 "SOLVESER.spad" 1914894 1914905 1916428 1916433) (-1158 "SOLVERAD.spad" 1910920 1910931 1914884 1914889) (-1157 "SOLVEFOR.spad" 1909382 1909400 1910910 1910915) (-1156 "SNTSCAT.spad" 1908982 1908999 1909350 1909377) (-1155 "SMTS.spad" 1907264 1907290 1908541 1908638) (-1154 "SMP.spad" 1904667 1904687 1905057 1905184) (-1153 "SMITH.spad" 1903512 1903537 1904657 1904662) (-1152 "SMATCAT.spad" 1901630 1901660 1903456 1903507) (-1151 "SMATCAT.spad" 1899680 1899712 1901508 1901513) (-1150 "SKAGG.spad" 1898649 1898660 1899648 1899675) (-1149 "SINT.spad" 1897589 1897598 1898515 1898644) (-1148 "SIMPAN.spad" 1897317 1897326 1897579 1897584) (-1147 "SIGNRF.spad" 1896442 1896453 1897307 1897312) (-1146 "SIGNEF.spad" 1895728 1895745 1896432 1896437) (-1145 "SIGAST.spad" 1895145 1895154 1895718 1895723) (-1144 "SIG.spad" 1894507 1894516 1895135 1895140) (-1143 "SHP.spad" 1892451 1892466 1894463 1894468) (-1142 "SHDP.spad" 1879806 1879833 1880323 1880422) (-1141 "SGROUP.spad" 1879414 1879423 1879796 1879801) (-1140 "SGROUP.spad" 1879020 1879031 1879404 1879409) (-1139 "SGCF.spad" 1872159 1872168 1879010 1879015) (-1138 "SFRTCAT.spad" 1871105 1871122 1872127 1872154) (-1137 "SFRGCD.spad" 1870168 1870188 1871095 1871100) (-1136 "SFQCMPK.spad" 1864981 1865001 1870158 1870163) (-1135 "SFORT.spad" 1864420 1864434 1864971 1864976) (-1134 "SEXOF.spad" 1864263 1864303 1864410 1864415) (-1133 "SEXCAT.spad" 1862091 1862131 1864253 1864258) (-1132 "SEX.spad" 1861983 1861992 1862081 1862086) (-1131 "SETMN.spad" 1860443 1860460 1861973 1861978) (-1130 "SETCAT.spad" 1859928 1859937 1860433 1860438) (-1129 "SETCAT.spad" 1859411 1859422 1859918 1859923) (-1128 "SETAGG.spad" 1855960 1855971 1859391 1859406) (-1127 "SETAGG.spad" 1852517 1852530 1855950 1855955) (-1126 "SET.spad" 1850790 1850801 1851887 1851926) (-1125 "SEQAST.spad" 1850493 1850502 1850780 1850785) (-1124 "SEGXCAT.spad" 1849649 1849662 1850483 1850488) (-1123 "SEGCAT.spad" 1848574 1848585 1849639 1849644) (-1122 "SEGBIND2.spad" 1848272 1848285 1848564 1848569) (-1121 "SEGBIND.spad" 1848030 1848041 1848219 1848224) (-1120 "SEGAST.spad" 1847760 1847769 1848020 1848025) (-1119 "SEG2.spad" 1847195 1847208 1847716 1847721) (-1118 "SEG.spad" 1847008 1847019 1847114 1847119) (-1117 "SDVAR.spad" 1846284 1846295 1846998 1847003) (-1116 "SDPOL.spad" 1843539 1843550 1843830 1843957) (-1115 "SCPKG.spad" 1841628 1841639 1843529 1843534) (-1114 "SCOPE.spad" 1840805 1840814 1841618 1841623) (-1113 "SCACHE.spad" 1839501 1839512 1840795 1840800) (-1112 "SASTCAT.spad" 1839410 1839419 1839491 1839496) (-1111 "SAOS.spad" 1839282 1839291 1839400 1839405) (-1110 "SAERFFC.spad" 1838995 1839015 1839272 1839277) (-1109 "SAEFACT.spad" 1838696 1838716 1838985 1838990) (-1108 "SAE.spad" 1836130 1836146 1836741 1836876) (-1107 "RURPK.spad" 1833789 1833805 1836120 1836125) (-1106 "RULESET.spad" 1833242 1833266 1833779 1833784) (-1105 "RULECOLD.spad" 1833094 1833107 1833232 1833237) (-1104 "RULE.spad" 1831342 1831366 1833084 1833089) (-1103 "RTVALUE.spad" 1831077 1831086 1831332 1831337) (-1102 "RSTRCAST.spad" 1830794 1830803 1831067 1831072) (-1101 "RSETGCD.spad" 1827236 1827256 1830784 1830789) (-1100 "RSETCAT.spad" 1817204 1817221 1827204 1827231) (-1099 "RSETCAT.spad" 1807192 1807211 1817194 1817199) (-1098 "RSDCMPK.spad" 1805692 1805712 1807182 1807187) (-1097 "RRCC.spad" 1804076 1804106 1805682 1805687) (-1096 "RRCC.spad" 1802458 1802490 1804066 1804071) (-1095 "RPTAST.spad" 1802160 1802169 1802448 1802453) (-1094 "RPOLCAT.spad" 1781664 1781679 1802028 1802155) (-1093 "RPOLCAT.spad" 1760863 1760880 1781229 1781234) (-1092 "ROUTINE.spad" 1756264 1756273 1759012 1759039) (-1091 "ROMAN.spad" 1755592 1755601 1756130 1756259) (-1090 "ROIRC.spad" 1754672 1754704 1755582 1755587) (-1089 "RNS.spad" 1753648 1753657 1754574 1754667) (-1088 "RNS.spad" 1752710 1752721 1753638 1753643) (-1087 "RNGBIND.spad" 1751870 1751884 1752665 1752670) (-1086 "RNG.spad" 1751605 1751614 1751860 1751865) (-1085 "RMODULE.spad" 1751386 1751397 1751595 1751600) (-1084 "RMCAT2.spad" 1750806 1750863 1751376 1751381) (-1083 "RMATRIX.spad" 1749576 1749595 1749919 1749958) (-1082 "RMATCAT.spad" 1745155 1745186 1749532 1749571) (-1081 "RMATCAT.spad" 1740624 1740657 1745003 1745008) (-1080 "RLINSET.spad" 1740328 1740339 1740614 1740619) (-1079 "RINTERP.spad" 1740216 1740236 1740318 1740323) (-1078 "RING.spad" 1739686 1739695 1740196 1740211) (-1077 "RING.spad" 1739164 1739175 1739676 1739681) (-1076 "RIDIST.spad" 1738556 1738565 1739154 1739159) (-1075 "RGCHAIN.spad" 1737077 1737093 1737971 1737998) (-1074 "RGBCSPC.spad" 1736866 1736878 1737067 1737072) (-1073 "RGBCMDL.spad" 1736428 1736440 1736856 1736861) (-1072 "RFFACTOR.spad" 1735890 1735901 1736418 1736423) (-1071 "RFFACT.spad" 1735625 1735637 1735880 1735885) (-1070 "RFDIST.spad" 1734621 1734630 1735615 1735620) (-1069 "RF.spad" 1732295 1732306 1734611 1734616) (-1068 "RETSOL.spad" 1731714 1731727 1732285 1732290) (-1067 "RETRACT.spad" 1731142 1731153 1731704 1731709) (-1066 "RETRACT.spad" 1730568 1730581 1731132 1731137) (-1065 "RETAST.spad" 1730380 1730389 1730558 1730563) (-1064 "RESULT.spad" 1727942 1727951 1728529 1728556) (-1063 "RESRING.spad" 1727289 1727336 1727880 1727937) (-1062 "RESLATC.spad" 1726613 1726624 1727279 1727284) (-1061 "REPSQ.spad" 1726344 1726355 1726603 1726608) (-1060 "REPDB.spad" 1726051 1726062 1726334 1726339) (-1059 "REP2.spad" 1715765 1715776 1725893 1725898) (-1058 "REP1.spad" 1709985 1709996 1715715 1715720) (-1057 "REP.spad" 1707539 1707548 1709975 1709980) (-1056 "REGSET.spad" 1705331 1705348 1707140 1707167) (-1055 "REF.spad" 1704666 1704677 1705286 1705291) (-1054 "REDORDER.spad" 1703872 1703889 1704656 1704661) (-1053 "RECLOS.spad" 1702631 1702651 1703335 1703428) (-1052 "REALSOLV.spad" 1701771 1701780 1702621 1702626) (-1051 "REAL0Q.spad" 1699069 1699084 1701761 1701766) (-1050 "REAL0.spad" 1695913 1695928 1699059 1699064) (-1049 "REAL.spad" 1695785 1695794 1695903 1695908) (-1048 "RDUCEAST.spad" 1695506 1695515 1695775 1695780) (-1047 "RDIV.spad" 1695161 1695186 1695496 1695501) (-1046 "RDIST.spad" 1694728 1694739 1695151 1695156) (-1045 "RDETRS.spad" 1693592 1693610 1694718 1694723) (-1044 "RDETR.spad" 1691731 1691749 1693582 1693587) (-1043 "RDEEFS.spad" 1690830 1690847 1691721 1691726) (-1042 "RDEEF.spad" 1689840 1689857 1690820 1690825) (-1041 "RCFIELD.spad" 1687058 1687067 1689742 1689835) (-1040 "RCFIELD.spad" 1684362 1684373 1687048 1687053) (-1039 "RCAGG.spad" 1682298 1682309 1684352 1684357) (-1038 "RCAGG.spad" 1680161 1680174 1682217 1682222) (-1037 "RATRET.spad" 1679521 1679532 1680151 1680156) (-1036 "RATFACT.spad" 1679213 1679225 1679511 1679516) (-1035 "RANDSRC.spad" 1678532 1678541 1679203 1679208) (-1034 "RADUTIL.spad" 1678288 1678297 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(-415 "FPS.spad" 657029 657039 660082 660087) (-414 "FPC.spad" 656075 656083 656931 657024) (-413 "FPC.spad" 655207 655217 656065 656070) (-412 "FPATMAB.spad" 654969 654979 655197 655202) (-411 "FPARFRAC.spad" 653811 653828 654959 654964) (-410 "FORTRAN.spad" 652317 652360 653801 653806) (-409 "FORTFN.spad" 649487 649495 652307 652312) (-408 "FORTCAT.spad" 649171 649179 649477 649482) (-407 "FORT.spad" 648120 648128 649161 649166) (-406 "FORDER.spad" 647811 647835 648110 648115) (-405 "FOP.spad" 647012 647020 647801 647806) (-404 "FNLA.spad" 646436 646458 646980 647007) (-403 "FNCAT.spad" 645031 645039 646426 646431) (-402 "FNAME.spad" 644923 644931 645021 645026) (-401 "FMTC.spad" 644721 644729 644849 644918) (-400 "FMONOID.spad" 644402 644412 644677 644682) (-399 "FMONCAT.spad" 641571 641581 644392 644397) (-398 "FMFUN.spad" 638601 638609 641561 641566) (-397 "FMCAT.spad" 636277 636295 638569 638596) (-396 "FMC.spad" 635329 635337 636267 636272) (-395 "FM1.spad" 634694 634706 635263 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"FGROUP.spad" 581244 581254 582561 582576) (-373 "FGLMICPK.spad" 580039 580054 581234 581239) (-372 "FFX.spad" 579422 579437 579755 579848) (-371 "FFSLPE.spad" 578933 578954 579412 579417) (-370 "FFPOLY2.spad" 577993 578010 578923 578928) (-369 "FFPOLY.spad" 569335 569346 577983 577988) (-368 "FFP.spad" 568740 568760 569051 569144) (-367 "FFNBX.spad" 567260 567280 568456 568549) (-366 "FFNBP.spad" 565781 565798 566976 567069) (-365 "FFNB.spad" 564246 564267 565462 565555) (-364 "FFINTBAS.spad" 561760 561779 564236 564241) (-363 "FFIELDC.spad" 559345 559353 561662 561755) (-362 "FFIELDC.spad" 557016 557026 559335 559340) (-361 "FFHOM.spad" 555788 555805 557006 557011) (-360 "FFF.spad" 553231 553242 555778 555783) (-359 "FFCGX.spad" 552086 552106 552947 553040) (-358 "FFCGP.spad" 550983 551003 551802 551895) (-357 "FFCG.spad" 549775 549796 550664 550757) (-356 "FFCAT2.spad" 549522 549562 549765 549770) (-355 "FFCAT.spad" 542687 542709 549361 549517) (-354 "FFCAT.spad" 535931 535955 542607 542612) (-353 "FF.spad" 535379 535395 535612 535705) (-352 "FEXPR.spad" 527079 527125 535126 535165) (-351 "FEVALAB.spad" 526787 526797 527069 527074) (-350 "FEVALAB.spad" 526271 526283 526555 526560) (-349 "FDIVCAT.spad" 524367 524391 526261 526266) (-348 "FDIVCAT.spad" 522461 522487 524357 524362) (-347 "FDIV2.spad" 522117 522157 522451 522456) (-346 "FDIV.spad" 521575 521599 522107 522112) (-345 "FCTRDATA.spad" 520583 520591 521565 521570) (-344 "FCPAK1.spad" 519118 519126 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) (-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 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. -1131) T) ((-528 . -19) 194447) ((-508 . -19) 194431) ((-58 . -616) 194408) ((-1033 . -239) 194345) ((-929 . -102) 194295) ((-877 . -746) T) ((-801 . -1131) T) ((-528 . -616) 194272) ((-508 . -616) 194249) ((-800 . -1131) T) ((-800 . -1095) 194216) ((-473 . -1131) T) ((-466 . -1131) T) ((-595 . -737) 194191) ((-669 . -1131) T) ((-1287 . -47) 194168) ((-1284 . -102) T) ((-1278 . -47) 194138) ((-1257 . -47) 194115) ((-1240 . -175) 194066) ((-1204 . -319) 194045) ((-1198 . -319) 194024) ((-1126 . -633) 194005) ((-1121 . -633) 193986) ((-1109 . -569) 193937) ((-1109 . -1252) 193888) ((-1103 . -633) 193869) ((-1034 . -926) NIL) ((-1096 . -633) 193850) ((-690 . -133) T) ((-644 . -1142) T) ((-1066 . -633) 193831) ((-1049 . -633) 193812) ((-734 . -1086) 193782) ((-732 . -920) 193685) ((-719 . -666) 193635) ((-286 . -1131) T) ((-86 . -453) T) ((-86 . -408) T) ((-731 . -175) T) ((-657 . -1086) 193619) ((-50 . -1131) T) ((-607 . -47) 193596) ((-229 . -668) 193561) ((-593 . -1131) T) ((-530 . 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. -1142) T) ((-490 . -93) T) ((-419 . -239) 191087) ((-368 . -630) 191069) ((-366 . -630) 191051) ((-358 . -630) 191033) ((-275 . -631) 190781) ((-275 . -630) 190763) ((-255 . -630) 190745) ((-255 . -631) 190606) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1171 . -630) 190588) ((-1150 . -660) 190575) ((-1150 . -1081) 190562) ((-841 . -746) T) ((-841 . -880) T) ((-614 . -300) 190539) ((-593 . -737) 190504) ((-491 . -631) NIL) ((-491 . -630) 190486) ((-530 . -737) 190431) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-934 . -630) 190413) ((-934 . -631) 190395) ((-400 . -746) T) ((-895 . -1086) 190347) ((-895 . -111) 190285) ((-734 . -1079) T) ((-732 . -1273) 190269) ((-714 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-531 . -630) 190201) ((-391 . -819) T) ((-170 . -1247) T) ((-227 . -1131) T) ((-391 . -814) T) ((-58 . -631) 190162) ((-229 . -816) T) ((-229 . -812) T) ((-58 . -630) 190074) ((-229 . -746) T) ((-528 . -631) 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-111) 186870) ((-1262 . -111) 186659) ((-252 . -1286) 186643) ((-558 . -869) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186630) ((-325 . -321) 186571) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1034 . -1050) T) ((-31 . -633) 186552) ((-108 . -23) T) ((-676 . -1081) 186536) ((-252 . -616) 186513) ((-659 . -737) 186497) ((-345 . -1131) T) ((-676 . -660) 186467) ((-1284 . -38) 186359) ((-1266 . -938) 186338) ((-114 . -1131) T) ((-838 . -1247) T) ((-425 . -1247) T) ((-1065 . -102) T) ((-1266 . -668) 186227) ((-894 . -816) NIL) ((-878 . -668) 186201) ((-894 . -812) NIL) ((-838 . -910) NIL) ((-894 . -746) T) ((-1117 . -526) 186068) ((-801 . -526) 186015) ((-800 . -526) 185967) ((-583 . -668) 185954) ((-838 . -1068) 185782) ((-466 . -526) 185725) ((-402 . -403) T) ((-1283 . -633) 185538) ((-1262 . -633) 185286) ((-60 . -1247) T) ((-636 . -870) 185265) ((-512 . -682) T) ((-1176 . -1006) 185234) ((-1054 . -666) 185171) ((-1033 . -464) T) ((-719 . -869) T) ((-523 . -814) T) 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T) ((-801 . -302) 183488) ((-339 . -19) 183472) ((-58 . -300) 183449) ((-800 . -302) 183380) ((-878 . -746) T) ((-119 . -869) NIL) ((-528 . -300) 183357) ((-339 . -616) 183334) ((-508 . -300) 183311) ((-466 . -302) 183242) ((-1065 . -321) 183093) ((-899 . -502) 183074) ((-899 . -630) 183040) ((-701 . -502) 183021) ((-583 . -746) T) ((-696 . -502) 183002) ((-701 . -630) 182952) ((-696 . -630) 182918) ((-672 . -630) 182900) ((-490 . -502) 182881) ((-490 . -630) 182847) ((-252 . -631) 182808) ((-252 . -502) 182785) ((-140 . -502) 182766) ((-139 . -502) 182747) ((-135 . -502) 182728) ((-252 . -630) 182620) ((-216 . -102) T) ((-140 . -630) 182586) ((-139 . -630) 182552) ((-135 . -630) 182518) ((-1178 . -34) T) ((-971 . -1247) T) ((-357 . -737) 182463) ((-690 . -25) T) ((-690 . -21) T) ((-1207 . -633) 182444) ((-343 . -1247) T) ((-486 . -1079) T) ((-650 . -430) 182409) ((-618 . -430) 182374) ((-1150 . -1182) T) ((-1278 . -319) 182353) ((-732 . -1081) 182176) ((-593 . -302) T) ((-530 . -302) T) ((-1257 . -319) 182155) ((-486 . -240) 182107) ((-486 . -250) 182086) ((-451 . -1247) T) ((-732 . -660) 181915) ((-1257 . -1050) NIL) ((-1109 . -133) T) ((-895 . -819) 181894) ((-146 . -102) T) ((-40 . -1131) T) ((-895 . -814) 181873) ((-661 . -1040) 181857) ((-592 . -1087) T) ((-558 . -1087) T) ((-507 . -1087) T) ((-419 . -464) T) ((-372 . -133) T) ((-326 . -412) 181841) ((-325 . -412) 181802) ((-367 . -133) T) ((-359 . -133) T) ((-1212 . -1131) T) ((-1150 . -38) 181789) ((-1119 . -630) 181756) ((-108 . -133) T) ((-982 . -1131) T) ((-947 . -1131) T) ((-791 . -1131) T) ((-692 . -1131) T) ((-721 . -149) T) ((-621 . -102) T) ((-118 . -149) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-684 . -1086) 181740) ((-543 . -870) T) ((-512 . -870) T) ((-377 . -1247) T) ((-368 . -1086) 181692) ((-366 . -1086) 181644) ((-358 . -1086) 181596) ((-260 . -1247) T) ((-259 . -1247) T) ((-275 . -1086) 181439) ((-255 . -1086) 181282) ((-684 . -111) 181261) ((-839 . -1252) 181240) ((-560 . -866) T) ((-326 . -928) 181206) ((-368 . -111) 181144) ((-366 . -111) 181082) ((-358 . -111) 181020) ((-275 . -111) 180849) ((-255 . -111) 180678) ((-325 . -928) NIL) ((-640 . -424) 180662) ((-44 . -21) T) ((-44 . -25) T) ((-930 . -873) 180613) ((-130 . -682) T) ((-837 . -658) 180519) ((-839 . -569) 180498) ((-499 . -873) T) ((-260 . -1068) 180325) ((-259 . -1068) 180152) ((-128 . -121) 180136) ((-221 . -873) T) ((-934 . -1086) 180101) ((-732 . -102) T) ((-719 . -1087) T) ((-609 . -633) 180082) ((-598 . -633) 180063) ((-547 . -635) 179966) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -630) 179948) ((-934 . -111) 179904) ((-40 . -737) 179849) ((-892 . -1131) T) ((-684 . -633) 179826) ((-665 . -633) 179807) ((-368 . -633) 179744) ((-366 . -633) 179681) ((-358 . -633) 179618) ((-560 . -1131) T) ((-339 . -631) 179579) ((-339 . -630) 179491) ((-275 . -633) 179244) ((-255 . -633) 179029) ((-190 . -1247) T) ((-1262 . -814) 178982) ((-1262 . -819) 178935) ((-260 . -390) 178904) ((-259 . -390) 178873) ((-562 . -873) T) ((-676 . -38) 178843) ((-625 . -34) T) ((-494 . -1142) 178821) ((-487 . -34) T) ((-1143 . -133) 178692) ((-992 . -25) 178503) ((-934 . -633) 178453) ((-897 . -630) 178435) ((-218 . -866) T) ((-992 . -21) 178390) ((-837 . -25) 178223) ((-837 . -21) 178134) ((-1254 . -381) T) ((-640 . -1087) T) ((-1209 . -569) 178113) ((-1201 . -47) 178090) ((-368 . -1079) T) ((-366 . -1079) T) ((-494 . -23) 177942) ((-358 . -1079) T) ((-275 . -1079) T) ((-255 . -1079) T) ((-1155 . -47) 177914) ((-119 . -1087) T) ((-1064 . -668) 177888) ((-986 . -34) T) ((-368 . -240) 177867) ((-368 . -250) T) ((-366 . -240) 177846) ((-366 . -250) T) ((-358 . -240) 177825) ((-358 . -250) T) ((-275 . -338) 177797) ((-255 . -338) 177754) ((-275 . -240) 177733) ((-1185 . -153) 177717) ((-260 . -926) 177649) ((-259 . -926) 177581) ((-1172 . -920) 177502) ((-1112 . -870) T) ((-1264 . -1247) 177480) ((-427 . -1142) T) ((-1240 . -1032) 177446) ((-1084 . -23) T) ((-1054 . -869) T) ((-934 . -1079) T) ((-334 . -668) 177428) ((-721 . -239) T) ((-690 . -236) 177373) ((-1204 . -949) 177352) ((-1198 . -949) 177331) ((-1198 . -842) NIL) ((-1026 . -1081) 177227) ((-995 . -1247) T) ((-934 . -250) T) ((-839 . -376) 177206) ((-218 . -1131) T) ((-394 . -23) T) ((-129 . -1131) 177184) ((-123 . -1131) 177162) ((-934 . -240) T) ((-131 . -34) T) ((-391 . -668) 177127) ((-1026 . -660) 177075) ((-892 . -737) 177062) ((-1327 . -666) 177034) ((-1076 . -153) 176999) ((-1023 . -1247) T) ((-886 . -1247) T) ((-40 . -175) T) ((-714 . -424) 176981) ((-732 . -321) 176968) ((-856 . -668) 176928) ((-850 . -668) 176902) ((-331 . -25) T) ((-331 . -21) T) ((-674 . -298) 176881) ((-592 . -1131) T) ((-558 . -1131) T) ((-507 . -1131) T) ((-1201 . -1247) T) ((-252 . -300) 176858) ((-1155 . -1247) T) ((-877 . -1247) T) ((-325 . -274) 176819) ((-325 . -234) 176780) ((-1253 . -873) T) ((-1201 . -910) NIL) ((-55 . -1131) T) ((-1155 . -910) 176639) ((-130 . -870) T) ((-1201 . -1068) 176519) 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T) ((-661 . -1247) T) ((-1109 . -658) 175384) ((-1201 . -926) 175327) ((-1155 . -926) 175311) ((-837 . -236) 175202) ((-672 . -1086) 175186) ((-108 . -658) 175168) ((-494 . -133) 175039) ((-1209 . -1142) T) ((-841 . -1247) T) ((-974 . -47) 175008) ((-640 . -1131) T) ((-672 . -111) 174987) ((-503 . -630) 174953) ((-339 . -300) 174930) ((-400 . -1247) T) ((-336 . -1247) T) ((-493 . -47) 174887) ((-1209 . -23) T) ((-119 . -1131) T) ((-103 . -102) 174837) ((-1310 . -1142) T) ((-561 . -870) T) ((-229 . -1247) T) ((-1084 . -133) T) ((-1054 . -1087) T) ((-1310 . -23) T) ((-1227 . -630) 174819) ((-841 . -1068) 174803) ((-1150 . -843) T) ((-1033 . -744) 174775) ((-1135 . -1131) T) ((-719 . -737) 174740) ((-595 . -630) 174722) ((-400 . -1068) 174706) ((-353 . -1087) T) ((-394 . -133) T) ((-336 . -1068) 174690) ((-1109 . -21) T) ((-1109 . -25) T) ((-1034 . -842) T) ((-229 . -910) 174672) ((-1034 . -949) T) ((-91 . -34) T) ((-1026 . -321) 174637) ((-942 . -949) T) ((-899 . -633) 174618) ((-734 . -668) 174578) ((-499 . -1252) T) ((-701 . -633) 174559) ((-696 . -633) 174540) ((-657 . -668) 174524) ((-221 . -1252) T) ((-419 . -920) 174445) ((-229 . -1068) 174405) ((-40 . -302) T) ((-499 . -569) T) ((-490 . -633) 174386) ((-372 . -25) T) ((-326 . -666) 174041) ((-325 . -666) 173955) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -569) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173901) ((-252 . -633) 173878) ((-140 . -633) 173859) ((-139 . -633) 173840) ((-135 . -633) 173821) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1087) T) ((-592 . -175) T) ((-558 . -175) T) ((-507 . -175) T) ((-1092 . -1247) T) ((-974 . -1247) T) ((-733 . -1247) T) ((-659 . -298) 173788) ((-674 . -630) 173770) ((-493 . -1247) T) ((-756 . -757) 173754) ((-346 . -630) 173736) ((-68 . -396) T) ((-68 . -408) T) ((-1127 . -107) 173720) ((-1092 . -910) 173702) ((-974 . -910) 173627) ((-675 . -1142) T) ((-640 . -737) 173614) ((-493 . -910) NIL) ((-1176 . -102) T) ((-1119 . -635) 173598) ((-1092 . -1068) 173580) ((-97 . -630) 173562) ((-489 . -149) T) ((-974 . -1068) 173442) ((-119 . -737) 173387) ((-732 . -928) 173294) ((-675 . -23) T) ((-493 . -1068) 173170) ((-1117 . -631) NIL) ((-1117 . -630) 173152) ((-801 . -631) NIL) ((-801 . -630) 173113) ((-800 . -631) 172747) ((-800 . -630) 172661) ((-1143 . -658) 172567) ((-820 . -873) 172546) ((-473 . -630) 172528) ((-466 . -630) 172510) ((-466 . -631) 172371) ((-1065 . -233) 172317) ((-895 . -938) 172296) ((-128 . -34) T) ((-839 . -133) T) ((-669 . -630) 172278) ((-590 . -102) T) ((-368 . -1316) 172262) ((-366 . -1316) 172246) ((-358 . -1316) 172230) ((-123 . -526) 172163) ((-129 . -526) 172096) ((-524 . -814) T) ((-524 . -819) T) ((-523 . -816) T) ((-103 . -321) 172034) ((-226 . -102) 171984) ((-719 . -175) T) ((-714 . -1131) T) ((-895 . -668) 171900) ((-65 . -398) T) ((-286 . -630) 171882) ((-65 . -408) T) ((-974 . -390) 171866) ((-892 . -302) T) ((-50 . -630) 171848) ((-1150 . -666) 171820) ((-1026 . -38) 171768) ((-624 . -1131) T) ((-619 . -1131) T) ((-593 . -630) 171750) ((-493 . -390) 171734) ((-593 . -631) 171716) ((-530 . -630) 171698) ((-934 . -1316) 171685) ((-894 . -1247) T) ((-721 . -464) T) ((-507 . -526) 171651) ((-1309 . -1247) T) ((-1308 . -1247) T) ((-499 . -376) T) ((-368 . -381) 171630) ((-366 . -381) 171609) ((-358 . -381) 171588) ((-734 . -746) T) ((-221 . -376) T) ((-118 . -464) T) ((-1321 . -1312) 171572) ((-894 . -908) 171549) ((-894 . -910) NIL) ((-992 . -870) 171448) ((-837 . -870) 171399) ((-1255 . -102) T) ((-676 . -678) 171383) ((-1234 . -34) T) ((-174 . -630) 171365) ((-1143 . -25) 171198) ((-1143 . -21) 171109) ((-894 . -1068) 171086) ((-974 . -926) 171067) ((-1266 . -47) 171044) ((-934 . -381) T) ((-605 . -873) T) ((-58 . -671) 171028) ((-528 . -671) 171012) ((-493 . -926) 170989) ((-71 . -453) T) ((-71 . -408) T) ((-508 . -671) 170973) ((-58 . -385) 170957) ((-640 . -175) T) ((-528 . -385) 170941) ((-508 . -385) 170925) ((-559 . -1247) T) ((-850 . -728) 170909) ((-1201 . -319) 170888) ((-1209 . -133) T) ((-1172 . -1081) 170872) ((-119 . -175) T) ((-1172 . -660) 170804) ((-1176 . -321) 170742) ((-171 . -1247) T) ((-1310 . -133) T) ((-1278 . -949) 170721) ((-1262 . -938) 170674) ((-1257 . -949) 170653) ((-889 . -1081) 170623) ((-650 . -764) 170607) ((-618 . -764) 170591) ((-1257 . -842) NIL) ((-1054 . -1131) T) ((-930 . -1142) T) ((-889 . -660) 170561) ((-714 . -737) 170511) ((-924 . -1247) T) ((-894 . -390) 170488) ((-894 . -351) 170465) ((-863 . -1247) T) ((-830 . -1247) T) ((-171 . -908) 170449) ((-171 . -910) 170374) ((-789 . -1247) T) ((-697 . -1247) T) ((-1297 . -526) 170307) ((-1283 . -668) 170204) ((-1109 . -236) 170077) ((-499 . -1142) T) ((-353 . -1131) T) ((-221 . -1142) T) ((-77 . -453) T) ((-77 . -408) T) ((-171 . -1068) 169973) ((-305 . -920) 169930) ((-331 . -870) T) ((-1262 . -668) 169738) ((-895 . -816) 169717) ((-895 . -812) 169696) ((-895 . -746) T) ((-499 . -23) T) ((-372 . -236) 169669) ((-367 . -236) 169642) ((-359 . -236) 169615) 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168449) ((-1033 . -660) 168394) ((-634 . -102) T) ((-614 . -34) T) ((-1178 . -1247) T) ((-1240 . -111) 168263) ((-486 . -668) 168160) ((-353 . -737) 168105) ((-171 . -926) 168064) ((-719 . -302) T) ((-714 . -175) T) ((-731 . -111) 168020) ((-1327 . -1087) T) ((-1266 . -390) 168004) ((-417 . -1252) 167982) ((-1145 . -630) 167964) ((-325 . -869) NIL) ((-417 . -569) T) ((-229 . -319) T) ((-1262 . -812) 167917) ((-1262 . -816) 167870) ((-1283 . -746) T) ((-1262 . -746) T) ((-48 . -737) 167835) ((-229 . -1050) T) ((-1284 . -424) 167801) ((-1266 . -926) 167744) ((-365 . -1305) 167721) ((-1240 . -633) 167603) ((-738 . -746) T) ((-345 . -630) 167585) ((-532 . -873) 167564) ((-1143 . -236) 167455) ((-114 . -630) 167437) ((-114 . -631) 167419) ((-738 . -485) T) ((-731 . -633) 167369) ((-1321 . -1081) 167353) ((-494 . -25) 167186) ((-129 . -501) 167170) ((-123 . -501) 167154) ((-494 . -21) 167065) ((-1321 . -660) 167035) ((-640 . -302) T) ((-595 . -1086) 167010) ((-448 . -1131) T) ((-1092 . -319) T) ((-119 . -302) T) ((-1133 . -102) T) ((-1033 . -102) T) ((-595 . -111) 166978) ((-1240 . -1079) T) ((-1172 . -321) 166916) ((-1092 . -1050) T) ((-1084 . -25) T) ((-66 . -1247) T) ((-914 . -1247) T) ((-1084 . -21) T) ((-731 . -1079) T) ((-394 . -21) T) ((-394 . -25) T) ((-714 . -526) NIL) ((-1054 . -175) T) ((-731 . -250) T) ((-1092 . -557) T) ((-732 . -666) 166826) ((-518 . -102) T) ((-514 . -102) T) ((-357 . -630) 166808) ((-353 . -175) T) ((-419 . -1081) 166760) ((-1150 . -869) T) ((-486 . -746) T) ((-914 . -1068) 166728) ((-419 . -660) 166680) ((-108 . -870) T) ((-674 . -1086) 166664) ((-499 . -133) T) ((-1284 . -1087) T) ((-221 . -133) T) ((-1185 . -102) 166614) ((-99 . -1131) T) ((-246 . -873) 166565) ((-252 . -686) 166549) ((-252 . -671) 166533) ((-674 . -111) 166512) ((-595 . -633) 166496) ((-326 . -424) 166480) ((-252 . -385) 166464) ((-1190 . -242) 166411) ((-1026 . -274) 166395) ((-1026 . -234) 166379) ((-74 . -1247) T) ((-48 . -175) T) ((-721 . -401) T) ((-721 . -145) T) 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-321) 155727) ((-1001 . -23) T) ((-143 . -526) NIL) ((-889 . -666) 155672) ((-942 . -1142) T) ((-942 . -23) T) ((-895 . -926) 155631) ((-365 . -38) 155596) ((-892 . -1086) 155583) ((-343 . -873) T) ((-83 . -630) 155565) ((-40 . -1079) T) ((-892 . -111) 155550) ((-738 . -1247) T) ((-721 . -102) T) ((-714 . -630) 155532) ((-614 . -1247) T) ((-608 . -569) 155511) ((-441 . -1142) T) ((-352 . -1081) 155495) ((-216 . -1131) T) ((-177 . -1081) 155427) ((-486 . -47) 155397) ((-40 . -240) 155369) ((-40 . -250) T) ((-136 . -102) T) ((-118 . -102) T) ((-607 . -569) 155348) ((-352 . -660) 155332) ((-714 . -631) 155240) ((-326 . -526) 155206) ((-177 . -660) 155138) ((-325 . -526) 155030) ((-499 . -236) 155017) ((-1283 . -1068) 155001) ((-1262 . -1068) 154787) ((-1026 . -424) 154771) ((-221 . -236) 154758) ((-441 . -23) T) ((-1150 . -175) T) ((-624 . -502) 154725) ((-619 . -502) 154707) ((-624 . -630) 154659) ((-619 . -630) 154626) ((-1284 . -302) T) ((-676 . -737) 154596) ((-146 . -1131) T) ((-48 . 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153397) ((-1198 . -505) 153363) ((-732 . -1131) T) ((-1156 . -505) 153329) ((-592 . -1086) 153316) ((-558 . -1086) 153303) ((-507 . -1086) 153268) ((-326 . -302) 153247) ((-325 . -302) T) ((-353 . -630) 153229) ((-417 . -25) T) ((-417 . -21) T) ((-99 . -298) 153208) ((-592 . -111) 153193) ((-558 . -111) 153178) ((-507 . -111) 153134) ((-1207 . -910) 153101) ((-929 . -501) 153085) ((-48 . -630) 153067) ((-48 . -631) 153012) ((-246 . -133) 152883) ((-1321 . -666) 152842) ((-1266 . -949) 152821) ((-838 . -1252) 152800) ((-402 . -502) 152781) ((-1065 . -526) 152625) ((-402 . -630) 152591) ((-838 . -569) 152522) ((-595 . -668) 152497) ((-275 . -47) 152469) ((-255 . -47) 152426) ((-543 . -521) 152403) ((-592 . -633) 152375) ((-558 . -633) 152347) ((-507 . -633) 152280) ((-1287 . -23) T) ((-1104 . -1247) T) ((-1030 . -1247) T) ((-1287 . -1142) T) ((-1278 . -1142) T) ((-1278 . -23) T) ((-1257 . -1142) T) ((-1257 . -23) T) ((-719 . -1086) 152245) ((-1253 . -682) T) ((-1240 . -746) T) ((-1150 . 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-938) 151343) ((-118 . -38) 151330) ((-212 . -822) T) ((-211 . -822) T) ((-210 . -822) T) ((-209 . -822) T) ((-895 . -1050) 151308) ((-684 . -1247) T) ((-665 . -1247) T) ((-801 . -938) 151287) ((-800 . -938) 151266) ((-1219 . -1247) T) ((-368 . -1247) T) ((-366 . -1247) T) ((-358 . -1247) T) ((-275 . -1247) T) ((-255 . -1247) T) ((-466 . -938) 151245) ((-756 . -501) 151229) ((-1117 . -668) 151118) ((-719 . -633) 151053) ((-801 . -668) 150942) ((-640 . -1086) 150929) ((-491 . -1247) T) ((-357 . -381) T) ((-143 . -501) 150911) ((-800 . -668) 150800) ((-1171 . -1247) T) ((-562 . -870) T) ((-473 . -668) 150771) ((-275 . -910) 150630) ((-255 . -910) NIL) ((-119 . -1086) 150575) ((-466 . -668) 150464) ((-684 . -1068) 150441) ((-640 . -111) 150426) ((-404 . -1081) 150410) ((-368 . -1068) 150394) ((-366 . -1068) 150378) ((-358 . -1068) 150362) ((-275 . -1068) 150206) ((-255 . -1068) 150082) ((-934 . -1247) T) ((-119 . -111) 150011) ((-58 . -1247) T) ((-404 . -660) 149995) ((-636 . -1081) 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-1086) 145898) ((-894 . -873) NIL) ((-1322 . -102) T) ((-395 . -102) T) ((-1284 . -630) 145880) ((-1163 . -1164) 145864) ((-1034 . -658) 145846) ((-899 . -1247) T) ((-48 . -111) 145802) ((-701 . -1247) T) ((-696 . -1247) T) ((-672 . -1247) T) ((-837 . -920) 145669) ((-490 . -1247) T) ((-252 . -1247) T) ((-543 . -102) T) ((-512 . -102) T) ((-154 . -1305) 145653) ((-140 . -1247) T) ((-139 . -1247) T) ((-135 . -1247) T) ((-1248 . -102) T) ((-1054 . -633) 145590) ((-839 . -239) T) ((-1201 . -1252) 145569) ((-218 . -381) T) ((-353 . -633) 145499) ((-1155 . -1252) 145478) ((-246 . -25) 145311) ((-246 . -21) 145222) ((-129 . -121) 145206) ((-123 . -121) 145190) ((-44 . -764) 145174) ((-1201 . -569) 145085) ((-1155 . -569) 145016) ((-1255 . -1131) T) ((-559 . -873) T) ((-1065 . -298) 144991) ((-1197 . -1113) T) ((-1024 . -1113) T) ((-838 . -133) T) ((-119 . -819) NIL) ((-119 . -814) NIL) ((-368 . -319) T) ((-366 . -319) T) ((-358 . -319) T) ((-1119 . -1247) 144969) ((-260 . -1142) 144947) 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143719) ((-48 . -250) T) ((-48 . -240) T) ((-676 . -298) 143680) ((-563 . -242) 143630) ((-583 . -873) T) ((-141 . -630) 143597) ((-137 . -630) 143579) ((-115 . -630) 143561) ((-489 . -38) 143526) ((-1322 . -1320) 143505) ((-1313 . -133) T) ((-1321 . -1087) T) ((-1112 . -102) T) ((-87 . -1247) T) ((-512 . -321) NIL) ((-1030 . -107) 143489) ((-912 . -1131) T) ((-909 . -1131) T) ((-1297 . -671) 143473) ((-1297 . -385) 143457) ((-339 . -1247) T) ((-605 . -870) T) ((-1172 . -1131) T) ((-1172 . -1083) 143397) ((-103 . -526) 143330) ((-953 . -630) 143312) ((-357 . -746) T) ((-30 . -630) 143294) ((-889 . -1131) T) ((-864 . -1087) 143273) ((-40 . -668) 143180) ((-229 . -1252) T) ((-419 . -1087) T) ((-1189 . -153) 143162) ((-1026 . -302) 143113) ((-897 . -1247) T) ((-634 . -1131) T) ((-229 . -569) T) ((-331 . -1280) 143097) ((-331 . -1276) 143067) ((-721 . -666) 143039) ((-1219 . -1224) 143018) ((-1106 . -630) 143000) ((-1219 . -107) 142950) ((-667 . -153) 142934) ((-649 . -153) 142880) ((-118 . -666) 142852) ((-491 . -1224) 142831) ((-499 . -149) T) ((-499 . -147) NIL) ((-1150 . -631) 142746) ((-450 . -630) 142728) ((-221 . -149) T) ((-221 . -147) NIL) ((-1150 . -630) 142710) ((-130 . -102) T) ((-51 . -102) T) ((-1257 . -658) 142662) ((-491 . -107) 142612) ((-1023 . -23) T) ((-1322 . -38) 142582) ((-1201 . -1142) T) ((-1155 . -1142) T) ((-1092 . -1252) T) ((-246 . -236) 142473) ((-324 . -102) T) ((-877 . -1142) T) ((-974 . -1252) 142452) ((-493 . -1252) 142431) ((-1092 . -569) T) ((-974 . -569) 142362) ((-1201 . -23) T) ((-1183 . -1113) T) ((-1155 . -23) T) ((-877 . -23) T) ((-493 . -569) 142293) ((-1172 . -737) 142225) ((-690 . -1081) 142209) ((-1176 . -526) 142142) ((-690 . -660) 142126) ((-1065 . -631) NIL) ((-1065 . -630) 142108) ((-96 . -1113) T) ((-1327 . -1086) 142095) ((-889 . -737) 142065) ((-1327 . -111) 142050) ((-1240 . -47) 142019) ((-1198 . -870) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1133 . -1131) T) ((-1033 . -1131) T) ((-63 . -630) 142001) ((-1109 . -920) 141870) ((-1054 . -814) T) ((-1054 . -819) T) ((-1287 . -25) T) ((-1287 . -21) T) ((-1278 . -21) T) ((-1278 . -25) T) ((-892 . -668) 141857) ((-1257 . -21) T) ((-1257 . -25) T) ((-1057 . -153) 141841) ((-1034 . -236) 141828) ((-895 . -842) 141807) ((-895 . -949) T) ((-732 . -298) 141734) ((-608 . -21) T) ((-352 . -666) 141693) ((-108 . -920) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-177 . -666) 141610) ((-40 . -746) T) ((-226 . -526) 141543) ((-607 . -25) T) ((-488 . -153) 141527) ((-475 . -153) 141511) ((-187 . -1247) T) ((-947 . -816) T) ((-947 . -746) T) ((-791 . -815) T) ((-791 . -816) T) ((-518 . -1131) T) ((-514 . -1131) T) ((-791 . -746) T) ((-229 . -376) T) ((-1319 . -1081) 141495) ((-1318 . -1081) 141479) ((-1319 . -660) 141449) ((-1185 . -1131) 141427) ((-894 . -1252) T) ((-1318 . -660) 141397) ((-1118 . -873) T) ((-676 . -630) 141379) ((-894 . -569) T) ((-714 . -381) NIL) ((-44 . -1081) 141363) ((-1327 . -633) 141345) ((-1321 . -1131) T) ((-690 . -102) T) ((-372 . -1305) 141329) ((-367 . -1305) 141313) ((-44 . -660) 141297) ((-359 . -1305) 141281) ((-561 . -102) T) ((-1240 . -1247) T) ((-532 . -870) 141260) ((-731 . -1247) T) ((-986 . -873) 141239) ((-871 . -873) T) ((-499 . -239) T) ((-221 . -239) T) ((-1076 . -1131) T) ((-839 . -464) 141218) ((-154 . -1081) 141202) ((-1076 . -1101) 141131) ((-1057 . -1006) 141100) ((-841 . -1142) T) ((-1033 . -737) 141045) ((-154 . -660) 141029) ((-400 . -1142) T) ((-488 . -1006) 140998) ((-475 . -1006) 140967) ((-1214 . -873) T) ((-110 . -153) 140949) ((-73 . -630) 140931) ((-917 . -630) 140913) ((-1213 . -873) T) ((-1109 . -744) 140892) ((-1327 . -1079) T) ((-838 . -658) 140840) ((-305 . -1087) 140782) ((-171 . -1252) 140687) ((-229 . -1142) T) ((-336 . -23) T) ((-1198 . -1021) 140639) ((-1284 . -1086) 140544) ((-864 . -1131) T) ((-131 . -873) T) ((-1156 . -760) 140523) ((-1283 . -949) 140502) ((-1262 . -949) 140481) ((-892 . -746) T) ((-171 . -569) 140392) ((-592 . -668) 140379) ((-558 . -668) 140351) 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139324) ((-1284 . -633) 139198) ((-493 . -23) T) ((-365 . -1087) T) ((-391 . -873) T) ((-1240 . -926) 139179) ((-690 . -321) 139117) ((-1287 . -236) 139070) ((-1143 . -1305) 139040) ((-719 . -668) 139005) ((-1034 . -870) T) ((-1033 . -175) T) ((-984 . -147) 138984) ((-650 . -1131) T) ((-618 . -1131) T) ((-984 . -149) 138963) ((-755 . -149) 138942) ((-755 . -147) 138921) ((-674 . -1247) T) ((-1001 . -870) T) ((-1278 . -236) 138867) ((-1257 . -236) 138684) ((-854 . -666) 138601) ((-486 . -949) 138580) ((-346 . -1247) T) ((-331 . -1081) 138415) ((-326 . -1086) 138325) ((-325 . -1086) 138254) ((-1026 . -298) 138212) ((-419 . -737) 138164) ((-331 . -660) 138005) ((-607 . -236) 137958) ((-721 . -869) T) ((-1284 . -1079) T) ((-326 . -111) 137854) ((-325 . -111) 137767) ((-97 . -1247) T) ((-992 . -102) T) ((-837 . -102) 137499) ((-732 . -631) NIL) ((-732 . -630) 137481) ((-1284 . -338) 137425) ((-674 . -1068) 137321) ((-1117 . -1247) T) ((-1065 . -300) 137296) ((-592 . -746) T) ((-558 . -816) T) ((-171 . -376) 137247) ((-558 . -812) T) ((-558 . -746) T) ((-507 . -746) T) ((-801 . -1247) T) ((-800 . -1247) T) ((-1176 . -501) 137231) ((-473 . -1247) T) ((-466 . -1247) T) ((-1319 . -1320) 137207) ((-1117 . -910) NIL) ((-894 . -1142) T) ((-119 . -938) NIL) ((-1318 . -1320) 137186) ((-669 . -1247) T) ((-801 . -910) NIL) ((-800 . -910) 137045) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137023) ((-1136 . -408) T) ((-640 . -668) 137010) ((-466 . -910) NIL) ((-695 . -102) 136960) ((-1117 . -1068) 136787) ((-894 . -23) T) ((-801 . -1068) 136646) ((-800 . -1068) 136503) ((-119 . -668) 136448) ((-466 . -1068) 136324) ((-286 . -1247) T) ((-326 . -633) 135888) ((-325 . -633) 135771) ((-50 . -1247) T) ((-404 . -666) 135740) ((-669 . -1068) 135724) ((-644 . -102) T) ((-593 . -1247) T) ((-530 . -1247) T) ((-226 . -501) 135708) ((-1297 . -34) T) ((-636 . -666) 135667) ((-301 . -1081) 135654) ((-137 . -633) 135638) ((-301 . -660) 135625) ((-650 . -737) 135609) ((-618 . -737) 135593) 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. -38) 134162) ((-1266 . -1142) T) ((-878 . -1142) T) ((-466 . -926) 134139) ((-881 . -1131) T) ((-1266 . -23) T) ((-1150 . -633) 134111) ((-1092 . -133) T) ((-878 . -23) T) ((-583 . -1142) T) ((-640 . -746) T) ((-523 . -873) T) ((-368 . -949) T) ((-366 . -949) T) ((-301 . -102) T) ((-358 . -949) T) ((-1000 . -1113) T) ((-974 . -133) T) ((-838 . -236) 134056) ((-119 . -816) NIL) ((-119 . -812) NIL) ((-119 . -746) T) ((-1076 . -526) 133957) ((-714 . -938) NIL) ((-583 . -23) T) ((-493 . -133) T) ((-417 . -239) 133908) ((-695 . -321) 133846) ((-227 . -1247) T) ((-655 . -1131) T) ((-650 . -781) T) ((-618 . -781) T) ((-1257 . -870) NIL) ((-1109 . -1081) 133756) ((-1033 . -302) T) ((-714 . -668) 133706) ((-260 . -25) T) ((-365 . -1131) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133690) ((-2 . -102) T) ((-934 . -949) T) ((-1109 . -660) 133558) ((-494 . -1305) 133528) ((-1150 . -1079) T) ((-731 . -319) T) ((-721 . -1087) T) ((-372 . -1081) 133480) ((-367 . -1081) 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T) ((-721 . -737) 127155) ((-352 . -1131) T) ((-177 . -1131) T) ((-343 . -870) T) ((-417 . -464) 127105) ((-391 . -23) T) ((-372 . -38) 127070) ((-367 . -38) 127035) ((-359 . -38) 127000) ((-80 . -453) T) ((-80 . -408) T) ((-229 . -25) T) ((-229 . -21) T) ((-856 . -1142) T) ((-108 . -38) 126950) ((-850 . -1142) T) ((-793 . -1131) T) ((-118 . -737) 126937) ((-692 . -1068) 126921) ((-628 . -102) T) ((-856 . -23) T) ((-850 . -23) T) ((-1185 . -298) 126873) ((-1143 . -321) 126811) ((-494 . -1081) 126712) ((-1127 . -242) 126696) ((-61 . -409) T) ((-61 . -408) T) ((-1183 . -102) T) ((-110 . -102) T) ((-494 . -660) 126618) ((-40 . -390) 126595) ((-96 . -102) T) ((-675 . -875) 126579) ((-1201 . -236) 126566) ((-1165 . -1113) T) ((-1092 . -21) T) ((-1092 . -25) T) ((-1084 . -1081) 126550) ((-837 . -274) 126519) ((-837 . -234) 126488) ((-974 . -25) T) ((-974 . -21) T) ((-1150 . -381) T) ((-1084 . -660) 126430) ((-636 . -1087) T) ((-1057 . -321) 126368) ((-912 . -630) 126350) ((-690 . -666) 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-1247) T) ((-1266 . -25) T) ((-1266 . -21) T) ((-1092 . -236) 122488) ((-878 . -25) T) ((-524 . -873) T) ((-256 . -1247) T) ((-44 . -380) 122472) ((-878 . -21) T) ((-751 . -464) 122423) ((-1321 . -630) 122405) ((-730 . -1247) T) ((-719 . -1247) T) ((-1310 . -1081) 122375) ((-1084 . -321) 122313) ((-691 . -1113) T) ((-617 . -1113) T) ((-404 . -1131) T) ((-583 . -25) T) ((-583 . -21) T) ((-183 . -1113) T) ((-164 . -1113) T) ((-158 . -1113) T) ((-156 . -1113) T) ((-1310 . -660) 122283) ((-636 . -1131) T) ((-719 . -910) 122265) ((-1297 . -1247) T) ((-231 . -321) 122203) ((-146 . -381) T) ((-1221 . -1247) T) ((-1076 . -631) 122145) ((-1076 . -630) 122088) ((-325 . -938) NIL) ((-1256 . -866) T) ((-1143 . -928) 121957) ((-719 . -1068) 121902) ((-731 . -949) T) ((-486 . -1252) 121881) ((-1204 . -464) 121860) ((-1198 . -464) 121839) ((-342 . -102) T) ((-895 . -1142) T) ((-331 . -666) 121721) ((-326 . -668) 121450) ((-325 . -668) 121379) ((-486 . -569) 121330) ((-352 . -526) 121296) ((-563 . -153) 121246) ((-40 . -319) T) ((-864 . -630) 121228) ((-721 . -302) T) ((-895 . -23) T) ((-391 . -505) T) ((-1109 . -274) 121198) ((-1109 . -234) 121168) ((-522 . -102) T) ((-419 . -631) 120975) ((-419 . -630) 120957) ((-270 . -630) 120939) ((-118 . -302) T) ((-1284 . -746) T) ((-640 . -1247) T) ((-1323 . -1131) T) ((-1283 . -376) 120918) ((-1262 . -376) 120897) ((-1311 . -34) T) ((-1256 . -1131) T) ((-119 . -1247) T) ((-108 . -274) 120879) ((-108 . -234) 120861) ((-1209 . -102) T) ((-489 . -1131) T) ((-535 . -501) 120845) ((-756 . -34) T) ((-675 . -1081) 120829) ((-675 . -660) 120799) ((-894 . -236) NIL) ((-143 . -34) T) ((-119 . -908) 120776) ((-119 . -910) NIL) ((-1310 . -102) T) ((-1287 . -239) 120735) ((-640 . -1068) 120618) ((-623 . -102) T) ((-622 . -102) T) ((-620 . -102) T) ((-661 . -870) 120597) ((-1278 . -239) 120549) ((-1257 . -239) 120372) ((-307 . -102) T) ((-732 . -381) 120351) ((-119 . -1068) 120328) ((-404 . -737) 120312) ((-607 . -239) 120271) ((-636 . -737) 120255) 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((-359 . -363) 118922) ((-326 . -485) 118901) ((-1283 . -23) T) ((-1262 . -23) T) ((-738 . -1142) T) ((-734 . -133) T) ((-675 . -102) T) ((-489 . -737) 118866) ((-672 . -873) 118845) ((-45 . -294) 118795) ((-105 . -1131) T) ((-68 . -630) 118777) ((-252 . -873) 118756) ((-1000 . -102) T) ((-887 . -102) T) ((-640 . -926) 118715) ((-1322 . -1131) T) ((-395 . -1131) T) ((-1) T) ((-1266 . -236) 118702) ((-1248 . -1131) T) ((-83 . -1247) T) ((-1143 . -274) 118671) ((-1092 . -870) T) ((-119 . -926) NIL) ((-801 . -949) 118650) ((-733 . -870) T) ((-543 . -1131) T) ((-512 . -1131) T) ((-368 . -1252) T) ((-366 . -1252) T) ((-358 . -1252) T) ((-275 . -1252) 118629) ((-255 . -1252) 118608) ((-545 . -884) T) ((-1143 . -234) 118577) ((-1189 . -843) T) ((-1172 . -1086) 118561) ((-404 . -781) T) ((-714 . -1247) T) ((-711 . -1068) 118545) ((-368 . -569) T) ((-366 . -569) T) ((-358 . -569) T) ((-275 . -569) 118476) ((-255 . -569) 118407) ((-537 . -1113) T) ((-1172 . -111) 118386) ((-465 . -764) 118356) 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116657) ((-714 . -351) 116639) ((-489 . -175) T) ((-395 . -737) 116609) ((-889 . -633) 116544) ((-894 . -870) NIL) ((-558 . -1050) T) ((-507 . -1050) T) ((-1163 . -630) 116526) ((-1143 . -245) 116505) ((-217 . -102) T) ((-1181 . -102) T) ((-71 . -630) 116487) ((-1054 . -1247) T) ((-1172 . -1079) T) ((-1209 . -38) 116384) ((-881 . -630) 116366) ((-558 . -557) T) ((-690 . -1087) T) ((-751 . -978) 116319) ((-1172 . -240) 116298) ((-353 . -1247) T) ((-1112 . -1131) T) ((-1064 . -25) T) ((-1064 . -21) T) ((-1033 . -1086) 116243) ((-339 . -873) 116222) ((-930 . -102) T) ((-889 . -1079) T) ((-714 . -926) NIL) ((-368 . -341) 116206) ((-368 . -376) T) ((-366 . -341) 116190) ((-366 . -376) T) ((-358 . -341) 116174) ((-358 . -376) T) ((-499 . -102) T) ((-1310 . -38) 116144) ((-559 . -870) T) ((-535 . -706) 116094) ((-221 . -102) T) ((-1054 . -1068) 115974) ((-1033 . -111) 115903) ((-655 . -630) 115885) ((-1205 . -1003) 115854) ((-1204 . -1003) 115816) ((-532 . -153) 115800) ((-1109 . -383) 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-1142) T) ((-275 . -1142) T) ((-255 . -1142) T) ((-1181 . -321) 114788) ((-1118 . -236) 114775) ((-640 . -319) 114754) ((-684 . -23) T) ((-536 . -1113) T) ((-324 . -1131) T) ((-494 . -274) 114723) ((-494 . -234) 114692) ((-154 . -1087) T) ((-368 . -23) T) ((-366 . -23) T) ((-358 . -23) T) ((-119 . -319) T) ((-275 . -23) T) ((-255 . -23) T) ((-1033 . -1079) T) ((-732 . -938) 114671) ((-1205 . -920) 114559) ((-1204 . -920) 114440) ((-1198 . -920) 114176) ((-1185 . -633) 114153) ((-1033 . -240) 114125) ((-1033 . -250) T) ((-1156 . -920) 114107) ((-119 . -1050) NIL) ((-934 . -1142) T) ((-1278 . -464) 114086) ((-1257 . -464) 114065) ((-535 . -630) 113997) ((-732 . -668) 113886) ((-419 . -1086) 113838) ((-516 . -630) 113820) ((-934 . -23) T) ((-499 . -321) NIL) ((-1321 . -633) 113776) ((-486 . -133) T) ((-221 . -321) NIL) ((-419 . -111) 113714) ((-837 . -1087) 113692) ((-756 . -1129) 113676) ((-1283 . -505) 113642) ((-1262 . -505) 113608) ((-448 . -1247) T) ((-561 . -866) T) ((-143 . -1129) 113590) ((-489 . -302) T) ((-1214 . -682) T) ((-1321 . -1079) T) ((-260 . -239) 113487) ((-259 . -239) 113384) ((-1253 . -102) T) ((-1093 . -102) T) ((-864 . -633) 113252) ((-512 . -526) NIL) ((-494 . -245) 113231) ((-419 . -633) 113129) ((-984 . -1081) 113012) ((-755 . -1081) 112982) ((-984 . -660) 112879) ((-1201 . -147) 112858) ((-755 . -660) 112828) ((-465 . -1081) 112798) ((-1201 . -149) 112777) ((-1155 . -149) 112756) ((-1155 . -147) 112735) ((-650 . -1086) 112719) ((-618 . -1086) 112703) ((-465 . -660) 112673) ((-1205 . -1290) 112657) ((-1205 . -1276) 112634) ((-1204 . -1282) 112595) ((-690 . -1131) T) ((-690 . -1083) 112535) ((-1204 . -1276) 112505) ((-561 . -1131) T) ((-499 . -1182) T) ((-1204 . -1280) 112489) ((-1198 . -1261) 112450) ((-840 . -277) 112434) ((-221 . -1182) T) ((-357 . -949) T) ((-99 . -1247) T) ((-650 . -111) 112413) ((-618 . -111) 112392) ((-1198 . -1276) 112369) ((-864 . -1079) 112348) ((-1198 . -1259) 112332) ((-527 . -25) T) ((-507 . -310) T) ((-524 . -23) T) ((-523 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-419 . -1079) T) ((-417 . -1081) 112306) ((-331 . -1087) T) ((-714 . -319) T) ((-417 . -660) 112280) ((-108 . -869) T) ((-732 . -746) T) ((-419 . -250) T) ((-419 . -240) 112259) ((-391 . -236) 112246) ((-499 . -38) 112196) ((-221 . -38) 112146) ((-486 . -505) 112112) ((-657 . -21) T) ((-657 . -25) T) ((-1255 . -381) T) ((-1189 . -1174) T) ((-1132 . -102) T) ((-850 . -236) 112085) ((-721 . -630) 112067) ((-721 . -631) 111982) ((-734 . -21) T) ((-734 . -25) T) ((-1165 . -102) T) ((-494 . -666) 111761) ((-246 . -920) 111628) ((-136 . -630) 111610) ((-118 . -630) 111592) ((-159 . -25) T) ((-1319 . -1131) T) ((-895 . -658) 111540) ((-1318 . -1131) T) ((-888 . -1247) T) ((-984 . -102) T) ((-755 . -102) T) ((-735 . -102) T) ((-465 . -102) T) ((-838 . -464) 111491) ((-44 . -1131) T) ((-1118 . -870) T) ((-1093 . -321) 111342) ((-684 . -133) T) ((-1084 . -666) 111311) ((-690 . -737) 111295) ((-301 . -1087) T) ((-368 . -133) T) ((-366 . -133) T) ((-358 . -133) T) ((-275 . -133) T) ((-255 . -133) T) ((-394 . -666) 111264) ((-1327 . -1247) T) ((-417 . -102) T) ((-154 . -1131) T) ((-45 . -233) 111214) ((-1034 . -920) NIL) ((-820 . -1081) 111198) ((-986 . -870) 111177) ((-1026 . -668) 111079) ((-820 . -660) 111063) ((-246 . -1305) 111033) ((-1054 . -319) T) ((-305 . -1086) 110954) ((-934 . -133) T) ((-40 . -949) T) ((-499 . -412) 110936) ((-353 . -319) T) ((-221 . -412) 110918) ((-1109 . -424) 110902) ((-305 . -111) 110818) ((-1214 . -870) T) ((-1213 . -870) T) ((-895 . -25) T) ((-895 . -21) T) ((-1284 . -47) 110762) ((-352 . -630) 110744) ((-1201 . -239) T) ((-229 . -149) T) ((-177 . -630) 110726) ((-793 . -630) 110708) ((-131 . -870) T) ((-625 . -242) 110655) ((-487 . -242) 110605) ((-1319 . -737) 110575) ((-48 . -319) T) ((-1318 . -737) 110545) ((-65 . -633) 110474) ((-992 . -1131) T) ((-837 . -1131) 110226) ((-323 . -102) T) ((-929 . -1247) T) ((-48 . -1050) T) ((-1262 . -658) 110134) ((-709 . -102) 110084) ((-44 . -737) 110068) ((-563 . -102) T) ((-305 . -633) 109999) ((-67 . -396) T) ((-499 . -928) NIL) ((-67 . -408) T) ((-286 . -873) T) ((-221 . -928) NIL) ((-672 . -23) T) ((-839 . -666) 109935) ((-690 . -781) T) ((-1245 . -1131) 109913) ((-365 . -1086) 109858) ((-695 . -1131) 109836) ((-1092 . -149) T) ((-974 . -149) 109815) ((-974 . -147) 109794) ((-820 . -102) T) ((-154 . -737) 109778) ((-493 . -149) 109757) ((-493 . -147) 109736) ((-365 . -111) 109665) ((-1109 . -1087) T) ((-334 . -870) 109644) ((-1287 . -1003) 109613) ((-1284 . -1247) T) ((-644 . -1131) T) ((-1278 . -1003) 109575) ((-524 . -133) T) ((-519 . -133) T) ((-307 . -233) 109525) ((-372 . -1087) T) ((-367 . -1087) T) ((-359 . -1087) T) ((-305 . -1079) 109467) ((-1257 . -1003) 109436) ((-391 . -870) T) ((-108 . -1087) T) ((-1026 . -746) T) ((-892 . -949) T) ((-864 . -819) 109415) ((-864 . -814) 109394) ((-417 . -321) 109333) ((-480 . -102) T) ((-607 . -1003) 109302) ((-331 . -1131) T) ((-419 . -819) 109281) ((-419 . -814) 109260) 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((-496 . -1131) 104653) ((-450 . -1247) T) ((-404 . -630) 104635) ((-523 . -870) T) ((-1150 . -1247) T) ((-1278 . -1282) 104596) ((-1278 . -1276) 104566) ((-1278 . -1280) 104550) ((-1257 . -1261) 104511) ((-1257 . -1276) 104488) ((-1257 . -1259) 104472) ((-1205 . -296) 104438) ((-636 . -630) 104420) ((-1204 . -296) 104386) ((-719 . -949) T) ((-1198 . -296) 104352) ((-1156 . -296) 104318) ((-1150 . -910) 104300) ((-1109 . -1131) T) ((-1091 . -1131) T) ((-48 . -310) T) ((-326 . -926) 104266) ((-325 . -926) NIL) ((-1091 . -1098) 104245) ((-820 . -38) 104229) ((-275 . -658) 104177) ((-114 . -873) T) ((-255 . -658) 104125) ((-721 . -1086) 104112) ((-607 . -1276) 104089) ((-1150 . -1068) 104071) ((-331 . -175) 104002) ((-372 . -1131) T) ((-367 . -1131) T) ((-359 . -1131) T) ((-512 . -19) 103984) ((-1127 . -153) 103968) ((-894 . -239) NIL) ((-108 . -1131) T) ((-118 . -1086) 103955) ((-731 . -376) T) ((-512 . -616) 103930) ((-721 . -111) 103915) ((-1323 . -630) 103881) ((-1323 . -502) 103862) 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-660) 101326) ((-372 . -737) 101278) ((-367 . -737) 101230) ((-352 . -1086) 101214) ((-359 . -737) 101166) ((-352 . -111) 101145) ((-177 . -1086) 101077) ((-177 . -111) 100988) ((-108 . -737) 100938) ((-221 . -666) 100888) ((-285 . -1131) T) ((-284 . -1131) T) ((-283 . -1131) T) ((-282 . -1131) T) ((-281 . -1131) T) ((-280 . -1131) T) ((-279 . -1131) T) ((-215 . -1131) T) ((-214 . -1131) T) ((-171 . -1236) 100866) ((-171 . -1233) 100844) ((-212 . -1131) T) ((-211 . -1131) T) ((-118 . -1079) T) ((-210 . -1131) T) ((-209 . -1131) T) ((-206 . -1131) T) ((-205 . -1131) T) ((-204 . -1131) T) ((-203 . -1131) T) ((-202 . -1131) T) ((-201 . -1131) T) ((-200 . -1131) T) ((-199 . -1131) T) ((-198 . -1131) T) ((-197 . -1131) T) ((-196 . -1131) T) ((-246 . -102) 100576) ((-171 . -35) 100554) ((-171 . -95) 100532) ((-676 . -1068) 100428) ((-494 . -1087) 100406) ((-1143 . -1131) 100158) ((-1172 . -34) T) ((-690 . -501) 100142) ((-73 . -1247) T) ((-105 . -630) 100124) ((-917 . -1247) T) ((-1322 . -630) 100106) ((-395 . -630) 100088) ((-352 . -633) 100040) ((-177 . -633) 99957) ((-1248 . -502) 99938) ((-751 . -38) 99787) ((-583 . -1236) T) ((-583 . -1233) T) ((-543 . -630) 99769) ((-532 . -321) 99707) ((-512 . -630) 99689) ((-512 . -631) 99671) ((-1248 . -630) 99637) ((-1198 . -1182) NIL) ((-216 . -1247) T) ((-1057 . -1101) 99606) ((-1057 . -1131) T) ((-1034 . -102) T) ((-1001 . -102) T) ((-942 . -102) T) ((-917 . -1068) 99583) ((-1172 . -746) T) ((-1033 . -668) 99490) ((-488 . -1131) T) ((-475 . -1131) T) ((-595 . -23) T) ((-583 . -35) T) ((-583 . -95) T) ((-441 . -102) T) ((-1093 . -233) 99436) ((-1205 . -38) 99333) ((-1204 . -38) 99174) ((-947 . -873) T) ((-889 . -746) T) ((-791 . -873) T) ((-714 . -949) T) ((-692 . -873) T) ((-524 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1198 . -38) 98970) ((-352 . -1079) T) ((-146 . -1247) T) ((-1109 . -175) T) ((-177 . -1079) T) ((-1156 . -38) 98867) ((-732 . -47) 98844) ((-372 . -175) T) ((-367 . -175) T) ((-531 . -57) 98818) ((-509 . -57) 98768) ((-365 . -1316) 98745) ((-229 . -464) T) ((-331 . -302) 98696) ((-359 . -175) T) ((-177 . -250) T) ((-1262 . -870) 98595) ((-108 . -175) T) ((-895 . -1021) 98579) ((-674 . -1142) T) ((-593 . -376) T) ((-593 . -341) 98566) ((-530 . -341) 98543) ((-530 . -376) T) ((-326 . -319) 98522) ((-325 . -319) T) ((-614 . -870) 98501) ((-1143 . -737) 98443) ((-621 . -1247) T) ((-532 . -294) 98427) ((-674 . -23) T) ((-417 . -234) 98411) ((-417 . -274) 98395) ((-325 . -1050) NIL) ((-346 . -23) T) ((-103 . -1040) 98379) ((-655 . -381) T) ((-45 . -36) 98358) ((-628 . -1131) T) ((-365 . -381) T) ((-536 . -102) T) ((-507 . -27) T) ((-246 . -321) 98296) ((-1117 . -1142) T) ((-1321 . -668) 98270) ((-801 . -1142) T) ((-800 . -1142) T) ((-1209 . -424) 98254) ((-466 . -1142) T) ((-1092 . -464) T) ((-1183 . -1131) T) ((-974 . -464) 98205) ((-1146 . -1113) T) ((-110 . -1131) T) ((-1117 . -23) T) ((-1190 . -526) 97988) ((-839 . -1087) T) ((-801 . -23) T) ((-800 . -23) T) ((-493 . -464) 97939) 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. -424) 94542) ((-1257 . -102) T) ((-1189 . -526) NIL) ((-672 . -25) T) ((-636 . -1086) 94526) ((-672 . -21) T) ((-984 . -666) 94436) ((-755 . -666) 94381) ((-735 . -666) 94353) ((-404 . -111) 94332) ((-226 . -263) 94316) ((-1084 . -1083) 94256) ((-1084 . -1131) T) ((-1034 . -1182) T) ((-840 . -1131) T) ((-465 . -666) 94171) ((-650 . -668) 94155) ((-636 . -111) 94134) ((-618 . -668) 94118) ((-357 . -1252) T) ((-608 . -102) T) ((-324 . -502) 94099) ((-595 . -133) T) ((-607 . -102) T) ((-427 . -1131) T) ((-394 . -1131) T) ((-324 . -630) 94065) ((-231 . -1131) 94043) ((-667 . -526) 93976) ((-649 . -526) 93820) ((-854 . -1079) 93799) ((-661 . -153) 93783) ((-357 . -569) T) ((-732 . -926) 93726) ((-563 . -233) 93676) ((-1287 . -296) 93642) ((-1278 . -296) 93608) ((-1109 . -302) 93559) ((-558 . -873) T) ((-499 . -869) T) ((-227 . -1142) T) ((-1257 . -296) 93525) ((-1240 . -505) 93491) ((-1034 . -38) 93441) ((-221 . -869) T) ((-417 . -666) 93400) ((-942 . -38) 93352) ((-864 . -816) 93331) 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-526) 92077) ((-1323 . -633) 92058) ((-465 . -380) 92028) ((-45 . -627) 92007) ((-411 . -1247) T) ((-326 . -310) T) ((-1297 . -873) 91986) ((-850 . -239) 91965) ((-489 . -633) 91915) ((-1257 . -321) 91800) ((-690 . -630) 91762) ((-58 . -870) 91741) ((-1034 . -412) 91723) ((-561 . -630) 91705) ((-820 . -666) 91664) ((-837 . -616) 91641) ((-528 . -870) 91620) ((-508 . -870) 91599) ((-1026 . -1068) 91495) ((-40 . -1252) T) ((-246 . -928) 91364) ((-50 . -133) T) ((-593 . -133) T) ((-530 . -133) T) ((-305 . -668) 91224) ((-357 . -341) 91201) ((-357 . -376) T) ((-334 . -335) 91178) ((-331 . -298) 91136) ((-40 . -569) T) ((-391 . -1233) T) ((-391 . -1236) T) ((-1065 . -1224) 91111) ((-1219 . -242) 91061) ((-1198 . -234) 91013) ((-1198 . -274) 90965) ((-342 . -1131) T) ((-391 . -95) T) ((-391 . -35) T) ((-1065 . -107) 90911) ((-489 . -1079) T) ((-1322 . -1086) 90895) ((-491 . -242) 90845) ((-1190 . -501) 90779) ((-1313 . -1081) 90763) ((-395 . -1086) 90747) ((-1313 . -660) 90717) ((-838 . 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89496) ((-221 . -1087) T) ((-357 . -23) T) ((-154 . -630) 89478) ((-854 . -819) 89457) ((-854 . -814) 89436) ((-1248 . -633) 89417) ((-608 . -38) 89390) ((-607 . -38) 89287) ((-892 . -569) T) ((-227 . -133) T) ((-331 . -1032) 89253) ((-79 . -630) 89235) ((-732 . -319) 89214) ((-305 . -746) 89116) ((-848 . -102) T) ((-887 . -866) T) ((-305 . -485) 89095) ((-1313 . -102) T) ((-40 . -376) T) ((-895 . -149) 89074) ((-497 . -666) 89056) ((-895 . -147) 89035) ((-1189 . -501) 89017) ((-1322 . -1079) T) ((-494 . -526) 88950) ((-659 . -133) T) ((-1176 . -1247) T) ((-992 . -630) 88932) ((-667 . -501) 88916) ((-649 . -501) 88847) ((-837 . -630) 88540) ((-48 . -27) T) ((-1209 . -737) 88437) ((-974 . -920) 88416) ((-675 . -1131) T) ((-885 . -884) T) ((-449 . -378) 88390) ((-751 . -666) 88300) ((-493 . -920) 88275) ((-1127 . -102) T) ((-1000 . -1131) T) ((-887 . -1131) T) ((-838 . -321) 88262) ((-545 . -539) T) ((-545 . -588) T) ((-1318 . -397) 88234) ((-714 . -873) T) ((-1084 . -526) 88167) ((-1190 . -298) 88143) ((-246 . -274) 88112) ((-246 . -234) 88081) ((-260 . -1081) 87982) ((-259 . -1081) 87883) ((-1310 . -737) 87853) ((-1197 . -93) T) ((-1024 . -93) T) ((-839 . -175) 87832) ((-260 . -660) 87754) ((-259 . -660) 87676) ((-1245 . -502) 87653) ((-590 . -1247) T) ((-231 . -526) 87586) ((-636 . -819) 87565) ((-636 . -814) 87544) ((-1245 . -630) 87456) ((-226 . -1247) T) ((-695 . -630) 87388) ((-1205 . -666) 87298) ((-1185 . -1040) 87282) ((-971 . -102) 87212) ((-365 . -746) T) ((-885 . -630) 87194) ((-1204 . -666) 87076) ((-1198 . -666) 86913) ((-1156 . -666) 86823) ((-1257 . -412) 86775) ((-1143 . -501) 86759) ((-60 . -321) 86697) ((-343 . -102) T) ((-1240 . -21) T) ((-1240 . -25) T) ((-40 . -1142) T) ((-731 . -21) T) ((-644 . -630) 86679) ((-527 . -335) 86658) ((-731 . -25) T) ((-451 . -102) T) ((-108 . -298) NIL) ((-947 . -1142) T) ((-40 . -23) T) ((-791 . -1142) T) ((-558 . -1252) T) ((-507 . -1252) T) ((-1034 . -274) 86640) ((-331 . -630) 86622) ((-1034 . -234) 86604) 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. -1081) 83597) ((-649 . -616) 83572) ((-1283 . -95) 83538) ((-1283 . -239) 83490) ((-1264 . -102) 83468) ((-1201 . -660) 83297) ((-1155 . -660) 83146) ((-877 . -660) 83116) ((-1262 . -1233) 83082) ((-1117 . -25) T) ((-562 . -1131) T) ((-1117 . -21) T) ((-984 . -1087) T) ((-543 . -814) T) ((-543 . -819) T) ((-119 . -1252) T) ((-889 . -1247) T) ((-640 . -569) T) ((-801 . -25) T) ((-801 . -21) T) ((-800 . -21) T) ((-800 . -25) T) ((-755 . -1087) T) ((-735 . -1087) T) ((-690 . -1086) 83066) ((-529 . -1113) T) ((-473 . -25) T) ((-119 . -569) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1262 . -1236) 83032) ((-1183 . -93) T) ((-1172 . -1068) 82928) ((-839 . -302) 82907) ((-1262 . -239) 82766) ((-846 . -1131) T) ((-994 . -997) T) ((-690 . -111) 82745) ((-634 . -1247) T) ((-307 . -526) 82537) ((-1257 . -234) 82489) ((-1257 . -274) 82441) ((-1256 . -381) T) ((-260 . -321) 82379) ((-259 . -321) 82317) ((-1253 . -866) T) ((-1190 . -631) NIL) ((-1190 . -630) 82299) ((-1172 . -390) 82283) ((-1150 . -842) T) ((-1150 . -949) T) ((-96 . -93) T) ((-1143 . -616) 82260) ((-1109 . -631) 82244) ((-1109 . -630) 82226) ((-1034 . -666) 82176) ((-942 . -666) 82113) ((-837 . -300) 82090) ((-496 . -630) 82022) ((-625 . -153) 81969) ((-499 . -737) 81919) ((-417 . -1087) T) ((-494 . -501) 81903) ((-441 . -666) 81862) ((-339 . -870) 81841) ((-352 . -668) 81815) ((-50 . -21) T) ((-50 . -25) T) ((-221 . -737) 81765) ((-171 . -744) 81736) ((-177 . -668) 81668) ((-593 . -21) T) ((-593 . -25) T) ((-530 . -25) T) ((-530 . -21) T) ((-487 . -153) 81618) ((-1091 . -630) 81600) ((-1023 . -102) T) ((-886 . -102) T) ((-838 . -928) 81500) ((-820 . -424) 81463) ((-40 . -133) T) ((-719 . -376) T) ((-721 . -746) T) ((-721 . -816) T) ((-721 . -812) T) ((-215 . -921) T) ((-592 . -1142) T) ((-558 . -1142) T) ((-507 . -1142) T) ((-372 . -630) 81445) ((-367 . -630) 81427) ((-359 . -630) 81409) ((-66 . -409) T) ((-66 . -408) T) ((-108 . -631) 81339) ((-108 . -630) 81281) ((-214 . -921) T) ((-986 . 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79497) ((-352 . -746) T) ((-279 . -630) 79479) ((-110 . -19) 79461) ((-177 . -746) T) ((-512 . -385) 79443) ((-215 . -630) 79425) ((-532 . -1180) 79409) ((-512 . -125) T) ((-110 . -616) 79384) ((-214 . -630) 79366) ((-486 . -35) 79332) ((-486 . -95) 79298) ((-212 . -630) 79280) ((-211 . -630) 79262) ((-210 . -630) 79244) ((-209 . -630) 79226) ((-206 . -630) 79208) ((-205 . -630) 79190) ((-204 . -630) 79172) ((-203 . -630) 79154) ((-202 . -630) 79136) ((-201 . -630) 79118) ((-200 . -630) 79100) ((-547 . -1134) 79052) ((-199 . -630) 79034) ((-198 . -630) 79016) ((-45 . -501) 78953) ((-197 . -630) 78935) ((-196 . -630) 78917) ((-154 . -633) 78886) ((-1146 . -102) T) ((-837 . -111) 78802) ((-661 . -102) 78732) ((-659 . -21) T) ((-659 . -25) T) ((-494 . -298) 78709) ((-1321 . -1068) 78693) ((-1143 . -630) 78386) ((-1132 . -1131) T) ((-1076 . -1247) T) ((-1201 . -321) 78373) ((-1092 . -1081) 78360) ((-1165 . -1131) T) ((-974 . -1081) 78203) ((-1155 . -321) 78190) ((-1126 . -1113) T) ((-640 . 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((-1277 . -149) 194106) ((-1277 . -147) 194085) ((-1277 . -1002) 194047) ((-1277 . -927) 193953) ((-1277 . -919) 193834) ((-1277 . -925) 193740) ((-1277 . -298) 193698) ((-1277 . -239) 193650) ((-1277 . -236) 193596) ((-1277 . -240) 193548) ((-1277 . -1279) 193532) ((-1277 . -1067) 193467) ((-1265 . -1272) 193451) ((-1265 . -1181) 193429) ((-1265 . -631) NIL) ((-1265 . -321) 193416) ((-1265 . -526) 193363) ((-1265 . -338) 193340) ((-1265 . -1067) 193220) ((-1265 . -424) 193204) ((-1265 . -38) 193033) ((-1265 . -111) 192842) ((-1265 . -1080) 192665) ((-1265 . -1085) 192488) ((-1265 . -666) 192398) ((-1265 . -668) 192287) ((-1265 . -660) 192116) ((-1265 . -737) 191945) ((-1265 . -633) 191693) ((-1265 . -147) 191672) ((-1265 . -149) 191651) ((-1265 . -47) 191628) ((-1265 . -390) 191612) ((-1265 . -658) 191560) ((-1265 . -925) 191503) ((-1265 . -919) 191406) ((-1265 . -927) 191313) ((-1265 . -909) NIL) ((-1265 . -937) 191292) ((-1265 . -1251) 191271) ((-1265 . -977) 191240) ((-1265 . -948) 191219) ((-1265 . -569) 191130) ((-1265 . -302) 191041) ((-1265 . -175) 190932) ((-1265 . -464) 190863) ((-1265 . -319) 190842) ((-1265 . -298) 190769) ((-1265 . -240) T) ((-1265 . -133) T) ((-1265 . -25) T) ((-1265 . -102) T) ((-1265 . -630) 190751) ((-1265 . -1130) T) ((-1265 . -23) T) ((-1265 . -21) T) ((-1265 . -746) T) ((-1265 . -1141) T) ((-1265 . -1086) T) ((-1265 . -1078) T) ((-1265 . -236) 190738) ((-1265 . -1246) T) ((-1265 . -239) T) ((-1265 . -274) 190722) ((-1265 . -234) 190706) ((-1263 . -1123) 190690) ((-1263 . -635) 190674) ((-1263 . -1130) 190652) ((-1263 . -630) 190619) ((-1263 . -1246) 190597) ((-1263 . -102) 190575) ((-1263 . -1124) 190532) ((-1261 . -1260) 190511) ((-1261 . -1031) 190477) ((-1261 . -1232) 190443) ((-1261 . -1235) 190409) ((-1261 . -505) 190375) ((-1261 . -296) 190341) ((-1261 . -95) 190307) ((-1261 . -35) 190273) ((-1261 . -1275) 190250) ((-1261 . -47) 190227) ((-1261 . -633) 189975) ((-1261 . -737) 189789) ((-1261 . -660) 189603) ((-1261 . -668) 189411) ((-1261 . -666) 189266) ((-1261 . -1085) 189074) ((-1261 . -1080) 188882) ((-1261 . -111) 188671) ((-1261 . -38) 188485) ((-1261 . -1002) 188454) ((-1261 . -298) 188354) ((-1261 . -1258) 188338) ((-1261 . -746) T) ((-1261 . -1141) T) ((-1261 . -1086) T) ((-1261 . -1078) T) ((-1261 . -21) T) ((-1261 . -23) T) ((-1261 . -1130) T) ((-1261 . -630) 188320) ((-1261 . -1246) T) ((-1261 . -102) T) ((-1261 . -25) T) ((-1261 . -133) T) ((-1261 . -147) 188245) ((-1261 . -149) 188170) ((-1261 . -631) 187841) ((-1261 . -234) 187811) ((-1261 . -925) 187662) ((-1261 . -927) 187459) ((-1261 . -919) 187254) ((-1261 . -274) 187224) ((-1261 . -239) 187083) ((-1261 . -236) 186936) ((-1261 . -240) 186841) ((-1261 . -376) 186820) ((-1261 . -1251) 186799) ((-1261 . -948) 186778) ((-1261 . -569) 186729) ((-1261 . -175) 186660) ((-1261 . -464) 186639) ((-1261 . -319) 186618) ((-1261 . -302) 186569) ((-1261 . -250) 186548) ((-1261 . -351) 186518) ((-1261 . -526) 186378) ((-1261 . -321) 186317) ((-1261 . -390) 186287) ((-1261 . -658) 186195) ((-1261 . -412) 186165) ((-1261 . -909) 186038) ((-1261 . -842) 185991) ((-1261 . -812) 185944) ((-1261 . -814) 185897) ((-1261 . -869) 185796) ((-1261 . -872) 185695) ((-1261 . -816) 185648) ((-1261 . -819) 185601) ((-1261 . -868) 185554) ((-1261 . -907) 185524) ((-1261 . -937) 185477) ((-1261 . -1049) 185429) ((-1261 . -1067) 185215) ((-1261 . -1181) 185167) ((-1261 . -1020) 185137) ((-1256 . -1260) 185098) ((-1256 . -1031) 185064) ((-1256 . -1232) 185030) ((-1256 . -1235) 184996) ((-1256 . -505) 184962) ((-1256 . -296) 184928) ((-1256 . -95) 184894) ((-1256 . -35) 184860) ((-1256 . -1275) 184837) ((-1256 . -47) 184814) ((-1256 . -633) 184609) ((-1256 . -737) 184405) ((-1256 . -660) 184201) ((-1256 . -668) 184053) ((-1256 . -666) 183890) ((-1256 . -1085) 183680) ((-1256 . -1080) 183470) ((-1256 . -111) 183239) ((-1256 . -38) 183035) ((-1256 . -1002) 183004) ((-1256 . -298) 182832) ((-1256 . -1258) 182816) ((-1256 . -746) T) ((-1256 . -1141) T) ((-1256 . -1086) T) ((-1256 . -1078) T) ((-1256 . -21) T) ((-1256 . -23) T) ((-1256 . -1130) T) ((-1256 . -630) 182798) ((-1256 . -1246) T) ((-1256 . -102) T) ((-1256 . -25) T) ((-1256 . -133) T) ((-1256 . -147) 182705) ((-1256 . -149) 182612) ((-1256 . -631) NIL) ((-1256 . -234) 182564) ((-1256 . -925) 182397) ((-1256 . -927) 182158) ((-1256 . -919) 181894) ((-1256 . -274) 181846) ((-1256 . -239) 181669) ((-1256 . -236) 181486) ((-1256 . -240) 181373) ((-1256 . -376) 181352) ((-1256 . -1251) 181331) ((-1256 . -948) 181310) ((-1256 . -569) 181261) ((-1256 . -175) 181192) ((-1256 . -464) 181171) ((-1256 . -319) 181150) ((-1256 . -302) 181101) ((-1256 . -250) 181080) ((-1256 . -351) 181032) ((-1256 . -526) 180801) ((-1256 . -321) 180686) ((-1256 . -390) 180638) ((-1256 . -658) 180590) ((-1256 . -412) 180542) ((-1256 . -909) NIL) ((-1256 . -842) NIL) ((-1256 . -812) NIL) ((-1256 . -814) NIL) ((-1256 . -869) NIL) ((-1256 . -872) NIL) ((-1256 . -816) NIL) ((-1256 . -819) NIL) ((-1256 . -868) NIL) ((-1256 . -907) 180494) ((-1256 . -937) NIL) ((-1256 . -1049) NIL) ((-1256 . -1067) 180460) ((-1256 . -1181) NIL) ((-1256 . -1020) 180412) ((-1255 . -865) T) ((-1255 . -872) T) ((-1255 . -869) T) ((-1255 . -1130) T) ((-1255 . -630) 180394) ((-1255 . -1246) T) ((-1255 . -102) T) ((-1255 . -381) T) ((-1255 . -682) T) ((-1254 . -865) T) ((-1254 . -872) T) ((-1254 . -869) T) ((-1254 . -1130) T) ((-1254 . -630) 180376) ((-1254 . -1246) T) ((-1254 . -102) T) ((-1254 . -381) T) ((-1254 . -682) T) ((-1253 . -865) T) ((-1253 . -872) T) ((-1253 . -869) T) ((-1253 . -1130) T) ((-1253 . -630) 180358) ((-1253 . -1246) T) ((-1253 . -102) T) ((-1253 . -381) T) ((-1253 . -682) T) ((-1252 . -865) T) ((-1252 . -872) T) ((-1252 . -869) T) ((-1252 . -1130) T) ((-1252 . -630) 180340) ((-1252 . -1246) T) ((-1252 . -102) T) ((-1252 . -381) T) ((-1252 . -682) T) ((-1247 . -1112) T) ((-1247 . -502) 180321) ((-1247 . -630) 180287) ((-1247 . -633) 180268) ((-1247 . -1130) T) ((-1247 . -1246) T) ((-1247 . -102) T) ((-1247 . -93) T) ((-1244 . -502) 180245) ((-1244 . -630) 180157) ((-1244 . -633) 180134) ((-1244 . -1130) 180112) ((-1244 . -1246) 180090) ((-1244 . -102) 180068) ((-1239 . -760) 180044) ((-1239 . -35) 180010) ((-1239 . -95) 179976) ((-1239 . -296) 179942) ((-1239 . -505) 179908) ((-1239 . -1235) 179874) ((-1239 . -1232) 179840) ((-1239 . -1031) 179806) ((-1239 . -47) 179775) ((-1239 . -38) 179672) ((-1239 . -660) 179569) ((-1239 . -737) 179466) ((-1239 . -633) 179348) ((-1239 . -302) 179327) ((-1239 . -569) 179306) ((-1239 . -111) 179175) ((-1239 . -1080) 179058) ((-1239 . -1085) 178941) ((-1239 . -175) 178892) ((-1239 . -149) 178871) ((-1239 . -147) 178850) ((-1239 . -668) 178775) ((-1239 . -666) 178685) ((-1239 . -1002) 178647) ((-1239 . -927) 178628) ((-1239 . -1246) T) ((-1239 . -919) 178607) ((-1239 . -1078) T) ((-1239 . -1086) T) ((-1239 . -1141) T) ((-1239 . -746) T) ((-1239 . -21) T) ((-1239 . -23) T) ((-1239 . -1130) T) ((-1239 . -630) 178589) ((-1239 . -102) T) ((-1239 . -25) T) ((-1239 . -133) T) ((-1239 . -925) 178570) ((-1239 . -526) 178537) ((-1239 . -321) 178524) ((-1233 . -1039) 178508) ((-1233 . -34) T) ((-1233 . -1246) T) ((-1233 . -102) 178458) ((-1233 . -630) 178390) ((-1233 . -321) 178328) ((-1233 . -526) 178261) ((-1233 . -1130) 178239) ((-1233 . -501) 178223) ((-1228 . -378) 178197) ((-1228 . -102) T) ((-1228 . -1246) T) ((-1228 . -630) 178179) ((-1228 . -1130) T) ((-1226 . -1130) T) ((-1226 . -630) 178161) ((-1226 . -1246) T) ((-1226 . -102) T) ((-1226 . -633) 178143) ((-1220 . -857) 178127) ((-1220 . -102) T) ((-1220 . -1246) T) ((-1220 . -630) 178109) ((-1220 . -1130) T) ((-1218 . -1223) 178088) ((-1218 . -233) 178038) ((-1218 . -107) 177988) ((-1218 . -321) 177792) ((-1218 . -526) 177584) ((-1218 . -501) 177521) ((-1218 . -153) 177471) ((-1218 . -631) NIL) ((-1218 . -242) 177421) ((-1218 . -627) 177400) ((-1218 . -300) 177379) ((-1218 . -1246) T) ((-1218 . -298) 177358) ((-1218 . -1130) T) ((-1218 . -630) 177340) ((-1218 . -102) T) ((-1218 . -34) T) ((-1218 . -616) 177319) ((-1216 . -1246) T) ((-1214 . -1130) T) ((-1214 . -630) 177301) ((-1214 . -1246) T) ((-1214 . -102) T) ((-1213 . -865) T) ((-1213 . -872) T) ((-1213 . -869) T) ((-1213 . -1130) T) ((-1213 . -630) 177283) ((-1213 . -1246) T) ((-1213 . -102) T) ((-1213 . -381) T) ((-1213 . -682) T) ((-1212 . -865) T) ((-1212 . -872) T) ((-1212 . -869) T) ((-1212 . -1130) T) ((-1212 . -630) 177265) ((-1212 . -1246) T) ((-1212 . -102) T) ((-1212 . -381) T) ((-1211 . -1292) T) ((-1211 . -1130) T) ((-1211 . -630) 177232) ((-1211 . -1246) T) ((-1211 . -102) T) ((-1211 . -1067) 177168) ((-1211 . -633) 177104) ((-1210 . -630) 177086) ((-1209 . -630) 177068) ((-1208 . -338) 177044) ((-1208 . -1067) 176940) ((-1208 . -424) 176924) ((-1208 . -38) 176821) ((-1208 . -633) 176674) ((-1208 . -668) 176599) ((-1208 . -666) 176509) ((-1208 . -746) T) ((-1208 . -1141) T) ((-1208 . -1086) T) ((-1208 . -1078) T) ((-1208 . -111) 176378) ((-1208 . -1080) 176261) ((-1208 . -1085) 176144) ((-1208 . -21) T) ((-1208 . -23) T) ((-1208 . -1130) T) ((-1208 . -630) 176126) ((-1208 . -1246) T) ((-1208 . -102) T) ((-1208 . -25) T) ((-1208 . -133) T) ((-1208 . -660) 176023) ((-1208 . -737) 175920) ((-1208 . -147) 175899) ((-1208 . -149) 175878) ((-1208 . -175) 175829) ((-1208 . -569) 175808) ((-1208 . -302) 175787) ((-1208 . -47) 175763) ((-1206 . -869) T) ((-1206 . -630) 175745) ((-1206 . -1130) T) ((-1206 . -102) T) ((-1206 . -1246) T) ((-1206 . -872) T) ((-1206 . -631) 175667) ((-1206 . -633) 175648) ((-1206 . -909) 175615) ((-1205 . -630) 175597) ((-1204 . -1289) 175581) ((-1204 . -240) 175540) ((-1204 . -633) 175422) ((-1204 . -668) 175347) ((-1204 . -666) 175257) ((-1204 . -133) T) ((-1204 . -25) T) ((-1204 . -102) T) ((-1204 . -630) 175239) ((-1204 . -1130) T) ((-1204 . -23) T) ((-1204 . -21) T) ((-1204 . -746) T) ((-1204 . -1141) T) ((-1204 . -1086) T) ((-1204 . -1078) T) ((-1204 . -236) 175192) ((-1204 . -1246) T) ((-1204 . -239) 175151) ((-1204 . -298) 175116) ((-1204 . -925) 175029) ((-1204 . -919) 174917) ((-1204 . -927) 174830) ((-1204 . -1002) 174799) ((-1204 . -38) 174696) ((-1204 . -111) 174565) ((-1204 . -1080) 174448) ((-1204 . -1085) 174331) ((-1204 . -660) 174228) ((-1204 . -737) 174125) ((-1204 . -147) 174104) ((-1204 . -149) 174083) ((-1204 . -175) 174034) ((-1204 . -569) 174013) ((-1204 . -302) 173992) ((-1204 . -47) 173969) ((-1204 . -1275) 173946) ((-1204 . -35) 173912) ((-1204 . -95) 173878) ((-1204 . -296) 173844) ((-1204 . -505) 173810) ((-1204 . -1235) 173776) ((-1204 . -1232) 173742) ((-1204 . -1031) 173708) ((-1203 . -1281) 173669) ((-1203 . -376) 173648) ((-1203 . -1251) 173627) ((-1203 . -948) 173606) ((-1203 . -569) 173557) ((-1203 . -175) 173488) ((-1203 . -633) 173231) ((-1203 . -737) 173072) ((-1203 . -660) 172913) ((-1203 . -38) 172754) ((-1203 . -464) 172733) ((-1203 . -319) 172712) ((-1203 . -668) 172609) ((-1203 . -666) 172491) ((-1203 . -746) T) ((-1203 . -1141) T) ((-1203 . -1086) T) ((-1203 . -1078) T) ((-1203 . -111) 172312) ((-1203 . -1080) 172147) ((-1203 . -1085) 171982) ((-1203 . -21) T) ((-1203 . -23) T) ((-1203 . -1130) T) ((-1203 . -630) 171964) ((-1203 . -1246) T) ((-1203 . -102) T) ((-1203 . -25) T) ((-1203 . -133) T) ((-1203 . -302) 171915) ((-1203 . -250) 171894) ((-1203 . -1031) 171860) ((-1203 . -1232) 171826) ((-1203 . -1235) 171792) ((-1203 . -505) 171758) ((-1203 . -296) 171724) ((-1203 . -95) 171690) ((-1203 . -35) 171656) ((-1203 . -1275) 171626) ((-1203 . -47) 171596) ((-1203 . -149) 171575) ((-1203 . -147) 171554) ((-1203 . -1002) 171516) ((-1203 . -927) 171422) ((-1203 . -919) 171303) ((-1203 . -925) 171209) ((-1203 . -298) 171167) ((-1203 . -239) 171119) ((-1203 . -236) 171065) ((-1203 . -240) 171017) ((-1203 . -1279) 171001) ((-1203 . -1067) 170936) ((-1200 . -1272) 170920) ((-1200 . -1181) 170898) ((-1200 . -631) NIL) ((-1200 . -321) 170885) ((-1200 . -526) 170832) ((-1200 . -338) 170809) ((-1200 . -1067) 170689) ((-1200 . -424) 170673) ((-1200 . -38) 170502) ((-1200 . -111) 170311) ((-1200 . -1080) 170134) ((-1200 . -1085) 169957) ((-1200 . -666) 169867) ((-1200 . -668) 169756) ((-1200 . -660) 169585) ((-1200 . -737) 169414) ((-1200 . -633) 169183) ((-1200 . -147) 169162) ((-1200 . -149) 169141) ((-1200 . -47) 169118) ((-1200 . -390) 169102) ((-1200 . -658) 169050) ((-1200 . -925) 168993) ((-1200 . -919) 168896) ((-1200 . -927) 168803) ((-1200 . -909) NIL) ((-1200 . -937) 168782) ((-1200 . -1251) 168761) ((-1200 . -977) 168730) ((-1200 . -948) 168709) ((-1200 . -569) 168620) ((-1200 . -302) 168531) ((-1200 . -175) 168422) ((-1200 . -464) 168353) ((-1200 . -319) 168332) ((-1200 . -298) 168259) ((-1200 . -240) T) ((-1200 . -133) T) ((-1200 . -25) T) ((-1200 . -102) T) ((-1200 . -630) 168241) ((-1200 . -1130) T) ((-1200 . -23) T) ((-1200 . -21) T) ((-1200 . -746) T) ((-1200 . -1141) T) ((-1200 . -1086) T) ((-1200 . -1078) T) ((-1200 . -236) 168228) ((-1200 . -1246) T) ((-1200 . -239) T) ((-1200 . -274) 168212) ((-1200 . -234) 168196) ((-1197 . -1260) 168157) ((-1197 . -1031) 168123) ((-1197 . -1232) 168089) ((-1197 . -1235) 168055) ((-1197 . -505) 168021) ((-1197 . -296) 167987) ((-1197 . -95) 167953) ((-1197 . -35) 167919) ((-1197 . -1275) 167896) ((-1197 . -47) 167873) ((-1197 . -633) 167668) ((-1197 . -737) 167464) ((-1197 . -660) 167260) ((-1197 . -668) 167112) ((-1197 . -666) 166949) ((-1197 . -1085) 166739) ((-1197 . -1080) 166529) ((-1197 . -111) 166298) ((-1197 . -38) 166094) ((-1197 . -1002) 166063) ((-1197 . -298) 165891) ((-1197 . -1258) 165875) ((-1197 . -746) T) ((-1197 . -1141) T) ((-1197 . -1086) T) ((-1197 . -1078) T) ((-1197 . -21) T) ((-1197 . -23) T) ((-1197 . -1130) T) ((-1197 . -630) 165857) ((-1197 . -1246) T) ((-1197 . -102) T) ((-1197 . -25) T) ((-1197 . -133) T) ((-1197 . -147) 165764) ((-1197 . -149) 165671) ((-1197 . -631) NIL) ((-1197 . -234) 165623) ((-1197 . -925) 165456) ((-1197 . -927) 165217) ((-1197 . -919) 164953) ((-1197 . -274) 164905) ((-1197 . -239) 164728) ((-1197 . -236) 164545) ((-1197 . -240) 164432) ((-1197 . -376) 164411) ((-1197 . -1251) 164390) ((-1197 . -948) 164369) ((-1197 . -569) 164320) ((-1197 . -175) 164251) ((-1197 . -464) 164230) ((-1197 . -319) 164209) ((-1197 . -302) 164160) ((-1197 . -250) 164139) ((-1197 . -351) 164091) ((-1197 . -526) 163860) ((-1197 . -321) 163745) ((-1197 . -390) 163697) ((-1197 . -658) 163649) ((-1197 . -412) 163601) ((-1197 . -909) NIL) ((-1197 . -842) NIL) ((-1197 . -812) NIL) ((-1197 . -814) NIL) ((-1197 . -869) NIL) ((-1197 . -872) NIL) ((-1197 . -816) NIL) ((-1197 . -819) NIL) ((-1197 . -868) NIL) ((-1197 . -907) 163553) ((-1197 . -937) NIL) ((-1197 . -1049) NIL) ((-1197 . -1067) 163519) ((-1197 . -1181) NIL) ((-1197 . -1020) 163471) ((-1196 . -1112) T) ((-1196 . -502) 163452) ((-1196 . -630) 163418) ((-1196 . -633) 163399) ((-1196 . -1130) T) ((-1196 . -1246) T) ((-1196 . -102) T) ((-1196 . -93) T) ((-1195 . -1130) T) ((-1195 . -630) 163381) ((-1195 . -1246) T) ((-1195 . -102) T) ((-1194 . -1130) T) ((-1194 . -630) 163363) ((-1194 . -1246) T) ((-1194 . -102) T) ((-1189 . -1223) 163339) ((-1189 . -233) 163286) ((-1189 . -107) 163233) ((-1189 . -321) 163028) ((-1189 . -526) 162811) ((-1189 . -501) 162745) ((-1189 . -153) 162692) ((-1189 . -631) NIL) ((-1189 . -242) 162639) ((-1189 . -627) 162615) ((-1189 . -300) 162591) ((-1189 . -1246) T) ((-1189 . -298) 162567) ((-1189 . -1130) T) ((-1189 . -630) 162549) ((-1189 . -102) T) ((-1189 . -34) T) ((-1189 . -616) 162525) ((-1188 . -1173) T) ((-1188 . -385) 162507) ((-1188 . -872) T) ((-1188 . -869) T) ((-1188 . -153) 162489) ((-1188 . -34) T) ((-1188 . -1246) T) ((-1188 . -102) T) ((-1188 . -630) 162471) ((-1188 . -321) NIL) ((-1188 . -526) NIL) ((-1188 . -1130) T) ((-1188 . -501) 162453) ((-1188 . -631) NIL) ((-1188 . -298) 162403) ((-1188 . -616) 162378) ((-1188 . -300) 162353) ((-1188 . -671) 162335) ((-1188 . -19) 162317) ((-1184 . -694) 162301) ((-1184 . -671) 162285) ((-1184 . -300) 162262) ((-1184 . -298) 162214) ((-1184 . -616) 162191) ((-1184 . -631) 162152) ((-1184 . -501) 162136) ((-1184 . -1130) 162114) ((-1184 . -526) 162047) ((-1184 . -321) 161985) ((-1184 . -630) 161917) ((-1184 . -102) 161867) ((-1184 . -1246) T) ((-1184 . -34) T) ((-1184 . -153) 161851) ((-1184 . -1285) 161835) ((-1184 . -1039) 161819) ((-1184 . -1179) 161803) ((-1184 . -633) 161780) ((-1182 . -1112) T) ((-1182 . -502) 161761) ((-1182 . -630) 161727) ((-1182 . -633) 161708) ((-1182 . -1130) T) ((-1182 . -1246) T) ((-1182 . -102) T) ((-1182 . -93) T) ((-1180 . -1223) 161687) ((-1180 . -233) 161637) ((-1180 . -107) 161587) ((-1180 . -321) 161391) ((-1180 . -526) 161183) ((-1180 . -501) 161120) ((-1180 . -153) 161070) ((-1180 . -631) NIL) ((-1180 . -242) 161020) ((-1180 . -627) 160999) ((-1180 . -300) 160978) ((-1180 . -1246) T) ((-1180 . -298) 160957) ((-1180 . -1130) T) ((-1180 . -630) 160939) ((-1180 . -102) T) ((-1180 . -34) T) ((-1180 . -616) 160918) ((-1177 . -1150) 160902) ((-1177 . -501) 160886) ((-1177 . -1130) 160864) ((-1177 . -526) 160797) ((-1177 . -321) 160735) ((-1177 . -630) 160667) ((-1177 . -102) 160617) ((-1177 . -1246) T) ((-1177 . -34) T) ((-1177 . -107) 160601) ((-1175 . -1138) 160570) ((-1175 . -1241) 160539) ((-1175 . -630) 160501) ((-1175 . -153) 160485) ((-1175 . -34) T) ((-1175 . -1246) T) ((-1175 . -102) T) ((-1175 . -321) 160423) ((-1175 . -526) 160356) ((-1175 . -1130) T) ((-1175 . -501) 160340) ((-1175 . -631) 160301) ((-1175 . -1005) 160270) ((-1175 . -1100) 160239) ((-1171 . -1152) 160184) ((-1171 . -501) 160168) ((-1171 . -526) 160101) ((-1171 . -321) 160039) ((-1171 . -34) T) ((-1171 . -1082) 159979) ((-1171 . -1067) 159875) ((-1171 . -633) 159793) ((-1171 . -424) 159777) ((-1171 . -658) 159725) ((-1171 . -668) 159663) ((-1171 . -390) 159647) ((-1171 . -240) 159626) ((-1171 . -236) 159571) ((-1171 . -239) 159522) ((-1171 . -274) 159506) ((-1171 . -919) 159427) ((-1171 . -927) 159350) ((-1171 . -925) 159309) ((-1171 . -234) 159293) ((-1171 . -737) 159225) ((-1171 . -660) 159157) ((-1171 . -666) 159116) ((-1171 . -133) T) ((-1171 . -25) T) ((-1171 . -102) T) ((-1171 . -1246) T) ((-1171 . -630) 159078) ((-1171 . -1130) T) ((-1171 . -23) T) ((-1171 . -21) T) ((-1171 . -1085) 159062) ((-1171 . -1080) 159046) ((-1171 . -111) 159025) ((-1171 . -1078) T) ((-1171 . -1086) T) ((-1171 . -1141) T) ((-1171 . -746) T) ((-1171 . -38) 158985) ((-1171 . -631) 158946) ((-1170 . -1039) 158917) ((-1170 . -34) T) ((-1170 . -1246) T) ((-1170 . -102) T) ((-1170 . -630) 158899) ((-1170 . -321) 158825) ((-1170 . -526) 158744) ((-1170 . -1130) T) ((-1170 . -501) 158715) ((-1169 . -1130) T) ((-1169 . -630) 158697) ((-1169 . -1246) T) ((-1169 . -102) T) ((-1164 . -1166) T) ((-1164 . -1292) T) ((-1164 . -93) T) ((-1164 . -102) T) ((-1164 . -1246) T) ((-1164 . -630) 158663) ((-1164 . -1130) T) ((-1164 . -633) 158644) ((-1164 . -502) 158625) ((-1164 . -1112) T) ((-1162 . -1163) 158609) ((-1162 . -102) T) ((-1162 . -1246) T) ((-1162 . -630) 158591) ((-1162 . -1130) T) ((-1155 . -760) 158570) ((-1155 . -35) 158536) ((-1155 . -95) 158502) ((-1155 . -296) 158468) ((-1155 . -505) 158434) ((-1155 . -1235) 158400) ((-1155 . -1232) 158366) ((-1155 . -1031) 158332) ((-1155 . -47) 158304) ((-1155 . -38) 158201) ((-1155 . -660) 158098) ((-1155 . -737) 157995) ((-1155 . -633) 157877) ((-1155 . -302) 157856) ((-1155 . -569) 157835) ((-1155 . -111) 157704) ((-1155 . -1080) 157587) ((-1155 . -1085) 157470) ((-1155 . -175) 157421) ((-1155 . -149) 157400) ((-1155 . -147) 157379) ((-1155 . -668) 157304) ((-1155 . -666) 157214) ((-1155 . -1002) 157181) ((-1155 . -927) 157165) ((-1155 . -1246) T) ((-1155 . -919) 157147) ((-1155 . -1078) T) ((-1155 . -1086) T) ((-1155 . -1141) T) ((-1155 . -746) T) ((-1155 . -21) T) ((-1155 . -23) T) ((-1155 . -1130) T) ((-1155 . -630) 157129) ((-1155 . -102) T) ((-1155 . -25) T) ((-1155 . -133) T) ((-1155 . -925) 157113) ((-1155 . -526) 157083) ((-1155 . -321) 157070) ((-1154 . -977) 157037) ((-1154 . -633) 156829) ((-1154 . -1067) 156712) ((-1154 . -1251) 156691) ((-1154 . -937) 156670) ((-1154 . -909) 156529) ((-1154 . -927) 156513) ((-1154 . -919) 156495) ((-1154 . -925) 156479) ((-1154 . -526) 156431) ((-1154 . -464) 156382) ((-1154 . -658) 156330) ((-1154 . -668) 156219) ((-1154 . -390) 156203) ((-1154 . -47) 156175) ((-1154 . -38) 156024) ((-1154 . -660) 155873) ((-1154 . -737) 155722) ((-1154 . -302) 155653) ((-1154 . -569) 155584) ((-1154 . -111) 155413) ((-1154 . -1080) 155256) ((-1154 . -1085) 155099) ((-1154 . -175) 155010) ((-1154 . -149) 154989) ((-1154 . -147) 154968) ((-1154 . -666) 154878) ((-1154 . -133) T) ((-1154 . -25) T) ((-1154 . -102) T) ((-1154 . -1246) T) ((-1154 . -630) 154860) ((-1154 . -1130) T) ((-1154 . -23) T) ((-1154 . -21) T) ((-1154 . -1078) T) ((-1154 . -1086) T) ((-1154 . -1141) T) ((-1154 . -746) T) ((-1154 . -424) 154844) ((-1154 . -338) 154816) ((-1154 . -321) 154803) ((-1154 . -631) 154551) ((-1149 . -557) T) ((-1149 . -1251) T) ((-1149 . -1181) T) ((-1149 . -1067) 154533) ((-1149 . -631) 154448) ((-1149 . -1049) T) ((-1149 . -909) 154430) ((-1149 . -868) T) ((-1149 . -819) T) ((-1149 . -816) T) ((-1149 . -872) T) ((-1149 . -869) T) ((-1149 . -814) T) ((-1149 . -812) T) ((-1149 . -842) T) ((-1149 . -668) 154402) ((-1149 . -658) 154384) ((-1149 . -948) T) ((-1149 . -569) T) ((-1149 . -302) T) ((-1149 . -175) T) ((-1149 . -633) 154356) ((-1149 . -737) 154343) ((-1149 . -660) 154330) ((-1149 . -1085) 154317) ((-1149 . -1080) 154304) ((-1149 . -111) 154289) ((-1149 . -38) 154276) ((-1149 . -464) T) ((-1149 . -319) T) ((-1149 . -239) T) ((-1149 . -236) 154263) ((-1149 . -240) T) ((-1149 . -145) T) ((-1149 . -1078) T) ((-1149 . -1086) T) ((-1149 . -1141) T) ((-1149 . -746) T) ((-1149 . -21) T) ((-1149 . -666) 154235) ((-1149 . -23) T) ((-1149 . -1130) T) ((-1149 . -630) 154217) ((-1149 . -1246) T) ((-1149 . -102) T) ((-1149 . -25) T) ((-1149 . -133) T) ((-1149 . -149) T) ((-1149 . -865) T) ((-1149 . -381) T) ((-1149 . -113) T) ((-1149 . -682) T) ((-1145 . -1112) T) ((-1145 . -502) 154198) ((-1145 . -630) 154164) ((-1145 . -633) 154145) ((-1145 . -1130) T) ((-1145 . -1246) T) ((-1145 . -102) T) ((-1145 . -93) T) ((-1144 . -1130) T) ((-1144 . -630) 154127) ((-1144 . -1246) T) ((-1144 . -102) T) ((-1142 . -245) 154106) ((-1142 . -1304) 154076) ((-1142 . -819) 154055) ((-1142 . -816) 154034) ((-1142 . -872) 153985) ((-1142 . -869) 153936) ((-1142 . -814) 153915) ((-1142 . -815) 153894) ((-1142 . -737) 153836) ((-1142 . -660) 153758) ((-1142 . -300) 153735) ((-1142 . -298) 153712) ((-1142 . -501) 153696) ((-1142 . -526) 153629) ((-1142 . -321) 153567) ((-1142 . -34) T) ((-1142 . -616) 153544) ((-1142 . -1067) 153371) ((-1142 . -633) 153169) ((-1142 . -424) 153138) ((-1142 . -658) 153044) ((-1142 . -668) 152877) ((-1142 . -390) 152846) ((-1142 . -381) 152825) ((-1142 . -240) 152777) ((-1142 . -666) 152556) ((-1142 . -746) 152534) ((-1142 . -1141) 152512) ((-1142 . -1086) 152490) ((-1142 . -1078) 152468) ((-1142 . -236) 152359) ((-1142 . -239) 152256) ((-1142 . -274) 152225) ((-1142 . -919) 152092) ((-1142 . -927) 151961) ((-1142 . -925) 151893) ((-1142 . -234) 151862) ((-1142 . -630) 151555) ((-1142 . -1085) 151476) ((-1142 . -1080) 151377) ((-1142 . -111) 151293) ((-1142 . -133) 151164) ((-1142 . -25) 150997) ((-1142 . -102) 150729) ((-1142 . -1246) T) ((-1142 . -1130) 150481) ((-1142 . -23) 150333) ((-1142 . -21) 150244) ((-1135 . -408) T) ((-1135 . -1246) T) ((-1135 . -630) 150226) ((-1134 . -1133) 150190) ((-1134 . -102) T) ((-1134 . -630) 150172) ((-1134 . -1130) T) ((-1134 . -298) 150128) ((-1134 . -1246) T) ((-1134 . -635) 150043) ((-1132 . -1133) 149995) ((-1132 . -102) T) ((-1132 . -630) 149977) ((-1132 . -1130) T) ((-1132 . -298) 149933) ((-1132 . -1246) T) ((-1132 . -635) 149836) ((-1131 . -381) T) ((-1131 . -102) T) ((-1131 . -1246) T) ((-1131 . -630) 149818) ((-1131 . -1130) T) ((-1126 . -438) 149802) ((-1126 . -1128) 149786) ((-1126 . -381) 149765) ((-1126 . -242) 149749) ((-1126 . -631) 149710) ((-1126 . -153) 149694) ((-1126 . -501) 149678) ((-1126 . -1130) T) ((-1126 . -526) 149611) ((-1126 . -321) 149549) ((-1126 . -630) 149531) ((-1126 . -102) T) ((-1126 . -1246) T) ((-1126 . -34) T) ((-1126 . -107) 149515) ((-1126 . -233) 149499) ((-1125 . -1112) T) ((-1125 . -502) 149480) ((-1125 . -630) 149446) ((-1125 . -633) 149427) ((-1125 . -1130) T) ((-1125 . -1246) T) ((-1125 . -102) T) ((-1125 . -93) T) ((-1121 . -1246) T) ((-1121 . -1130) 149397) ((-1121 . -630) 149356) ((-1121 . -102) 149326) ((-1120 . -1112) T) ((-1120 . -502) 149307) ((-1120 . -630) 149273) ((-1120 . -633) 149254) ((-1120 . -1130) T) ((-1120 . -1246) T) ((-1120 . -102) T) ((-1120 . -93) T) ((-1118 . -1123) 149238) ((-1118 . -635) 149222) ((-1118 . -1130) 149200) ((-1118 . -630) 149167) ((-1118 . -1246) 149145) ((-1118 . -102) 149123) ((-1118 . -1124) 149081) ((-1117 . -277) 149065) ((-1117 . -633) 149049) ((-1117 . -1067) 149033) ((-1117 . -872) T) ((-1117 . -102) T) ((-1117 . -1130) T) ((-1117 . -630) 149015) ((-1117 . -869) T) ((-1117 . -236) 149002) ((-1117 . -1246) T) ((-1117 . -239) T) ((-1116 . -262) 148939) ((-1116 . -633) 148675) ((-1116 . -1067) 148502) ((-1116 . -631) NIL) ((-1116 . -338) 148463) ((-1116 . -424) 148447) ((-1116 . -38) 148296) ((-1116 . -111) 148125) ((-1116 . -1080) 147968) ((-1116 . -1085) 147811) ((-1116 . -666) 147721) ((-1116 . -668) 147610) ((-1116 . -660) 147459) ((-1116 . -737) 147308) ((-1116 . -147) 147287) ((-1116 . -149) 147266) ((-1116 . -175) 147177) ((-1116 . -569) 147108) ((-1116 . -302) 147039) ((-1116 . -47) 147000) ((-1116 . -390) 146984) ((-1116 . -658) 146932) ((-1116 . -464) 146883) ((-1116 . -526) 146750) ((-1116 . -925) 146685) ((-1116 . -919) 146580) ((-1116 . -927) 146479) ((-1116 . -909) NIL) ((-1116 . -937) 146458) ((-1116 . -1251) 146437) ((-1116 . -977) 146382) ((-1116 . -321) 146369) ((-1116 . -240) 146348) ((-1116 . -133) T) ((-1116 . -25) T) ((-1116 . -102) T) ((-1116 . -630) 146330) ((-1116 . -1130) T) ((-1116 . -23) T) ((-1116 . -21) T) ((-1116 . -746) T) ((-1116 . -1141) T) ((-1116 . -1086) T) ((-1116 . -1078) T) ((-1116 . -236) 146275) ((-1116 . -1246) T) ((-1116 . -239) 146226) ((-1116 . -274) 146210) ((-1116 . -234) 146194) ((-1114 . -630) 146176) ((-1111 . -869) T) ((-1111 . -630) 146158) ((-1111 . -1130) T) ((-1111 . -102) T) ((-1111 . -1246) T) ((-1111 . -872) T) ((-1111 . -631) 146139) ((-1108 . -744) 146118) ((-1108 . -1067) 146014) ((-1108 . -424) 145998) ((-1108 . -658) 145946) ((-1108 . -668) 145820) ((-1108 . -390) 145804) ((-1108 . -383) 145783) ((-1108 . -149) 145762) ((-1108 . -633) 145580) ((-1108 . -737) 145448) ((-1108 . -660) 145316) ((-1108 . -666) 145211) ((-1108 . -1085) 145121) ((-1108 . -1080) 145031) ((-1108 . -111) 144927) ((-1108 . -38) 144795) ((-1108 . -422) 144774) ((-1108 . -414) 144753) ((-1108 . -147) 144704) ((-1108 . -1181) 144683) ((-1108 . -363) 144662) ((-1108 . -381) 144613) ((-1108 . -250) 144564) ((-1108 . -302) 144515) ((-1108 . -319) 144466) ((-1108 . -464) 144417) ((-1108 . -569) 144368) ((-1108 . -948) 144319) ((-1108 . -1251) 144270) ((-1108 . -376) 144221) ((-1108 . -240) 144146) ((-1108 . -236) 144019) ((-1108 . -239) 143898) ((-1108 . -274) 143868) ((-1108 . -919) 143737) ((-1108 . -927) 143608) ((-1108 . -925) 143541) ((-1108 . -234) 143511) ((-1108 . -631) 143495) ((-1108 . -21) T) ((-1108 . -23) T) ((-1108 . -1130) T) ((-1108 . -630) 143477) ((-1108 . -1246) T) ((-1108 . -102) T) ((-1108 . -25) T) ((-1108 . -133) T) ((-1108 . -1078) T) ((-1108 . -1086) T) ((-1108 . -1141) T) ((-1108 . -746) T) ((-1108 . -175) T) ((-1106 . -1130) T) ((-1106 . -630) 143459) ((-1106 . -1246) T) ((-1106 . -102) T) ((-1106 . -298) 143438) ((-1105 . -1130) T) ((-1105 . -630) 143420) ((-1105 . -1246) T) ((-1105 . -102) T) ((-1104 . -1130) T) ((-1104 . -630) 143402) ((-1104 . -1246) T) ((-1104 . -102) T) ((-1104 . -298) 143381) ((-1104 . -1067) 143358) ((-1104 . -633) 143335) ((-1103 . -1246) T) ((-1102 . -1112) T) ((-1102 . -502) 143316) ((-1102 . -630) 143282) ((-1102 . -633) 143263) ((-1102 . -1130) T) ((-1102 . -1246) T) ((-1102 . -102) T) ((-1102 . -93) T) ((-1095 . -1112) T) ((-1095 . -502) 143244) ((-1095 . -630) 143210) ((-1095 . -633) 143191) ((-1095 . -1130) T) ((-1095 . -1246) T) ((-1095 . -102) T) ((-1095 . -93) T) ((-1092 . -1223) 143166) ((-1092 . -233) 143112) ((-1092 . -107) 143058) ((-1092 . -321) 142909) ((-1092 . -526) 142753) ((-1092 . -501) 142684) ((-1092 . -153) 142630) ((-1092 . -631) NIL) ((-1092 . -242) 142576) ((-1092 . -627) 142551) ((-1092 . -300) 142526) ((-1092 . -1246) T) ((-1092 . -298) 142501) ((-1092 . -1130) T) ((-1092 . -630) 142483) ((-1092 . -102) T) ((-1092 . -34) T) ((-1092 . -616) 142458) ((-1091 . -557) T) ((-1091 . -1251) T) ((-1091 . -1181) T) ((-1091 . -1067) 142440) ((-1091 . -631) 142355) ((-1091 . -1049) T) ((-1091 . -909) 142337) ((-1091 . -868) T) ((-1091 . -819) T) ((-1091 . -816) T) ((-1091 . -872) T) ((-1091 . -869) T) ((-1091 . -814) T) ((-1091 . -812) T) ((-1091 . -842) T) ((-1091 . -668) 142309) ((-1091 . -658) 142291) ((-1091 . -948) T) ((-1091 . -569) T) ((-1091 . -302) T) ((-1091 . -175) T) ((-1091 . -633) 142263) ((-1091 . -737) 142250) ((-1091 . -660) 142237) ((-1091 . -1085) 142224) ((-1091 . -1080) 142211) ((-1091 . -111) 142196) ((-1091 . -38) 142183) ((-1091 . -464) T) ((-1091 . -319) T) ((-1091 . -239) T) ((-1091 . -236) 142170) ((-1091 . -240) T) ((-1091 . -145) T) ((-1091 . -1078) T) ((-1091 . -1086) T) ((-1091 . -1141) T) ((-1091 . -746) T) ((-1091 . -21) T) ((-1091 . -666) 142142) ((-1091 . -23) T) ((-1091 . -1130) T) ((-1091 . -630) 142124) ((-1091 . -1246) T) ((-1091 . -102) T) ((-1091 . -25) T) ((-1091 . -133) T) ((-1091 . -149) T) ((-1091 . -635) 142105) ((-1090 . -1097) 142084) ((-1090 . -102) T) ((-1090 . -1246) T) ((-1090 . -630) 142066) ((-1090 . -1130) T) ((-1087 . -1246) T) ((-1087 . -1130) 142044) ((-1087 . -630) 142011) ((-1087 . -102) 141989) ((-1083 . -1082) 141929) ((-1083 . -660) 141871) ((-1083 . -737) 141813) ((-1083 . -34) T) ((-1083 . -321) 141751) ((-1083 . -526) 141684) ((-1083 . -501) 141668) ((-1083 . -668) 141652) ((-1083 . -666) 141621) ((-1083 . -133) T) ((-1083 . -25) T) ((-1083 . -102) T) ((-1083 . -1246) T) ((-1083 . -630) 141583) ((-1083 . -1130) T) ((-1083 . -23) T) ((-1083 . -21) T) ((-1083 . -1085) 141567) ((-1083 . -1080) 141551) ((-1083 . -111) 141530) ((-1083 . -1304) 141500) ((-1083 . -631) 141461) ((-1075 . -1100) 141390) ((-1075 . -1005) 141319) ((-1075 . -631) 141261) ((-1075 . -501) 141226) ((-1075 . -1130) T) ((-1075 . -526) 141127) ((-1075 . -321) 141035) ((-1075 . -630) 140978) ((-1075 . -102) T) ((-1075 . -1246) T) ((-1075 . -34) T) ((-1075 . -153) 140943) ((-1075 . -1241) 140872) ((-1065 . -1112) T) ((-1065 . -502) 140853) ((-1065 . -630) 140819) ((-1065 . -633) 140800) ((-1065 . -1130) T) ((-1065 . -1246) T) ((-1065 . -102) T) ((-1065 . -93) T) ((-1064 . -1223) 140775) ((-1064 . -233) 140721) ((-1064 . -107) 140667) ((-1064 . -321) 140518) ((-1064 . -526) 140362) ((-1064 . -501) 140293) ((-1064 . -153) 140239) ((-1064 . -631) NIL) ((-1064 . -242) 140185) ((-1064 . -627) 140160) ((-1064 . -300) 140135) ((-1064 . -1246) T) ((-1064 . -298) 140110) ((-1064 . -1130) T) ((-1064 . -630) 140092) ((-1064 . -102) T) ((-1064 . -34) T) ((-1064 . -616) 140067) ((-1063 . -175) T) ((-1063 . -633) 140036) ((-1063 . -746) T) ((-1063 . -1141) T) ((-1063 . -1086) T) ((-1063 . -1078) T) ((-1063 . -668) 140010) ((-1063 . -666) 139969) ((-1063 . -133) T) ((-1063 . -25) T) ((-1063 . -102) T) ((-1063 . -1246) T) ((-1063 . -630) 139951) ((-1063 . -1130) T) ((-1063 . -23) T) ((-1063 . -21) T) ((-1063 . -1085) 139925) ((-1063 . -1080) 139899) ((-1063 . -111) 139866) ((-1063 . -38) 139850) ((-1063 . -660) 139834) ((-1063 . -737) 139818) ((-1056 . -1100) 139787) ((-1056 . -1005) 139756) ((-1056 . -631) 139717) ((-1056 . -501) 139701) ((-1056 . -1130) T) ((-1056 . -526) 139634) ((-1056 . -321) 139572) ((-1056 . -630) 139534) ((-1056 . -102) T) ((-1056 . -1246) T) ((-1056 . -34) T) ((-1056 . -153) 139518) ((-1056 . -1241) 139487) ((-1055 . -1246) T) ((-1055 . -1130) 139465) ((-1055 . -630) 139432) ((-1055 . -102) 139410) ((-1053 . -1041) T) ((-1053 . -1031) T) ((-1053 . -812) T) ((-1053 . -814) T) ((-1053 . -869) T) ((-1053 . -872) T) ((-1053 . -816) T) ((-1053 . -819) T) ((-1053 . -868) T) ((-1053 . -1067) 139290) ((-1053 . -424) 139252) ((-1053 . -250) T) ((-1053 . -302) T) ((-1053 . -319) T) ((-1053 . -464) T) ((-1053 . -38) 139189) ((-1053 . -660) 139126) ((-1053 . -737) 139063) ((-1053 . -633) 139000) ((-1053 . -569) T) ((-1053 . -948) T) ((-1053 . -1251) T) ((-1053 . -376) T) ((-1053 . -111) 138916) ((-1053 . -1080) 138853) ((-1053 . -1085) 138790) ((-1053 . -175) T) ((-1053 . -149) T) ((-1053 . -668) 138727) ((-1053 . -666) 138664) ((-1053 . -133) T) ((-1053 . -25) T) ((-1053 . -102) T) ((-1053 . -1246) T) ((-1053 . -630) 138646) ((-1053 . -1130) T) ((-1053 . -23) T) ((-1053 . -21) T) ((-1053 . -1078) T) ((-1053 . -1086) T) ((-1053 . -1141) T) ((-1053 . -746) T) ((-1048 . -1112) T) ((-1048 . -502) 138627) ((-1048 . -630) 138593) ((-1048 . -633) 138574) ((-1048 . -1130) T) ((-1048 . -1246) T) ((-1048 . -102) T) ((-1048 . -93) T) ((-1033 . -1020) 138556) ((-1033 . -1181) T) ((-1033 . -633) 138506) ((-1033 . -1067) 138466) ((-1033 . -631) 138396) ((-1033 . -1049) T) ((-1033 . -937) NIL) ((-1033 . -907) 138378) ((-1033 . -868) T) ((-1033 . -819) T) ((-1033 . -816) T) ((-1033 . -872) T) ((-1033 . -869) T) ((-1033 . -814) T) ((-1033 . -812) T) ((-1033 . -842) T) ((-1033 . -909) 138360) ((-1033 . -412) 138342) ((-1033 . -658) 138324) ((-1033 . -390) 138306) ((-1033 . -298) NIL) ((-1033 . -321) NIL) ((-1033 . -526) NIL) ((-1033 . -351) 138288) ((-1033 . -250) T) ((-1033 . -111) 138222) ((-1033 . -1080) 138172) ((-1033 . -1085) 138122) ((-1033 . -302) T) ((-1033 . -737) 138072) ((-1033 . -660) 138022) ((-1033 . -668) 137972) ((-1033 . -666) 137922) ((-1033 . -38) 137872) ((-1033 . -319) T) ((-1033 . -464) T) ((-1033 . -175) T) ((-1033 . -569) T) ((-1033 . -948) T) ((-1033 . -1251) T) ((-1033 . -376) T) ((-1033 . -240) T) ((-1033 . -236) 137859) ((-1033 . -239) T) ((-1033 . -274) 137841) ((-1033 . -919) NIL) ((-1033 . -927) NIL) ((-1033 . -925) NIL) ((-1033 . -234) 137823) ((-1033 . -149) T) ((-1033 . -147) NIL) ((-1033 . -133) T) ((-1033 . -25) T) ((-1033 . -102) T) ((-1033 . -1246) T) ((-1033 . -630) 137783) ((-1033 . -1130) T) ((-1033 . -23) T) ((-1033 . -21) T) ((-1033 . -1078) T) ((-1033 . -1086) T) ((-1033 . -1141) T) ((-1033 . -746) T) ((-1032 . -355) 137757) ((-1032 . -175) T) ((-1032 . -633) 137687) ((-1032 . -746) T) ((-1032 . -1141) T) ((-1032 . -1086) T) ((-1032 . -1078) T) ((-1032 . -668) 137594) ((-1032 . -666) 137524) ((-1032 . -133) T) ((-1032 . -25) T) ((-1032 . -102) T) ((-1032 . -1246) T) ((-1032 . -630) 137506) ((-1032 . -1130) T) ((-1032 . -23) T) ((-1032 . -21) T) ((-1032 . -1085) 137451) ((-1032 . -1080) 137396) ((-1032 . -111) 137325) ((-1032 . -631) 137309) ((-1032 . -234) 137286) ((-1032 . -925) 137238) ((-1032 . -927) 137147) ((-1032 . -919) 137054) ((-1032 . -274) 137031) ((-1032 . -239) 136968) ((-1032 . -236) 136899) ((-1032 . -240) 136871) ((-1032 . -376) T) ((-1032 . -1251) T) ((-1032 . -948) T) ((-1032 . -569) T) ((-1032 . -737) 136816) ((-1032 . -660) 136761) ((-1032 . -38) 136706) ((-1032 . -464) T) ((-1032 . -319) T) ((-1032 . -302) T) ((-1032 . -250) T) ((-1032 . -381) NIL) ((-1032 . -363) NIL) ((-1032 . -1181) NIL) ((-1032 . -147) 136678) ((-1032 . -414) NIL) ((-1032 . -422) 136650) ((-1032 . -149) 136622) ((-1032 . -383) 136594) ((-1032 . -390) 136571) ((-1032 . -658) 136510) ((-1032 . -424) 136487) ((-1032 . -1067) 136375) ((-1032 . -744) 136347) ((-1029 . -1024) 136331) ((-1029 . -501) 136315) ((-1029 . -1130) 136293) ((-1029 . -526) 136226) ((-1029 . -321) 136164) ((-1029 . -630) 136096) ((-1029 . -102) 136046) ((-1029 . -1246) T) ((-1029 . -34) T) ((-1029 . -107) 136030) ((-1025 . -1027) 136014) ((-1025 . -872) 135993) ((-1025 . -869) 135972) ((-1025 . -1067) 135868) ((-1025 . -424) 135852) ((-1025 . 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-1130) T) ((-1023 . -1246) T) ((-1023 . -102) T) ((-1023 . -93) T) ((-1022 . -21) T) ((-1022 . -666) 134223) ((-1022 . -23) T) ((-1022 . -1130) T) ((-1022 . -630) 134205) ((-1022 . -1246) T) ((-1022 . -102) T) ((-1022 . -25) T) ((-1022 . -133) T) ((-1022 . -298) 134172) ((-1018 . -630) 134154) ((-1015 . -1130) T) ((-1015 . -630) 134136) ((-1015 . -1246) T) ((-1015 . -102) T) ((-1000 . -819) T) ((-1000 . -816) T) ((-1000 . -872) T) ((-1000 . -869) T) ((-1000 . -814) T) ((-1000 . -23) T) ((-1000 . -1130) T) ((-1000 . -630) 134096) ((-1000 . -1246) T) ((-1000 . -102) T) ((-1000 . -25) T) ((-1000 . -133) T) ((-999 . -1112) T) ((-999 . -502) 134077) ((-999 . -630) 134043) ((-999 . -633) 134024) ((-999 . -1130) T) ((-999 . -1246) T) ((-999 . -102) T) ((-999 . -93) T) ((-995 . -1246) T) ((-994 . -1246) T) ((-993 . -996) T) ((-993 . -102) T) ((-993 . -630) 134006) ((-993 . -1130) T) ((-993 . -682) T) ((-993 . -1246) T) ((-993 . -113) T) ((-993 . -633) 133990) ((-992 . -630) 133972) ((-991 . -1130) T) ((-991 . -630) 133954) ((-991 . -1246) T) ((-991 . -102) T) ((-991 . -381) 133907) ((-991 . -746) 133806) ((-991 . -1141) 133705) ((-991 . -23) 133516) ((-991 . -25) 133327) ((-991 . -133) 133182) ((-991 . -485) 133135) ((-991 . -21) 133090) ((-991 . -666) 133034) ((-991 . -815) 132987) ((-991 . -814) 132940) ((-991 . -869) 132839) ((-991 . -872) 132738) ((-991 . -816) 132691) ((-991 . -819) 132644) ((-985 . -19) 132628) ((-985 . -671) 132612) ((-985 . -300) 132589) ((-985 . -298) 132541) ((-985 . -616) 132518) ((-985 . -631) 132479) ((-985 . -501) 132463) ((-985 . -1130) 132413) ((-985 . -526) 132346) ((-985 . -321) 132284) ((-985 . -630) 132196) ((-985 . -102) 132126) ((-985 . -1246) T) ((-985 . -34) T) ((-985 . -153) 132110) ((-985 . -869) 132089) ((-985 . -872) 132068) ((-985 . -385) 132052) ((-983 . -338) 132031) ((-983 . -1067) 131927) ((-983 . -424) 131911) ((-983 . -38) 131808) ((-983 . -633) 131661) ((-983 . -668) 131586) ((-983 . -666) 131496) ((-983 . -746) T) 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127102) ((-933 . -737) 127067) ((-933 . -660) 127032) ((-933 . -38) 126997) ((-933 . -464) T) ((-933 . -319) T) ((-933 . -111) 126953) ((-933 . -1080) 126918) ((-933 . -1085) 126883) ((-933 . -666) 126833) ((-933 . -668) 126798) ((-933 . -302) T) ((-933 . -250) T) ((-933 . -414) T) ((-933 . -239) T) ((-933 . -1246) T) ((-933 . -236) 126785) ((-933 . -1078) T) ((-933 . -1086) T) ((-933 . -1141) T) ((-933 . -746) T) ((-933 . -21) T) ((-933 . -23) T) ((-933 . -1130) T) ((-933 . -630) 126767) ((-933 . -102) T) ((-933 . -25) T) ((-933 . -133) T) ((-933 . -240) T) ((-933 . -341) 126754) ((-933 . -149) 126736) ((-933 . -1067) 126723) ((-933 . -1304) 126710) ((-933 . -1315) 126697) ((-933 . -631) 126679) ((-932 . -1130) T) ((-932 . -630) 126661) ((-932 . -1246) T) ((-932 . -102) T) ((-929 . -931) 126645) ((-929 . -872) 126596) ((-929 . -869) 126547) ((-929 . -746) T) ((-929 . -1130) T) ((-929 . -630) 126529) ((-929 . -102) T) ((-929 . -1141) T) ((-929 . -485) T) ((-929 . -1246) T) ((-929 . -298) 126508) ((-928 . -121) 126492) ((-928 . -501) 126476) ((-928 . -1130) 126454) ((-928 . -526) 126387) ((-928 . -321) 126325) ((-928 . -630) 126236) ((-928 . -102) 126186) ((-928 . -1246) T) ((-928 . -34) T) ((-928 . -1039) 126170) ((-923 . -1130) T) ((-923 . -630) 126152) ((-923 . -1246) T) ((-923 . -102) T) ((-916 . -869) T) ((-916 . -630) 126134) ((-916 . -1130) T) ((-916 . -102) T) ((-916 . -1246) T) ((-916 . -872) T) ((-916 . -1067) 126111) ((-916 . -633) 126088) ((-913 . -1130) T) ((-913 . -630) 126070) ((-913 . -1246) T) ((-913 . -102) T) ((-913 . -1067) 126038) ((-913 . -633) 126006) ((-911 . -1130) T) ((-911 . -630) 125988) ((-911 . -1246) T) ((-911 . -102) T) ((-908 . -1130) T) ((-908 . -630) 125970) ((-908 . -1246) T) ((-908 . -102) T) ((-898 . -1112) T) ((-898 . -502) 125951) ((-898 . -630) 125917) ((-898 . -633) 125898) ((-898 . -1130) T) ((-898 . -1246) T) ((-898 . -102) T) ((-898 . -93) T) ((-898 . -1292) T) ((-896 . -1130) T) ((-896 . -630) 125880) ((-896 . -1246) T) ((-896 . -102) T) ((-895 . -1246) T) ((-895 . -630) 125752) ((-895 . -1130) 125703) ((-895 . -102) 125654) ((-894 . -1020) 125638) ((-894 . -1181) 125616) ((-894 . -1067) 125482) ((-894 . -633) 125380) ((-894 . -631) 125187) ((-894 . -1049) 125165) ((-894 . -937) 125144) ((-894 . -907) 125128) ((-894 . -868) 125107) ((-894 . -819) 125086) ((-894 . -816) 125065) ((-894 . -872) 125016) ((-894 . -869) 124967) ((-894 . -814) 124946) ((-894 . -812) 124925) ((-894 . -842) 124904) ((-894 . -909) 124829) ((-894 . -412) 124813) ((-894 . -658) 124761) ((-894 . -668) 124677) ((-894 . -390) 124661) ((-894 . -298) 124619) ((-894 . -321) 124584) ((-894 . -526) 124496) ((-894 . -351) 124480) ((-894 . -250) T) ((-894 . -111) 124418) ((-894 . -1080) 124370) ((-894 . -1085) 124322) ((-894 . -302) T) ((-894 . -737) 124274) ((-894 . -660) 124226) ((-894 . -666) 124163) ((-894 . -38) 124115) ((-894 . -319) T) ((-894 . -464) T) ((-894 . -175) T) ((-894 . -569) T) ((-894 . -948) T) ((-894 . -1251) T) 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. -102) T) ((-886 . -381) T) ((-886 . -631) 122048) ((-885 . -1130) T) ((-885 . -630) 122030) ((-885 . -1246) T) ((-885 . -102) T) ((-884 . -883) T) ((-884 . -176) T) ((-884 . -630) 122012) ((-880 . -869) T) ((-880 . -630) 121994) ((-880 . -1130) T) ((-880 . -102) T) ((-880 . -1246) T) ((-880 . -872) T) ((-877 . -874) 121978) ((-877 . -1067) 121874) ((-877 . -633) 121771) ((-877 . -424) 121755) ((-877 . -737) 121725) ((-877 . -660) 121695) ((-877 . -668) 121669) ((-877 . -666) 121628) ((-877 . -133) T) ((-877 . -25) T) ((-877 . -102) T) ((-877 . -1246) T) ((-877 . -630) 121610) ((-877 . -1130) T) ((-877 . -23) T) ((-877 . -21) T) ((-877 . -1085) 121594) ((-877 . -1080) 121578) ((-877 . -111) 121557) ((-877 . -1078) T) ((-877 . -1086) T) ((-877 . -1141) T) ((-877 . -746) T) ((-877 . -38) 121527) ((-876 . -874) 121511) ((-876 . -1067) 121407) ((-876 . -633) 121325) ((-876 . -424) 121309) ((-876 . -737) 121279) ((-876 . -660) 121249) ((-876 . -668) 121223) ((-876 . -666) 121182) ((-876 . 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. -240) T) ((-801 . -133) T) ((-801 . -25) T) ((-801 . -102) T) ((-801 . -630) 107171) ((-801 . -1130) T) ((-801 . -23) T) ((-801 . -21) T) ((-801 . -746) T) ((-801 . -1141) T) ((-801 . -1086) T) ((-801 . -1078) T) ((-801 . -236) 107158) ((-801 . -1246) T) ((-801 . -239) T) ((-801 . -274) 107142) ((-801 . -234) 107126) ((-800 . -1094) 107093) ((-800 . -631) 106727) ((-800 . -321) 106714) ((-800 . -526) 106666) ((-800 . -338) 106638) ((-800 . -1067) 106495) ((-800 . -424) 106479) ((-800 . -38) 106328) ((-800 . -633) 106094) ((-800 . -668) 105983) ((-800 . -666) 105893) ((-800 . -746) T) ((-800 . -1141) T) ((-800 . -1086) T) ((-800 . -1078) T) ((-800 . -111) 105722) ((-800 . -1080) 105565) ((-800 . -1085) 105408) ((-800 . -21) T) ((-800 . -23) T) ((-800 . -1130) T) ((-800 . -630) 105322) ((-800 . -1246) T) ((-800 . -102) T) ((-800 . -25) T) ((-800 . -133) T) ((-800 . -660) 105171) ((-800 . -737) 105020) ((-800 . -147) 104999) ((-800 . -149) 104978) ((-800 . -175) 104889) ((-800 . -569) 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102187) ((-751 . -569) 102118) ((-751 . -111) 101947) ((-751 . -1080) 101790) ((-751 . -1085) 101633) ((-751 . -175) 101544) ((-751 . -149) 101523) ((-751 . -147) 101502) ((-751 . -666) 101412) ((-751 . -133) T) ((-751 . -25) T) ((-751 . -102) T) ((-751 . -1246) T) ((-751 . -630) 101394) ((-751 . -1130) T) ((-751 . -23) T) ((-751 . -21) T) ((-751 . -1078) T) ((-751 . -1086) T) ((-751 . -1141) T) ((-751 . -746) T) ((-751 . -424) 101378) ((-751 . -338) 101343) ((-751 . -321) 101330) ((-751 . -631) 101191) ((-738 . -485) T) ((-738 . -1141) T) ((-738 . -102) T) ((-738 . -1246) T) ((-738 . -630) 101173) ((-738 . -1130) T) ((-738 . -746) T) ((-735 . -1078) T) ((-735 . -1086) T) ((-735 . -1141) T) ((-735 . -746) T) ((-735 . -21) T) ((-735 . -666) 101145) ((-735 . -23) T) ((-735 . -1130) T) ((-735 . -630) 101127) ((-735 . -1246) T) ((-735 . -102) T) ((-735 . -25) T) ((-735 . -133) T) ((-735 . -668) 101114) ((-735 . -633) 101096) ((-734 . -1078) T) ((-734 . -1086) T) ((-734 . -1141) T) ((-734 . 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-1246) T) ((-391 . -630) 54090) ((-391 . -1130) T) ((-391 . -23) T) ((-391 . -21) T) ((-391 . -746) T) ((-391 . -1141) T) ((-391 . -1086) T) ((-391 . -1078) T) ((-391 . -631) 54004) ((-391 . -376) T) ((-391 . -1251) T) ((-391 . -948) T) ((-391 . -569) T) ((-391 . -175) T) ((-391 . -737) 53969) ((-391 . -660) 53934) ((-391 . -38) 53899) ((-391 . -464) T) ((-391 . -319) T) ((-391 . -111) 53855) ((-391 . -1080) 53820) ((-391 . -1085) 53785) ((-391 . -302) T) ((-391 . -250) T) ((-391 . -868) T) ((-391 . -819) T) ((-391 . -816) T) ((-391 . -872) T) ((-391 . -869) T) ((-391 . -814) T) ((-391 . -812) T) ((-391 . -909) 53767) ((-391 . -1031) T) ((-391 . -1049) T) ((-391 . -1067) 53727) ((-391 . -1089) T) ((-391 . -240) T) ((-391 . -236) 53714) ((-391 . -239) T) ((-391 . -1232) T) ((-391 . -1235) T) ((-391 . -505) T) ((-391 . -296) T) ((-391 . -95) T) ((-391 . -35) T) ((-391 . -635) 53696) ((-377 . -378) 53673) ((-377 . -102) T) ((-377 . -1246) T) ((-377 . -630) 53655) ((-377 . -1130) T) ((-374 . -485) T) ((-374 . -1141) T) ((-374 . -102) T) ((-374 . -1246) T) ((-374 . -630) 53637) ((-374 . -1130) T) ((-374 . -746) T) ((-374 . -1067) 53621) ((-374 . -633) 53605) ((-372 . -341) 53589) ((-372 . -240) 53568) ((-372 . -236) 53541) ((-372 . -239) 53520) ((-372 . -381) 53499) ((-372 . -1181) 53478) ((-372 . -363) 53457) ((-372 . -149) 53436) ((-372 . -633) 53373) ((-372 . -668) 53325) ((-372 . -666) 53262) ((-372 . -133) T) ((-372 . -25) T) ((-372 . -102) T) ((-372 . -1246) T) ((-372 . -630) 53244) ((-372 . -1130) T) ((-372 . -23) T) ((-372 . -21) T) ((-372 . -746) T) ((-372 . -1141) T) ((-372 . -1086) T) ((-372 . -1078) T) ((-372 . -376) T) ((-372 . -1251) T) ((-372 . -948) T) ((-372 . -569) T) ((-372 . -175) T) ((-372 . -737) 53196) ((-372 . -660) 53148) ((-372 . -38) 53113) ((-372 . -464) T) ((-372 . -319) T) ((-372 . -111) 53051) ((-372 . -1080) 53003) ((-372 . -1085) 52955) ((-372 . -302) T) ((-372 . -250) T) ((-372 . -414) 52906) ((-372 . -147) 52857) ((-372 . -1067) 52841) 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|BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| - |BinaryTree| |Byte| |ByteBuffer| |ByteOrder| - |CancellationAbelianMonoid| |CachableSet| |CapsuleAst| - |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| - |CaseAst| |CategoryAst| |CategoryConstructor| |Category| - |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory| - |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage| - |CharacteristicZero| |ChangeOfVariable| - |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| - |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| - |CollectAst| |ComplexRootPackage| |ColonAst| |Color| - |CombinatorialFunction| |IntegerCombinatoricFunctions| - |CombinatorialOpsCategory| |Commutator| |CommaAst| |CommonOperators| - |CommuteUnivariatePolynomialCategory| |ComplexCategory&| - |ComplexCategory| |ComplexFactorization| |CompilerPackage| |Complex| - |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| - |CommutativeRing| |Conduit| |ContinuedFraction| |Contour| - |CoordinateSystems| |CharacteristicPolynomialInMonogenicalAlgebra| - |ComplexPatternMatch| |CRApackage| |CoerceAst| - |ComplexRootFindingPackage| |CyclicStreamTools| |Constructor| - |ConstructorCall| |ConstructorCategory&| |ConstructorCategory| + |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| |BinaryTree| + |Byte| |ByteBuffer| |ByteOrder| |CancellationAbelianMonoid| |CachableSet| + |CapsuleAst| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| + |CaseAst| |CategoryAst| |CategoryConstructor| |Category| |CharacterClass| + |CommonDenominator| |CombinatorialFunctionCategory| |Character| + |CharacteristicNonZero| |CharacteristicPolynomialPackage| |CharacteristicZero| + |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| + |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| |CollectAst| + |ComplexRootPackage| |ColonAst| |Color| |CombinatorialFunction| + |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| + |CommaAst| |CommonOperators| |CommuteUnivariatePolynomialCategory| + |ComplexCategory&| |ComplexCategory| |ComplexFactorization| |CompilerPackage| + |Complex| |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| + |CommutativeRing| |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems| + |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch| + |CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools| + |Constructor| |ConstructorCall| |ConstructorCategory&| |ConstructorCategory| |ConstructorKind| |ComplexTrigonometricManipulations| - |CoerceVectorMatrixPackage| |CycleIndicators| - |CyclotomicPolynomialPackage| |d01AgentsPackage| |d01ajfAnnaType| - |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| - |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| - |d01gbfAnnaType| |d01TransformFunctionType| |d01WeightsPackage| - |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| - |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |d03fafAnnaType| - |DataArray| |Database| |DualBasis| |DoubleResultantPackage| + |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage| + |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| + |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| + |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| + |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| + |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| + |d03fafAnnaType| |DataArray| |Database| |DualBasis| |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion| |DefinitionAst| - |ElementaryFunctionDefiniteIntegration| - |RationalFunctionDefiniteIntegration| |DegreeReductionPackage| - |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat| - |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| |Dictionary&| - |Dictionary| |DifferentialExtension| |DifferentialDomain&| + |ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration| + |DegreeReductionPackage| |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| + |DoubleFloat| |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| + |Dictionary&| |Dictionary| |DifferentialExtension| |DifferentialDomain&| |DifferentialDomain| |DifferentialModule| |DifferentialSpace&| |DifferentialSpace| |DifferentialRing| |DictionaryOperations&| - |DictionaryOperations| |DiophantineSolutionPackage| - |DirectProductCategory&| |DirectProductCategory| |DirectProduct| - |DirectProductFunctions2| |DisplayPackage| |DivisionRing&| - |DivisionRing| |DoublyLinkedAggregate| |DataList| - |DiscreteLogarithmPackage| |DifferentialModuleExtension| + |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| + |DirectProductCategory| |DirectProduct| |DirectProductFunctions2| + |DisplayPackage| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| + |DataList| |DiscreteLogarithmPackage| |DifferentialModuleExtension| |DistributedMultivariatePolynomial| |Domain| |DomainConstructor| |DomainTemplate| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| - |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| - |DrawNumericHack| |TopLevelDrawFunctionsForPoints| |DrawOption| - |DrawOptionFunctions0| |DrawOptionFunctions1| - |DifferentialSpaceExtension&| |DifferentialSpaceExtension| - |DifferentialSparseMultivariatePolynomial| + |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| + |TopLevelDrawFunctionsForPoints| |DrawOption| |DrawOptionFunctions0| + |DrawOptionFunctions1| |DifferentialSpaceExtension&| + |DifferentialSpaceExtension| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| - |ExtAlgBasis| |ElementaryFunction| - |ElementaryFunctionStructurePackage| + |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElaboratedExpression| |Elaboration| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| - |EllipticFunctionsUnivariateTaylorSeries| |Eltable| - |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| - |EntireRing| |Environment| |EigenPackage| |Equation| - |EquationFunctions2| |EqTable| |ErrorFunctions| |ExpressionSpace&| - |ExpressionSpace| |ExpressionSpaceFunctions1| + |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| + |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| + |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| + |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| - |EuclideanDomain&| |EuclideanDomain| |Evalable&| |Evalable| - |EvaluateCycleIndicators| |Exit| |ExitAst| |ExponentialExpansion| - |Expression| |ExpressionFunctions2| + |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| + |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| + |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| - |FreeAbelianMonoidCategory| |FreeAbelianMonoid| - |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing| |FlexibleArray| - |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| - |FortranCode| |FourierComponent| |FortranCodePackage1| |FunctorData| - |FiniteDivisor| |FiniteDivisorFunctions2| |FiniteDivisorCategory&| - |FiniteDivisorCategory| |FullyEvalableOver&| |FullyEvalableOver| - |FortranExpression| |FiniteField| |FunctionFieldCategory&| + |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| + |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| + |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| + |FortranCodePackage1| |FunctorData| |FiniteDivisor| |FiniteDivisorFunctions2| + |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| + |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| - |FiniteFieldHomomorphisms| |FiniteFieldCategory&| - |FiniteFieldCategory| |FunctionFieldIntegralBasis| - |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| + |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| + |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| + |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldNormalBasisExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory| - |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| - |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| - |FiniteLinearAggregate&| |FiniteLinearAggregate| - |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| + |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| + |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&| + |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| - |FloatingRealPackage| |FreeModule| |FreeModule1| - |FortranMatrixCategory| |FreeModuleCat| - |FortranMatrixFunctionCategory| |FreeMonoidCategory| |FreeMonoid| - |FortranMachineTypeCategory| |FileName| |FileNameCategory| + |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| + |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoidCategory| + |FreeMonoid| |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| |FortranPackage| |FortranProgramCategory| |FortranFunctionCategory| - |FortranProgram| |FullPartialFractionExpansion| - |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| - |FieldOfPrimeCharacteristic| |FloatingPointSystem&| - |FloatingPointSystem| |Factored| |FactoredFunctions2| |Fraction| - |FractionFunctions2| |FramedAlgebra&| |FramedAlgebra| + |FortranProgram| |FullPartialFractionExpansion| |FullyPatternMatchable| + |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| + |FloatingPointSystem&| |FloatingPointSystem| |Factored| |FactoredFunctions2| + |Fraction| |FractionFunctions2| |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| - |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| - |FunctionSpace&| |FunctionSpace| |FunctionSpaceFunctions2| - |FunctionSpaceToExponentialExpansion| - |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregate&| - |FiniteSetAggregate| |FiniteSetAggregateFunctions2| - |FunctionSpaceComplexIntegration| |FourierSeries| - |FunctionSpaceIntegration| |FunctionalSpecialFunction| - |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| - |FortranScalarType| |FunctionSpaceUnivariatePolynomialFactor| - |FortranType| |FortranTemplate| |FunctionCalled| |FunctionDescriptor| - |FortranVectorCategory| |FortranVectorFunctionCategory| - |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| - |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| - |GaussianFactorizationPackage| |GroebnerPackage| + |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&| + |FunctionSpace| |FunctionSpaceFunctions2| + |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| + |FiniteSetAggregate&| |FiniteSetAggregate| |FiniteSetAggregateFunctions2| + |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| + |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| + |FunctionSpaceReduce| |FortranScalarType| + |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| + |FunctionCalled| |FunctionDescriptor| |FortranVectorCategory| + |FortranVectorFunctionCategory| |GaloisGroupFactorizer| + |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| + |GaloisGroupUtilities| |GaussianFactorizationPackage| |GroebnerPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GcdDomain&| |GcdDomain| - |GenericNonAssociativeAlgebra| - |GeneralDistributedMultivariatePolynomial| |GenExEuclid| - |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| + |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| + |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| - |GeneralModulePolynomial| |GosperSummationMethod| - |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| - |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| - |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| - |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HasAst| |HashTable| - |HallBasis| |HomogeneousDistributedMultivariatePolynomial| - |HomogeneousDirectProduct| |HeadAst| |Heap| - |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| - |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| - |Hostname| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| - |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| + |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| + |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| + |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| + |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| + |Pi| |HasAst| |HashTable| |HallBasis| + |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| + |HeadAst| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| + |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname| + |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| + |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| - |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| - |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| - |IdealDecompositionPackage| |Identifier| - |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| - |IndexedDirectProductCategory| |IndexedDirectProductObject| - |IndexedDirectProductOrderedAbelianMonoid| - |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| - |InnerEvalable| |InnerFreeAbelianMonoid| |IndexedFlexibleArray| - |IfAst| |InnerFiniteField| |InnerIndexedTwoDimensionalArray| - |IndexedList| |InnerMatrixLinearAlgebraFunctions| - |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| - |InAst| |InputByteConduit&| |InputByteConduit| + |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| + |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| + |Identifier| |IndexedDirectProductAbelianGroup| + |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| + |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| + |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable| + |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField| + |InnerIndexedTwoDimensionalArray| |IndexedList| + |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| + |IndexedMatrix| |ImportAst| |InAst| |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions| |InputBinaryFile| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |InetClientStreamSocket| |Infinity| |InputForm| |InputFormFunctions1| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| - |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64| |Int8| - |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| - |IntervalCategory| |IntegralDomain&| |IntegralDomain| - |ElementaryIntegration| |IntegerFactorizationPackage| - |IntegrationFunctionsTable| |GenusZeroIntegration| - |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| - |TranscendentalHermiteIntegration| |AnnaNumericalIntegrationPackage| - |PureAlgebraicIntegration| |PatternMatchIntegration| - |RationalIntegration| |IntegerRetractions| + |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64| |Int8| |InnerTable| + |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| + |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| + |IntegerFactorizationPackage| |IntegrationFunctionsTable| + |GenusZeroIntegration| |IntegerNumberTheoryFunctions| + |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| + |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| + |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| - |TranscendentalIntegration| |InverseLaplaceTransform| - |InputOutputByteConduit| |InputOutputBinaryFile| |IOMode| |IP4Address| - |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| - |IntegrationResult| |IntegrationResultFunctions2| - |IntegrationResultToFunction| |InternalRepresentationForm| - |IntegerRoots| |IrredPolyOverFiniteField| + |TranscendentalIntegration| |InverseLaplaceTransform| |InputOutputByteConduit| + |InputOutputBinaryFile| |IOMode| |IP4Address| |InnerPAdicInteger| + |InnerPrimeField| |InternalPrintPackage| |IntegrationResult| + |IntegrationResultFunctions2| |IntegrationResultToFunction| + |InternalRepresentationForm| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| - |InternalRationalUnivariateRepresentationPackage| |IsAst| - |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| - |InnerTaylorSeries| |InternalTypeForm| |InfiniteTupleFunctions2| - |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| - |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| - |JoinAst| |AssociatedJordanAlgebra| |JVMBytecode| |JVMClassFileAccess| - |JVMConstantTag| |JVMFieldAccess| |JVMMethodAccess| |JVMOpcode| - |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |Kernel| - |KernelFunctions2| |CoercibleTo| |ConvertibleTo| |Kovacic| - |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| + |InternalRationalUnivariateRepresentationPackage| |IsAst| |IndexedString| + |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| + |InternalTypeForm| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| + |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| + |IndexedAggregate&| |IndexedAggregate| |JoinAst| |AssociatedJordanAlgebra| + |JVMBytecode| |JVMClassFileAccess| |JVMConstantTag| |JVMFieldAccess| + |JVMMethodAccess| |JVMOpcode| |KeyedAccessFile| |KeyedDictionary&| + |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| + |Kovacic| |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| - |LeadingCoefDetermination| |LetAst| |LieExponentials| - |LexTriangularPackage| |LiouvillianFunction| + |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| + |LetAst| |LieExponentials| |LexTriangularPackage| |LiouvillianFunction| |LiouvillianFunctionCategory| |LinGroebnerPackage| |Library| - |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| - |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearBasis| - |LinearDependence| |LinearElement| |LinearlyExplicitRingOver| - |LinearForm| |LinearSet| |List| |ListFunctions2| |ListToMap| - |ListFunctions3| |Literal| |LeftLinearSet| |ListMultiDictionary| - |LeftModule| |ListMonoidOps| |LinearAggregate&| |LinearAggregate| - |Localize| |ElementaryFunctionLODESolver| - |LinearOrdinaryDifferentialOperator| - |LinearOrdinaryDifferentialOperator1| + |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| |PowerSeriesLimitPackage| + |RationalFunctionLimitPackage| |LinearBasis| |LinearDependence| + |LinearElement| |LinearlyExplicitRingOver| |LinearForm| |LinearSet| |List| + |ListFunctions2| |ListToMap| |ListFunctions3| |Literal| |LeftLinearSet| + |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| + |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| + |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| - |ListAggregate| |LinearSystemMatrixPackage| - |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| - |LieSquareMatrix| |ConstructAst| |LyndonWord| |LazyStreamAggregate&| - |LazyStreamAggregate| |ThreeDimensionalMatrix| |MacroAst| |Magma| - |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| - |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| - |MappingPackage2| |MappingPackage3| |MatrixCategory&| |MatrixCategory| - |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |Matrix| - |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| - |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| - |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| - |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| - |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| - |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| - |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| - |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| - |Monad&| |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| + |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| + |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| + |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| + |MacroAst| |Magma| |MappingPackageInternalHacks1| + |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| + |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| + |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| + |Matrix| |StorageEfficientMatrixOperations| |Maybe| + |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| + |MultiDictionary| |ModularDistinctDegreeFactorizer| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| + |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| + |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| + |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| + |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| + |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| + |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |Multiset| |MultisetAggregate| |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| |MultivariateFactorize| - |MultivariateSquareFree| |NonAssociativeAlgebra&| - |NonAssociativeAlgebra| |NagPolynomialRootsPackage| - |NagRootFindingPackage| |NagSeriesSummationPackage| - |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| + |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| + |NagPolynomialRootsPackage| |NagRootFindingPackage| + |NagSeriesSummationPackage| |NagIntegrationPackage| + |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| - |NagFittingPackage| |NagOptimisationPackage| - |NagMatrixOperationsPackage| |NagEigenPackage| - |NagLinearEquationSolvingPackage| |NagLapack| - |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| - |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| - |NonAssociativeRing| |NumericComplexEigenPackage| - |NumericContinuedFraction| |NonCommutativeOperatorDivision| - |NetworkClientSocket| |NumberFieldIntegralBasis| - |NumericalIntegrationProblem| |NonLinearSolvePackage| - |NonNegativeInteger| |NonLinearFirstOrderODESolver| |None| - |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| + |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| + |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| + |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| + |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| + |NumericComplexEigenPackage| |NumericContinuedFraction| + |NonCommutativeOperatorDivision| |NetworkClientSocket| + |NumberFieldIntegralBasis| |NumericalIntegrationProblem| + |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| + |None| |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| - |NewSparseUnivariatePolynomialFunctions2| - |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| - |Numeric| |NumberFormats| |NumericalIntegrationCategory| - |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| - |NumericTubePlot| |OrderedAbelianGroup&| |OrderedAbelianGroup| - |OrderedAbelianMonoid&| |OrderedAbelianMonoid| - |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| - |OctonionCategory&| |OctonionCategory| - |OrderedCancellationAbelianMonoid| |Octonion| - |OctonionCategoryFunctions2| - |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| - |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| - |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| - |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| - |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| - |SystemODESolver| |ODETools| |OrderedDirectProduct| - |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| - |OrderlyDifferentialVariable| |OrderedFreeMonoid| - |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| - |OpenMathDevice| |OpenMathEncoding| |OpenMathError| - |OpenMathErrorKind| |ExpressionToOpenMath| - |OppositeMonogenicLinearOperator| |OpenMathPackage| - |OrderedMultisetAggregate| |OpenMathServerPackage| + |NewSparseUnivariatePolynomialFunctions2| |NumberTheoreticPolynomialFunctions| + |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| + |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| + |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup&| + |OrderedAbelianGroup| |OrderedAbelianMonoid&| |OrderedAbelianMonoid| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OctonionCategory&| + |OctonionCategory| |OrderedCancellationAbelianMonoid| |Octonion| + |OctonionCategoryFunctions2| |OrdinaryDifferentialEquationsSolverCategory| + |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| + |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| + |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| + |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| + |OrderedDirectProduct| |OrderlyDifferentialPolynomial| + |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| + |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice| + |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| + |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| |OnePointCompletion| |OnePointCompletionFunctions2| |Operator| - |OperatorCategory&| |OperatorCategory| |OperationsQuery| - |OperatorSignature| |NumericalOptimizationCategory| - |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| - |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| - |OrderingFunctions| |OrderedMonoid| |OrderedRing| |OrderedSet| - |OrderedStructure| |OrderedType&| |OrderedType| - |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| - |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| - |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| - |OrderedSemiGroup| |OrdSetInts| |OutputPackage| |OutputByteConduit&| - |OutputByteConduit| |OutputBinaryFile| |OutputForm| - |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| + |OperatorCategory&| |OperatorCategory| |OperationsQuery| |OperatorSignature| + |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| + |NumericalOptimizationProblem| |OrderedCompletion| + |OrderedCompletionFunctions2| |OrderedFinite| |OrderingFunctions| + |OrderedMonoid| |OrderedRing| |OrderedSet| |OrderedStructure| |OrderedType&| + |OrderedType| |UnivariateSkewPolynomialCategory&| + |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| + |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| + |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| + |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputBinaryFile| + |OutputForm| |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| - |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| - |Pair| |Palette| |PolynomialAN2Expression| |ParameterAst| + |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Pair| + |Palette| |PolynomialAN2Expression| |ParameterAst| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser| - |ParametricSurfaceFunctions2| |ParametricSurface| - |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| - |PatternMatchable| |PatternMatch| |PatternMatchResult| - |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| - |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| + |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| + |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| + |PatternMatchResult| |PatternMatchResultFunctions2| |Pattern| + |PatternFunctions1| |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialDomain&| - |PartialDifferentialDomain| - |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| - |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| - |PartialDifferentialModule| |PartialDifferentialRing| + |PartialDifferentialDomain| |PartialDifferentialEquationsSolverCategory| + |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| + |NumericalPDEProblem| |PartialDifferentialModule| |PartialDifferentialRing| |PartialDifferentialSpace&| |PartialDifferentialSpace| |PendantTree| |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| |PrimeField| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| - |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| - |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| - |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| - |PositiveInteger| |PiCoercions| |PrincipalIdealDomain| - |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| - |ParametricLinearEquations| |Plot| |PlotFunctions1| |Plot3D| - |PlotTools| |PatternMatchAssertions| |FunctionSpaceAssertions| - |PatternMatchPushDown| |PatternMatchFunctionSpace| + |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| + |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| + |PermutationGroupExamples| |PolyGroebner| |PositiveInteger| |PiCoercions| + |PrincipalIdealDomain| |PolynomialInterpolation| + |PolynomialInterpolationAlgorithms| |ParametricLinearEquations| |Plot| + |PlotFunctions1| |Plot3D| |PlotTools| |PatternMatchAssertions| + |FunctionSpaceAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |AttachPredicates| |FunctionSpaceAttachPredicates| - |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| - |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| - |PolToPol| |RealPolynomialUtilitiesPackage| |Polynomial| - |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| - |PolynomialCategory&| |PolynomialCategory| + |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| + |PolynomialNumberTheoryFunctions| |Point| |PolToPol| + |RealPolynomialUtilitiesPackage| |Polynomial| |PolynomialFunctions2| + |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| - |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| - |PolynomialRing| |PrecomputedAssociatedEquations| |PrimitiveArray| - |PrimitiveArrayFunctions2| |PrimitiveFunctionCategory| - |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |Product| - |Property| |PropositionalFormula| |PropositionalFormulaFunctions1| - |PropositionalFormulaFunctions2| |PropositionalLogic| - |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| - |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| - |PlottableSpaceCurveCategory| |PolynomialSetCategory&| - |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| - |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| - |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| - |PushVariables| |PAdicWildFunctionFieldIntegralBasis| - |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |QuasiComponentPackage| - |QueryEquation| |QuotientFieldCategory&| |QuotientFieldCategory| - |QuotientFieldCategoryFunctions2| |QuadraticForm| |QuasiquoteAst| - |QueueAggregate| |Quaternion| |QuaternionCategory&| - |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| - |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| - |RadixExpansion| |RadixUtilities| |RandomNumberSource| - |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| - |RecursiveAggregate| |RealClosedField&| |RealClosedField| - |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| - |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| - |ReduceAst| |RealConstant| |RealZeroPackage| |RealZeroPackageQ| - |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| - |RegularTriangularSet| |RadicalEigenPackage| |RepresentationPackage1| - |RepresentationPackage2| |RepeatedDoubling| |RepeatedSquaring| - |ResolveLatticeCompletion| |ResidueRing| |Result| |ReturnAst| - |RetractableTo&| |RetractableTo| |RetractSolvePackage| + |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| |PolynomialRing| + |PrecomputedAssociatedEquations| |PrimitiveArray| |PrimitiveArrayFunctions2| + |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| + |PrintPackage| |Product| |Property| |PropositionalFormula| + |PropositionalFormulaFunctions1| |PropositionalFormulaFunctions2| + |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| + |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| + |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| + |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| + |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| + |PartialTranscendentalFunctions| |PushVariables| + |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| + |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategory&| + |QuotientFieldCategory| |QuotientFieldCategoryFunctions2| |QuadraticForm| + |QuasiquoteAst| |QueueAggregate| |Quaternion| |QuaternionCategory&| + |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| |RadicalCategory&| + |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| + |RandomNumberSource| |RationalFactorize| |RationalRetractions| + |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| + |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| + |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| + |ReducedDivisor| |ReduceAst| |RealConstant| |RealZeroPackage| + |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| + |Reference| |RegularTriangularSet| |RadicalEigenPackage| + |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| + |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| + |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| - |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| - |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| - |RationalInterpolation| |RightLinearSet| |RectangularMatrixCategory&| - |RectangularMatrixCategory| |RectangularMatrix| - |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| + |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain| + |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| + |RightLinearSet| |RectangularMatrixCategory&| |RectangularMatrixCategory| + |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RangeBinding| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| - |RecursivePolynomialCategory&| |RecursivePolynomialCategory| - |RepeatAst| |RealRootCharacterizationCategory&| - |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| - |RegularTriangularSetCategory&| |RegularTriangularSetCategory| - |RegularTriangularSetGcdPackage| |RestrictAst| |RuntimeValue| - |RewriteRule| |RuleCalled| |Ruleset| + |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| + |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| + |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| + |RegularTriangularSetCategory| |RegularTriangularSetGcdPackage| |RestrictAst| + |RuntimeValue| |RewriteRule| |RuleCalled| |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| |SpadSyntaxCategory| |SortedCache| |Scope| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| - |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| - |SegmentAst| |SegmentBinding| |SegmentBindingFunctions2| - |SegmentCategory| |SegmentExpansionCategory| |SequenceAst| |Set| - |SetAggregate&| |SetAggregate| |SetCategory&| |SetCategory| - |SetOfMIntegersInOneToN| |SExpression| |SExpressionCategory| - |SExpressionOf| |SimpleFortranProgram| - |SquareFreeQuasiComponentPackage| - |SquareFreeRegularTriangularSetGcdPackage| - |SquareFreeRegularTriangularSetCategory| - |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| - |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |Signature| - |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| - |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| - |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| - |SmithNormalForm| |SparseMultivariatePolynomial| - |SparseMultivariateTaylorSeries| - |SquareFreeNormalizedTriangularSetCategory| - |PolynomialSolveByFormulas| |RadicalSolvePackage| - |TransSolvePackageService| |TransSolvePackage| |SortPackage| - |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| + |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| |SegmentAst| + |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| + |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| + |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| + |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| + |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| + |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| + |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| + |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| + |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| + |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| + |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| + |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| + |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| + |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| |SpadAstExports| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SemiRing| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepThrough| |StepAst| |StreamInfiniteProduct| |Stream| |StreamFunctions1| |StreamFunctions2| - |StreamFunctions3| |String| |StringTable| - |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| - |StreamTranscendentalFunctionsNonCommutative| |SubResultantPackage| - |SubSpace| |SuchThat| |SuchThatAst| |SparseUnivariateLaurentSeries| - |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomial| - |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| - |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| - |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| - |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| - |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| - |System| |TableauxBumpers| |Table| |Tableau| |TermAlgebraOperator| - |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat| - |TexFormat1| |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| - |Tree| |TrigonometricFunctionCategory&| + |StreamFunctions3| |String| |StringTable| |StreamTaylorSeriesOperations| + |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| + |SubResultantPackage| |SubSpace| |SuchThat| |SuchThatAst| + |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| + |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| + |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| + |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| + |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| + |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| |System| + |TableauxBumpers| |Table| |Tableau| |TermAlgebraOperator| |TangentExpansions| + |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| + |TemplateUtilities| |TexFormat| |TexFormat1| |TextFile| |ToolsForSign| + |TopLevelThreeSpace| |TranscendentalFunctionCategory&| + |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| - |TaylorSeries| |TriangularSetCategory&| |TriangularSetCategory| - |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |TypeAst| - |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| - |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UInt16| - |UInt32| |UInt64| |UInt8| |UnivariateLaurentSeries| - |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| + |TriangularMatrixOperations| |TranscendentalManipulations| |TaylorSeries| + |TriangularSetCategory&| |TriangularSetCategory| |TubePlot| |TubePlotTools| + |Tuple| |TwoFactorize| |Type| |TypeAst| |UserDefinedPartialOrdering| + |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt64| |UInt8| + |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| + |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| - |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| - |UniversalSegment| |UniversalSegmentFunctions2| |UnivariatePolynomial| - |UnivariatePolynomialFunctions2| - |UnivariatePolynomialCommonDenominator| + |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| |UniversalSegment| + |UniversalSegmentFunctions2| |UnivariatePolynomial| + |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| - |UnivariatePolynomialMultiplicationPackage| - |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| - |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialCategory&| + |UnivariatePolynomialCategory| |UnivariatePolynomialCategoryFunctions2| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructor| - |UnivariatePuiseuxSeriesWithExponentialSingularity| - |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| - |UnivariateTaylorSeries| |UnivariateTaylorSeriesFunctions2| - |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesCategory| - |UnivariateTaylorSeriesODESolver| |UTSodetools| |UnionType| |Variable| - |VectorCategory&| |VectorCategory| |Vector| |VectorFunctions2| - |ViewportPackage| |TwoDimensionalViewport| |ThreeDimensionalViewport| - |ViewDefaultsPackage| |Void| |VectorSpace&| |VectorSpace| - |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| |WhereAst| - |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| - |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| + |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| + |UnaryRecursiveAggregate| |UnivariateTaylorSeries| + |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| + |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesODESolver| + |UTSodetools| |UnionType| |Variable| |VectorCategory&| |VectorCategory| + |Vector| |VectorFunctions2| |ViewportPackage| |TwoDimensionalViewport| + |ThreeDimensionalViewport| |ViewDefaultsPackage| |Void| |VectorSpace&| + |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| + |WhereAst| |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| + |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| |ExtensionField| |XFreeAlgebra| |XPBWPolynomial| |XPolynomial| - |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| - |YoungDiagram| |ParadoxicalCombinatorsForStreams| - |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |ip4Address| |environment| - |OMgetBind| |uniform01| |eisensteinIrreducible?| |sqrt| - |var2StepsDefault| |intChoose| |setMinPoints3D| |df2fi| |iprint| - |irForm| |OMgetBVar| |normal01| |tryFunctionalDecomposition?| |real| - |tubePointsDefault| |coefChoose| |minPoints3D| |subNodeOf?| |edf2fi| - |elem?| |elaboration| |OMgetError| |exponential1| - |tryFunctionalDecomposition| |imag| |tubeRadiusDefault| |myDegree| - |tValues| |nodeOf?| |edf2df| |notelem| |select!| |OMgetObject| - |chiSquare1| |directProduct| |initial| |btwFact| |dimension| - |normDeriv2| |tRange| |updateStatus!| |float| |expenseOfEvaluation| - |logpart| |title| |delete!| |OMgetEndApp| |exponential| - |beauzamyBound| |plenaryPower| |plot| |extractSplittingLeaf| - |numberOfOperations| |ratpart| |dn| |OMgetEndAtp| |chiSquare| - |divideExponents| |bombieriNorm| |c02aff| |pointPlot| |squareMatrix| - |edf2efi| |mkAnswer| |sncndn| |OMgetEndAttr| |factorFraction| - |unmakeSUP| |close| |rootBound| |li| |c02agf| |calcRanges| |transpose| - |dfRange| |irDef| |categoryFrame| |OMgetEndBind| |componentUpperBound| - |makeSUP| |singleFactorBound| |arguments| |c05adf| |fixPredicate| - |trim| |dflist| |irCtor| |interactiveEnv| |OMgetEndBVar| |blue| - |display| |vectorise| |quadraticNorm| |c05nbf| |patternMatch| |split| - |df2mf| |irVar| |putProperties| |OMgetEndError| |green| |extend| - |infinityNorm| |error| |c05pbf| |patternMatchTimes| |replace| - |ldf2vmf| |perfectNthPower?| |getProperties| |OMgetEndObject| |red| - |truncate| |scaleRoots| |c06eaf| |bernoulli| |upperCase!| |edf2ef| - |perfectNthRoot| |putProperty| |OMgetInteger| |whitePoint| |order| - |shiftRoots| |zeroOf| |c06ebf| |chebyshevT| |upperCase| GE |vedf2vef| - |getProperty| |approxNthRoot| |hash| |OMgetFloat| |uniform| |terms| - |degreePartition| |rootsOf| |c06ecf| |chebyshevU| |lowerCase!| GT - |df2st| |scopes| |perfectSquare?| |count| |OMgetVariable| |binomial| - |input| |squareFreePart| |makeSketch| |factorOfDegree| |next| |c06ekf| - |cyclotomic| |lowerCase| LE |f2st| |weight| |perfectSqrt| - |eigenvalues| |OMgetString| |poisson| |zero| |library| |BumInSepFFE| - |factorsOfDegree| |rightTrim| |inrootof| |c06fpf| |euler| - |KrullNumber| LT |ldf2lst| |approxSqrt| |OMgetSymbol| |geometric| - |makeVariable| |multiplyExponents| |pascalTriangle| |leftTrim| |droot| - |c06fqf| |fixedDivisor| |numberOfVariables| |sdf2lst| - |generateIrredPoly| |OMgetType| |ridHack1| |And| |finiteBound| - |laurentIfCan| |rangePascalTriangle| |iroot| |c06frf| |laguerre| - |algebraicDecompose| |getlo| |complexExpand| |OMencodingBinary| - |interpolate| |Or| |laurentRep| |sizePascalTriangle| |eq?| |c06fuf| - |legendre| |transcendentalDecompose| |gethi| |complexIntegrate| - |OMencodingSGML| |nullSpace| |Not| |rationalPower| - |fillPascalTriangle| |reset| |doublyTransitive?| |c06gbf| |dmpToHdmp| - |internalDecompose| |outputMeasure| - 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|extendedResultant| |asechIfCan| |times| |cot2trig| |realRoots| - |recur| |orbit| |stoseInvertible?| |reciprocalPolynomial| |reduction| - |subResultantsChain| |acschIfCan| |message| |coth2trigh| |leadingTerm| - |const| |permutationGroup| |stoseInvertibleSet| |rootRadius| - |signAround| |iiatan| |lazyPseudoQuotient| |pushdown| |suchThat| - |csc2sin| |overlap| |curry| |wordsForStrongGenerators| |parts| |log10| - |stoseSquareFreePart| |schwerpunkt| |invmod| |lazyPseudoRemainder| - |pushup| |kroneckerDelta| |csch2sinh| |hcrf| |construct| |diag| - |strongGenerators| |coleman| |bitand| |setErrorBound| |powmod| - |bernoulliB| |reducedDiscriminant| |sec2cos| |reindex| |hclf| - |curryRight| |generators| |inverseColeman| |bitior| |startPolynomial| - |mulmod| |eulerE| |idealSimplify| |sech2cosh| |parents| |writable?| - |curryLeft| |bivariateSLPEBR| |listYoungTableaus| |cycleElt| |submod| - |numericIfCan| |definingInequation| |sin2csc| |readable?| - |constantRight| |solveLinearPolynomialEquationByRecursion| |node| - |makeYoungTableau| |computeCycleLength| |addmod| |setPosition| - |complexNumericIfCan| |definingEquations| |sinh2csch| |exists?| - SEGMENT |constantLeft| |digit| |factorByRecursion| |nextColeman| - |computeCycleEntry| |symmetricRemainder| - |generalizedContinuumHypothesisAssumed| |FormatArabic| |setStatus| - |tan2trig| |extension| |twist| |charClass| - |factorSquareFreeByRecursion| |nextLatticePermutation| - |findConstructor| |positiveRemainder| - |generalizedContinuumHypothesisAssumed?| |ScanArabic| - |quasiAlgebraicSet| |tanh2trigh| |shallowExpand| |setsubMatrix!| - |alphanumeric?| |randomR| |nextPartition| |dualSignature| |bit?| - |FormatRoman| |radicalSimplify| |tan2cot| |deepExpand| |rem| |sn| - |subMatrix| |factorSFBRlcUnit| |common| |numberOfImproperPartitions| - |coerceP| |algint| |ScanRoman| |reducedForm| |denominator| |tanh2coth| - |clearFortranOutputStack| |quo| |swapColumns!| |charthRoot| |subSet| - |powerSum| |algintegrate| |bezoutMatrix| |ScanFloatIgnoreSpaces| - |partialQuotients| |numerator| |cot2tan| |showFortranOutputStack| - |qelt| |swapRows!| |conditionP| |unrankImproperPartitions0| - |elementary| |palgintegrate| |ScanFloatIgnoreSpacesIfCan| - |bezoutResultant| |quadraticForm| |qsetelt| |coth2tanh| - |topFortranOutputStack| |div| |vertConcat| - |solveLinearPolynomialEquation| |unrankImproperPartitions1| - |alternating| |palginfieldint| |bezoutDiscriminant| - |numericalIntegration| |linkToFortran| |back| |retractIfCan| - |removeCosSq| |exquo| |xRange| |horizConcat| - |factorSquareFreePolynomial| |subresultantSequence| |cyclic| - |bitLength| |rk4| |principalAncestors| |front| - |setLegalFortranSourceExtensions| |removeSinSq| ~= |yRange| - |derivative| |squareTop| |factorPolynomial| |SturmHabichtSequence| - |dihedral| |bitCoef| |rk4a| |exportedOperators| |rotate!| |fracPart| - |removeCoshSq| |#| |zRange| |elRow1!| |squareFreePolynomial| - |SturmHabichtCoefficients| |cap| |bitTruth| |rk4qc| |dequeue!| - |removeSinhSq| |associatedSystem| ~ |constantOperator| |elRow2!| - |gcdPolynomial| |SturmHabicht| |cup| |contains?| |rk4f| |range| - |enqueue!| |integralMatrix| |expandTrigProducts| |uncouplingMatrices| - |constantOpIfCan| |elColumn2!| |torsion?| |center| |countRealRoots| - |wreath| |inf| |bfEntry| |aromberg| |colorFunction| |quatern| - |reduceBasisAtInfinity| |fintegrate| |associatedEquations| - |integerBound| |fractionFreeGauss!| |torsionIfCan| |equation| - |SturmHabichtMultiple| |SFunction| |qinterval| |bfKeys| |asimpson| - |comment| |imagK| |normalizeAtInfinity| |coefficient| |/\\| - |invertIfCan| |getGoodPrime| |countRealRootsMultiple| |skewSFunction| - |inspect| |iibinom| |atrapezoidal| |hexDigit?| |imagJ| - |complementaryBasis| |coHeight| |\\/| |copy!| |badNum| |signatureAst| - |testDim| |digit?| |romberg| |integral?| |imagI| |extendIfCan| |map| - |plus!| |mix| |pop!| |cyclotomicDecomposition| |genericPosition| - |iiperm| |simpson| |leaves| |escape| |conjugate| |integralAtInfinity?| - |algebraicVariables| |minus!| |doubleDisc| |push!| - |cyclotomicFactorization| |lfunc| |iipow| |trapezoidal| |queue| - |integralBasisAtInfinity| |zeroSetSplitIntoTriangularSystems| - |polyred| |rangeIsFinite| |minordet| |inHallBasis?| |index| |iidsum| - |rombergo| |nthRoot| |ramified?| |zeroSetSplit| |jvmProtected| - |padicFraction| |determinant| |reorder| |nor| |simpsono| - |ramifiedAtInfinity?| |fractRadix| |inputBinaryFile| - |reduceByQuasiMonic| |jvmPrivate| |padicallyExpand| |diagonalProduct| - |headAst| |nand| |singular?| |trapezoidalo| |collectQuasiMonic| - |wholeRadix| |convert| |outputBinaryFile| |jvmPublic| - |numberOfFractionalTerms| |diagonal| |heap| |cycleRagits| - |singularAtInfinity?| |removeZero| |key?| |nthFractionalTerm| - |diagonalMatrix| |gcdprim| |f02awf| |prefixRagits| |branchPoint?| - |initiallyReduce| |symbolIfCan| |firstNumer| |scalarMatrix| - |gcdcofact| |f02axf| |fractRagits| |branchPointAtInfinity?| - |headReduce| |argument| |firstDenom| |hermite| |gcdcofactprim| - |f02bbf| |wholeRagits| |rationalPoint?| |stronglyReduce| - |constantKernel| |completeHermite| |lintgcd| |f02bjf| |radix| - |absolutelyIrreducible?| |rewriteSetWithReduction| |showAttributes| - |constantIfCan| |vconcat| |smith| |hex| |setleaves!| |f02fjf| |nrows| - |randnum| |genus| |autoReduced?| |kovacic| |hconcat| |completeSmith| - |every?| |balancedBinaryTree| |f02wef| |ncols| |reseed| |getZechTable| - |initiallyReduced?| |laplace| |rspace| |apply| |diophantineSystem| - |any?| |sylvesterMatrix| |f02xef| |createZechTable| |headReduced?| - |trailingCoefficient| |vspace| |csubst| |first| |host| |f04adf| - |roughEqualIdeals?| |log| |createMultiplicationTable| - |stronglyReduced?| |normalizeIfCan| |hspace| |particularSolution| - |rest| |trueEqual| |f04arf| |linear| |roughSubIdeal?| - |createMultiplicationMatrix| |reduced?| |polCase| |superHeight| - |mapSolve| |factorList| |f04asf| |roughBase?| - |createLowComplexityTable| |normalized?| |distFact| |subHeight| - |listConjugateBases| |f04atf| |polynomial| |trivialIdeal?| - |createLowComplexityNormalBasis| |quasiComponent| |identification| - |doubleFloatFormat| |lift| |algebraicCoefficients?| |matrixGcd| - |f04axf| |collectUpper| |representationType| |initials| - |LyndonCoordinates| |messagePrint| |purelyTranscendental?| |reduce| - |curveColor| |divideIfCan!| |f04faf| |collect| |extract!| - |createPrimitiveElement| |basicSet| |LyndonBasis| |members| - |purelyAlgebraic?| |pointColor| |leastPower| |f04jgf| |collectUnder| - |bag| |tableForDiscreteLogarithm| |zeroDimensional?| |padecf| - |prepareSubResAlgo| |clip| |idealiser| |f04maf| |result| - |mainVariable?| |binding| |buildSyntax| |factorsOfCyclicGroupSize| - |fglmIfCan| |pade| |internalLastSubResultant| |idealiserMatrix| - |f04mbf| |mainVariables| |category| |solve| |sizeMultiplication| - |groebner| |root| |integralLastSubResultant| |moduleSum| |f04mcf| - |removeSquaresIfCan| |domain| |triangularSystems| - |getMultiplicationMatrix| |lexTriangular| |quotientByP| - |toseLastSubResultant| |mapUnivariate| |f04qaf| - |unprotectedRemoveRedundantFactors| |package| |nativeModuleExtension| - |getMultiplicationTable| |paraboloidal| |squareFreeLexTriangular| - |moduloP| |loadNativeModule| |toseInvertible?| |crest| - |mapUnivariateIfCan| |f07adf| |removeRedundantFactors| |hostByteOrder| - |primitive?| |ellipticCylindrical| |belong?| |modulus| - |toseInvertibleSet| |quadratic?| |cfirst| |mapMatrixIfCan| |dec| - |f07aef| |table| |certainlySubVariety?| |hostPlatform| - |numberOfIrreduciblePoly| |prolateSpheroidal| |Ci| |digits| - |toseSquareFreePart| |arrayStack| |sts2stst| |mapBivariate| |f07fdf| - |possiblyNewVariety?| |t| |rootDirectory| |numberOfPrimitivePoly| |Si| - |continuedFraction| |lowerCase?| |quotedOperators| |setButtonValue| - |clikeUniv| |fullDisplay| |f07fef| |probablyZeroDim?| |bumprow| - |numberOfNormalPoly| |Ei| |light| |upperCase?| |rur| - |setAttributeButtonStep| |weierstrass| |relationsIdeal| |s01eaf| |new| - |selectPolynomials| |bumptab| |createIrreduciblePoly| |linGenPos| - |outputList| |pastel| |alphabetic?| |create| |qqq| |saturate| - |changeNameToObjf| |s13aaf| |selectOrPolynomials| |last| |bumptab1| - |createPrimitivePoly| |groebgen| |dark| |enterInCache| |integralBasis| - |groebner?| |optAttributes| |s13acf| |assoc| |selectAndPolynomials| - |untab| |createNormalPoly| |totolex| |getSyntaxFormsFromFile| |byte| - |currentCategoryFrame| |substring?| |localIntegralBasis| - |groebnerIdeal| |Nul| |s13adf| |quasiMonicPolynomials| |bat1| - |createNormalPrimitivePoly| |minPol| |surface| |currentScope| - |qualifier| |ideal| |s14aaf| |numeric| |univariate?| |bat| - |createPrimitiveNormalPoly| |computeBasis| |coordinate| |label| - |pushNewContour| |suffix?| |mainExpression| |leadingIdeal| |radical| - |s14abf| |univariatePolynomials| |tab1| |exponents| - |nextIrreduciblePoly| |coord| |conjugates| |findBinding| EQ - |changeWeightLevel| |backOldPos| |s14baf| |linear?| |tab| |iisqrt2| - |nextPrimitivePoly| |anticoord| |comp| |shuffle| |rule| |contours| - |prefix?| |characteristicSerie| |generalPosition| |s15adf| - |linearPolynomials| |lex| |nextNormalPoly| |intcompBasis| |shufflein| - |structuralConstants| |characteristicSet| |quotient| |s15aef| |left| - |bivariate?| |slex| |iisqrt3| |nextNormalPrimitivePoly| - |curveColorPalette| |choosemon| |sequences| |coordinates| |medialSet| - |sort| |zeroDim?| |eval| |s17acf| |right| |bivariatePolynomials| - |drawComplex| |inverse| |iiexp| |nextPrimitiveNormalPoly| |var1Steps| - |transform| |permutations| |bounds| |int| |option| |Hausdorff| - |inRadical?| |s17adf| |denom| |removeRoughlyRedundantFactorsInPols| - |drawComplexVectorField| |maxrow| |iilog| |leastAffineMultiple| - |var2Steps| |pack!| |makeResult| |high| |Frobenius| |random| |in?| - |s17aef| |removeRoughlyRedundantFactorsInPol| |tableau| - |reducedQPowers| |setRealSteps| |complexLimit| |is?| |low| |operation| - |transcendenceDegree| |element?| |coerce| |s17aff| |pi| |interReduce| - |failed| |listOfLists| |rootOfIrreduciblePoly| |limit| |Is| - |condition| |subset?| |extensionDegree| |infix?| |zeroDimPrime?| - |s17agf| |infinity| |roughBasicSet| |tanSum| |write!| - |linearlyDependent?| |addMatchRestricted| |symmetricDifference| |mask| - |inGroundField?| |zeroDimPrimary?| |s17ahf| |crushedSet| |tanAn| - |read!| |linearDependence| |insertMatch| |difference| |transcendent?| - |primaryDecomp| |categories| |s17ajf| - |rewriteSetByReducingWithParticularGenerators| |tanNa| |iomode| - |solveLinear| |addMatch| |intersect| |algebraic?| |contract| |kernel| - |s17akf| |rewriteIdealWithQuasiMonicGenerators| |initTable!| |close!| - |linearElement| |getMatch| |part?| |sh| |gensym| |lhs| |s17dcf| |list| - |function| |squareFreeFactors| |printInfo!| |reopen!| |reducedSystem| - |failed?| |latex| |mirror| |leadingSupport| |rhs| |draw| |s17def| - |univariatePolynomialsGcds| |startStats!| |rightUnit| - |leftReducedSystem| |optpair| |clipBoolean| |member?| |monomial?| - |pattern| |e| |shrinkable| |s17dgf| - |removeRoughlyRedundantFactorsInContents| |printStats!| |leftUnit| - |linearForm| |getBadValues| |constant| |enumerate| |rquo| - |physicalLength!| |s17dhf| |removeRedundantFactorsInContents| - |clearTable!| |rightMinimalPolynomial| |setIntersection| - |resetBadValues| |setOfMinN| |capacity| |lquo| |physicalLength| - |setelt| |s17dlf| |symbol| |removeRedundantFactorsInPols| - |usingTable?| |leftMinimalPolynomial| |nil| |setUnion| - |hasTopPredicate?| |byteBuffer| |elements| |makeObject| |mindegTerm| - |flexibleArray| |copy| |s18acf| |expression| |irreducibleFactors| - |printingInfo?| |associatorDependence| |generator| |duplicates?| - |topPredicate| |unknownEndian| |replaceKthElement| |elseBranch| - |product| |s18adf| |autoCoerce| |coef| |integer| - |lazyIrreducibleFactors| |makingStats?| |mapGen| |setTopPredicate| - |incrementKthElement| |has?| |LiePolyIfCan| |thenBranch| |s18aef| - |resetAttributeButtons| |removeIrreducibleRedundantFactors| - |simplifyPower| |extractIfCan| |approximate| |mapExpon| - |patternVariable| |cdr| |comparison| |trunc| |generalizedInverse| - |s18aff| |getButtonValue| |normalForm| |number?| |insert!| |complex| - |commutativeEquality| |withPredicates| |car| |equality| |degree| - |imports| |width| |s18dcf| |decrease| |changeBase| |seriesSolve| - |interpretString| |leftMult| |setPredicates| |float?| |quasiRegular| - |s18def| |companionBlocks| |constantToUnaryFunction| - |stripCommentsAndBlanks| |rightMult| |predicates| |integer?| |redPo| - |quasiRegular?| |s19aaf| |lcm| |xCoord| |tubePlot| |setPrologue!| - |makeUnit| |hasPredicate?| |symbol?| |hMonic| |constant?| |s19abf| - |yCoord| |exponentialOrder| |setTex!| |nthFactor| |optional?| |updatF| - |string?| |mindeg| |vector| |s19acf| |gcd| |zCoord| |completeEval| - |setEpilogue!| |multiple?| |sPol| |list?| |maxdeg| |differentiate| - |s19adf| |false| |rCoord| |lowerPolynomial| |prologue| |cCsc| - |generic?| |pair?| |updatD| |RemainderList| |s20acf| |thetaCoord| - |raisePolynomial| |epilogue| |cSec| |incr| |quoted?| |atom?| - |minGbasis| |unexpand| |s20adf| |phiCoord| |normalDeriv| |endOfFile?| - |cCot| |hi| |inR?| |super| |null?| |lepol| |shape| |color| |ran| - |readIfCan!| |cTan| |isList| |nary?| |startTable!| |prinshINFO| - |youngDiagram| |d03eef| |hue| |highCommonTerms| |readLineIfCan!| - |newline| |cCos| |isOp| |unary?| |stopTable!| |prindINFO| - |triangSolve| |d03faf| |flatten| |shade| |mapCoef| |readLine!| - |underscore| |cSin| |satisfy?| |nullary?| |supDimElseRittWu?| - |fprindINFO| |univariateSolve| |nothing| |e01baf| |nthRootIfCan| - |nthCoef| |writeLine!| |ord| |cLog| |algebraicSort| |prinpolINFO| - |realSolve| |e01bef| |expIfCan| |binomThmExpt| |sign| |cExp| |arity| - |moreAlgebraic?| |prinb| |positiveSolve| |binaryTournament| |e01bff| - |logIfCan| |pomopo!| |nonQsign| |cRationalPower| |getDatabase| - |subTriSet?| |critpOrder| |squareFree| |binaryTree| |e01bgf| |unknown| - |sinIfCan| |mapExponents| |direction| |cPower| |numericalOptimization| - |subPolSet?| |makeCrit| |linearlyDependentOverZ?| |setLength!| - |e01bhf| |linearAssociatedLog| |createThreeSpace| |seriesToOutputForm| - |goodnessOfFit| |internalSubPolSet?| |virtualDegree| - |linearDependenceOverZ| |e01daf| |property| |linearAssociatedOrder| - |cyclicParents| |iCompose| |whatInfinity| |internalInfRittWu?| - |conditionsForIdempotents| |solveLinearlyOverQ| |e01saf| |disjunction| - |rank| |linearAssociatedExp| |cyclicEqual?| |taylorQuoByVar| - |infinite?| |internalSubQuasiComponent?| |genericRightDiscriminant| - |e01sbf| |conjunction| |createNormalElement| |cyclicEntries| |iExquo| - |finite?| |genericRightTraceForm| |e01sef| |exp| |isEquiv| - |alphanumeric| |setLabelValue| |cyclicCopy| |getStream| |generate| - |cond| |pureLex| |inc| |selectODEIVPRoutines| - |genericLeftDiscriminant| |e01sff| |isImplies| |alphabetic| |getCode| - |cyclic?| |getRef| |totalLex| |selectPDERoutines| |predicate| - |genericLeftTraceForm| |e02adf| |isOr| |hexDigit| |printCode| |arg1| - |complexNormalize| |incrementBy| |makeSeries| |reverseLex| - |selectOptimizationRoutines| |genericRightNorm| |concat| |e02aef| - |isAnd| |printStatement| |mappingMode| |expand| |leftLcm| - |selectIntegrationRoutines| |ravel| |genericRightTrace| |e02agf| - |isNot| |subresultantVector| |block| |categoryMode| |filterWhile| - |rightExtendedGcd| |routines| |genericRightMinimalPolynomial| - |reshape| |e02ahf| |lists| |isAtom| |primitivePart| |returns| - |voidMode| |filterUntil| |rightGcd| |mainSquareFreePart| - |rightRankPolynomial| |e02ajf| |atoms| |pointData| |goto| - |noValueMode| |select| |rightExactQuotient| |mainPrimitivePart| - |genericLeftNorm| |e02akf| |dual| |parent| |constructor| - |repeatUntilLoop| |jokerMode| |rightRemainder| |second| |mainContent| - |scale| |genericLeftTrace| |e02baf| |equiv| |extractProperty| - |whileLoop| GF2FG |rightQuotient| |third| |primitivePart!| |connect| - |genericLeftMinimalPolynomial| |e02bbf| |implies| |extractClosed| - |forLoop| FG2F |rightLcm| |nextsubResultant2| |region| - |leftRankPolynomial| |e02bcf| |merge!| |extractIndex| |sin?| F2FG - |leftExtendedGcd| |call| |LazardQuotient2| |parameters| |points| - |generic| |e02bdf| |max| |extractPoint| |zeroVector| |explogs2trigs| - |leftGcd| |LazardQuotient| |getGraph| |rightUnits| |e02bef| - |resultantEuclidean| |traverse| |zeroSquareMatrix| |trigs2explogs| - |leftExactQuotient| |subResultantChain| |isQuotient| |putGraph| - |leftUnits| |e02daf| |semiResultantEuclidean2| |defineProperty| - |identitySquareMatrix| |swap!| |leftRemainder| - |halfExtendedSubResultantGcd2| |graphs| |compBound| |e02dcf| - |extractTop!| |semiResultantEuclidean1| |closeComponent| - |lookupFunction| |double| |fill!| |leftQuotient| - |halfExtendedSubResultantGcd1| |graphStates| |brillhartTrials| - |tablePow| |e02ddf| |insertBottom!| |indiceSubResultant| |modifyPoint| - |encodingDirectory| |minIndex| |monicLeftDivide| - |extendedSubResultantGcd| |setright!| |graphState| |solveid| - |position| |e02def| |insertTop!| |indiceSubResultantEuclidean| - |addPointLast| |attributeData| |maxIndex| |monicRightDivide| - |setleft!| |exactQuotient!| |testModulus| |makeViewport2D| |insert| - |length| |e02dff| |semiIndiceSubResultantEuclidean| |addPoint2| - |domainTemplate| |entry?| |leftDivide| |brillhartIrreducible?| - |exactQuotient| |height| |viewport2D| |HenselLift| |scripts| |e02gaf| - |degreeSubResultant| |addPoint| |lSpaceBasis| |indices| |rightDivide| - |primPartElseUnitCanonical!| |getPickedPoints| |completeHensel| - |e02zaf| |degreeSubResultantEuclidean| BY |merge| |finiteBasis| - |index?| |brace| |hermiteH| |primPartElseUnitCanonical| |colorDef| - |multMonom| |variable| |e04dgf| |semiDegreeSubResultantEuclidean| - |deepCopy| |principal?| |entries| |destruct| |laguerreL| - |lazyResidueClass| |intensity| |build| |iterators| |e04fdf| - |mkIntegral| |lastSubResultantEuclidean| |shallowCopy| |divisor| - |declare!| |jvmInterface| |legendreP| |monicModulo| |lighting| - |leadingIndex| |radPoly| |e04gcf| |bottom!| - |semiLastSubResultantEuclidean| |numberOfChildren| |useNagFunctions| - |jvmSuper| |writeBytes!| |lazyPseudoDivide| |clipSurface| - |leadingExponent| |e04jaf| |rootPoly| |subResultantGcdEuclidean| - |children| |rationalPoints| |jvmNameAndTypeConstantTag| |writeUInt8!| - |lazyPremWithDefault| |showClipRegion| |GospersMethod| |e04mbf| - |semiSubResultantGcdEuclidean2| |child| |formfeed| |nonSingularModel| - |jvmInterfaceMethodConstantTag| |monomial| |writeInt8!| |lazyPquo| - |showRegion| |nextSubsetGray| |e04naf| |semiSubResultantGcdEuclidean1| - |linefeed| |birth| |algSplitSimple| |box| |jvmMethodrefConstantTag| - |multivariate| |writeByte!| |lazyPrem| NOT |hitherPlane| - |firstSubsetGray| |e04ucf| |discriminantEuclidean| |assert| - |internal?| |carriageReturn| |hyperelliptic| |jvmFieldrefConstantTag| - |variables| |isOpen?| |pquo| OR |eyeDistance| |clipPointsDefault| - |e04ycf| |semiDiscriminantEuclidean| |root?| |elliptic| - |jvmStringConstantTag| |blankSeparate| |prem| AND |perspective| - |drawToScale| |f01brf| |chainSubResultants| |leaf?| - |integralDerivationMatrix| |segment| |jvmClassConstantTag| - |semicolonSeparate| |shift| |supRittWu?| |zoom| |adaptive| |f01bsf| - |schema| |outputForm| |tree| |integralRepresents| |cons| - |jvmDoubleConstantTag| |commaSeparate| |RittWuCompare| |rotate| - |filename| |figureUnits| |f01maf| |resultantReduit| |argscript| - |integralCoordinates| |tail| |jvmLongConstantTag| |currentEnv| |pile| - |mainMonomials| |drawStyle| |putColorInfo| |f01mcf| - |resultantReduitEuclidean| |interpret| |superscript| |yCoordinates| - |jvmFloatConstantTag| |taylor| |paren| |mainCoefficients| - |outlineRender| |appendPoint| |parse| |f01qcf| - |semiResultantReduitEuclidean| |precision| |subscript| - |inverseIntegralMatrixAtInfinity| |jvmIntegerConstantTag| |laurent| - |bracket| |leastMonomial| |diagonals| |component| |f01qdf| |divide| - |script| |integralMatrixAtInfinity| |source| |jvmUTF8ConstantTag| - |puiseux| |iicot| |prod| |mainMonomial| |axes| |ranges| |f01qef| - |top!| |Lazard| |scripted?| |inverseIntegralMatrix| |jvmTransient| - |iisec| |overlabel| |quasiMonic?| |controlPanel| |pointLists| |f01rcf| - |Lazard2| |level| |resetNew| |jvmVolatile| |inv| |iicsc| |overbar| - |monic?| |viewpoint| |makeGraphImage| |f01rdf| |eigenvector| - |nextsousResultant2| |symFunc| |monom| |ground?| |jvmStrict| |prime| - |deepestInitial| * |dimensions| |graphImage| |f01ref| |resultantnaif| - |generalizedEigenvector| |symbolTableOf| |iidprod| |ground| - |jvmAbstract| |update| |quote| |iteratedInitials| |resize| - |groebSolve| |f02aaf| |goodPoint| |resultantEuclideannaif| - |generalizedEigenvectors| |argumentListOf| |jvmNative| |id| - |leadingMonomial| |supersub| |deepestTail| |move| |f02abf| |chvar| - |semiResultantEuclideannaif| |eigenvectors| |returnTypeOf| - |jvmSynchronized| |leadingCoefficient| |lo| |sum| |ipow| |presuper| - |fortranComplex| |head| = |modifyPointData| |f02adf| - |removeDuplicates| |pdct| |factorAndSplit| |printHeader| |jvmFinal| - |primitiveMonomials| |step| |factorial| |presub| |mdeg| - |fortranLogical| |subspace| |f02aef| |powers| |rightOne| |returnType!| - |multinomial| |datalist| |jvmStatic| |reductum| |mantissa| |sub| - |fortranInteger| |mvar| < |makeViewport3D| |f02aff| |partitions| - |leftOne| |argumentList!| |rarrow| |fortranDouble| |relativeApprox| > - |viewport3D| |f02agf| |partition| |rightZero| |endSubProgram| - |tanintegrate| |showSummary| |assign| |fortranReal| |rootOf| <= - |viewDeltaYDefault| |f02ajf| |eq| |complete| |leftZero| - |currentSubProgram| |primextendedint| |slash| |external?| |allRootsOf| - >= |viewDeltaXDefault| |iter| |f02akf| |any| |pole?| |swap| - |newSubProgram| |iiacoth| |expextendedint| |typeForm| |tower| |over| - |key| |definingPolynomial| |options| |scalarTypeOf| |viewZoomDefault| - |listBranches| |minPoly| |clearTheSymbolTable| |primlimitedint| - |iiasech| |zag| |positive?| |fortranCarriageReturn| |viewPhiDefault| - |map!| |normalDenom| |triangular?| |freeOf?| |showTheSymbolTable| - |explimitedint| |iiacsch| |fortranLiteral| |rules| |postfix| - |negative?| |string| + |viewThetaDefault| |qsetelt!| |totalfract| - |applyRules| |rewriteIdealWithRemainder| |operators| |printTypes| - |specialTrigs| |primextintfrac| |fortranLiteralLine| |compile| |infix| - |expr| |plus| |zero?| - |pointColorDefault| |pushdterm| |dequeue| - |rewriteIdealWithHeadRemainder| |mainKernel| |newTypeLists| - |basisOfRightNucloid| |primlimintfrac| |setColumn!| |localReal?| - |localUnquote| |iisinh| |processTemplate| |augment| |lineColorDefault| - / |pushucoef| |recolor| |sortConstraints| |remainder| |distribute| - |typeLists| |setRow!| |primintfldpoly| |rischNormalize| - |OMputEndObject| |basisOfCentroid| |arbitrary| |iicosh| - |lastSubResultant| |makeFR| |axesColorDefault| |pushuconst| - |sumOfSquares| |headRemainder| |functionIsFracPolynomial?| - |externalList| |oneDimensionalArray| |expintfldpoly| |realElementary| - |OMputInteger| |radicalOfLeftTraceForm| |musserTrials| |dim| - |lastSubResultantElseSplit| |complexNumeric| |unitsColorDefault| - |numberOfMonomials| |splitLinear| |roughUnitIdeal?| |problemPoints| - |typeList| |dom| |monomialIntegrate| |validExponential| |OMputFloat| - |invertibleSet| |stopMusserTrials| |pointSizeDefault| |multiset| - |acsch| |zerosOf| |parametersOf| |obj| |monomialIntPoly| - |rootNormalize| |OMputVariable| |kernels| |invertible?| - |numberOfFactors| |viewPosDefault| |mergeDifference| |setAdaptive3D| - |singularitiesOf| |fortranTypeOf| |find| |inverseLaplace| |tanQ| - |OMputString| |modularFactor| |invertibleElseSplit?| |operator| - |viewSizeDefault| |squareFreePrim| |adaptive3D?| |clipParametric| - |polynomialZeros| |empty| |callForm?| |inputOutputBinaryFile| - |OMputSymbol| |op| |useSingleFactorBound?| - |purelyAlgebraicLeadingMonomial?| |univariate| |viewDefaults| - |compdegd| |setScreenResolution3D| |f2df| |compound?| |clipWithRanges| - |closed| |getIdentifier| |OMgetApp| |useSingleFactorBound| - |viewWriteDefault| |univcase| |screenResolution3D| |ef2edf| - |getOperands| |bothWays| |variable?| |OMgetAtp| |solveRetract| - |useEisensteinCriterion?| |viewWriteAvailable| |consnewpol| - |setMaxPoints3D| |ocf2ocdf| |getOperator| |bytes| |getConstant| - |OMgetAttr| |mainVariable| |useEisensteinCriterion| |factor| - |var1StepsDefault| |nsqfree| |maxPoints3D| |char| |socf2socdf| |nil?| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| + |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| + |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| + |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |eq?| + |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| |ratPoly| + |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| |rightRank| + |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| + |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| + |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| + |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| + |radicalOfLeftTraceForm| |obj| |dom| |any| |applyRules| |localUnquote| + |arbitrary| |setColumn!| |setRow!| |oneDimensionalArray| |associatedSystem| + |uncouplingMatrices| |associatedEquations| |arrayStack| |setButtonValue| + |setAttributeButtonStep| |resetAttributeButtons| |getButtonValue| |decrease| + |increase| |morphism| |balancedFactorisation| |before?| |mapDown!| |mapUp!| + |setleaves!| |balancedBinaryTree| |sylvesterMatrix| |bezoutMatrix| + |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys| |inspect| |extract!| + |bag| |binding| |setProperties| |setProperty| |deleteProperty!| |has?| + |comparison| |equality| |nary?| |unary?| |nullary?| |properties| |derivative| + |constantOperator| |constantOpIfCan| |integerBound| |setright!| |setleft!| + |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| + |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| |byte| + |setLength!| |capacity| |byteBuffer| |unknownEndian| |bigEndian| + |littleEndian| |subtractIfCan| |setPosition| + |generalizedContinuumHypothesisAssumed| + |generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel| + |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |parents| + |principalAncestors| |exportedOperators| |alphanumeric| |alphabetic| + |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?| |upperCase?| + |alphabetic?| |hexDigit?| |digit?| |escape| |verticalTab| |horizontalTab| + |backspace| |formfeed| |linefeed| |carriageReturn| |newline| |underscore| + |char| |ord| |mkIntegral| |radPoly| |rootPoly| |goodPoint| |chvar| + |removeDuplicates| |find| |e| |clipParametric| |clipWithRanges| |numberOfHues| + |yellow| |iifact| |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| + |factorial| |multinomial| |permutation| |stirling1| |stirling2| |summation| + |factorials| |mkcomm| |polarCoordinates| |complex| |imaginary| |elaborateFile| + |elaborate| |macroExpand| |solid| |solid?| |denominators| |numerators| + |convergents| |approximants| |reducedForm| |partialQuotients| + |partialDenominators| |partialNumerators| |reducedContinuedFraction| |push| + |bindings| |cartesian| |polar| |cylindrical| |spherical| |parabolic| + |parabolicCylindrical| |paraboloidal| |ellipticCylindrical| + |prolateSpheroidal| |oblateSpheroidal| |bipolar| |bipolarCylindrical| + |toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros| + |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| + |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| + |computeCycleLength| |computeCycleEntry| |findConstructor| |arguments| + |operations| |dualSignature| |kind| |package| |domain| |category| |coerceP| + |powerSum| |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath| + |SFunction| |skewSFunction| |cyclotomicDecomposition| + |cyclotomicFactorization| |rangeIsFinite| |functionIsContinuousAtEndPoints| + |functionIsOscillatory| |changeName| |exprHasWeightCosWXorSinWX| + |exprHasAlgebraicWeight| |exprHasLogarithmicWeights| + |combineFeatureCompatibility| |sparsityIF| |stiffnessAndStabilityFactor| + |stiffnessAndStabilityOfODEIF| |systemSizeIF| |expenseOfEvaluationIF| + |accuracyIF| |intermediateResultsIF| |subscriptedVariables| |central?| + |elliptic?| |qsetelt| |doubleResultant| |distdfact| |separateDegrees| + |trace2PowMod| |tracePowMod| |irreducible?| |decimal| |innerint| + |exteriorDifferential| |totalDifferential| |homogeneous?| |leadingBasisTerm| + |ignore?| |computeInt| |checkForZero| |nan?| |logGamma| |hypergeometric0F1| + |rotatez| |rotatey| |rotatex| |identity| |dictionary| |dioSolve| + |directProduct| |newLine| |copies| |say| |sayLength| |setnext!| |setprevious!| + |next| |previous| |datalist| |shanksDiscLogAlgorithm| |showSummary| |reflect| + |reify| |constructor| |functorData| |separant| |initial| |leader| |isobaric?| + |weights| |differentialVariables| |extractBottom!| |extractTop!| + |insertBottom!| |insertTop!| |bottom!| |top!| |dequeue| |makeObject| |recolor| + |drawComplex| |drawComplexVectorField| |setRealSteps| |setImagSteps| + |setClipValue| |draw| |option?| |range| |colorFunction| |curveColor| + |pointColor| |clip| |clipBoolean| |style| |toScale| |pointColorPalette| + |curveColorPalette| |var1Steps| |var2Steps| |space| |tubePoints| |tubeRadius| + |option| |weight| |makeVariable| |finiteBound| |sortConstraints| + |sumOfSquares| |splitLinear| |simpleBounds?| |linearMatrix| |linearPart| + |nonLinearPart| |quadratic?| |changeNameToObjf| |optAttributes| |Nul| + |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| |iicos| |iitan| + |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| + |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| + |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| |localReal?| + |rischNormalize| |realElementary| |validExponential| |rootNormalize| |tanQ| + |callForm?| |getIdentifier| |variable?| |getConstant| |type| |environment| + |typeForm| |irForm| |elaboration| |select!| |delete!| |sn| |cn| |dn| |sncndn| + |qsetelt!| |categoryFrame| |interactiveEnv| |currentEnv| |putProperties| + |getProperties| |putProperty| |getProperty| |scopes| |eigenvalues| + |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| + |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| + |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| + |distribute| |subst| |functionIsFracPolynomial?| |problemPoints| |zerosOf| + |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| |ocf2ocdf| |socf2socdf| + |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| |numberOfOperations| |edf2efi| + |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| |vedf2vef| |df2st| |f2st| + |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| |measure2Result| + |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| |fi2df| |mat| |neglist| + |multiEuclidean| |extendedEuclidean| |euclideanSize| |sizeLess?| + |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| |tubePlot| + |exponentialOrder| |completeEval| |lowerPolynomial| |raisePolynomial| + |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| + |pomopo!| |mapExponents| |linearAssociatedLog| |linearAssociatedOrder| + |linearAssociatedExp| |createNormalElement| |setLabelValue| |getCode| + |printCode| |code| |operation| |common| |printStatement| |save| |stop| |block| + |cond| |returns| |call| |comment| |continue| |goto| |repeatUntilLoop| + |whileLoop| |forLoop| |sin?| |zeroVector| |zeroSquareMatrix| + |identitySquareMatrix| |lookupFunction| |encodingDirectory| |attributeData| + |domainTemplate| |lSpaceBasis| |finiteBasis| |principal?| |divisor| + |useNagFunctions| |rationalPoints| |nonSingularModel| |algSplitSimple| + |hyperelliptic| |elliptic| |integralDerivationMatrix| |integralRepresents| + |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| + |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| + |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| + |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| + |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| + |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| + |getZechTable| |createZechTable| |createMultiplicationTable| + |createMultiplicationMatrix| |createLowComplexityTable| + |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| + |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| + |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| + |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| + |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| + |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| + |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| + |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| + |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| + |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| + |associatorDependence| |lieAlgebra?| |jordanAlgebra?| + |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| + |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| + |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| + |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| + |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| + |someBasis| |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| + |shellSort| |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| + |exp1| |log10| |log2| |rationalApproximation| |relerror| |complexSolve| + |complexRoots| |realRoots| |leadingTerm| |overlap| |hcrf| |hclf| |writable?| + |readable?| |exists?| |extension| |directory| |filename| |shallowExpand| + |deepExpand| |clearFortranOutputStack| |showFortranOutputStack| + |popFortranOutputStack| |pushFortranOutputStack| |topFortranOutputStack| + |linkToFortran| |setLegalFortranSourceExtensions| |fracPart| |polyPart| + |fullPartialFraction| |primeFrobenius| |discreteLog| |decreasePrecision| + |increasePrecision| |bits| |unitNormalize| |unit| |flagFactor| |sqfrFactor| + |primeFactor| |nthFlag| |nthExponent| |irreducibleFactor| |factors| + |nilFactor| |regularRepresentation| |traceMatrix| |randomLC| |minimize| + |module| |rightRegularRepresentation| |leftRegularRepresentation| + |rightTraceMatrix| |leftTraceMatrix| |rightDiscriminant| |leftDiscriminant| + |represents| |mergeFactors| |isMult| |applyQuote| |ground| |ground?| + |exprToXXP| |exprToUPS| |exprToGenUPS| |localAbs| |universe| |complement| + |cardinality| |internalIntegrate0| |makeCos| |makeSin| |iiGamma| |iiabs| + |bringDown| |newReduc| |logical?| |character?| |doubleComplex?| |complex?| + |double?| |ffactor| |qfactor| |UP2ifCan| |anfactor| |fortranCharacter| + |fortranDoubleComplex| |fortranComplex| |fortranLogical| |fortranInteger| + |fortranDouble| |fortranReal| |external?| |scalarTypeOf| + |fortranCarriageReturn| |fortranLiteral| |fortranLiteralLine| + |processTemplate| |makeFR| |musserTrials| |stopMusserTrials| |numberOfFactors| + |modularFactor| |useSingleFactorBound?| |useSingleFactorBound| + |useEisensteinCriterion?| |useEisensteinCriterion| |eisensteinIrreducible?| + |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| + |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| + |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| + |factorsOfDegree| |pascalTriangle| |rangePascalTriangle| |sizePascalTriangle| + |fillPascalTriangle| |safeCeiling| |safeFloor| |safetyMargin| |sumSquares| + |euclideanNormalForm| |euclideanGroebner| |factorGroebnerBasis| + |groebnerFactorize| |credPol| |redPol| |gbasis| |critT| |critM| |critB| + |critBonD| |critMTonD1| |critMonD1| |redPo| |hMonic| |updatF| |sPol| |updatD| + |minGbasis| |lepol| |prinshINFO| |prindINFO| |fprindINFO| |prinpolINFO| + |prinb| |critpOrder| |makeCrit| |virtualDegree| |lcm| + |conditionsForIdempotents| |genericRightDiscriminant| |genericRightTraceForm| + |genericLeftDiscriminant| |genericLeftTraceForm| |genericRightNorm| + |genericRightTrace| |genericRightMinimalPolynomial| |rightRankPolynomial| + |genericLeftNorm| |genericLeftTrace| |genericLeftMinimalPolynomial| + |leftRankPolynomial| |generic| |rightUnits| |leftUnits| |compBound| |tablePow| + |solveid| |testModulus| |HenselLift| |completeHensel| |multMonom| |build| + |leadingIndex| |leadingExponent| |GospersMethod| |nextSubsetGray| + |firstSubsetGray| |clipPointsDefault| |drawToScale| |adaptive| |figureUnits| + |putColorInfo| |appendPoint| |component| |ranges| |pointLists| + |makeGraphImage| |graphImage| |groebSolve| |testDim| |genericPosition| |lfunc| + |inHallBasis?| |reorder| |parameters| |headAst| |heap| |gcdprim| |gcdcofact| + |gcdcofactprim| |lintgcd| |hex| |count| |every?| |any?| |map!| |host| + |trueEqual| |factorList| |listConjugateBases| |matrixGcd| |divideIfCan!| + |leastPower| |idealiser| |idealiserMatrix| |moduleSum| |mapUnivariate| + |mapUnivariateIfCan| |mapMatrixIfCan| |mapBivariate| |fullDisplay| + |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal| + |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?| + |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp| + |contract| |gensym| |leadingSupport| |shrinkable| |physicalLength!| + |physicalLength| |flexibleArray| |elseBranch| |thenBranch| + |generalizedInverse| |imports| |sequence| |readBytes!| |readUInt32!| + |readInt32!| |readUInt16!| |readInt16!| |readUInt8!| |readInt8!| |readByte!| + |setFieldInfo| |pol| |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup| + |normal?| |basis| |normalElement| |minimalPolynomial| |position!| |eof?| + |inputBinaryFile| |increment| |incrementBy| |charpol| |solve1| + |innerEigenvectors| |compile| |declare| |parseString| |unparse| |flatten| + |lambda| |binary| |packageCall| |interpret| |innerSolve1| |innerSolve| + |makeEq| |modularGcdPrimitive| |modularGcd| |reduction| |signAround| |invmod| + |powmod| |mulmod| |submod| |addmod| |mask| |dec| |inc| |symmetricRemainder| + |positiveRemainder| |bit?| |algint| |algintegrate| |palgintegrate| + |palginfieldint| |bitLength| |bitCoef| |bitTruth| |contains?| |inf| + |qinterval| |interval| |unit?| |associates?| |unitCanonical| |unitNormal| + |lfextendedint| |lflimitedint| |lfinfieldint| |lfintegrate| |lfextlimint| + |BasicMethod| |PollardSmallFactor| |showTheFTable| |clearTheFTable| |fTable| + |showAttributes| |entry| |palgint0| |palgextint0| |palglimint0| |palgRDE0| + |palgLODE0| |chineseRemainder| |divisors| |eulerPhi| |fibonacci| |harmonic| + |jacobi| |moebiusMu| |numberOfDivisors| |sumOfDivisors| + |sumOfKthPowerDivisors| |HermiteIntegrate| |palgint| |palgextint| |palglimint| + |palgRDE| |palgLODE| |splitConstant| |pmComplexintegrate| |pmintegrate| + |infieldint| |extendedint| |limitedint| |integerIfCan| |internalIntegrate| + |infieldIntegrate| |limitedIntegrate| |extendedIntegrate| |varselect| |kmax| + |ksec| |vark| |removeConstantTerm| |mkPrim| |intPatternMatch| |primintegrate| + |expintegrate| |tanintegrate| |primextendedint| |expextendedint| + |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| + |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| + |inverseLaplace| |inputOutputBinaryFile| |closed| |bothWays| |input| |resolve| + |bytes| |ip4Address| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| + |irDef| |irCtor| |irVar| |perfectNthPower?| |perfectNthRoot| |approxNthRoot| + |perfectSquare?| |perfectSqrt| |approxSqrt| |generateIrredPoly| + |complexExpand| |complexIntegrate| |dimensionOfIrreducibleRepresentation| + |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| + |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| + |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| + |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| + |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| |mappingMode| + |categoryMode| |voidMode| |noValueMode| |jokerMode| GF2FG FG2F F2FG + |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| + |indices| |index?| |entries| |categories| |jvmInterface| |jvmSuper| + |jvmNameAndTypeConstantTag| |jvmInterfaceMethodConstantTag| + |jvmMethodrefConstantTag| |jvmFieldrefConstantTag| |jvmStringConstantTag| + |jvmClassConstantTag| |jvmDoubleConstantTag| |jvmLongConstantTag| + |jvmFloatConstantTag| |jvmIntegerConstantTag| |jvmUTF8ConstantTag| + |jvmTransient| |jvmVolatile| |jvmStrict| |jvmAbstract| |jvmNative| + |jvmSynchronized| |jvmFinal| |jvmStatic| |jvmProtected| |jvmPrivate| + |jvmPublic| |search| |key?| |symbolIfCan| |kernel| |argument| |constantKernel| + |constantIfCan| |kovacic| |unknown| |laplace| |trailingCoefficient| + |normalizeIfCan| |polCase| |distFact| |identification| |LyndonCoordinates| + |LyndonBasis| |zeroDimensional?| |fglmIfCan| |groebner| |lexTriangular| + |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| |Si| |Ei| + |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| |anticoord| + |intcompBasis| |choosemon| |transform| |pack!| |library| |complexLimit| + |limit| |linearlyDependent?| |linearDependence| |solveLinear| |linearElement| + |reducedSystem| |leftReducedSystem| |linearForm| |setDifference| + |setIntersection| |setUnion| |append| |null| |nil| |substitute| |duplicates?| + |mapGen| |mapExpon| |commutativeEquality| |leftMult| |rightMult| |makeUnit| + |reverse!| |reverse| |nthFactor| |nthExpon| |makeMulti| |makeTerm| + |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| + |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ + |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| + |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| + |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| + |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| + |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| + |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| + |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| + |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| + |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| + |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| + |rightScalarTimes!| |times!| |power!| |nothing| |just| |gradient| |divergence| + |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| + |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| + |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| + |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| + |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| + |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| + |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| + |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| + |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| + |derivationCoordinates| |generator| |one?| |splitSquarefree| |normalDenom| + |reshape| |totalfract| |pushdterm| |pushucoef| |pushuconst| + |numberOfMonomials| |multiset| |systemCommand| |mergeDifference| + |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| + |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |c02aff| |c02agf| |c05adf| + |c05nbf| |c05pbf| |c06eaf| |c06ebf| |c06ecf| |c06ekf| |c06fpf| |c06fqf| + |c06frf| |c06fuf| |c06gbf| |c06gcf| |c06gqf| |c06gsf| |d01ajf| |d01akf| + |d01alf| |d01amf| |d01anf| |d01apf| |d01aqf| |d01asf| |d01bbf| |d01fcf| + |d01gaf| |d01gbf| |d02bbf| |d02bhf| |d02cjf| |d02ejf| |d02gaf| |d02gbf| + |d02kef| |d02raf| |d03edf| |d03eef| |d03faf| |e01baf| |e01bef| |e01bff| + |e01bgf| |e01bhf| |e01daf| |e01saf| |e01sbf| |e01sef| |e01sff| |e02adf| + |e02aef| |e02agf| |e02ahf| |e02ajf| |e02akf| |e02baf| |e02bbf| |e02bcf| + |e02bdf| |e02bef| |e02daf| |e02dcf| |e02ddf| |e02def| |e02dff| |e02gaf| + |e02zaf| |e04dgf| |e04fdf| |e04gcf| |e04jaf| |e04mbf| |e04naf| |e04ucf| + |e04ycf| |f01brf| |f01bsf| |f01maf| |f01mcf| |f01qcf| |f01qdf| |f01qef| + |f01rcf| |f01rdf| |f01ref| |f02aaf| |f02abf| |f02adf| |f02aef| |f02aff| + |f02agf| |f02ajf| |f02akf| |f02awf| |f02axf| |f02bbf| |f02bjf| |f02fjf| + |f02wef| |f02xef| |f04adf| |f04arf| |f04asf| |f04atf| |f04axf| |f04faf| + |f04jgf| |f04maf| |f04mbf| |f04mcf| |f04qaf| |f07adf| |f07aef| |f07fdf| + |f07fef| |s01eaf| |s13aaf| |s13acf| |s13adf| |s14aaf| |s14abf| |s14baf| + |s15adf| |s15aef| |s17acf| |s17adf| |s17aef| |s17aff| |s17agf| |s17ahf| + |s17ajf| |s17akf| |s17dcf| |s17def| |s17dgf| |s17dhf| |s17dlf| |s18acf| + |s18adf| |s18aef| |s18aff| |s18dcf| |s18def| |s19aaf| |s19abf| |s19acf| + |s19adf| |s20acf| |s20adf| |s21baf| |s21bbf| |s21bcf| |s21bdf| + |fortranCompilerName| |fortranLinkerArgs| |aspFilename| |dimensionsOf| + |checkPrecision| |restorePrecision| |antiCommutator| |commutator| |associator| + |complexEigenvalues| |complexEigenvectors| |isConnected?| |connectTo| |shift| + |normalizedAssociate| |normalize| |outputArgs| |normInvertible?| |normFactors| + |npcoef| |listexp| |characteristicPolynomial| |realEigenvalues| + |realEigenvectors| |halfExtendedResultant2| |halfExtendedResultant1| + |extendedResultant| |subResultantsChain| |lazyPseudoQuotient| + |lazyPseudoRemainder| |bernoulliB| |eulerE| |numeric| |complexNumeric| + |numericIfCan| |complexNumericIfCan| |FormatArabic| |ScanArabic| |FormatRoman| + |ScanRoman| |ScanFloatIgnoreSpaces| |ScanFloatIgnoreSpacesIfCan| + |numericalIntegration| |rk4| |rk4a| |rk4qc| |rk4f| |aromberg| |asimpson| + |atrapezoidal| |romberg| |simpson| |trapezoidal| |rombergo| |simpsono| + |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| |imagi| |octon| |ODESolve| + |constDsolve| |showTheIFTable| |clearTheIFTable| |keys| |iFTable| + |showIntensityFunctions| |expint| |diff| |algDsolve| |denomLODE| + |indicialEquations| |indicialEquation| |denomRicDE| |leadingCoefficientRicDE| + |constantCoefficientRicDE| |changeVar| |ratDsolve| + |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| + |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| + |lexico| |OMmakeConn| |OMcloseConn| |OMconnInDevice| |OMconnOutDevice| + |OMconnectTCP| |OMbindTCP| |OMopenFile| |OMopenString| |OMclose| + |OMsetEncoding| |OMputApp| |OMputAtp| |OMputAttr| |OMputBind| |OMputBVar| + |OMputError| |OMputObject| |OMputEndApp| |OMputEndAtp| |OMputEndAttr| + |OMputEndBind| |OMputEndBVar| |OMputEndError| |OMputEndObject| |OMputInteger| + |OMputFloat| |OMputVariable| |OMputString| |OMputSymbol| |OMgetApp| |OMgetAtp| + |OMgetAttr| |OMgetBind| |OMgetBVar| |OMgetError| |OMgetObject| |OMgetEndApp| + |OMgetEndAtp| |OMgetEndAttr| |OMgetEndBind| |OMgetEndBVar| |OMgetEndError| + |OMgetEndObject| |OMgetInteger| |OMgetFloat| |OMgetVariable| |OMgetString| + |OMgetSymbol| |OMgetType| |OMencodingBinary| |OMencodingSGML| |OMencodingXML| + |OMencodingUnknown| |omError| |errorInfo| |errorKind| |OMReadError?| + |OMUnknownSymbol?| |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread| + |OMreadFile| |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?| + |OMsupportsSymbol?| |OMunhandledSymbol| |infinity| |makeop| |opeval| + |evaluateInverse| |evaluate| |conjug| |adjoint| |arity| |getDatabase| + |numericalOptimization| |optimize| |goodnessOfFit| |whatInfinity| |infinite?| + |finite?| |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex| + |min| |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient| + |rightRemainder| |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| + |leftExactQuotient| |leftRemainder| |leftQuotient| |times| |apply| + |monicLeftDivide| |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| + |laguerreL| |legendreP| |outputList| |writeBytes!| |writeUInt8!| |writeInt8!| + |writeByte!| |isOpen?| |outputBinaryFile| |not| |or| |and| |quo| |rem| |div| + >= > ~= |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren| + |bracket| |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper| + |presub| |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| + |infix?| |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| + |hspace| |superHeight| |subHeight| |height| |width| |doubleFloatFormat| + |messagePrint| |message| |members| |padecf| |pade| |root| |quotientByP| + |moduloP| |modulus| |digits| |continuedFraction| |pair| |light| |pastel| + |bright| |dim| |dark| |getSyntaxFormsFromFile| |surface| |coordinate| + |conjugates| |shuffle| |shufflein| |sequences| |permutations| |lists| + |makeResult| |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| + |getMatch| |failed| |failed?| |optpair| |getBadValues| |resetBadValues| + |hasTopPredicate?| |topPredicate| |setTopPredicate| |patternVariable| + |withPredicates| |setPredicates| |predicates| |hasPredicate?| |optional?| + |multiple?| |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| + |satisfy?| |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| + |PDESolve| |leftFactor| |rightFactorCandidate| |measure| D |ptree| + |coerceImages| |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| + |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| + |cycles| |cycle| |initializeGroupForWordProblem| <= < |support| + |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| + |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| + |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| + |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| + |charthRoot| |conditionP| |solveLinearPolynomialEquation| + |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| + |gcdPolynomial| |torsion?| |torsionIfCan| |getGoodPrime| |badNum| |mix| + |doubleDisc| |polyred| |padicFraction| |padicallyExpand| + |numberOfFractionalTerms| |nthFractionalTerm| |firstNumer| |firstDenom| + |compactFraction| |partialFraction| |gcdPrimitive| |symmetricGroup| + |alternatingGroup| |abelianGroup| |cyclicGroup| |dihedralGroup| |mathieu11| + |mathieu12| |mathieu22| |mathieu23| |mathieu24| |janko2| |rubiksGroup| + |youngGroup| |lexGroebner| |totalGroebner| |expressIdealMember| + |principalIdeal| |LagrangeInterpolation| |psolve| |wrregime| |rdregime| + |bsolve| |dmp2rfi| |se2rfi| |pr2dmp| |hasoln| |ParCondList| |redpps| |B1solve| + |factorset| |maxrank| |minrank| |minset| |nextSublist| |overset?| |ParCond| + |redmat| |regime| |sqfree| |inconsistent?| |debug| |numFunEvals| |setAdaptive| + |adaptive?| |setScreenResolution| |screenResolution| |setMaxPoints| + |maxPoints| |setMinPoints| |minPoints| |parametric?| |plotPolar| |debug3D| + |numFunEvals3D| |setAdaptive3D| |adaptive3D?| |setScreenResolution3D| + |screenResolution3D| |setMaxPoints3D| |maxPoints3D| |setMinPoints3D| + |minPoints3D| |tValues| |tRange| |plot| |pointPlot| |calcRanges| |assert| + |optional| |multiple| |fixPredicate| |patternMatch| |patternMatchTimes| + |bernoulli| |chebyshevT| |chebyshevU| |cyclotomic| |euler| |fixedDivisor| + |laguerre| |legendre| |dmpToHdmp| |hdmpToDmp| |pToHdmp| |hdmpToP| |dmpToP| + |pToDmp| |sylvesterSequence| |sturmSequence| |boundOfCauchy| + |sturmVariationsOf| |lazyVariations| |content| |primitiveMonomials| + |totalDegree| |minimumDegree| |monomials| |isPlus| |isTimes| |isExpt| + |isPower| |rroot| |qroot| |froot| |nthr| |port| |firstUncouplingMatrix| + |integral| |primitiveElement| |nextPrime| |prevPrime| |primes| |print| + |selectsecond| |selectfirst| |makeprod| |property| |disjunction| |conjunction| + |isEquiv| |isImplies| |isOr| |isAnd| |isNot| |isAtom| |atoms| |dual| |equiv| + |implies| |false| |true| |merge!| |max| |resultantEuclidean| + |semiResultantEuclidean2| |semiResultantEuclidean1| |indiceSubResultant| + |indiceSubResultantEuclidean| |semiIndiceSubResultantEuclidean| + |degreeSubResultant| |degreeSubResultantEuclidean| + |semiDegreeSubResultantEuclidean| |lastSubResultantEuclidean| + |semiLastSubResultantEuclidean| |subResultantGcdEuclidean| + |semiSubResultantGcdEuclidean2| |semiSubResultantGcdEuclidean1| + |discriminantEuclidean| |semiDiscriminantEuclidean| |chainSubResultants| + |schema| |resultantReduit| |resultantReduitEuclidean| + |semiResultantReduitEuclidean| |divide| |Lazard| |Lazard2| + |nextsousResultant2| |resultantnaif| |resultantEuclideannaif| + |semiResultantEuclideannaif| |pdct| |powers| |partitions| |parts| |partition| + |complete| |pole?| |monomial| |leadingMonomial| |zRange| |yRange| |xRange| + |listBranches| |triangular?| |rewriteIdealWithRemainder| + |rewriteIdealWithHeadRemainder| |remainder| |headRemainder| |roughUnitIdeal?| + |roughEqualIdeals?| |roughSubIdeal?| |roughBase?| |trivialIdeal?| |sort| + |collectUpper| |collect| |collectUnder| |mainVariable?| |mainVariables| + |removeSquaresIfCan| |unprotectedRemoveRedundantFactors| + |removeRedundantFactors| |certainlySubVariety?| |possiblyNewVariety?| + |probablyZeroDim?| |selectPolynomials| |selectOrPolynomials| + |selectAndPolynomials| |quasiMonicPolynomials| |univariate?| + |univariatePolynomials| |linear?| |linearPolynomials| |bivariate?| + |bivariatePolynomials| |removeRoughlyRedundantFactorsInPols| + |removeRoughlyRedundantFactorsInPol| |interReduce| |roughBasicSet| + |crushedSet| |rewriteSetByReducingWithParticularGenerators| + |rewriteIdealWithQuasiMonicGenerators| |squareFreeFactors| + |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInContents| + |removeRedundantFactorsInContents| |removeRedundantFactorsInPols| + |irreducibleFactors| |lazyIrreducibleFactors| + |removeIrreducibleRedundantFactors| |normalForm| |changeBase| + |companionBlocks| |xCoord| |yCoord| |zCoord| |rCoord| |thetaCoord| |phiCoord| + |color| |hue| |shade| |nthRootIfCan| |expIfCan| |logIfCan| |sinIfCan| + |cosIfCan| |tanIfCan| |cotIfCan| |secIfCan| |cscIfCan| |asinIfCan| |acosIfCan| + |atanIfCan| |acotIfCan| |asecIfCan| |acscIfCan| |sinhIfCan| |coshIfCan| + |tanhIfCan| |cothIfCan| |sechIfCan| |cschIfCan| |asinhIfCan| |acoshIfCan| + |atanhIfCan| |acothIfCan| |asechIfCan| |acschIfCan| |pushdown| |pushup| + |reducedDiscriminant| |idealSimplify| |definingInequation| |definingEquations| + |setStatus| |quasiAlgebraicSet| |radicalSimplify| |random| |denominator| + |numerator| |denom| |numer| |quadraticForm| |back| |front| |rotate!| + |dequeue!| |enqueue!| |quatern| |imagK| |imagJ| |imagI| |conjugate| |queue| + |nthRoot| |fractRadix| |wholeRadix| |cycleRagits| |prefixRagits| |fractRagits| + |wholeRagits| |radix| |randnum| |reseed| |seed| |rational| |rational?| + |rationalIfCan| |setvalue!| |setchildren!| |node?| |child?| |distance| + |leaves| |nodes| |rename| |rename!| |mainValue| |mainDefiningPolynomial| + |mainForm| |sqrt| |rischDE| |rischDEsys| |monomRDE| |baseRDE| |polyRDE| + |monomRDEsys| |baseRDEsys| |weighted| |rdHack1| |midpoint| |midpoints| + |realZeros| |mainCharacterization| |algebraicOf| |ReduceOrder| = |setref| + |deref| |ref| |radicalEigenvectors| |radicalEigenvector| |radicalEigenvalues| + |eigenMatrix| |normalise| |gramschmidt| |orthonormalBasis| + |antisymmetricTensors| |createGenericMatrix| |symmetricTensors| + |tensorProduct| |permutationRepresentation| |completeEchelonBasis| + |createRandomElement| |cyclicSubmodule| |standardBasisOfCyclicSubmodule| + |areEquivalent?| |isAbsolutelyIrreducible?| |meatAxe| |scanOneDimSubspaces| + |double| |expt| |lift| |showArrayValues| |showScalarValues| |solveRetract| + |variables| |mainVariable| |univariate| |multivariate| |uniform01| |normal01| + |exponential1| |chiSquare1| |normal| |exponential| |chiSquare| F |t| + |factorFraction| |componentUpperBound| |blue| |green| |red| |whitePoint| + |uniform| |binomial| |poisson| |geometric| |ridHack1| |interpolate| + |nullSpace| |nullity| |rank| |rowEchelon| |column| |row| |qelt| |ncols| + |nrows| |maxColIndex| |minColIndex| |maxRowIndex| |minRowIndex| + |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| + |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart| + |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right| + |left| |roman| |recoverAfterFail| |showTheRoutinesTable| |deleteRoutine!| + |getExplanations| |getMeasure| |changeMeasure| |changeThreshhold| + |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| + |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| + |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| + |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| + |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| + |subResultantChain| |halfExtendedSubResultantGcd2| + |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| + |exactQuotient| |primPartElseUnitCanonical!| |primPartElseUnitCanonical| + |retract| |retractIfCan| |lazyResidueClass| |monicModulo| |lazyPseudoDivide| + |lazyPremWithDefault| |lazyPquo| |lazyPrem| |pquo| |prem| |supRittWu?| + |RittWuCompare| |mainMonomials| |mainCoefficients| |leastMonomial| + |mainMonomial| |quasiMonic?| |monic?| |leadingCoefficient| |deepestInitial| + |iteratedInitials| |deepestTail| |head| |mdeg| |mvar| |iterators| + |relativeApprox| |rootOf| |allRootsOf| |definingPolynomial| |positive?| + |negative?| |zero?| |augment| |lastSubResultant| |lastSubResultantElseSplit| + |invertibleSet| |invertible?| |invertibleElseSplit?| + |purelyAlgebraicLeadingMonomial?| |algebraicCoefficients?| + |purelyTranscendental?| |purelyAlgebraic?| |prepareSubResAlgo| + |internalLastSubResultant| |integralLastSubResultant| |toseLastSubResultant| + |toseInvertible?| |toseInvertibleSet| |toseSquareFreePart| |expression| + |quotedOperators| |pattern| |suchThat| |rule| |rules| |ruleset| |rur| |create| + |clearCache| |cache| |enterInCache| |currentCategoryFrame| |currentScope| + |pushNewContour| |findBinding| |contours| |structuralConstants| |coordinates| + |bounds| |equation| |incr| |high| |low| |hi| |lo| BY |body| |union| |subset?| + |symmetricDifference| |difference| |intersect| |set| |brace| |part?| |latex| + |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| + |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| + |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| + |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| + |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| + |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| + |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| + |removeSuperfluousCases| |prepareDecompose| |branchIfCan| |startTableGcd!| + |stopTableGcd!| |startTableInvSet!| |stopTableInvSet!| + |stosePrepareSubResAlgo| |stoseInternalLastSubResultant| + |stoseIntegralLastSubResultant| |stoseLastSubResultant| + |stoseInvertible?sqfreg| |stoseInvertibleSetsqfreg| |stoseInvertible?reg| + |stoseInvertibleSetreg| |stoseInvertible?| |stoseInvertibleSet| + |stoseSquareFreePart| |coleman| |inverseColeman| |listYoungTableaus| + |makeYoungTableau| |nextColeman| |nextLatticePermutation| |nextPartition| + |numberOfImproperPartitions| |subSet| |unrankImproperPartitions0| + |unrankImproperPartitions1| |subresultantSequence| |SturmHabichtSequence| + |SturmHabichtCoefficients| |SturmHabicht| |countRealRoots| + |SturmHabichtMultiple| |countRealRootsMultiple| |source| |target| |signature| + |signatureAst| |Or| |And| |Not| |xor| |depth| |top| |pop!| |push!| |minordet| + |determinant| |diagonalProduct| |trace| |diagonal| |diagonalMatrix| + |scalarMatrix| |hermite| |completeHermite| |smith| |completeSmith| + |diophantineSystem| |csubst| |particularSolution| |mapSolve| |linear| + |quadratic| |cubic| |quartic| |aLinear| |aQuadratic| |aCubic| |aQuartic| + |radicalSolve| |radicalRoots| |contractSolve| |decomposeFunc| |unvectorise| + |bubbleSort!| |insertionSort!| |check| |objects| |lprop| |llprop| |lllp| + |lllip| |lp| |mesh?| |mesh| |polygon?| |polygon| |closedCurve?| |closedCurve| + |curve?| |curve| |point?| |enterPointData| |composites| |components| + |numberOfComposites| |numberOfComponents| |create3Space| |parse| + |outputAsFortran| |outputAsScript| |outputAsTex| |abs| |Beta| |digamma| + |polygamma| |Gamma| |besselJ| |besselY| |besselI| |besselK| |airyAi| |airyBi| + |subNode?| |infLex?| |setEmpty!| |setStatus!| |setCondition!| |setValue!| + |copy| |status| |value| |empty?| |splitNodeOf!| |remove!| |remove| + |subNodeOf?| |nodeOf?| |result| |conditions| |updateStatus!| + |extractSplittingLeaf| |squareMatrix| |transpose| |rightTrim| |leftTrim| + |trim| |split| |position| |replace| |match?| |match| |substring?| |suffix?| + |prefix?| |upperCase!| |upperCase| |lowerCase!| |lowerCase| |KrullNumber| + |numberOfVariables| |algebraicDecompose| |transcendentalDecompose| + |internalDecompose| |decompose| |upDateBranches| |printInfo| |preprocess| + |internalZeroSetSplit| |internalAugment| |stack| |size?| |possiblyInfinite?| + |explicitlyFinite?| |nextItem| |init| |step| |upperBound| |lowerBound| + |iterationVar| |infiniteProduct| |evenInfiniteProduct| |oddInfiniteProduct| + |generalInfiniteProduct| |filterUntil| |filterWhile| |generate| |showAll?| + |showAllElements| |output| |cons| |delay| |findCycle| |repeating?| |repeating| + |exquo| |recip| |integers| |oddintegers| |int| |mapmult| |deriv| |gderiv| + |compose| |addiag| |lazyIntegrate| |nlde| |powern| |mapdiv| |lazyGintegrate| + |power| |sincos| |sinhcosh| |asin| |acos| |atan| |acot| |asec| |acsc| |sinh| + |cosh| |tanh| |coth| |sech| |csch| |asinh| |acosh| |atanh| |acoth| |asech| + |acsch| |subresultantVector| |primitivePart| |pointData| |parent| |level| + |extractProperty| |extractClosed| |extractIndex| |extractPoint| |traverse| + |defineProperty| |closeComponent| |modifyPoint| |addPointLast| |addPoint2| + |addPoint| |merge| |deepCopy| |shallowCopy| |numberOfChildren| |children| + |child| |birth| |internal?| |root?| |leaf?| |rhs| |lhs| |construct| + |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT LT |list| |string| + |argscript| |superscript| |subscript| |script| |scripts| |scripted?| |name| + |resetNew| |symFunc| |symbolTableOf| |argumentListOf| |returnTypeOf| + |printHeader| |returnType!| |argumentList!| |endSubProgram| + |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| + |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| + |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| + |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| + |solve| |triangularSystems| |loadNativeModule| |nativeModuleExtension| + |hostByteOrder| |hostPlatform| |rootDirectory| |bumprow| |bumptab| |bumptab1| + |untab| |bat1| |bat| |tab1| |tab| |lex| |slex| |inverse| |maxrow| |mr| + |tableau| |listOfLists| |operator| |tanSum| |tanAn| |tanNa| |table| + |initTable!| |printInfo!| |startStats!| |printStats!| |clearTable!| + |usingTable?| |printingInfo?| |makingStats?| |extractIfCan| |insert!| + |interpretString| |stripCommentsAndBlanks| |setPrologue!| |setTex!| + |setEpilogue!| |prologue| |new| |tex| |epilogue| |display| |endOfFile?| + |readIfCan!| |readLineIfCan!| |readLine!| |writeLine!| |sign| |nonQsign| + |direction| |createThreeSpace| |pi| |cyclicParents| |cyclicEqual?| + |cyclicEntries| |cyclicCopy| |tree| |cyclic?| |cos| |cot| |csc| |sec| |sin| + |tan| |complexNormalize| |complexElementary| |trigs| |real| |imag| |real?| + |complexForm| |UpTriBddDenomInv| |LowTriBddDenomInv| |simplify| |htrigs| + |simplifyExp| |simplifyLog| |expandPower| |expandLog| |cos2sec| |cosh2sech| + |cot2trig| |coth2trigh| |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| + |sinh2csch| |tan2trig| |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| + |coth2tanh| |removeCosSq| |removeSinSq| |removeCoshSq| |removeSinhSq| + |expandTrigProducts| |fintegrate| |coefficient| |coHeight| |extendIfCan| + |algebraicVariables| |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| + |reduceByQuasiMonic| |collectQuasiMonic| |removeZero| |initiallyReduce| + |headReduce| |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| + |initiallyReduced?| |headReduced?| |stronglyReduced?| |reduced?| |normalized?| + |quasiComponent| |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| + |closed?| |open?| |setClosed| |tube| |point| |unitVector| |cosSinInfo| + |loopPoints| |select| |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| + |getOrder| |less?| |userOrdered?| |largest| |more?| |setVariableOrder| + |getVariableOrder| |resetVariableOrder| |prime?| |sample| |bitior| |bitand| + |rationalFunction| |taylorIfCan| |taylor| |removeZeroes| |taylorRep| |factor| + |factorSquareFree| |henselFact| |hasHi| |segment| SEGMENT |fmecg| + |commonDenominator| |clearDenominator| |splitDenominator| + |monicRightFactorIfCan| |rightFactorIfCan| |leftFactorIfCan| + |monicDecomposeIfCan| |monicCompleteDecompose| |divideIfCan| |noKaratsuba| + |karatsubaOnce| |karatsuba| |separate| |pseudoDivide| |pseudoQuotient| + |composite| |subResultantGcd| |resultant| |discriminant| |differentiate| + |pseudoRemainder| |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| + |divideExponents| |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| + |approximate| |truncate| |order| |center| |terms| |squareFreePart| + |BumInSepFFE| |multiplyExponents| |laurentIfCan| |laurent| |laurentRep| + |rationalPower| |puiseux| |dominantTerm| |limitPlus| |split!| |setlast!| + |setrest!| |setelt| |setfirst!| |cycleSplit!| |concat!| |cycleTail| + |cycleLength| |cycleEntry| |third| |second| |tail| |last| |rest| |elt| |first| + |concat| |invmultisect| |multisect| |revert| |generalLambert| |evenlambert| + |oddlambert| |lambert| |lagrange| |univariatePolynomial| |integrate| ** + |polynomial| |multiplyCoefficients| |quoByVar| |coefficients| |series| + |stFunc1| |stFunc2| |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| |mpsode| + UP2UTS UTS2UP LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| + |outerProduct| |dot| - |zero| + |vector| |scan| |reduce| |graphCurves| + |drawCurves| |update| |show| |scale| |connect| |region| |points| |units| + |getGraph| |putGraph| |graphs| |graphStates| |graphState| |makeViewport2D| + |viewport2D| |getPickedPoints| |key| |close| |write| |colorDef| |reset| + |intensity| |lighting| |clipSurface| |showClipRegion| |showRegion| + |hitherPlane| |eyeDistance| |perspective| |translate| |zoom| |rotate| + |drawStyle| |outlineRender| |diagonals| |axes| |controlPanel| |viewpoint| + |dimensions| |title| |resize| |move| |options| |modifyPointData| |subspace| + |makeViewport3D| |viewport3D| |viewDeltaYDefault| |viewDeltaXDefault| + |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| |pointColorDefault| + |lineColorDefault| |axesColorDefault| |unitsColorDefault| |pointSizeDefault| + |viewPosDefault| |viewSizeDefault| |viewDefaults| |viewWriteDefault| + |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| |tubePointsDefault| + |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| |sts2stst| |clikeUniv| + |weierstrass| |qqq| |integralBasis| |localIntegralBasis| |qualifier| + |mainExpression| |condition| |changeWeightLevel| |characteristicSerie| + |characteristicSet| |medialSet| |Hausdorff| |Frobenius| |transcendenceDegree| + |extensionDegree| |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| + |mirror| |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| + |LiePolyIfCan| |coerce| |trunc| |degree| / |quasiRegular| |quasiRegular?| + |constant| |constant?| |coef| |mindeg| |maxdeg| |#| |map| |reductum| * + |RemainderList| |unexpand| |expand| |shape| |youngDiagram| Y |triangSolve| + |univariateSolve| |realSolve| |positiveSolve| |squareFree| |convert| + |linearlyDependentOverZ?| |linearDependenceOverZ| |solveLinearlyOverQ| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-558))) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4089 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-633 #0#) -4089 (|has| |#1| (-1068 (-419 (-558)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-630 (-886)) . T) ((-175) . T) ((-631 (-171 (-229))) |has| |#1| (-1050)) ((-631 (-171 (-391))) |has| |#1| (-1050)) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-631 (-914 (-391))) |has| |#1| (-631 (-914 (-391)))) ((-631 (-914 (-558))) |has| |#1| (-631 (-914 (-558)))) ((-631 #1=(-1201 |#1|)) . T) ((-236 $) -4089 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -4089 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -4089 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1233)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -4089 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-414) |has| |#1| (-363)) ((-381) -4089 (|has| |#1| (-381)) (|has| |#1| (-363))) ((-363) |has| |#1| (-363)) ((-383 |#1| #1#) . T) ((-422 |#1| #1#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-412 |#1|) . T) ((-424 |#1|) . T) ((-464) -4089 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-505) |has| |#1| (-1233)) ((-526 (-1207) |#1|) |has| |#1| (-526 (-1207) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-569) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-666 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 #2=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 |#1|) . T) ((-660 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-658 #2#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-737 |#1|) . T) ((-737 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-744 |#1| #1#) . T) ((-746) . T) ((-920 $ #3=(-1207)) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-926 (-1207)) |has| |#1| (-926 (-1207))) ((-928 #3#) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-910 (-391)) |has| |#1| (-910 (-391))) ((-910 (-558)) |has| |#1| (-910 (-558))) ((-908 |#1|) . T) ((-938) -12 (|has| |#1| (-319)) (|has| |#1| (-938))) ((-949) -4089 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1032) -12 (|has| |#1| (-1032)) (|has| |#1| (-1233))) ((-1068 (-419 (-558))) |has| |#1| (-1068 (-419 (-558)))) ((-1068 (-558)) |has| |#1| (-1068 (-558))) ((-1068 |#1|) . T) ((-1081 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1081 |#1|) . T) ((-1081 $) . T) ((-1086 #0#) -4089 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1086 |#1|) . T) ((-1086 $) . T) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1182) |has| |#1| (-363)) ((-1233) |has| |#1| (-1233)) ((-1236) |has| |#1| (-1233)) ((-1247) . 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T) ((-23) . T) ((-25) . T) ((-38 #1=(-419 (-558))) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1232)) ((-95) |has| |#1| (-1232)) ((-102) . T) ((-111 #1# #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4034 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-633 #1#) -4034 (|has| |#1| (-1067 (-419 (-558)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-630 (-885)) . T) ((-175) . T) ((-631 (-171 (-229))) |has| |#1| (-1049)) ((-631 (-171 (-391))) |has| |#1| (-1049)) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-631 (-913 (-391))) |has| |#1| (-631 (-913 (-391)))) ((-631 (-913 (-558))) |has| |#1| (-631 (-913 (-558)))) ((-631 #2=(-1200 |#1|)) . T) ((-236 $) -4034 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -4034 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -4034 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1232)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -4034 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-414) |has| |#1| (-363)) ((-381) -4034 (|has| |#1| (-363)) (|has| |#1| (-381))) ((-363) |has| |#1| (-363)) ((-383 |#1| #2#) . T) ((-422 |#1| #2#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-412 |#1|) . T) ((-424 |#1|) . T) ((-464) -4034 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-505) |has| |#1| (-1232)) ((-526 (-1206) |#1|) |has| |#1| (-526 (-1206) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-569) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-666 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 #3=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 |#1|) . T) ((-660 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-658 #3#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-737 |#1|) . T) ((-737 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-744 |#1| #2#) . T) ((-746) . T) ((-919 $ #4=(-1206)) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-925 (-1206)) |has| |#1| (-925 (-1206))) ((-927 #4#) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-909 (-391)) |has| |#1| (-909 (-391))) ((-909 (-558)) |has| |#1| (-909 (-558))) ((-907 |#1|) . T) ((-937) -12 (|has| |#1| (-319)) (|has| |#1| (-937))) ((-948) -4034 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1031) -12 (|has| |#1| (-1031)) (|has| |#1| (-1232))) ((-1067 (-419 (-558))) |has| |#1| (-1067 (-419 (-558)))) ((-1067 (-558)) |has| |#1| (-1067 (-558))) ((-1067 |#1|) . T) ((-1080 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1080 |#1|) . T) ((-1080 $) . T) ((-1085 #1#) -4034 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1085 |#1|) . T) ((-1085 $) . T) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1181) |has| |#1| (-363)) ((-1232) |has| |#1| (-1232)) ((-1235) |has| |#1| (-1232)) ((-1246) . 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(|:| |relerr| (-229)))) (-5 *2 (-1184 (-229))) (-5 *1 (-195)))) (-1757 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1206)) (-5 *5 (-1118 (-863 (-229)))) (-5 *2 (-661 (-229))) (-5 *1 (-195)))) (-1567 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-391)) (-5 *1 (-195)))) (-1782 (*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-1781 (*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-1566 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (-5 *1 (-195)))) (-1565 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-195))))) +(-10 -7 (-15 -1565 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1566 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1781 ((-229) (-1118 (-863 (-229))))) (-15 -1782 ((-229) (-1118 (-863 (-229))))) (-15 -1567 ((-391) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1757 ((-661 (-229)) (-326 (-229)) (-1206) (-1118 (-863 (-229))))) (-15 -1759 ((-1184 (-229)) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1777 ((-1188) (-229))) (-15 -1779 ((-661 (-1188)) (-661 (-229)))) (-15 -1780 ((-661 (-1188)) (-1184 (-229)))) (-15 -3047 ((-1188) 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$) NIL T ELT))) (((-196) (-807)) (T -196)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 66 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 66 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) (((-197) (-807)) (T -197)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 80 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 80 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) (((-198) (-807)) (T -198)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 63 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 63 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) (((-199) (-807)) (T -199)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 76 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 76 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) (((-200) (-807)) (T -200)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 93 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 93 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) (((-201) (-807)) (T -201)) NIL (-807) -((-2940 (((-114) $ $) NIL T ELT)) (-2923 (((-1065) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) 90 T ELT) (((-1065) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1065)) NIL T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189)) (|:| |extra| (-1065))) (-1093) (-2 (|:| |fn| (-326 (-229))) (|:| -2972 (-661 (-1119 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3514 (((-1189) $) NIL T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT)) (-2638 (((-114) $ $) NIL T ELT)) (-4241 (((-114) $ $) NIL T ELT))) +((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 90 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) 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T) ((-102) -4089 (|has| |#2| (-1131)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|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|) -4089 (|has| |#2| (-1079)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -4089 (|has| |#2| (-1079)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-633 #0=(-419 (-558))) -12 (|has| |#2| (-1068 (-419 (-558)))) (|has| |#2| (-1131))) ((-633 (-558)) -4089 (|has| |#2| (-1079)) (-12 (|has| |#2| (-1068 (-558))) (|has| |#2| (-1131)))) ((-633 |#2|) |has| |#2| (-1131)) ((-630 (-886)) -4089 (|has| |#2| (-1131)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-630 (-886))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-630 (-1297 |#2|)) . T) ((-236 $) -4089 (-12 (|has| |#2| (-239)) (|has| |#2| (-1079))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1079)))) ((-234 |#2|) |has| |#2| (-1079)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1079))) ((-239) -4089 (-12 (|has| |#2| (-239)) (|has| |#2| (-1079))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1079)))) ((-274 |#2|) |has| |#2| (-1079)) ((-298 #1=(-558) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1079)) ((-424 |#2|) |has| |#2| (-1131)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((-666 (-558)) -4089 (|has| |#2| (-1079)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-666 |#2|) -4089 (|has| |#2| (-1079)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-666 $) |has| |#2| (-1079)) ((-668 #2=(-558)) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1079))) ((-668 |#2|) -4089 (|has| |#2| (-1079)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1079)) ((-660 |#2|) -4089 (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-658 #2#) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1079))) ((-658 |#2|) |has| |#2| (-1079)) ((-737 |#2|) -4089 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-746) |has| |#2| (-1079)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-870) -4089 (|has| |#2| (-870)) (|has| |#2| (-815))) ((-873) -4089 (|has| |#2| (-870)) (|has| |#2| (-815))) ((-920 $ #3=(-1207)) -4089 (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) (-12 (|has| |#2| (-926 (-1207))) (|has| |#2| (-1079)))) ((-926 (-1207)) -12 (|has| |#2| (-926 (-1207))) (|has| |#2| (-1079))) ((-928 #3#) -4089 (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) (-12 (|has| |#2| (-926 (-1207))) (|has| |#2| (-1079)))) ((-1068 #0#) -12 (|has| |#2| (-1068 (-419 (-558)))) (|has| |#2| (-1131))) ((-1068 (-558)) -12 (|has| |#2| (-1068 (-558))) (|has| |#2| (-1131))) ((-1068 |#2|) |has| |#2| (-1131)) ((-1081 |#2|) -4089 (|has| |#2| (-1079)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1086 |#2|) -4089 (|has| |#2| (-1079)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1079) |has| |#2| (-1079)) ((-1087) |has| |#2| (-1079)) ((-1142) |has| |#2| (-1079)) ((-1131) -4089 (|has| |#2| (-1131)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . T) ((-1305 |#2|) |has| |#2| (-376))) -((-2940 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-4353 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-2048 (($ (-947)) 63 (|has| |#2| (-1079)) ELT)) (-3937 (((-1303) $ (-558) (-558)) NIL (|has| $ (-6 -4507)) ELT)) (-1856 (($ $ $) 69 (|has| |#2| (-815)) ELT)) (-2284 (((-3 $ "failed") $ $) 54 (|has| |#2| (-133)) ELT)) (-2739 (((-791)) NIL (|has| |#2| (-381)) ELT)) (-3551 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4507)) ELT)) (-2219 (($) NIL T CONST)) (-2926 (((-3 (-558) "failed") $) NIL (-12 (|has| |#2| (-1068 (-558))) (|has| |#2| (-1131))) ELT) (((-3 (-419 (-558)) "failed") $) NIL (-12 (|has| |#2| (-1068 (-419 (-558)))) (|has| |#2| (-1131))) ELT) (((-3 |#2| "failed") $) 31 (|has| |#2| (-1131)) ELT)) (-1870 (((-558) $) NIL (-12 (|has| |#2| (-1068 (-558))) (|has| |#2| (-1131))) ELT) (((-419 (-558)) $) NIL (-12 (|has| |#2| (-1068 (-419 (-558)))) (|has| |#2| (-1131))) ELT) ((|#2| $) 29 (|has| |#2| (-1131)) ELT)) (-3512 (((-709 (-558)) (-709 $)) NIL (-12 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|#2| (-23)) CONST)) (-2150 (($) 41 (|has| |#2| (-1079)) CONST)) (-1907 (($ $ (-791)) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1079))) ELT) (($ $) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1079))) ELT) (($ $ (-661 (-1207)) (-661 (-791))) NIL (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) ELT) (($ $ (-1207) (-791)) NIL (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) ELT) (($ $ (-661 (-1207))) NIL (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) ELT) (($ $ (-1207)) NIL (-12 (|has| |#2| (-928 (-1207))) (|has| |#2| (-1079))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1079)) ELT) (($ $ (-1 |#2| |#2|) (-791)) NIL (|has| |#2| (-1079)) ELT)) (-4299 (((-114) $ $) NIL (|has| |#2| (-870)) ELT)) (-4277 (((-114) $ $) NIL (|has| |#2| (-870)) ELT)) (-4241 (((-114) $ $) 28 (|has| |#2| (-102)) ELT)) (-4288 (((-114) $ $) NIL (|has| |#2| (-870)) ELT)) (-4268 (((-114) $ $) 67 (|has| |#2| (-870)) ELT)) (-4370 (($ $ |#2|) NIL (|has| |#2| (-376)) ELT)) (-4354 (($ $ $) NIL (|has| |#2| 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T) ((-102) -4034 (|has| |#2| (-1130)) (|has| |#2| (-1078)) (|has| |#2| (-869)) (|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|) -4034 (|has| |#2| (-1078)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -4034 (|has| |#2| (-1078)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-633 #1=(-419 (-558))) -12 (|has| |#2| (-1067 (-419 (-558)))) (|has| |#2| (-1130))) ((-633 (-558)) -4034 (|has| |#2| (-1078)) (-12 (|has| |#2| (-1067 (-558))) (|has| |#2| (-1130)))) ((-633 |#2|) |has| |#2| (-1130)) ((-630 (-885)) -4034 (|has| |#2| (-1130)) (|has| |#2| (-1078)) (|has| |#2| (-869)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-630 (-885))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-630 (-1296 |#2|)) . T) ((-236 $) -4034 (-12 (|has| |#2| (-239)) (|has| |#2| (-1078))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1078)))) ((-234 |#2|) |has| |#2| (-1078)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1078))) ((-239) -4034 (-12 (|has| |#2| (-239)) (|has| |#2| (-1078))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1078)))) ((-274 |#2|) |has| |#2| (-1078)) ((-298 #2=(-558) |#2|) . T) ((-300 #2# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1130))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1078)) ((-424 |#2|) |has| |#2| (-1130)) ((-501 |#2|) . T) ((-616 #2# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1130))) ((-666 (-558)) -4034 (|has| |#2| (-1078)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-666 |#2|) -4034 (|has| |#2| (-1078)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-666 $) |has| |#2| (-1078)) ((-668 #3=(-558)) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1078))) ((-668 |#2|) -4034 (|has| |#2| (-1078)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1078)) ((-660 |#2|) -4034 (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-658 #3#) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1078))) ((-658 |#2|) |has| |#2| (-1078)) ((-737 |#2|) -4034 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-746) |has| |#2| (-1078)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-869) -4034 (|has| |#2| (-869)) (|has| |#2| (-815))) ((-872) -4034 (|has| |#2| (-869)) (|has| |#2| (-815))) ((-919 $ #4=(-1206)) -4034 (-12 (|has| |#2| (-927 (-1206))) (|has| |#2| (-1078))) (-12 (|has| |#2| (-925 (-1206))) (|has| |#2| (-1078)))) ((-925 (-1206)) -12 (|has| |#2| (-925 (-1206))) (|has| |#2| (-1078))) ((-927 #4#) -4034 (-12 (|has| |#2| (-927 (-1206))) (|has| |#2| (-1078))) (-12 (|has| |#2| (-925 (-1206))) (|has| |#2| (-1078)))) ((-1067 #1#) -12 (|has| |#2| (-1067 (-419 (-558)))) (|has| |#2| (-1130))) ((-1067 (-558)) -12 (|has| |#2| (-1067 (-558))) (|has| |#2| (-1130))) ((-1067 |#2|) |has| |#2| (-1130)) ((-1080 |#2|) -4034 (|has| |#2| (-1078)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1085 |#2|) -4034 (|has| |#2| (-1078)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1078) |has| |#2| (-1078)) ((-1086) |has| |#2| (-1078)) ((-1141) |has| |#2| (-1078)) ((-1130) -4034 (|has| |#2| (-1130)) (|has| |#2| (-1078)) (|has| |#2| (-869)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1246) . T) ((-1304 |#2|) |has| |#2| (-376))) +((-3044 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-3683 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-4214 (($ (-946)) 63 (|has| |#2| (-1078)) ELT)) (-2421 (((-1302) $ (-558) (-558)) NIL (|has| $ (-6 -4503)) ELT)) (-2881 (($ $ $) 69 (|has| |#2| (-815)) ELT)) (-1434 (((-3 $ "failed") $ $) 54 (|has| |#2| (-133)) ELT)) (-3615 (((-791)) NIL (|has| |#2| (-381)) ELT)) (-4295 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4503)) ELT)) (-4231 (($) NIL T CONST)) (-3652 (((-3 (-558) #1="failed") $) NIL (-12 (|has| |#2| (-1067 (-558))) (|has| |#2| (-1130))) ELT) (((-3 (-419 (-558)) #1#) $) NIL (-12 (|has| |#2| (-1067 (-419 (-558)))) (|has| |#2| (-1130))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1130)) ELT)) (-3651 (((-558) $) NIL (-12 (|has| |#2| (-1067 (-558))) (|has| |#2| (-1130))) ELT) (((-419 (-558)) $) NIL (-12 (|has| |#2| (-1067 (-419 (-558)))) (|has| |#2| (-1130))) ELT) ((|#2| $) 29 (|has| |#2| (-1130)) ELT)) (-2501 (((-709 (-558)) (-709 $)) NIL (-12 (|has| 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T) ((-569) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-666 #0#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #0#) |has| |#1| (-38 (-419 (-558)))) ((-668 #1=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-658 #1#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #0#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-746) . T) ((-920 $ #2=(-1207)) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-920 $ |#3|) . T) ((-926 (-1207)) |has| |#1| (-926 (-1207))) ((-926 |#3|) . T) ((-928 #2#) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-928 |#3|) . T) ((-910 (-391)) -12 (|has| |#1| (-910 (-391))) (|has| |#3| (-910 (-391)))) ((-910 (-558)) -12 (|has| |#1| (-910 (-558))) (|has| |#3| (-910 (-558)))) ((-978 |#1| |#4| |#3|) . T) ((-938) |has| |#1| (-938)) ((-1068 (-419 (-558))) |has| |#1| (-1068 (-419 (-558)))) ((-1068 (-558)) |has| |#1| (-1068 (-558))) ((-1068 |#1|) . T) ((-1068 |#2|) . T) ((-1068 |#3|) . T) ((-1081 #0#) |has| |#1| (-38 (-419 (-558)))) ((-1081 |#1|) . T) ((-1081 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1086 #0#) |has| |#1| (-38 (-419 (-558)))) ((-1086 |#1|) . T) ((-1086 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1247) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #1=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1#) -4034 (|has| |#1| (-1067 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 |#2|) . T) ((-633 |#3|) . T) ((-633 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-630 (-885)) . 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range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) 36 T ELT)) (-1911 (((-1303)) 11 T ELT))) -(((-572) (-10 -8 (-15 -1900 ($)) (-15 -1911 ((-1303))) (-15 -2693 ((-661 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) $)) (-15 -1920 ($ (-661 (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3606 ($ (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not 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range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (-15 -2065 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) (T -572)) -((-2065 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-572)))) (-4016 (*1 *2 *1) (-12 (-5 *2 (-661 (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-572)))) (-3118 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| 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(-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (-5 *1 (-572)))) (-1920 (*1 *1 *2) (-12 (-5 *2 (-661 (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-572)))) (-2693 (*1 *2 *1) (-12 (-5 *2 (-661 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-572)))) 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|lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3606 ($ (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-15 -3118 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -4016 ((-661 (-2 (|:| -4312 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2065 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (-15 -2065 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2972 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) -((-4449 (((-1201 (-419 (-1201 |#2|))) |#2| (-628 |#2|) (-628 |#2|) (-1201 |#2|)) 35 T ELT)) (-1946 (((-3 (-2 (|:| 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T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1=(-419 (-558))) |has| |#1| (-1067 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-630 (-885)) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-381) |has| |#1| (-381)) ((-351 |#1|) . T) ((-424 |#1|) . T) ((-526 (-1206) |#1|) |has| |#1| (-526 (-1206) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-660 |#1|) . T) ((-737 |#1|) . T) ((-746) . T) ((-869) |has| |#1| (-869)) ((-872) |has| |#1| (-869)) ((-1067 #1#) |has| |#1| (-1067 (-419 (-558)))) ((-1067 (-558)) |has| |#1| (-1067 (-558))) ((-1067 |#1|) . T) ((-1080 |#1|) . T) ((-1085 |#1|) . T) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1246) . 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T)) -((-2940 (((-114) $ $) NIL T ELT)) (-4353 (((-114) $) NIL T ELT)) (-2284 (((-3 $ "failed") $ $) NIL T ELT)) (-2739 (((-791)) NIL (|has| |#1| (-381)) ELT)) (-2219 (($) NIL T CONST)) (-2926 (((-3 |#1| "failed") $) NIL T ELT) (((-3 (-1026 |#1|) "failed") $) 35 T ELT) (((-3 (-558) "failed") $) NIL (-4089 (|has| (-1026 |#1|) (-1068 (-558))) (|has| |#1| (-1068 (-558)))) ELT) (((-3 (-419 (-558)) "failed") $) NIL (-4089 (|has| (-1026 |#1|) (-1068 (-419 (-558)))) (|has| |#1| (-1068 (-419 (-558))))) ELT)) (-1870 ((|#1| $) NIL T ELT) (((-1026 |#1|) $) 33 T ELT) (((-558) $) NIL (-4089 (|has| (-1026 |#1|) (-1068 (-558))) (|has| |#1| (-1068 (-558)))) ELT) (((-419 (-558)) $) NIL (-4089 (|has| (-1026 |#1|) (-1068 (-419 (-558)))) (|has| |#1| (-1068 (-419 (-558))))) ELT)) (-1802 (((-3 $ "failed") $) NIL T ELT)) (-1347 ((|#1| $) 16 T ELT)) (-1948 (((-3 (-419 (-558)) "failed") $) NIL (|has| |#1| (-557)) ELT)) (-1940 (((-114) $) NIL (|has| |#1| (-557)) ELT)) (-1931 (((-419 (-558)) $) NIL (|has| |#1| (-557)) ELT)) (-3438 (($) NIL (|has| |#1| (-381)) ELT)) (-2361 (((-114) $) NIL T ELT)) (-1901 (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 28 T ELT) (($ (-1026 |#1|) (-1026 |#1|)) 29 T ELT)) (-1768 ((|#1| $) NIL T ELT)) (-2625 (($ $ $) NIL (|has| |#1| (-870)) ELT)) (-3915 (($ $ $) NIL (|has| |#1| (-870)) ELT)) (-3026 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-2541 (((-947) $) NIL (|has| |#1| (-381)) ELT)) (-3514 (((-1189) $) NIL T ELT)) (-4187 (($ $) NIL (|has| |#1| (-376)) ELT)) (-3053 (($ (-947)) NIL (|has| |#1| (-381)) ELT)) (-1873 ((|#1| $) 22 T ELT)) (-1880 ((|#1| $) 20 T ELT)) (-1890 ((|#1| $) 18 T ELT)) (-3001 ((|#1| $) 26 T ELT)) (-3013 ((|#1| $) 25 T ELT)) (-3024 ((|#1| $) 24 T ELT)) (-1864 ((|#1| $) 23 T ELT)) (-1466 (((-1150) $) NIL T ELT)) (-3410 (($ $ (-661 |#1|) (-661 |#1|)) NIL (|has| |#1| (-321 |#1|)) ELT) (($ $ |#1| |#1|) NIL (|has| |#1| (-321 |#1|)) ELT) (($ $ (-305 |#1|)) NIL (|has| |#1| (-321 |#1|)) ELT) (($ $ (-661 (-305 |#1|))) NIL (|has| |#1| (-321 |#1|)) ELT) (($ $ (-661 (-1207)) (-661 |#1|)) NIL (|has| |#1| (-526 (-1207) |#1|)) ELT) (($ $ (-1207) |#1|) NIL (|has| |#1| (-526 (-1207) |#1|)) ELT)) (-2204 (($ $ |#1|) NIL (|has| |#1| (-298 |#1| |#1|)) ELT)) (-3078 (((-547) $) NIL (|has| |#1| (-631 (-547))) ELT)) (-3036 (($ $) NIL T ELT)) (-3451 (((-886) $) NIL T ELT) (($ (-558)) NIL T ELT) (($ |#1|) NIL T ELT) (($ (-1026 |#1|)) 30 T ELT) (($ (-419 (-558))) NIL (-4089 (|has| (-1026 |#1|) (-1068 (-419 (-558)))) (|has| |#1| (-1068 (-419 (-558))))) ELT)) (-2894 (((-711 $) $) NIL (|has| |#1| (-147)) ELT)) (-1711 (((-791)) NIL T CONST)) (-2638 (((-114) $ $) NIL T ELT)) (-2322 ((|#1| $) NIL (|has| |#1| (-1090)) ELT)) (-2139 (($) 8 T CONST)) (-2150 (($) 12 T CONST)) (-4299 (((-114) $ $) NIL (|has| |#1| (-870)) ELT)) (-4277 (((-114) $ $) NIL (|has| |#1| (-870)) ELT)) (-4241 (((-114) $ $) NIL T ELT)) (-4288 (((-114) $ $) NIL (|has| |#1| (-870)) ELT)) (-4268 (((-114) $ $) NIL (|has| |#1| (-870)) ELT)) (-4354 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-4338 (($ $ $) NIL T ELT)) (** (($ $ (-947)) NIL T ELT) (($ $ (-791)) NIL T ELT)) (* (($ (-947) $) NIL T ELT) (($ (-791) $) NIL T ELT) (($ (-558) $) NIL T ELT) (($ $ $) 40 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) NIL T ELT))) -(((-820 |#1|) (-13 (-818 |#1|) (-424 (-1026 |#1|)) (-10 -8 (-15 -1901 ($ (-1026 |#1|) (-1026 |#1|))))) (-175)) (T -820)) -((-1901 (*1 *1 *2 *2) (-12 (-5 *2 (-1026 *3)) (-4 *3 (-175)) (-5 *1 (-820 *3))))) -(-13 (-818 |#1|) (-424 (-1026 |#1|)) (-10 -8 (-15 -1901 ($ (-1026 |#1|) (-1026 |#1|))))) -((-3026 ((|#3| (-1 |#4| |#2|) |#1|) 20 T ELT))) -(((-821 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3026 (|#3| (-1 |#4| |#2|) |#1|))) (-818 |#2|) (-175) (-818 |#4|) (-175)) (T -821)) -((-3026 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-818 *6)) (-5 *1 (-821 *4 *5 *2 *6)) (-4 *4 (-818 *5))))) -(-10 -7 (-15 -3026 (|#3| (-1 |#4| |#2|) |#1|))) -((-2940 (((-114) $ $) 7 T ELT)) (-2563 (((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189))) (-1093) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 18 T ELT)) (-3514 (((-1189) $) 11 T ELT)) (-1466 (((-1150) $) 12 T ELT)) (-3451 (((-886) $) 13 T ELT)) (-2638 (((-114) $ $) 6 T ELT)) (-1912 (((-1065) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 17 T ELT)) (-4241 (((-114) $ $) 8 T ELT))) +(((-23) . 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T)) +((-3044 (((-114) $ $) NIL T ELT)) (-3683 (((-114) $) NIL T ELT)) (-1434 (((-3 $ "failed") $ $) NIL T ELT)) (-3615 (((-791)) NIL (|has| |#1| (-381)) ELT)) (-4231 (($) NIL T CONST)) (-3652 (((-3 |#1| #1="failed") $) NIL T ELT) (((-3 (-1025 |#1|) #1#) $) 35 T ELT) (((-3 (-558) #1#) $) NIL (-4034 (|has| (-1025 |#1|) (-1067 (-558))) (|has| |#1| (-1067 (-558)))) ELT) (((-3 (-419 (-558)) #1#) $) NIL (-4034 (|has| (-1025 |#1|) (-1067 (-419 (-558)))) (|has| |#1| (-1067 (-419 (-558))))) ELT)) (-3651 ((|#1| $) NIL T ELT) (((-1025 |#1|) $) 33 T ELT) (((-558) $) NIL (-4034 (|has| (-1025 |#1|) (-1067 (-558))) (|has| |#1| (-1067 (-558)))) ELT) (((-419 (-558)) $) NIL (-4034 (|has| (-1025 |#1|) (-1067 (-419 (-558)))) (|has| |#1| (-1067 (-419 (-558))))) ELT)) (-3964 (((-3 $ "failed") $) NIL T ELT)) (-4150 ((|#1| $) 16 T ELT)) (-3502 (((-3 (-419 (-558)) "failed") $) NIL (|has| |#1| (-557)) ELT)) (-3501 (((-114) $) NIL (|has| |#1| (-557)) ELT)) (-3500 (((-419 (-558)) $) NIL (|has| |#1| (-557)) ELT)) 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(** (($ $ (-946)) NIL T ELT) (($ $ (-791)) NIL T ELT)) (* (($ (-946) $) NIL T ELT) (($ (-791) $) NIL T ELT) (($ (-558) $) NIL T ELT) (($ $ $) 40 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) NIL T ELT))) +(((-820 |#1|) (-13 (-818 |#1|) (-424 (-1025 |#1|)) (-10 -8 (-15 -2887 ($ (-1025 |#1|) (-1025 |#1|))))) (-175)) (T -820)) +((-2887 (*1 *1 *2 *2) (-12 (-5 *2 (-1025 *3)) (-4 *3 (-175)) (-5 *1 (-820 *3))))) +(-13 (-818 |#1|) (-424 (-1025 |#1|)) (-10 -8 (-15 -2887 ($ (-1025 |#1|) (-1025 |#1|))))) +((-4465 ((|#3| (-1 |#4| |#2|) |#1|) 20 T ELT))) +(((-821 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -4465 (|#3| (-1 |#4| |#2|) |#1|))) (-818 |#2|) (-175) (-818 |#4|) (-175)) (T -821)) +((-4465 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-818 *6)) (-5 *1 (-821 *4 *5 *2 *6)) (-4 *4 (-818 *5))))) +(-10 -7 (-15 -4465 (|#3| (-1 |#4| |#2|) |#1|))) +((-3044 (((-114) $ $) 7 T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188))) (-1092) (-2 (|:| |xinit| (-229)) (|:| 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(-229)) (|:| |xend| (-229)) (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-1065))))) -(-13 (-1131) (-10 -7 (-15 -2563 ((-2 (|:| -2563 (-391)) (|:| |explanations| (-1189))) (-1093) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1912 ((-1065) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) -(((-102) . T) ((-630 (-886)) . T) ((-1131) . T) ((-1247) . T)) -((-1921 (((-2 (|:| |particular| |#2|) (|:| -2565 (-661 |#2|))) |#3| |#2| (-1207)) 19 T ELT))) -(((-823 |#1| |#2| |#3|) (-10 -7 (-15 -1921 ((-2 (|:| |particular| |#2|) (|:| -2565 (-661 |#2|))) |#3| |#2| (-1207)))) (-13 (-319) (-1068 (-558)) (-658 (-558)) (-149)) (-13 (-29 |#1|) (-1233) (-988)) (-678 |#2|)) (T -823)) -((-1921 (*1 *2 *3 *4 *5) (-12 (-5 *5 (-1207)) (-4 *6 (-13 (-319) (-1068 (-558)) (-658 (-558)) (-149))) (-4 *4 (-13 (-29 *6) (-1233) (-988))) (-5 *2 (-2 (|:| |particular| *4) (|:| -2565 (-661 *4)))) (-5 *1 (-823 *6 *4 *3)) (-4 *3 (-678 *4))))) -(-10 -7 (-15 -1921 ((-2 (|:| |particular| |#2|) (|:| -2565 (-661 |#2|))) |#3| |#2| (-1207)))) -((-3231 (((-3 |#2| "failed") |#2| (-115) (-305 |#2|) (-661 |#2|)) 28 T ELT) (((-3 |#2| "failed") (-305 |#2|) (-115) (-305 |#2|) (-661 |#2|)) 29 T ELT) (((-3 (-2 (|:| |particular| |#2|) (|:| -2565 (-661 |#2|))) |#2| "failed") |#2| (-115) (-1207)) 17 T ELT) (((-3 (-2 (|:| |particular| |#2|) (|:| -2565 (-661 |#2|))) |#2| "failed") (-305 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #1=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1#) -4034 (|has| |#1| (-1067 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 |#3|) . T) ((-633 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464))) ((-630 (-885)) . 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T) ((-1080 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1085 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1085 |#1|) . T) ((-1085 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-175))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1246) . 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T) ((-23) . T) ((-47 |#1| #0=(-558)) . T) ((-25) . T) ((-38 #1=(-419 (-558))) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 #1# #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-633 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1068 (-1207)))) ((-633 |#1|) |has| |#1| (-175)) ((-633 |#2|) . T) ((-633 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-630 (-886)) . T) ((-175) -4089 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1050))) ((-631 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1050))) ((-631 (-547)) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-547)))) ((-631 (-914 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-914 (-391))))) ((-631 (-914 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-914 (-558))))) ((-236 $) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-239) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1142)) ((-302) -4089 (|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 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1207) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -4089 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-666 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 |#2|) |has| |#1| (-376)) ((-666 $) . T) ((-668 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-668 #3=(-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-660 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-660 |#1|) |has| |#1| (-175)) ((-660 |#2|) |has| |#1| (-376)) ((-660 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-658 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-658 |#2|) |has| |#1| (-376)) ((-737 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-737 |#1|) |has| |#1| (-175)) ((-737 |#2|) |has| |#1| (-376)) ((-737 $) -4089 (|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))) ((-869) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-870))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-873) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-870))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-920 $ #4=(-1207)) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-926 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-926 (-1207))))) ((-926 (-1207)) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-926 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-926 (-1207))))) ((-928 #4#) -4089 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-926 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-926 (-1207))))) ((-910 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-910 (-391)))) ((-910 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-910 (-558)))) ((-908 |#2|) |has| |#1| (-376)) ((-938) -12 (|has| |#1| (-376)) (|has| |#2| (-938))) ((-1003 |#1| #0# (-1112)) . T) ((-949) |has| |#1| (-376)) ((-1021 |#2|) |has| |#1| (-376)) ((-1032) |has| |#1| (-38 (-419 (-558)))) ((-1050) -12 (|has| |#1| (-376)) (|has| |#2| (-1050))) ((-1068 (-419 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-1068 (-558)))) ((-1068 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-1068 (-558)))) ((-1068 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1068 (-1207)))) ((-1068 |#2|) . T) ((-1081 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-376)) ((-1081 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1086 #1#) -4089 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1086 |#1|) . T) ((-1086 |#2|) |has| |#1| (-376)) ((-1086 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-419 (-558)))) ((-1236) |has| |#1| (-38 (-419 (-558)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1259 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-791)) . T) ((-25) . T) ((-38 #1=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1#) -4089 (|has| |#1| (-1068 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 #2=(-1112)) . T) ((-633 |#1|) . T) ((-633 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-630 (-886)) . T) ((-175) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-547)) -12 (|has| (-1112) (-631 (-547))) (|has| |#1| (-631 (-547)))) ((-631 (-914 (-391))) -12 (|has| (-1112) (-631 (-914 (-391)))) (|has| |#1| (-631 (-914 (-391))))) ((-631 (-914 (-558))) -12 (|has| (-1112) (-631 (-914 (-558)))) (|has| |#1| (-631 (-914 (-558))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-419 $) (-419 $)) |has| |#1| (-569)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-424 |#1|) . T) ((-464) -4089 (|has| |#1| (-938)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-569) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-666 #1#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #1#) |has| |#1| (-38 (-419 (-558)))) ((-668 #3=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-658 #3#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #1#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-746) . T) ((-920 $ #2#) . T) ((-920 $ #4=(-1207)) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-926 #2#) . T) ((-926 (-1207)) |has| |#1| (-926 (-1207))) ((-928 #2#) . T) ((-928 #4#) -4089 (|has| |#1| (-928 (-1207))) (|has| |#1| (-926 (-1207)))) ((-910 (-391)) -12 (|has| (-1112) (-910 (-391))) (|has| |#1| (-910 (-391)))) ((-910 (-558)) -12 (|has| (-1112) (-910 (-558))) (|has| |#1| (-910 (-558)))) ((-978 |#1| #0# #2#) . T) ((-938) |has| |#1| (-938)) ((-949) |has| |#1| (-376)) ((-1068 (-419 (-558))) |has| |#1| (-1068 (-419 (-558)))) ((-1068 (-558)) |has| |#1| (-1068 (-558))) ((-1068 #2#) . T) ((-1068 |#1|) . T) ((-1081 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1081 |#1|) . T) ((-1081 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1086 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1086 |#1|) . T) ((-1086 $) -4089 (|has| |#1| (-938)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . T) ((-1252) |has| |#1| (-938))) -((-3026 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) -(((-1274 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3026 (|#4| (-1 |#3| |#1|) |#2|))) (-1079) (-1273 |#1|) (-1079) (-1273 |#3|)) (T -1274)) -((-3026 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1079)) (-4 *6 (-1079)) (-4 *2 (-1273 *6)) (-5 *1 (-1274 *5 *4 *6 *2)) (-4 *4 (-1273 *5))))) -(-10 -7 (-15 -3026 (|#4| (-1 |#3| |#1|) |#2|))) -((-4086 (((-661 (-1112)) $) 34 T ELT)) (-4263 (($ $) 31 T ELT)) (-4061 (($ |#2| |#3|) NIL T ELT) (($ $ (-1112) |#3|) 28 T ELT) (($ $ (-661 (-1112)) (-661 |#3|)) 27 T ELT)) (-4224 (($ $) 14 T ELT)) (-4234 ((|#2| $) 12 T ELT)) (-3612 ((|#3| $) 10 T ELT))) -(((-1275 |#1| |#2| |#3|) (-10 -8 (-15 -4086 ((-661 (-1112)) |#1|)) (-15 -4061 (|#1| |#1| (-661 (-1112)) (-661 |#3|))) (-15 -4061 (|#1| |#1| (-1112) |#3|)) (-15 -4263 (|#1| |#1|)) (-15 -4061 (|#1| |#2| |#3|)) (-15 -3612 (|#3| |#1|)) (-15 -4224 (|#1| |#1|)) (-15 -4234 (|#2| |#1|))) (-1276 |#2| |#3|) (-1079) (-814)) (T -1275)) -NIL -(-10 -8 (-15 -4086 ((-661 (-1112)) |#1|)) (-15 -4061 (|#1| |#1| (-661 (-1112)) (-661 |#3|))) (-15 -4061 (|#1| |#1| (-1112) |#3|)) (-15 -4263 (|#1| |#1|)) (-15 -4061 (|#1| |#2| |#3|)) (-15 -3612 (|#3| |#1|)) (-15 -4224 (|#1| |#1|)) (-15 -4234 (|#2| |#1|))) -((-2940 (((-114) $ $) 7 T ELT)) (-4353 (((-114) $) 21 T ELT)) (-4086 (((-661 (-1112)) $) 92 T ELT)) (-4011 (((-1207) $) 126 T ELT)) (-1830 (((-2 (|:| -1833 $) (|:| -4493 $) (|:| |associate| $)) $) 68 (|has| |#1| (-569)) ELT)) (-1820 (($ $) 69 (|has| |#1| (-569)) ELT)) (-1803 (((-114) $) 71 (|has| |#1| (-569)) ELT)) (-1446 (($ $ |#2|) 121 T ELT) (($ $ |#2| |#2|) 120 T ELT)) (-1469 (((-1185 (-2 (|:| |k| |#2|) (|:| |c| |#1|))) $) 127 T ELT)) (-2284 (((-3 $ "failed") $ $) 25 T ELT)) (-2219 (($) 22 T CONST)) (-4263 (($ $) 77 T ELT)) (-1802 (((-3 $ "failed") $) 42 T ELT)) (-4304 (((-114) $) 91 T ELT)) (-1456 ((|#2| $) 123 T ELT) ((|#2| $ |#2|) 122 T ELT)) (-2361 (((-114) $) 40 T ELT)) (-1512 (($ $ (-947)) 124 T ELT)) (-3527 (((-114) $) 79 T ELT)) (-4061 (($ |#1| |#2|) 78 T ELT) (($ $ (-1112) |#2|) 94 T ELT) (($ $ (-661 (-1112)) (-661 |#2|)) 93 T ELT)) (-3026 (($ (-1 |#1| |#1|) $) 80 T ELT)) (-4224 (($ $) 82 T ELT)) (-4234 ((|#1| $) 83 T ELT)) (-3514 (((-1189) $) 11 T ELT)) (-1466 (((-1150) $) 12 T ELT)) (-1435 (($ $ |#2|) 118 T ELT)) (-2928 (((-3 $ "failed") $ $) 67 (|has| |#1| (-569)) ELT)) (-3410 (((-1185 |#1|) $ |#1|) 117 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) ELT)) (-2204 ((|#1| $ |#2|) 128 T ELT) (($ $ $) 104 (|has| |#2| (-1142)) ELT)) (-3662 (($ $ (-1207)) 116 (-12 (|has| |#1| (-926 (-1207))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-661 (-1207))) 114 (-12 (|has| |#1| (-926 (-1207))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1207) (-791)) 113 (-12 (|has| |#1| (-926 (-1207))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-661 (-1207)) (-661 (-791))) 112 (-12 (|has| |#1| (-926 (-1207))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 108 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ 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(-661 (-1207)) (-661 (-791))) 109 (-12 (|has| |#1| (-926 (-1207))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 107 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-791)) 105 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-4241 (((-114) $ $) 8 T ELT)) (-4370 (($ $ |#1|) 75 (|has| |#1| (-376)) ELT)) (-4354 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4338 (($ $ $) 18 T ELT)) (** (($ $ (-947)) 33 T ELT) (($ $ (-791)) 41 T ELT)) (* (($ (-947) $) 17 T ELT) (($ (-791) $) 20 T ELT) (($ (-558) $) 29 T ELT) (($ $ $) 32 T ELT) (($ $ |#1|) 85 T ELT) (($ |#1| $) 84 T ELT) (($ (-419 (-558)) $) 73 (|has| |#1| (-38 (-419 (-558)))) ELT) (($ $ (-419 (-558))) 72 (|has| |#1| (-38 (-419 (-558)))) ELT))) -(((-1276 |#1| |#2|) (-142) (-1079) (-814)) (T -1276)) -((-1469 (*1 *2 *1) (-12 (-4 *1 (-1276 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-814)) (-5 *2 (-1185 (-2 (|:| |k| *4) (|:| |c| *3)))))) (-4011 (*1 *2 *1) (-12 (-4 *1 (-1276 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-814)) (-5 *2 (-1207)))) (-2980 (*1 *2 *1) (-12 (-4 *1 (-1276 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1079)))) (-1512 (*1 *1 *1 *2) (-12 (-5 *2 (-947)) (-4 *1 (-1276 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-814)))) (-1456 (*1 *2 *1) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-814)))) (-1456 (*1 *2 *1 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-814)))) (-1446 (*1 *1 *1 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-814)))) (-1446 (*1 *1 *1 *2 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-814)))) (-3595 (*1 *2 *1 *3) (-12 (-4 *1 (-1276 *2 *3)) (-4 *3 (-814)) (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3451 (*2 (-1207)))) (-4 *2 (-1079)))) (-1435 (*1 *1 *1 *2) (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-814)))) (-3410 (*1 *2 *1 *3) (-12 (-4 *1 (-1276 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-814)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1185 *3))))) -(-13 (-1003 |t#1| |t#2| (-1112)) (-298 |t#2| |t#1|) (-10 -8 (-15 -1469 ((-1185 (-2 (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (-15 -4011 ((-1207) $)) (-15 -2980 (|t#1| $)) (-15 -1512 ($ $ (-947))) (-15 -1456 (|t#2| $)) (-15 -1456 (|t#2| $ |t#2|)) (-15 -1446 ($ $ |t#2|)) (-15 -1446 ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (-15 -3451 (|t#1| (-1207)))) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -3595 (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (-15 -1435 ($ $ |t#2|)) (IF (|has| |t#2| (-1142)) (-6 (-298 $ $)) |%noBranch|) (IF (|has| |t#1| (-15 * (|t#1| |t#2| |t#1|))) (PROGN (-6 (-240)) (IF (|has| |t#1| (-926 (-1207))) (-6 (-926 (-1207))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -3410 ((-1185 |t#1|) $ |t#1|)) |%noBranch|))) -(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4089 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #0#) |has| |#1| (-38 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) |has| |#1| (-175)) ((-633 $) |has| |#1| (-569)) ((-630 (-886)) . T) ((-175) -4089 (|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| (-1142)) ((-302) |has| |#1| (-569)) ((-569) |has| |#1| (-569)) ((-666 #0#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #0#) |has| |#1| (-38 (-419 (-558)))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) |has| |#1| (-569)) ((-737 #0#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) |has| |#1| (-569)) ((-746) . T) ((-920 $ #1=(-1207)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1207)))) ((-926 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1207)))) ((-928 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1207)))) ((-1003 |#1| |#2| (-1112)) . T) ((-1081 #0#) |has| |#1| (-38 (-419 (-558)))) ((-1081 |#1|) . T) ((-1081 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1086 #0#) |has| |#1| (-38 (-419 (-558)))) ((-1086 |#1|) . T) ((-1086 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1247) . T)) -((-1483 ((|#2| |#2|) 12 T ELT)) (-3754 (((-417 |#2|) |#2|) 14 T ELT)) (-1499 (((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-558))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-558)))) 30 T ELT))) -(((-1277 |#1| |#2|) (-10 -7 (-15 -3754 ((-417 |#2|) |#2|)) (-15 -1483 (|#2| |#2|)) (-15 -1499 ((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-558))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-558)))))) (-569) (-13 (-1273 |#1|) (-569) (-10 -8 (-15 -3654 ($ $ $))))) (T -1277)) -((-1499 (*1 *2 *2) (-12 (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-558)))) (-4 *4 (-13 (-1273 *3) (-569) (-10 -8 (-15 -3654 ($ $ $))))) (-4 *3 (-569)) (-5 *1 (-1277 *3 *4)))) (-1483 (*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-1277 *3 *2)) (-4 *2 (-13 (-1273 *3) (-569) (-10 -8 (-15 -3654 ($ $ $))))))) (-3754 (*1 *2 *3) (-12 (-4 *4 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T) ((-1081 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1086 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1086 |#1|) . T) ((-1086 $) -4089 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1079) . T) ((-1087) . T) ((-1142) . T) ((-1131) . T) ((-1233) |has| |#1| (-38 (-419 (-558)))) ((-1236) |has| |#1| (-38 (-419 (-558)))) ((-1247) . T) ((-1276 |#1| #0#) . 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(-1302 3394983 3395778 3396515 "VIEWDEF" 3398000 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3383927 3386531 3388704 "VIEW3D" 3392832 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3375944 3377838 3379417 "VIEW2D" 3382370 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3374044 3374439 3374845 "VIEW" 3375560 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3372597 3372880 3373198 "VECTOR2" 3373774 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3367617 3372367 3372459 "VECTOR" 3372540 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3360676 3365321 3365364 "VECTCAT" 3366359 NIL VECTCAT (NIL T) -9 NIL 3366946 NIL) (-1295 3359618 3359944 3360334 "VECTCAT-" 3360339 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3359024 3359269 3359389 "VARIABLE" 3359533 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3358957 3358962 3358992 "UTYPE" 3358997 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3357765 3357941 3358203 "UTSODETL" 3358783 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3355157 3355665 3356189 "UTSODE" 3357306 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3345167 3351090 3351133 "UTSCAT" 3352245 NIL UTSCAT (NIL T) -9 NIL 3353003 NIL) (-1289 3342293 3343237 3344226 "UTSCAT-" 3344231 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3341914 3341963 3342096 "UTS2" 3342244 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3333231 3339675 3340155 "UTS" 3341492 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3327209 3330041 3330084 "URAGG" 3332154 NIL URAGG (NIL T) -9 NIL 3332877 NIL) (-1285 3324241 3325209 3326233 "URAGG-" 3326238 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3319617 3322876 3323341 "UPXSSING" 3323905 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3312046 3319521 3319593 "UPXSCONS" 3319598 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3300804 3308248 3308310 "UPXSCCA" 3308884 NIL UPXSCCA (NIL T T) -9 NIL 3309117 NIL) (-1281 3300424 3300527 3300701 "UPXSCCA-" 3300706 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3289082 3296251 3296294 "UPXSCAT" 3296942 NIL UPXSCAT (NIL T) -9 NIL 3297551 NIL) (-1279 3288506 3288591 3288770 "UPXS2" 3288997 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3279998 3287888 3288152 "UPXS" 3288300 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3278634 3278905 3279256 "UPSQFREE" 3279741 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3271465 3274900 3274955 "UPSCAT" 3276035 NIL UPSCAT (NIL T T) -9 NIL 3276801 NIL) (-1275 3270621 3270876 3271203 "UPSCAT-" 3271208 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3270242 3270291 3270424 "UPOLYC2" 3270572 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3254390 3263369 3263412 "UPOLYC" 3265513 NIL UPOLYC (NIL T) -9 NIL 3266734 NIL) (-1272 3245259 3248158 3251298 "UPOLYC-" 3251303 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3244580 3244705 3244869 "UPMP" 3245148 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3244127 3244214 3244353 "UPDIVP" 3244493 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3242665 3242944 3243260 "UPDECOMP" 3243876 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3241878 3242008 3242194 "UPCDEN" 3242549 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3241391 3241466 3241615 "UP2" 3241803 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3231987 3241074 3241203 "UP" 3241310 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3231192 3231329 3231534 "UNISEG2" 3231830 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3229545 3230396 3230673 "UNISEG" 3230950 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3228587 3228785 3229011 "UNIFACT" 3229361 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3215318 3228491 3228563 "ULSCONS" 3228568 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3195135 3208398 3208460 "ULSCCAT" 3209098 NIL ULSCCAT (NIL T T) -9 NIL 3209387 NIL) (-1260 3194131 3194430 3194818 "ULSCCAT-" 3194823 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3182586 3189677 3189720 "ULSCAT" 3190583 NIL ULSCAT (NIL T) -9 NIL 3191314 NIL) (-1258 3182010 3182095 3182274 "ULS2" 3182501 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3163841 3181322 3181564 "ULS" 3181826 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3162760 3163460 3163574 "UINT8" 3163685 T UINT8 (NIL) -8 NIL NIL 3163777) (-1255 3161678 3162378 3162492 "UINT64" 3162603 T UINT64 (NIL) -8 NIL NIL 3162695) (-1254 3160596 3161296 3161410 "UINT32" 3161521 T UINT32 (NIL) -8 NIL NIL 3161613) (-1253 3159514 3160214 3160328 "UINT16" 3160439 T UINT16 (NIL) -8 NIL NIL 3160531) (-1252 3157593 3158760 3158790 "UFD" 3159002 T UFD (NIL) -9 NIL 3159116 NIL) (-1251 3157375 3157433 3157528 "UFD-" 3157533 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3156433 3156640 3156856 "UDVO" 3157181 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3154199 3154658 3155129 "UDPO" 3155997 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3153911 3154154 3154185 "TYPEAST" 3154190 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3153844 3153849 3153879 "TYPE" 3153884 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3152797 3153017 3153257 "TWOFACT" 3153638 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3151772 3152206 3152441 "TUPLE" 3152597 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3149409 3149982 3150521 "TUBETOOL" 3151255 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3148215 3148456 3148698 "TUBE" 3149202 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3136464 3140972 3141069 "TSETCAT" 3146338 NIL TSETCAT (NIL T T T T) -9 NIL 3147870 NIL) (-1241 3130932 3132796 3134687 "TSETCAT-" 3134692 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3125118 3129904 3130187 "TS" 3130684 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3119591 3120604 3121533 "TRMANIP" 3124254 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3119020 3119095 3119258 "TRIMAT" 3119523 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3116832 3117123 3117480 "TRIGMNIP" 3118769 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3116316 3116465 3116495 "TRIGCAT" 3116708 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3115961 3116064 3116205 "TRIGCAT-" 3116210 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3112686 3114819 3115100 "TREE" 3115715 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3111792 3112488 3112518 "TRANFUN" 3112553 T TRANFUN (NIL) -9 NIL 3112619 NIL) (-1232 3111011 3111262 3111542 "TRANFUN-" 3111547 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3110809 3110847 3110908 "TOPSP" 3110972 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3110139 3110272 3110426 "TOOLSIGN" 3110690 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3108653 3109316 3109555 "TEXTFILE" 3109922 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3108428 3108465 3108537 "TEX1" 3108616 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3106232 3106881 3107310 "TEX" 3108021 T TEX (NIL) -8 NIL NIL NIL) (-1226 3105868 3105943 3106033 "TEMUTL" 3106164 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3103962 3104302 3104627 "TBCMPPK" 3105591 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3095396 3102048 3102104 "TBAGG" 3102504 NIL TBAGG (NIL T T) -9 NIL 3102715 NIL) (-1223 3090280 3091954 3093708 "TBAGG-" 3093713 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3089646 3089771 3089916 "TANEXP" 3090169 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3089097 3089421 3089511 "TALGOP" 3089591 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3088491 3088608 3088746 "TABLEAU" 3088994 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3081619 3088348 3088441 "TABLE" 3088446 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3076149 3077447 3078695 "TABLBUMP" 3080405 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3075359 3075518 3075699 "SYSTEM" 3075990 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3071764 3072517 3073300 "SYSSOLP" 3074610 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3071526 3071719 3071750 "SYSPTR" 3071755 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3070365 3071057 3071183 "SYSNNI" 3071369 NIL SYSNNI (NIL NIL) -8 NIL NIL 3071461) (-1213 3069572 3070127 3070206 "SYSINT" 3070266 NIL SYSINT (NIL NIL) -8 NIL NIL 3070311) (-1212 3065670 3066850 3067560 "SYNTAX" 3068884 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3062750 3063430 3064062 "SYMTAB" 3065060 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3057849 3058901 3059884 "SYMS" 3061789 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3054755 3057300 3057533 "SYMPOLY" 3057651 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3054260 3054347 3054470 "SYMFUNC" 3054667 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3050058 3051572 3052385 "SYMBOL" 3053469 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3043531 3045286 3047006 "SWITCH" 3048360 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3036292 3042487 3042781 "SUTS" 3043295 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3027784 3035674 3035938 "SUPXS" 3036086 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3026931 3027070 3027287 "SUPFRACF" 3027652 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3026546 3026611 3026724 "SUP2" 3026866 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3017090 3026164 3026290 "SUP" 3026455 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3015514 3015812 3016168 "SUMRF" 3016789 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3014837 3014915 3015107 "SUMFS" 3015435 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 2996703 3014149 3014391 "SULS" 3014653 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 2996251 2996525 2996595 "SUCHTAST" 2996655 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 2995492 2995776 2995916 "SUCH" 2996159 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 2989131 2990398 2991357 "SUBSPACE" 2994580 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 2988551 2988651 2988815 "SUBRESP" 2989019 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2982562 2983844 2984991 "STTFNC" 2987451 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2975756 2977227 2978538 "STTF" 2981298 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2966872 2968938 2970732 "STTAYLOR" 2973997 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2959740 2966736 2966819 "STRTBL" 2966824 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2954251 2959449 2959548 "STRING" 2959663 T STRING (NIL) -8 NIL NIL NIL) (-1188 2953755 2953838 2953982 "STREAM3" 2954168 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2952719 2952920 2953155 "STREAM2" 2953568 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2952401 2952459 2952552 "STREAM1" 2952661 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2944515 2950020 2950631 "STREAM" 2951825 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2943507 2943712 2943943 "STINPROD" 2944331 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2942622 2942996 2943144 "STEPAST" 2943381 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2942118 2942363 2942393 "STEP" 2942487 T STEP (NIL) -9 NIL 2942558 NIL) (-1181 2935288 2942017 2942094 "STBL" 2942099 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2929469 2934082 2934125 "STAGG" 2934557 NIL STAGG (NIL T) -9 NIL 2934736 NIL) (-1179 2927021 2927773 2928645 "STAGG-" 2928650 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2925107 2926791 2926883 "STACK" 2926964 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2924424 2924937 2924967 "SRING" 2924972 T SRING (NIL) -9 NIL 2924992 NIL) (-1176 2916546 2922565 2923021 "SREGSET" 2924054 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1175 2908893 2910340 2911853 "SRDCMPK" 2915152 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1174 2901307 2906252 2906282 "SRAGG" 2907585 T SRAGG (NIL) -9 NIL 2908193 NIL) (-1173 2900258 2900579 2900958 "SRAGG-" 2900963 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1172 2893956 2899205 2899626 "SQMATRIX" 2899884 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1171 2887482 2890674 2891401 "SPLTREE" 2893301 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1170 2883307 2884138 2884784 "SPLNODE" 2886908 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1169 2882282 2882587 2882617 "SPFCAT" 2883061 T SPFCAT (NIL) -9 NIL NIL NIL) (-1168 2880977 2881229 2881493 "SPECOUT" 2882040 T SPECOUT (NIL) -7 NIL NIL NIL) (-1167 2871623 2873941 2873971 "SPADXPT" 2878649 T SPADXPT (NIL) -9 NIL 2880815 NIL) (-1166 2871378 2871424 2871493 "SPADPRSR" 2871576 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1165 2868981 2871333 2871364 "SPADAST" 2871369 T SPADAST (NIL) -8 NIL NIL NIL) (-1164 2860582 2862685 2862728 "SPACEC" 2867101 NIL SPACEC (NIL T) -9 NIL 2868917 NIL) (-1163 2858382 2860514 2860563 "SPACE3" 2860568 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1162 2857114 2857305 2857596 "SORTPAK" 2858187 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1161 2855176 2855509 2855921 "SOLVETRA" 2856778 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1160 2854214 2854448 2854709 "SOLVESER" 2854949 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1159 2849446 2850406 2851401 "SOLVERAD" 2853266 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1158 2845171 2845870 2846599 "SOLVEFOR" 2848813 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1157 2838889 2844519 2844616 "SNTSCAT" 2844621 NIL SNTSCAT (NIL T T T T) -9 NIL 2844691 NIL) (-1156 2832440 2837212 2837603 "SMTS" 2838579 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1155 2826162 2832328 2832405 "SMP" 2832410 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1154 2824291 2824622 2825020 "SMITH" 2825859 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1153 2815930 2820870 2820973 "SMATCAT" 2822324 NIL SMATCAT (NIL NIL T T T) -9 NIL 2822874 NIL) (-1152 2812702 2813693 2814871 "SMATCAT-" 2814876 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1151 2810282 2811910 2811953 "SKAGG" 2812214 NIL SKAGG (NIL T) -9 NIL 2812349 NIL) (-1150 2805802 2809765 2809942 "SINT" 2810094 T SINT (NIL) -8 NIL NIL 2810249) (-1149 2805568 2805612 2805678 "SIMPAN" 2805758 T SIMPAN (NIL) -7 NIL NIL NIL) (-1148 2804388 2804627 2804902 "SIGNRF" 2805327 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1147 2803203 2803372 2803656 "SIGNEF" 2804217 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1146 2802443 2802786 2802910 "SIGAST" 2803101 T SIGAST (NIL) -8 NIL NIL NIL) (-1145 2801668 2801978 2802118 "SIG" 2802325 T SIG (NIL) -8 NIL NIL NIL) (-1144 2799320 2799812 2800318 "SHP" 2801209 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1143 2792758 2799221 2799297 "SHDP" 2799302 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1142 2792269 2792509 2792539 "SGROUP" 2792632 T SGROUP (NIL) -9 NIL 2792694 NIL) (-1141 2792121 2792153 2792226 "SGROUP-" 2792231 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1140 2788840 2789610 2790333 "SGCF" 2791420 T SGCF (NIL) -7 NIL NIL NIL) (-1139 2782656 2788286 2788383 "SFRTCAT" 2788388 NIL SFRTCAT (NIL T T T T) -9 NIL 2788427 NIL) (-1138 2775975 2777095 2778231 "SFRGCD" 2781639 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1137 2768993 2770174 2771360 "SFQCMPK" 2774908 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1136 2768595 2768702 2768813 "SFORT" 2768934 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1135 2767521 2768435 2768556 "SEXOF" 2768561 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1134 2763110 2764017 2764112 "SEXCAT" 2766734 NIL SEXCAT (NIL T T T T T) -9 NIL 2767294 NIL) (-1133 2762025 2762991 2763059 "SEX" 2763064 T SEX (NIL) -8 NIL NIL NIL) (-1132 2760147 2760738 2761043 "SETMN" 2761766 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1131 2759677 2759865 2759895 "SETCAT" 2760012 T SETCAT (NIL) -9 NIL 2760097 NIL) (-1130 2759445 2759509 2759608 "SETCAT-" 2759613 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1129 2755659 2757906 2757949 "SETAGG" 2758819 NIL SETAGG (NIL T) -9 NIL 2759159 NIL) (-1128 2755081 2755233 2755470 "SETAGG-" 2755475 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1127 2752004 2755015 2755063 "SET" 2755068 NIL SET (NIL T) -8 NIL NIL NIL) (-1126 2751387 2751700 2751801 "SEQAST" 2751925 T SEQAST (NIL) -8 NIL NIL NIL) (-1125 2750514 2750880 2750941 "SEGXCAT" 2751227 NIL SEGXCAT (NIL T T) -9 NIL 2751347 NIL) (-1124 2749439 2749707 2749750 "SEGCAT" 2750272 NIL SEGCAT (NIL T) -9 NIL 2750493 NIL) (-1123 2749054 2749119 2749232 "SEGBIND2" 2749374 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1122 2747944 2748417 2748625 "SEGBIND" 2748881 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1121 2747463 2747745 2747822 "SEGAST" 2747889 T SEGAST (NIL) -8 NIL NIL NIL) (-1120 2746672 2746808 2747012 "SEG2" 2747307 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1119 2745588 2746338 2746520 "SEG" 2746525 NIL SEG (NIL T) -8 NIL NIL NIL) (-1118 2744821 2745523 2745570 "SDVAR" 2745575 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1117 2736179 2744591 2744721 "SDPOL" 2744726 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1116 2734748 2735038 2735357 "SCPKG" 2735894 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1115 2733870 2734084 2734276 "SCOPE" 2734578 T SCOPE (NIL) -8 NIL NIL NIL) (-1114 2733066 2733224 2733403 "SCACHE" 2733725 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1113 2732650 2732884 2732914 "SASTCAT" 2732919 T SASTCAT (NIL) -9 NIL 2732932 NIL) (-1112 2732053 2732485 2732561 "SAOS" 2732596 T SAOS (NIL) -8 NIL NIL NIL) (-1111 2731612 2731653 2731826 "SAERFFC" 2732012 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1110 2731199 2731240 2731399 "SAEFACT" 2731571 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1109 2724247 2731096 2731176 "SAE" 2731181 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1108 2722550 2722882 2723283 "RURPK" 2723913 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1107 2721127 2721493 2721798 "RULESET" 2722384 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1106 2720697 2720921 2721004 "RULECOLD" 2721079 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1105 2717812 2718450 2718908 "RULE" 2720378 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1104 2717596 2717630 2717701 "RTVALUE" 2717763 T RTVALUE (NIL) -8 NIL NIL NIL) (-1103 2717007 2717313 2717407 "RSTRCAST" 2717524 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1102 2711777 2712650 2713570 "RSETGCD" 2716206 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2700455 2706085 2706182 "RSETCAT" 2710301 NIL RSETCAT (NIL T T T T) -9 NIL 2711398 NIL) (-1100 2698274 2698921 2699745 "RSETCAT-" 2699750 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1099 2690582 2692036 2693556 "RSDCMPK" 2696873 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1098 2688451 2689014 2689088 "RRCC" 2690174 NIL RRCC (NIL T T) -9 NIL 2690518 NIL) (-1097 2687772 2687976 2688255 "RRCC-" 2688260 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1096 2687155 2687468 2687569 "RPTAST" 2687693 T RPTAST (NIL) -8 NIL NIL NIL) (-1095 2659541 2670267 2670334 "RPOLCAT" 2681000 NIL RPOLCAT (NIL T T T) -9 NIL 2684160 NIL) (-1094 2650511 2653379 2656501 "RPOLCAT-" 2656506 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1093 2641078 2648722 2649204 "ROUTINE" 2650051 T ROUTINE (NIL) -8 NIL NIL NIL) (-1092 2637141 2640704 2640844 "ROMAN" 2640960 T ROMAN (NIL) -8 NIL NIL NIL) (-1091 2635253 2636001 2636261 "ROIRC" 2636946 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1090 2631026 2633795 2633825 "RNS" 2634094 T RNS (NIL) -9 NIL 2634350 NIL) (-1089 2629433 2629918 2630452 "RNS-" 2630527 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1088 2628394 2628798 2629000 "RNGBIND" 2629284 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1087 2627687 2628191 2628221 "RNG" 2628226 T RNG (NIL) -9 NIL 2628247 NIL) (-1086 2626982 2627460 2627503 "RMODULE" 2627508 NIL RMODULE (NIL T) -9 NIL 2627535 NIL) (-1085 2625806 2625912 2626248 "RMCAT2" 2626883 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1084 2622422 2625152 2625449 "RMATRIX" 2625568 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1083 2615032 2617509 2617624 "RMATCAT" 2620983 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2621965 NIL) (-1082 2614371 2614554 2614861 "RMATCAT-" 2614866 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1081 2613944 2614158 2614201 "RLINSET" 2614263 NIL RLINSET (NIL T) -9 NIL 2614307 NIL) (-1080 2613505 2613586 2613714 "RINTERP" 2613863 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1079 2612429 2613103 2613133 "RING" 2613189 T RING (NIL) -9 NIL 2613281 NIL) (-1078 2612209 2612265 2612362 "RING-" 2612367 NIL RING- (NIL T) -8 NIL NIL NIL) (-1077 2611020 2611287 2611545 "RIDIST" 2611973 T RIDIST (NIL) -7 NIL NIL NIL) (-1076 2601759 2610488 2610694 "RGCHAIN" 2610868 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1075 2601017 2601501 2601542 "RGBCSPC" 2601600 NIL RGBCSPC (NIL T) -9 NIL 2601652 NIL) (-1074 2600083 2600542 2600583 "RGBCMDL" 2600815 NIL RGBCMDL (NIL T) -9 NIL 2600929 NIL) (-1073 2599723 2599792 2599895 "RFFACTOR" 2600014 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1072 2599442 2599483 2599580 "RFFACT" 2599682 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1071 2597493 2597923 2598305 "RFDIST" 2599082 T RFDIST (NIL) -7 NIL NIL NIL) (-1070 2594433 2595101 2595771 "RF" 2596857 NIL RF (NIL T) -7 NIL NIL NIL) (-1069 2593880 2593978 2594141 "RETSOL" 2594335 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1068 2593498 2593596 2593639 "RETRACT" 2593772 NIL RETRACT (NIL T) -9 NIL 2593859 NIL) (-1067 2593341 2593372 2593459 "RETRACT-" 2593464 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1066 2592889 2593163 2593233 "RETAST" 2593293 T RETAST (NIL) -8 NIL NIL NIL) (-1065 2585353 2592542 2592669 "RESULT" 2592784 T RESULT (NIL) -8 NIL NIL NIL) (-1064 2583788 2584622 2584821 "RESRING" 2585256 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1063 2583412 2583473 2583571 "RESLATC" 2583725 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1062 2583111 2583152 2583259 "REPSQ" 2583371 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1061 2582802 2582843 2582954 "REPDB" 2583070 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1060 2576634 2578091 2579314 "REP2" 2581614 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1059 2572937 2573692 2574500 "REP1" 2575861 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1058 2570317 2570939 2571541 "REP" 2572357 T REP (NIL) -7 NIL NIL NIL) (-1057 2562439 2568458 2568914 "REGSET" 2569947 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1056 2561148 2561587 2561837 "REF" 2562224 NIL REF (NIL T) -8 NIL NIL NIL) (-1055 2560513 2560628 2560795 "REDORDER" 2561032 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1054 2555884 2559726 2559953 "RECLOS" 2560341 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1053 2554918 2555117 2555332 "REALSOLV" 2555691 T REALSOLV (NIL) -7 NIL NIL NIL) (-1052 2551365 2552203 2553087 "REAL0Q" 2554083 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1051 2546918 2547954 2549015 "REAL0" 2550346 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1050 2546752 2546805 2546835 "REAL" 2546840 T REAL (NIL) -9 NIL 2546875 NIL) (-1049 2546163 2546469 2546563 "RDUCEAST" 2546680 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1048 2545562 2545640 2545847 "RDIV" 2546085 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1047 2544612 2544804 2545017 "RDIST" 2545384 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1046 2543197 2543496 2543868 "RDETRS" 2544320 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1045 2540991 2541463 2542001 "RDETR" 2542739 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1044 2539610 2539894 2540291 "RDEEFS" 2540707 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1043 2538113 2538425 2538850 "RDEEF" 2539298 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1042 2531592 2535067 2535097 "RCFIELD" 2536392 T RCFIELD (NIL) -9 NIL 2537123 NIL) (-1041 2529548 2530160 2530856 "RCFIELD-" 2530931 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1040 2525711 2527621 2527664 "RCAGG" 2528748 NIL RCAGG (NIL T) -9 NIL 2529213 NIL) (-1039 2525321 2525433 2525596 "RCAGG-" 2525601 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1038 2524638 2524768 2524933 "RATRET" 2525205 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1037 2524179 2524258 2524379 "RATFACT" 2524566 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1036 2523457 2523607 2523759 "RANDSRC" 2524049 T RANDSRC (NIL) -7 NIL NIL NIL) (-1035 2523185 2523235 2523308 "RADUTIL" 2523406 T RADUTIL (NIL) -7 NIL NIL NIL) (-1034 2515330 2522016 2522327 "RADIX" 2522908 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1033 2504945 2515172 2515302 "RADFF" 2515307 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1032 2504574 2504667 2504697 "RADCAT" 2504857 T RADCAT (NIL) -9 NIL NIL NIL) (-1031 2504344 2504404 2504504 "RADCAT-" 2504509 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1030 2502369 2504114 2504206 "QUEUE" 2504287 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1029 2501994 2502043 2502174 "QUATCT2" 2502320 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1028 2494372 2498417 2498459 "QUATCAT" 2499250 NIL QUATCAT (NIL T) -9 NIL 2500016 NIL) (-1027 2490253 2491548 2492938 "QUATCAT-" 2493034 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1026 2486099 2490186 2490234 "QUAT" 2490239 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1025 2483466 2485147 2485190 "QUAGG" 2485571 NIL QUAGG (NIL T) -9 NIL 2485746 NIL) (-1024 2483014 2483288 2483358 "QQUTAST" 2483418 T QQUTAST (NIL) -8 NIL NIL NIL) (-1023 2481925 2482527 2482692 "QFORM" 2482895 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1022 2481550 2481599 2481730 "QFCAT2" 2481876 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1021 2471247 2477397 2477439 "QFCAT" 2478107 NIL QFCAT (NIL T) -9 NIL 2479108 NIL) (-1020 2466581 2468029 2469616 "QFCAT-" 2469712 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1019 2466012 2466146 2466278 "QEQUAT" 2466471 T QEQUAT (NIL) -8 NIL NIL NIL) (-1018 2459030 2460211 2461397 "QCMPACK" 2464945 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2458259 2458441 2458677 "QALGSET2" 2458848 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1016 2455709 2456245 2456675 "QALGSET" 2457914 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1015 2454376 2454618 2454937 "PWFFINTB" 2455482 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1014 2452521 2452719 2453075 "PUSHVAR" 2454190 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1013 2448248 2449464 2449507 "PTRANFN" 2451418 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1012 2446585 2446930 2447254 "PTPACK" 2447959 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1011 2446208 2446271 2446382 "PTFUNC2" 2446522 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1010 2440238 2444997 2445040 "PTCAT" 2445340 NIL PTCAT (NIL T) -9 NIL 2445493 NIL) (-1009 2439887 2439928 2440054 "PSQFR" 2440197 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1008 2438459 2438775 2439111 "PSEUDLIN" 2439585 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1007 2424979 2427554 2429880 "PSETPK" 2436219 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1006 2417798 2420715 2420813 "PSETCAT" 2423854 NIL PSETCAT (NIL T T T T) -9 NIL 2424668 NIL) (-1005 2415523 2416265 2417089 "PSETCAT-" 2417094 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1004 2414836 2415031 2415061 "PSCURVE" 2415333 T PSCURVE (NIL) -9 NIL 2415500 NIL) (-1003 2410559 2412326 2412393 "PSCAT" 2413245 NIL PSCAT (NIL T T T) -9 NIL 2413485 NIL) (-1002 2409553 2409835 2410238 "PSCAT-" 2410243 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1001 2407721 2408612 2408877 "PRTITION" 2409310 T PRTITION (NIL) -8 NIL NIL NIL) (-1000 2407132 2407438 2407532 "PRTDAST" 2407649 T PRTDAST (NIL) -8 NIL NIL NIL) (-999 2396014 2398436 2400624 "PRS" 2404994 NIL PRS (NIL T T) -7 NIL NIL NIL) (-998 2393745 2395336 2395376 "PRQAGG" 2395559 NIL PRQAGG (NIL T) -9 NIL 2395661 NIL) (-997 2392924 2393373 2393401 "PROPLOG" 2393540 T PROPLOG (NIL) -9 NIL 2393655 NIL) (-996 2392522 2392585 2392708 "PROPFUN2" 2392847 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-995 2391819 2391958 2392130 "PROPFUN1" 2392383 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-994 2389800 2390566 2390863 "PROPFRML" 2391555 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-993 2389245 2389376 2389504 "PROPERTY" 2389692 T PROPERTY (NIL) -8 NIL NIL NIL) (-992 2383058 2387411 2388231 "PRODUCT" 2388471 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-991 2382848 2382886 2382945 "PRINT" 2383019 T PRINT (NIL) -7 NIL NIL NIL) (-990 2382164 2382305 2382457 "PRIMES" 2382728 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-989 2380211 2380630 2381096 "PRIMELT" 2381743 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-988 2379928 2379989 2380017 "PRIMCAT" 2380141 T PRIMCAT (NIL) -9 NIL NIL NIL) (-987 2378917 2379113 2379341 "PRIMARR2" 2379746 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-986 2374753 2378855 2378900 "PRIMARR" 2378905 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-985 2374390 2374452 2374563 "PREASSOC" 2374691 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-984 2371355 2373848 2374082 "PR" 2374201 NIL PR (NIL T T) -8 NIL NIL NIL) (-983 2370806 2370963 2370991 "PPCURVE" 2371196 T PPCURVE (NIL) -9 NIL 2371332 NIL) (-982 2370353 2370601 2370684 "PORTNUM" 2370743 T PORTNUM (NIL) -8 NIL NIL NIL) (-981 2367690 2368111 2368703 "POLYROOT" 2369934 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-980 2367067 2367131 2367365 "POLYLIFT" 2367626 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-979 2363288 2363791 2364420 "POLYCATQ" 2366612 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-978 2348936 2355035 2355100 "POLYCAT" 2358614 NIL POLYCAT (NIL T T T) -9 NIL 2360492 NIL) (-977 2342076 2344261 2346638 "POLYCAT-" 2346643 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-976 2341657 2341731 2341851 "POLY2UP" 2342002 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-975 2341283 2341346 2341455 "POLY2" 2341594 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-974 2334498 2340887 2341047 "POLY" 2341156 NIL POLY (NIL T) -8 NIL NIL NIL) (-973 2333159 2333422 2333698 "POLUTIL" 2334272 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-972 2331478 2331791 2332122 "POLTOPOL" 2332881 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-971 2326588 2331412 2331459 "POINT" 2331464 NIL POINT (NIL T) -8 NIL NIL NIL) (-970 2324721 2325132 2325507 "PNTHEORY" 2326233 T PNTHEORY (NIL) -7 NIL NIL NIL) (-969 2323167 2323476 2323875 "PMTOOLS" 2324419 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-968 2322754 2322838 2322955 "PMSYM" 2323083 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-967 2322256 2322331 2322506 "PMQFCAT" 2322679 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-966 2321637 2321735 2321897 "PMPREDFS" 2322157 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-965 2320980 2321102 2321258 "PMPRED" 2321514 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-964 2319634 2319852 2320230 "PMPLCAT" 2320742 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-963 2319160 2319245 2319397 "PMLSAGG" 2319549 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-962 2318627 2318709 2318891 "PMKERNEL" 2319078 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-961 2318238 2318319 2318432 "PMINS" 2318546 NIL PMINS (NIL T) -7 NIL NIL NIL) (-960 2317674 2317749 2317958 "PMFS" 2318163 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-959 2316890 2317020 2317225 "PMDOWN" 2317551 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-958 2316139 2316273 2316436 "PMASSFS" 2316777 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-957 2315282 2315464 2315645 "PMASS" 2315978 T PMASS (NIL) -7 NIL NIL NIL) (-956 2314931 2315005 2315099 "PLOTTOOL" 2315208 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-955 2310583 2311777 2312699 "PLOT3D" 2314029 T PLOT3D (NIL) -8 NIL NIL NIL) (-954 2309471 2309672 2309907 "PLOT1" 2310387 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-953 2303892 2305282 2306430 "PLOT" 2308343 T PLOT (NIL) -8 NIL NIL NIL) (-952 2279067 2283958 2288809 "PLEQN" 2299158 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-951 2278754 2278807 2278910 "PINTERPA" 2279014 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-950 2278060 2278194 2278374 "PINTERP" 2278619 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-949 2276144 2277310 2277338 "PID" 2277535 T PID (NIL) -9 NIL 2277662 NIL) (-948 2275889 2275932 2276007 "PICOERCE" 2276101 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-947 2274985 2275653 2275740 "PI" 2275780 T PI (NIL) -8 NIL NIL 2275847) (-946 2274293 2274444 2274620 "PGROEB" 2274841 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-945 2269732 2270691 2271597 "PGE" 2273407 T PGE (NIL) -7 NIL NIL NIL) (-944 2267813 2268102 2268468 "PGCD" 2269449 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-943 2267139 2267254 2267415 "PFRPAC" 2267697 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-942 2263397 2265687 2266040 "PFR" 2266818 NIL PFR (NIL T) -8 NIL NIL NIL) (-941 2261750 2262030 2262355 "PFOTOOLS" 2263144 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-940 2260265 2260522 2260873 "PFOQ" 2261507 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-939 2258748 2258978 2259334 "PFO" 2260049 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-938 2255832 2257338 2257366 "PFECAT" 2257959 T PFECAT (NIL) -9 NIL 2258336 NIL) (-937 2255280 2255445 2255652 "PFECAT-" 2255657 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-936 2253853 2254135 2254436 "PFBRU" 2255029 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-935 2251682 2252071 2252503 "PFBR" 2253504 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-934 2247628 2251571 2251640 "PF" 2251645 NIL PF (NIL NIL) -8 NIL NIL NIL) (-933 2242682 2243835 2244705 "PERMGRP" 2246791 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-932 2240594 2241706 2241747 "PERMCAT" 2242147 NIL PERMCAT (NIL T) -9 NIL 2242445 NIL) (-931 2240241 2240288 2240412 "PERMAN" 2240547 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-930 2236043 2237750 2238398 "PERM" 2239626 NIL PERM (NIL T) -8 NIL NIL NIL) (-929 2233398 2235708 2235830 "PENDTREE" 2235954 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-928 2232279 2232542 2232583 "PDSPC" 2233116 NIL PDSPC (NIL T) -9 NIL 2233361 NIL) (-927 2231334 2231600 2231962 "PDSPC-" 2231967 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-926 2230048 2230984 2231025 "PDRING" 2231030 NIL PDRING (NIL T) -9 NIL 2231058 NIL) (-925 2228791 2229553 2229607 "PDMOD" 2229612 NIL PDMOD (NIL T T) -9 NIL 2229716 NIL) (-924 2225958 2226784 2227452 "PDEPROB" 2228143 T PDEPROB (NIL) -8 NIL NIL NIL) (-923 2223467 2224007 2224562 "PDEPACK" 2225423 T PDEPACK (NIL) -7 NIL NIL NIL) (-922 2222355 2222569 2222820 "PDECOMP" 2223266 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-921 2219872 2220763 2220791 "PDECAT" 2221578 T PDECAT (NIL) -9 NIL 2222291 NIL) (-920 2219489 2219556 2219610 "PDDOM" 2219775 NIL PDDOM (NIL T T) -9 NIL 2219855 NIL) (-919 2219302 2219338 2219445 "PDDOM-" 2219450 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-918 2219047 2219086 2219176 "PCOMP" 2219263 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-917 2217087 2217848 2218145 "PBWLB" 2218776 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-916 2216713 2216776 2216885 "PATTERN2" 2217024 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-915 2214422 2214858 2215315 "PATTERN1" 2216302 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-914 2206601 2208495 2209833 "PATTERN" 2213105 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-913 2206159 2206232 2206364 "PATRES2" 2206528 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-912 2203425 2204108 2204589 "PATRES" 2205724 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-911 2201278 2201713 2202120 "PATMATCH" 2203092 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-910 2200732 2200983 2201024 "PATMAB" 2201131 NIL PATMAB (NIL T) -9 NIL 2201214 NIL) (-909 2199178 2199586 2199844 "PATLRES" 2200537 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-908 2198716 2198847 2198888 "PATAB" 2198893 NIL PATAB (NIL T) -9 NIL 2199065 NIL) (-907 2196856 2197293 2197716 "PARTPERM" 2198313 T PARTPERM (NIL) -7 NIL NIL NIL) (-906 2196465 2196540 2196642 "PARSURF" 2196787 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-905 2196091 2196154 2196263 "PARSU2" 2196402 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-904 2195849 2195895 2195962 "PARSER" 2196044 T PARSER (NIL) -7 NIL NIL NIL) (-903 2195458 2195533 2195635 "PARSCURV" 2195780 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-902 2195084 2195147 2195256 "PARSC2" 2195395 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-901 2194711 2194781 2194878 "PARPCURV" 2195020 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-900 2194337 2194400 2194509 "PARPC2" 2194648 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-899 2193326 2193710 2193892 "PARAMAST" 2194175 T PARAMAST (NIL) -8 NIL NIL NIL) (-898 2192834 2192932 2193051 "PAN2EXPR" 2193227 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-897 2191527 2191955 2192183 "PALETTE" 2192626 T PALETTE (NIL) -8 NIL NIL NIL) (-896 2189872 2190532 2190892 "PAIR" 2191213 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-895 2182805 2189129 2189324 "PADICRC" 2189726 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-894 2175062 2182149 2182334 "PADICRAT" 2182652 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-893 2171859 2173722 2173762 "PADICCT" 2174343 NIL PADICCT (NIL NIL) -9 NIL 2174625 NIL) (-892 2169875 2171796 2171841 "PADIC" 2171846 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-891 2168820 2169032 2169300 "PADEPAC" 2169662 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-890 2168020 2168165 2168371 "PADE" 2168682 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-889 2166253 2167228 2167508 "OWP" 2167824 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-888 2165698 2165959 2166056 "OVERSET" 2166176 T OVERSET (NIL) -8 NIL NIL NIL) (-887 2164618 2165303 2165475 "OVAR" 2165566 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-886 2152854 2155727 2157927 "OUTFORM" 2162438 T OUTFORM (NIL) -8 NIL NIL NIL) (-885 2152136 2152451 2152578 "OUTBFILE" 2152747 T OUTBFILE (NIL) -8 NIL NIL NIL) (-884 2151413 2151608 2151636 "OUTBCON" 2151954 T OUTBCON (NIL) -9 NIL 2152120 NIL) (-883 2150996 2151126 2151283 "OUTBCON-" 2151288 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-882 2150236 2150381 2150542 "OUT" 2150855 T OUT (NIL) -7 NIL NIL NIL) (-881 2149532 2149965 2150054 "OSI" 2150167 T OSI (NIL) -8 NIL NIL NIL) (-880 2148951 2149373 2149401 "OSGROUP" 2149406 T OSGROUP (NIL) -9 NIL 2149428 NIL) (-879 2147662 2147923 2148208 "ORTHPOL" 2148698 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-878 2144913 2147497 2147618 "OREUP" 2147623 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-877 2142016 2144604 2144731 "ORESUP" 2144855 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-876 2139516 2140044 2140605 "OREPCTO" 2141505 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-875 2132894 2135389 2135430 "OREPCAT" 2137778 NIL OREPCAT (NIL T) -9 NIL 2138882 NIL) (-874 2129867 2130823 2131881 "OREPCAT-" 2131886 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-873 2129059 2129337 2129365 "ORDTYPE" 2129674 T ORDTYPE (NIL) -9 NIL 2129837 NIL) (-872 2128360 2128576 2128831 "ORDTYPE-" 2128836 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-871 2127716 2128099 2128257 "ORDSTRCT" 2128262 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-870 2127214 2127584 2127612 "ORDSET" 2127617 T ORDSET (NIL) -9 NIL 2127639 NIL) (-869 2125865 2126836 2126864 "ORDRING" 2126869 T ORDRING (NIL) -9 NIL 2126898 NIL) (-868 2125116 2125681 2125709 "ORDMON" 2125714 T ORDMON (NIL) -9 NIL 2125735 NIL) (-867 2124260 2124425 2124620 "ORDFUNS" 2124965 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2123475 2123990 2124018 "ORDFIN" 2124083 T ORDFIN (NIL) -9 NIL 2124157 NIL) (-865 2122729 2122868 2123054 "ORDCOMP2" 2123335 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2119076 2121315 2121724 "ORDCOMP" 2122353 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2115597 2116567 2117381 "OPTPROB" 2118282 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2112339 2113038 2113742 "OPTPACK" 2114913 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2109952 2110778 2110806 "OPTCAT" 2111625 T OPTCAT (NIL) -9 NIL 2112275 NIL) (-860 2109270 2109629 2109734 "OPSIG" 2109867 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2109032 2109077 2109143 "OPQUERY" 2109224 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2108338 2108618 2108659 "OPERCAT" 2108871 NIL OPERCAT (NIL T) -9 NIL 2108968 NIL) (-857 2108081 2108149 2108266 "OPERCAT-" 2108271 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2104997 2106392 2106896 "OP" 2107610 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2104290 2104417 2104591 "ONECOMP2" 2104869 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2100903 2103087 2103456 "ONECOMP" 2103954 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2100304 2100428 2100558 "OMSERVER" 2100793 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2096929 2099744 2099784 "OMSAGG" 2099845 NIL OMSAGG (NIL T) -9 NIL 2099909 NIL) (-851 2095504 2095815 2096097 "OMPKG" 2096667 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2093851 2095053 2095222 "OMLO" 2095385 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2092787 2092958 2093178 "OMEXPR" 2093677 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2091872 2092208 2092368 "OMERRK" 2092647 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2091109 2091418 2091554 "OMERR" 2091756 T OMERR (NIL) -8 NIL NIL NIL) (-846 2090500 2090786 2090894 "OMENC" 2091021 T OMENC (NIL) -8 NIL NIL NIL) (-845 2084137 2085580 2086751 "OMDEV" 2089349 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2083170 2083377 2083571 "OMCONN" 2083963 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2082576 2082703 2082731 "OM" 2083030 T OM (NIL) -9 NIL NIL NIL) (-842 2080854 2082046 2082074 "OINTDOM" 2082079 T OINTDOM (NIL) -9 NIL 2082100 NIL) (-841 2077929 2079542 2079879 "OFMONOID" 2080549 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2077163 2077866 2077911 "ODVAR" 2077916 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2074307 2076908 2077063 "ODR" 2077068 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2065719 2074083 2074209 "ODPOL" 2074214 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2059127 2065591 2065696 "ODP" 2065701 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2057869 2058108 2058383 "ODETOOLS" 2058901 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2054812 2055494 2056210 "ODESYS" 2057202 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2049642 2050602 2051627 "ODERTRIC" 2053887 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2049062 2049150 2049344 "ODERED" 2049554 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2045914 2046498 2047175 "ODERAT" 2048485 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2042830 2043338 2043935 "ODEPRRIC" 2045443 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2040725 2041369 2041855 "ODEPROB" 2042364 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2037191 2037730 2038377 "ODEPRIM" 2040204 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2036434 2036542 2036802 "ODEPAL" 2037083 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2032536 2033387 2034251 "ODEPACK" 2035590 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2031579 2031704 2031926 "ODEINT" 2032425 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2025644 2027105 2028552 "ODEIFTBL" 2030152 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2020994 2021828 2022780 "ODEEF" 2024803 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2020337 2020432 2020655 "ODECONST" 2020899 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2018400 2019109 2019137 "ODECAT" 2019742 T ODECAT (NIL) -9 NIL 2020273 NIL) (-821 2018032 2018081 2018208 "OCTCT2" 2018351 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2014532 2017737 2017859 "OCT" 2017942 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2013725 2014325 2014353 "OCAMON" 2014358 T OCAMON (NIL) -9 NIL 2014379 NIL) (-818 2007996 2010768 2010808 "OC" 2011905 NIL OC (NIL T) -9 NIL 2012763 NIL) (-817 2005031 2005971 2006961 "OC-" 2007055 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2004451 2004876 2004904 "OASGP" 2004909 T OASGP (NIL) -9 NIL 2004929 NIL) (-815 2003547 2004174 2004202 "OAMONS" 2004242 T OAMONS (NIL) -9 NIL 2004285 NIL) (-814 2002723 2003282 2003310 "OAMON" 2003368 T OAMON (NIL) -9 NIL 2003420 NIL) (-813 2002581 2002614 2002682 "OAMON-" 2002687 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-812 2001362 2002115 2002143 "OAGROUP" 2002290 T OAGROUP (NIL) -9 NIL 2002383 NIL) (-811 2001065 2001153 2001271 "OAGROUP-" 2001276 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-810 2000747 2000803 2000892 "NUMTUBE" 2001009 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-809 1994266 1995838 1997374 "NUMQUAD" 1999231 T NUMQUAD (NIL) -7 NIL NIL NIL) (-808 1989946 1990980 1992015 "NUMODE" 1993251 T NUMODE (NIL) -7 NIL NIL NIL) (-807 1987227 1988167 1988195 "NUMINT" 1989118 T NUMINT (NIL) -9 NIL 1989882 NIL) (-806 1986139 1986372 1986590 "NUMFMT" 1987029 T NUMFMT (NIL) -7 NIL NIL NIL) (-805 1972322 1975443 1977975 "NUMERIC" 1983646 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-804 1966140 1971770 1971865 "NTSCAT" 1971870 NIL NTSCAT (NIL T T T T) -9 NIL 1971909 NIL) (-803 1965320 1965499 1965692 "NTPOLFN" 1965979 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-802 1964946 1965009 1965118 "NSUP2" 1965257 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1951728 1961771 1962583 "NSUP" 1964167 NIL NSUP (NIL T) -8 NIL NIL NIL) (-800 1940571 1951502 1951635 "NSMP" 1951640 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-799 1938979 1939304 1939661 "NREP" 1940259 NIL NREP (NIL T) -7 NIL NIL NIL) (-798 1937558 1937822 1938180 "NPCOEF" 1938722 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-797 1936606 1936739 1936955 "NORMRETR" 1937439 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-796 1934617 1934937 1935346 "NORMPK" 1936314 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-795 1934296 1934330 1934454 "NORMMA" 1934583 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-794 1934079 1934114 1934183 "NONE1" 1934260 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1933843 1934036 1934065 "NONE" 1934070 T NONE (NIL) -8 NIL NIL NIL) (-792 1933334 1933402 1933581 "NODE1" 1933775 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-791 1931395 1932457 1932712 "NNI" 1933059 T NNI (NIL) -8 NIL NIL 1933294) (-790 1929791 1930128 1930492 "NLINSOL" 1931063 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-789 1925972 1927027 1927926 "NIPROB" 1928912 T NIPROB (NIL) -8 NIL NIL NIL) (-788 1924711 1924963 1925265 "NFINTBAS" 1925734 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-787 1923795 1924361 1924402 "NETCLT" 1924574 NIL NETCLT (NIL T) -9 NIL 1924656 NIL) (-786 1922467 1922734 1923015 "NCODIV" 1923563 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-785 1922223 1922266 1922341 "NCNTFRAC" 1922424 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-784 1920379 1920767 1921187 "NCEP" 1921848 NIL NCEP (NIL T) -7 NIL NIL NIL) (-783 1919042 1919989 1920017 "NASRING" 1920127 T NASRING (NIL) -9 NIL 1920207 NIL) (-782 1918825 1918881 1918975 "NASRING-" 1918980 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-781 1917792 1918443 1918471 "NARNG" 1918588 T NARNG (NIL) -9 NIL 1918679 NIL) (-780 1917466 1917551 1917685 "NARNG-" 1917690 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-779 1916303 1916552 1916787 "NAGSP" 1917251 T NAGSP (NIL) -7 NIL NIL NIL) (-778 1907347 1909259 1910932 "NAGS" 1914650 T NAGS (NIL) -7 NIL NIL NIL) (-777 1905871 1906203 1906534 "NAGF07" 1907036 T NAGF07 (NIL) -7 NIL NIL NIL) (-776 1900343 1901700 1903007 "NAGF04" 1904584 T NAGF04 (NIL) -7 NIL NIL NIL) (-775 1893215 1894925 1896558 "NAGF02" 1898730 T NAGF02 (NIL) -7 NIL NIL NIL) (-774 1888379 1889539 1890656 "NAGF01" 1892118 T NAGF01 (NIL) -7 NIL NIL NIL) (-773 1881959 1883573 1885158 "NAGE04" 1886814 T NAGE04 (NIL) -7 NIL NIL NIL) (-772 1873020 1875249 1877379 "NAGE02" 1879849 T NAGE02 (NIL) -7 NIL NIL NIL) (-771 1868913 1869920 1870884 "NAGE01" 1872076 T NAGE01 (NIL) -7 NIL NIL NIL) (-770 1866690 1867242 1867800 "NAGD03" 1868375 T NAGD03 (NIL) -7 NIL NIL NIL) (-769 1858386 1860368 1862322 "NAGD02" 1864756 T NAGD02 (NIL) -7 NIL NIL NIL) (-768 1852125 1853622 1855062 "NAGD01" 1856966 T NAGD01 (NIL) -7 NIL NIL NIL) (-767 1848262 1849156 1849993 "NAGC06" 1851308 T NAGC06 (NIL) -7 NIL NIL NIL) (-766 1846709 1847059 1847415 "NAGC05" 1847926 T NAGC05 (NIL) -7 NIL NIL NIL) (-765 1846073 1846204 1846348 "NAGC02" 1846585 T NAGC02 (NIL) -7 NIL NIL NIL) (-764 1844874 1845601 1845641 "NAALG" 1845720 NIL NAALG (NIL T) -9 NIL 1845781 NIL) (-763 1844703 1844738 1844828 "NAALG-" 1844833 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-762 1838575 1839761 1840948 "MULTSQFR" 1843599 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-761 1837882 1837969 1838153 "MULTFACT" 1838487 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-760 1830027 1834465 1834518 "MTSCAT" 1835588 NIL MTSCAT (NIL T T) -9 NIL 1836104 NIL) (-759 1829733 1829793 1829885 "MTHING" 1829967 NIL MTHING (NIL T) -7 NIL NIL NIL) (-758 1829519 1829558 1829618 "MSYSCMD" 1829693 T MSYSCMD (NIL) -7 NIL NIL NIL) (-757 1826375 1829080 1829121 "MSETAGG" 1829126 NIL MSETAGG (NIL T) -9 NIL 1829160 NIL) (-756 1822203 1825130 1825450 "MSET" 1826088 NIL MSET (NIL T) -8 NIL NIL NIL) (-755 1817805 1819582 1820327 "MRING" 1821503 NIL MRING (NIL T T) -8 NIL NIL NIL) (-754 1817365 1817438 1817569 "MRF2" 1817732 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-753 1816977 1817018 1817162 "MRATFAC" 1817324 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-752 1814547 1814884 1815315 "MPRFF" 1816682 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-751 1807881 1814401 1814498 "MPOLY" 1814503 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-750 1807365 1807406 1807614 "MPCPF" 1807840 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-749 1806873 1806922 1807106 "MPC3" 1807316 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1806056 1806149 1806370 "MPC2" 1806788 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1804333 1804694 1805084 "MONOTOOL" 1805716 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-746 1803478 1803861 1803889 "MONOID" 1804108 T MONOID (NIL) -9 NIL 1804255 NIL) (-745 1802994 1803143 1803324 "MONOID-" 1803329 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-744 1791967 1798814 1798873 "MONOGEN" 1799547 NIL MONOGEN (NIL T T) -9 NIL 1800003 NIL) (-743 1789017 1789920 1790920 "MONOGEN-" 1791039 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-742 1787734 1788282 1788310 "MONADWU" 1788702 T MONADWU (NIL) -9 NIL 1788940 NIL) (-741 1787064 1787265 1787513 "MONADWU-" 1787518 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-740 1786349 1786653 1786681 "MONAD" 1786888 T MONAD (NIL) -9 NIL 1787000 NIL) (-739 1786016 1786112 1786244 "MONAD-" 1786249 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-738 1784155 1784929 1785208 "MOEBIUS" 1785769 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-737 1783323 1783823 1783863 "MODULE" 1783868 NIL MODULE (NIL T) -9 NIL 1783907 NIL) (-736 1782861 1782987 1783177 "MODULE-" 1783182 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-735 1780391 1781225 1781552 "MODRING" 1782685 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-734 1777120 1778496 1779017 "MODOP" 1779920 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-733 1775606 1776187 1776464 "MODMONOM" 1776983 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-732 1764366 1773897 1774311 "MODMON" 1775243 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-731 1761199 1763210 1763486 "MODFIELD" 1764241 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1760110 1760480 1760670 "MMLFORM" 1761029 T MMLFORM (NIL) -8 NIL NIL NIL) (-729 1759630 1759679 1759858 "MMAP" 1760061 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-728 1757523 1758462 1758503 "MLO" 1758926 NIL MLO (NIL T) -9 NIL 1759168 NIL) (-727 1754871 1755405 1756007 "MLIFT" 1757004 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-726 1754250 1754346 1754500 "MKUCFUNC" 1754782 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-725 1753843 1753919 1754042 "MKRECORD" 1754173 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-724 1752866 1753052 1753280 "MKFUNC" 1753654 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-723 1752242 1752358 1752514 "MKFLCFN" 1752749 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-722 1751507 1751621 1751806 "MKBCFUNC" 1752135 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-721 1747504 1751061 1751197 "MINT" 1751391 T MINT (NIL) -8 NIL NIL NIL) (-720 1746286 1746559 1746836 "MHROWRED" 1747259 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-719 1741037 1744821 1745226 "MFLOAT" 1745901 T MFLOAT (NIL) -8 NIL NIL NIL) (-718 1740382 1740470 1740641 "MFINFACT" 1740949 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-717 1736661 1737545 1738429 "MESH" 1739518 T MESH (NIL) -7 NIL NIL NIL) (-716 1735015 1735363 1735716 "MDDFACT" 1736348 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-715 1731662 1734146 1734187 "MDAGG" 1734442 NIL MDAGG (NIL T) -9 NIL 1734585 NIL) (-714 1719385 1730955 1731162 "MCMPLX" 1731475 T MCMPLX (NIL) -8 NIL NIL NIL) (-713 1718504 1718668 1718869 "MCDEN" 1719234 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-712 1716352 1716664 1717044 "MCALCFN" 1718234 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-711 1715229 1715517 1715750 "MAYBE" 1716158 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-710 1712787 1713364 1713926 "MATSTOR" 1714700 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-709 1708323 1712159 1712407 "MATRIX" 1712572 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-708 1704023 1704796 1705532 "MATLIN" 1707680 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-707 1702599 1702770 1703103 "MATCAT2" 1703858 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1692052 1695656 1695733 "MATCAT" 1700765 NIL MATCAT (NIL T T T) -9 NIL 1702237 NIL) (-705 1688005 1689315 1690728 "MATCAT-" 1690733 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-704 1686081 1686441 1686825 "MAPPKG3" 1687680 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-703 1685038 1685235 1685457 "MAPPKG2" 1685905 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-702 1683495 1683821 1684148 "MAPPKG1" 1684744 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-701 1682496 1682901 1683078 "MAPPAST" 1683338 T MAPPAST (NIL) -8 NIL NIL NIL) (-700 1682101 1682165 1682288 "MAPHACK3" 1682432 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-699 1681681 1681754 1681868 "MAPHACK2" 1682033 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-698 1681107 1681222 1681364 "MAPHACK1" 1681572 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-697 1679030 1679807 1680111 "MAGMA" 1680835 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-696 1678449 1678754 1678845 "MACROAST" 1678959 T MACROAST (NIL) -8 NIL NIL NIL) (-695 1674806 1676688 1677149 "M3D" 1678021 NIL M3D (NIL T) -8 NIL NIL NIL) (-694 1668278 1673117 1673158 "LZSTAGG" 1673940 NIL LZSTAGG (NIL T) -9 NIL 1674235 NIL) (-693 1663960 1665409 1666866 "LZSTAGG-" 1666871 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-692 1660873 1661851 1662338 "LWORD" 1663505 NIL LWORD (NIL T) -8 NIL NIL NIL) (-691 1660395 1660677 1660752 "LSTAST" 1660818 T LSTAST (NIL) -8 NIL NIL NIL) (-690 1652437 1660166 1660300 "LSQM" 1660305 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-689 1651655 1651800 1652028 "LSPP" 1652292 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-688 1648392 1649108 1649838 "LSMP1" 1650957 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1646174 1646505 1646961 "LSMP" 1648081 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-686 1639302 1645264 1645305 "LSAGG" 1645367 NIL LSAGG (NIL T) -9 NIL 1645445 NIL) (-685 1635811 1636921 1638134 "LSAGG-" 1638139 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-684 1633106 1634955 1635204 "LPOLY" 1635606 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-683 1632682 1632773 1632896 "LPEFRAC" 1633015 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-682 1632365 1632444 1632472 "LOGIC" 1632583 T LOGIC (NIL) -9 NIL 1632665 NIL) (-681 1632221 1632250 1632321 "LOGIC-" 1632326 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-680 1631396 1631554 1631747 "LODOOPS" 1632077 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1629920 1630169 1630522 "LODOF" 1631143 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1625796 1628555 1628596 "LODOCAT" 1629034 NIL LODOCAT (NIL T) -9 NIL 1629245 NIL) (-677 1625511 1625587 1625714 "LODOCAT-" 1625719 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1622497 1625352 1625470 "LODO2" 1625475 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1619604 1622434 1622479 "LODO1" 1622484 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1616699 1619520 1619586 "LODO" 1619591 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1615568 1615745 1616050 "LODEEF" 1616522 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1613554 1614662 1614915 "LO" 1615400 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1608637 1611720 1611761 "LNAGG" 1612623 NIL LNAGG (NIL T) -9 NIL 1613058 NIL) (-670 1607730 1607998 1608340 "LNAGG-" 1608345 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-669 1603710 1604655 1605294 "LMOPS" 1607145 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-668 1603009 1603487 1603528 "LMODULE" 1603533 NIL LMODULE (NIL T) -9 NIL 1603559 NIL) (-667 1600078 1602654 1602777 "LMDICT" 1602919 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-666 1599654 1599868 1599909 "LLINSET" 1599970 NIL LLINSET (NIL T) -9 NIL 1600014 NIL) (-665 1599299 1599562 1599622 "LITERAL" 1599627 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-664 1598818 1598898 1599037 "LIST3" 1599219 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1596916 1597264 1597663 "LIST2MAP" 1598465 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1595905 1596101 1596329 "LIST2" 1596734 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-661 1588359 1594839 1595143 "LIST" 1595634 NIL LIST (NIL T) -8 NIL NIL NIL) (-660 1587942 1588178 1588219 "LINSET" 1588224 NIL LINSET (NIL T) -9 NIL 1588258 NIL) (-659 1586756 1587450 1587617 "LINFORM" 1587827 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-658 1585055 1585783 1585824 "LINEXP" 1586314 NIL LINEXP (NIL T) -9 NIL 1586587 NIL) (-657 1583631 1584535 1584716 "LINELT" 1584926 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-656 1582188 1582468 1582779 "LINDEP" 1583383 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-655 1581324 1581920 1582030 "LINBASIS" 1582118 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-654 1578061 1578810 1579587 "LIMITRF" 1580579 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-653 1576346 1576660 1577069 "LIMITPS" 1577756 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-652 1575174 1575749 1575789 "LIECAT" 1575929 NIL LIECAT (NIL T) -9 NIL 1576080 NIL) (-651 1575009 1575042 1575130 "LIECAT-" 1575135 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-650 1569029 1574520 1574748 "LIE" 1574830 NIL LIE (NIL T T) -8 NIL NIL NIL) (-649 1561328 1568569 1568725 "LIB" 1568893 T LIB (NIL) -8 NIL NIL NIL) (-648 1556897 1557846 1558781 "LGROBP" 1560445 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-647 1555521 1556429 1556457 "LFCAT" 1556664 T LFCAT (NIL) -9 NIL 1556803 NIL) (-646 1553459 1553793 1554143 "LF" 1555242 NIL LF (NIL T T) -7 NIL NIL NIL) (-645 1550319 1550991 1551679 "LEXTRIPK" 1552823 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-644 1546907 1547889 1548392 "LEXP" 1549899 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-643 1546323 1546628 1546720 "LETAST" 1546835 T LETAST (NIL) -8 NIL NIL NIL) (-642 1544709 1545034 1545435 "LEADCDET" 1546005 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-641 1543887 1543973 1544202 "LAZM3PK" 1544630 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-640 1538412 1541964 1542502 "LAUPOL" 1543399 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-639 1537985 1538035 1538196 "LAPLACE" 1538362 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-638 1536833 1537549 1537590 "LALG" 1537652 NIL LALG (NIL T) -9 NIL 1537711 NIL) (-637 1536529 1536606 1536742 "LALG-" 1536747 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-636 1534266 1535630 1535881 "LA" 1536362 NIL LA (NIL T T T) -8 NIL NIL NIL) (-635 1534095 1534125 1534166 "KVTFROM" 1534228 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-634 1532852 1533462 1533647 "KTVLOGIC" 1533930 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-633 1532681 1532711 1532752 "KRCFROM" 1532814 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-632 1531573 1531772 1532071 "KOVACIC" 1532481 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-631 1531402 1531432 1531473 "KONVERT" 1531535 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-630 1531231 1531261 1531302 "KOERCE" 1531364 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-629 1530715 1530808 1530940 "KERNEL2" 1531145 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1528402 1529308 1529685 "KERNEL" 1530371 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-627 1521984 1526879 1526933 "KDAGG" 1527310 NIL KDAGG (NIL T T) -9 NIL 1527516 NIL) (-626 1521495 1521637 1521842 "KDAGG-" 1521847 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-625 1514309 1521156 1521311 "KAFILE" 1521373 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-624 1513913 1514198 1514261 "JVMOP" 1514266 T JVMOP (NIL) -8 NIL NIL NIL) (-623 1512649 1513153 1513402 "JVMMDACC" 1513684 T JVMMDACC (NIL) -8 NIL NIL NIL) (-622 1511585 1512039 1512244 "JVMFDACC" 1512464 T JVMFDACC (NIL) -8 NIL NIL NIL) (-621 1510166 1510661 1510961 "JVMCSTTG" 1511305 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-620 1509302 1509706 1509867 "JVMCFACC" 1510025 T JVMCFACC (NIL) -8 NIL NIL NIL) (-619 1508980 1509219 1509268 "JVMBCODE" 1509273 T JVMBCODE (NIL) -8 NIL NIL NIL) (-618 1502999 1508491 1508719 "JORDAN" 1508801 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1502312 1502648 1502769 "JOINAST" 1502898 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1498458 1500489 1500543 "IXAGG" 1501472 NIL IXAGG (NIL T T) -9 NIL 1501931 NIL) (-615 1497311 1497683 1498102 "IXAGG-" 1498107 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1492514 1497233 1497292 "IVECTOR" 1497297 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1491239 1491517 1491783 "ITUPLE" 1492281 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1489711 1489918 1490213 "ITRIGMNP" 1491061 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1488438 1488660 1488943 "ITFUN3" 1489487 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1488036 1488099 1488222 "ITFUN2" 1488361 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-609 1487141 1487516 1487690 "ITFORM" 1487882 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1484910 1486161 1486439 "ITAYLOR" 1486896 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1473314 1479047 1480210 "ISUPS" 1483780 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1472406 1472558 1472794 "ISUMP" 1473161 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1467370 1472351 1472392 "ISTRING" 1472397 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1466786 1467091 1467183 "ISAST" 1467298 T ISAST (NIL) -8 NIL NIL NIL) (-603 1465984 1466077 1466293 "IRURPK" 1466700 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1464896 1465121 1465361 "IRSN" 1465764 T IRSN (NIL) -7 NIL NIL NIL) (-601 1462941 1463322 1463751 "IRRF2F" 1464534 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1462682 1462726 1462802 "IRREDFFX" 1462897 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1461255 1461556 1461855 "IROOT" 1462415 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1460394 1460748 1460899 "IRFORM" 1461124 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1459476 1459607 1459821 "IR2F" 1460277 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1457065 1457584 1458150 "IR2" 1458954 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1453505 1454749 1455441 "IR" 1456405 NIL IR (NIL T) -8 NIL NIL NIL) (-594 1453290 1453330 1453390 "IPRNTPK" 1453465 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1449264 1453179 1453248 "IPF" 1453253 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1447292 1449189 1449246 "IPADIC" 1449251 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1446550 1446852 1446982 "IP4ADDR" 1447182 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1445888 1446179 1446311 "IOMODE" 1446438 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1444859 1445485 1445612 "IOBFILE" 1445781 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1444269 1444763 1444791 "IOBCON" 1444796 T IOBCON (NIL) -9 NIL 1444817 NIL) (-587 1443774 1443838 1444021 "INVLAPLA" 1444205 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1433344 1435776 1438162 "INTTR" 1441438 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1429637 1430421 1431286 "INTTOOLS" 1432529 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1429217 1429314 1429431 "INTSLPE" 1429540 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1426684 1429140 1429199 "INTRVL" 1429204 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1424262 1424798 1425373 "INTRF" 1426169 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1423655 1423770 1423912 "INTRET" 1424160 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1421628 1422041 1422511 "INTRAT" 1423263 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1418873 1419474 1420093 "INTPM" 1421113 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1415590 1416217 1416955 "INTPAF" 1418259 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1410691 1411731 1412782 "INTPACK" 1414559 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1409937 1410095 1410303 "INTHERTR" 1410533 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1409370 1409456 1409644 "INTHERAL" 1409851 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1407138 1407659 1408116 "INTHEORY" 1408933 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1398470 1400165 1401937 "INTG0" 1405490 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1378995 1383833 1388643 "INTFTBL" 1393680 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1378220 1378382 1378555 "INTFACT" 1378854 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1375617 1376093 1376650 "INTEF" 1377774 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1373814 1374709 1374737 "INTDOM" 1375038 T INTDOM (NIL) -9 NIL 1375245 NIL) (-568 1373153 1373357 1373599 "INTDOM-" 1373604 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1369021 1371442 1371496 "INTCAT" 1372295 NIL INTCAT (NIL T) -9 NIL 1372616 NIL) (-566 1368475 1368596 1368724 "INTBIT" 1368913 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1367156 1367328 1367635 "INTALG" 1368320 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1366633 1366729 1366886 "INTAF" 1367060 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1359714 1366443 1366583 "INTABL" 1366588 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1358955 1359517 1359582 "INT8" 1359616 T INT8 (NIL) -8 NIL NIL 1359661) (-561 1358195 1358757 1358822 "INT64" 1358856 T INT64 (NIL) -8 NIL NIL 1358901) (-560 1357435 1357997 1358062 "INT32" 1358096 T INT32 (NIL) -8 NIL NIL 1358141) (-559 1356675 1357237 1357302 "INT16" 1357336 T INT16 (NIL) -8 NIL NIL 1357381) (-558 1352879 1356472 1356581 "INT" 1356586 T INT (NIL) -8 NIL NIL NIL) (-557 1346988 1350427 1350455 "INS" 1351389 T INS (NIL) -9 NIL 1352054 NIL) (-556 1344145 1345065 1346006 "INS-" 1346079 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1342902 1343147 1343445 "INPSIGN" 1343898 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1341996 1342137 1342334 "INPRODPF" 1342782 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1340866 1341007 1341244 "INPRODFF" 1341876 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1339854 1340018 1340278 "INNMFACT" 1340702 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1339033 1339148 1339336 "INMODGCD" 1339753 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1337517 1337786 1338110 "INFSP" 1338778 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1336677 1336818 1337001 "INFPROD0" 1337397 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1336275 1336347 1336445 "INFORM1" 1336612 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1332842 1334340 1334855 "INFORM" 1335768 T INFORM (NIL) -8 NIL NIL NIL) (-546 1332347 1332454 1332568 "INFINITY" 1332748 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1331421 1332067 1332168 "INETCLTS" 1332266 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1330019 1330287 1330608 "INEP" 1331169 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1329049 1329916 1329981 "INDE" 1329986 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1328601 1328681 1328798 "INCRMAPS" 1328976 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1327323 1327870 1328076 "INBFILE" 1328415 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1322503 1323559 1324503 "INBFF" 1326411 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1321357 1321680 1321708 "INBCON" 1322221 T INBCON (NIL) -9 NIL 1322487 NIL) (-538 1320567 1320832 1321108 "INBCON-" 1321113 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1319986 1320291 1320382 "INAST" 1320496 T INAST (NIL) -8 NIL NIL NIL) (-536 1319353 1319665 1319771 "IMPTAST" 1319900 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1315388 1319197 1319301 "IMATRIX" 1319306 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1314080 1314219 1314535 "IMATQF" 1315244 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1312260 1312527 1312864 "IMATLIN" 1313836 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1306175 1312184 1312242 "ILIST" 1312247 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1303955 1306035 1306148 "IIARRAY2" 1306153 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1298776 1303866 1303930 "IFF" 1303935 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1298057 1298393 1298509 "IFAST" 1298680 T IFAST (NIL) -8 NIL NIL NIL) (-528 1292683 1297349 1297537 "IFARRAY" 1297914 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1291721 1292587 1292660 "IFAMON" 1292665 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1291293 1291370 1291424 "IEVALAB" 1291631 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1290956 1291036 1291196 "IEVALAB-" 1291201 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1289989 1290845 1290920 "IDPOAMS" 1290925 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1289091 1289878 1289953 "IDPOAM" 1289958 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1288472 1289006 1289068 "IDPO" 1289073 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1286952 1287479 1287531 "IDPC" 1288043 NIL IDPC (NIL T T) -9 NIL 1288324 NIL) (-520 1286284 1286844 1286917 "IDPAM" 1286922 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1285499 1286176 1286249 "IDPAG" 1286254 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1285043 1285305 1285395 "IDENT" 1285429 T IDENT (NIL) -8 NIL NIL NIL) (-517 1281262 1282146 1283041 "IDECOMP" 1284200 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1273897 1275185 1276232 "IDEAL" 1280298 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1273039 1273169 1273369 "ICDEN" 1273781 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1272014 1272519 1272666 "ICARD" 1272912 T ICARD (NIL) -8 NIL NIL NIL) (-513 1270044 1270387 1270792 "IBPTOOLS" 1271691 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1265273 1269664 1269777 "IBITS" 1269963 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1261948 1262572 1263267 "IBATOOL" 1264690 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1259709 1260189 1260722 "IBACHIN" 1261483 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1257413 1259555 1259658 "IARRAY2" 1259663 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1253240 1257339 1257396 "IARRAY1" 1257401 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1246257 1251652 1252133 "IAN" 1252779 T IAN (NIL) -8 NIL NIL NIL) (-506 1245762 1245825 1245998 "IALGFACT" 1246194 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1245254 1245403 1245431 "HYPCAT" 1245638 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1244756 1244909 1245095 "HYPCAT-" 1245100 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1244303 1244551 1244634 "HOSTNAME" 1244693 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1244136 1244185 1244226 "HOMOTOP" 1244231 NIL HOMOTOP (NIL T) -9 NIL 1244264 NIL) (-501 1240680 1242068 1242109 "HOAGG" 1243090 NIL HOAGG (NIL T) -9 NIL 1243819 NIL) (-500 1239196 1239673 1240199 "HOAGG-" 1240204 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1232253 1238789 1238939 "HEXADEC" 1239066 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1230965 1231223 1231486 "HEUGCD" 1232030 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1229897 1230802 1230932 "HELLFDIV" 1230937 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1228021 1229674 1229762 "HEAP" 1229841 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1227218 1227573 1227707 "HEADAST" 1227907 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1220670 1227133 1227195 "HDP" 1227200 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1213689 1220305 1220457 "HDMP" 1220571 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1212995 1213153 1213317 "HB" 1213545 T HB (NIL) -7 NIL NIL NIL) (-491 1206119 1212841 1212945 "HASHTBL" 1212950 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1205535 1205840 1205932 "HASAST" 1206047 T HASAST (NIL) -8 NIL NIL NIL) (-489 1202948 1205157 1205339 "HACKPI" 1205373 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1198234 1202801 1202914 "GTSET" 1202919 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1191387 1198112 1198210 "GSTBL" 1198215 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1183150 1190552 1190808 "GSERIES" 1191187 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1182181 1182694 1182722 "GROUP" 1182925 T GROUP (NIL) -9 NIL 1183059 NIL) (-484 1181505 1181706 1181957 "GROUP-" 1181962 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1179854 1180193 1180580 "GROEBSOL" 1181182 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1178682 1179042 1179093 "GRMOD" 1179622 NIL GRMOD (NIL T T) -9 NIL 1179790 NIL) (-481 1178438 1178486 1178614 "GRMOD-" 1178619 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1173578 1174792 1175792 "GRIMAGE" 1177458 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1171972 1172305 1172629 "GRDEF" 1173274 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1171404 1171532 1171673 "GRAY" 1171851 T GRAY (NIL) -7 NIL NIL NIL) (-477 1170481 1170983 1171034 "GRALG" 1171187 NIL GRALG (NIL T T) -9 NIL 1171280 NIL) (-476 1170118 1170215 1170378 "GRALG-" 1170383 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1166713 1169701 1169880 "GPOLSET" 1170024 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1166061 1166124 1166382 "GOSPER" 1166650 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1161631 1162499 1163025 "GMODPOL" 1165760 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1160618 1160820 1161058 "GHENSEL" 1161443 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1154690 1155617 1156637 "GENUPS" 1159702 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1154381 1154438 1154527 "GENUFACT" 1154633 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1153781 1153870 1154035 "GENPGCD" 1154299 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1153249 1153290 1153503 "GENMFACT" 1153740 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1151786 1152072 1152379 "GENEEZ" 1152992 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1144964 1151397 1151559 "GDMP" 1151709 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1133702 1138735 1139841 "GCNAALG" 1143947 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1131829 1132877 1132905 "GCDDOM" 1133160 T GCDDOM (NIL) -9 NIL 1133317 NIL) (-463 1131269 1131426 1131641 "GCDDOM-" 1131646 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1119741 1122215 1124607 "GBINTERN" 1128960 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1117542 1117870 1118291 "GBF" 1119416 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1116299 1116488 1116755 "GBEUCLID" 1117358 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1114949 1115156 1115460 "GB" 1116078 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1114280 1114423 1114572 "GAUSSFAC" 1114820 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1112601 1112949 1113263 "GALUTIL" 1113999 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1110861 1111183 1111507 "GALPOLYU" 1112328 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1108160 1108516 1108923 "GALFACTU" 1110558 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1099774 1101465 1103073 "GALFACT" 1106592 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1097060 1097820 1097848 "FVFUN" 1099004 T FVFUN (NIL) -9 NIL 1099724 NIL) (-452 1096290 1096508 1096536 "FVC" 1096827 T FVC (NIL) -9 NIL 1097010 NIL) (-451 1095891 1096115 1096183 "FUNDESC" 1096242 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1095464 1095688 1095769 "FUNCTION" 1095843 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1094141 1094765 1094968 "FTEM" 1095281 T FTEM (NIL) -8 NIL NIL NIL) (-448 1091771 1092463 1092929 "FT" 1093695 T FT (NIL) -8 NIL NIL NIL) (-447 1090040 1090351 1090748 "FSUPFACT" 1091462 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1088359 1088726 1089058 "FST" 1089728 T FST (NIL) -8 NIL NIL NIL) (-445 1087540 1087664 1087852 "FSRED" 1088241 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1086229 1086495 1086842 "FSPRMELT" 1087255 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1083439 1083973 1084459 "FSPECF" 1085792 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1082961 1083021 1083191 "FSINT" 1083380 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1081097 1081954 1082257 "FSERIES" 1082740 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1080121 1080255 1080479 "FSCINT" 1080977 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1079145 1079306 1079533 "FSAGG2" 1079974 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 1075120 1078089 1078130 "FSAGG" 1078500 NIL FSAGG (NIL T) -9 NIL 1078759 NIL) (-437 1072720 1073483 1074279 "FSAGG-" 1074374 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1070380 1070678 1071226 "FS2UPS" 1072438 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1069246 1069429 1069731 "FS2EXPXP" 1070205 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 1068874 1068923 1069052 "FS2" 1069197 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1049112 1058648 1058689 "FS" 1062573 NIL FS (NIL T) -9 NIL 1064862 NIL) (-432 1037173 1040748 1044805 "FS-" 1045105 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 1036587 1036714 1036866 "FRUTIL" 1037053 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 1031098 1034276 1034316 "FRNAALG" 1035636 NIL FRNAALG (NIL T) -9 NIL 1036234 NIL) (-429 1026579 1027847 1029122 "FRNAALG-" 1029872 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1026211 1026260 1026387 "FRNAAF2" 1026530 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1024498 1025060 1025356 "FRMOD" 1026023 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1023683 1023776 1024067 "FRIDEAL2" 1024405 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1021288 1022058 1022376 "FRIDEAL" 1023474 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 1020379 1020835 1020876 "FRETRCT" 1020881 NIL FRETRCT (NIL T) -9 NIL 1021057 NIL) (-423 1019437 1019722 1020073 "FRETRCT-" 1020078 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1016258 1017721 1017780 "FRAMALG" 1018662 NIL FRAMALG (NIL T T) -9 NIL 1018954 NIL) (-421 1014296 1014847 1015477 "FRAMALG-" 1015700 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1013926 1013989 1014096 "FRAC2" 1014233 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1006919 1013399 1013676 "FRAC" 1013681 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 1006549 1006612 1006719 "FR2" 1006856 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 997466 1002044 1003402 "FR" 1005223 NIL FR (NIL T) -8 NIL NIL NIL) (-416 991385 994845 994873 "FPS" 995992 T FPS (NIL) -9 NIL 996549 NIL) (-415 990810 990943 991107 "FPS-" 991253 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 987776 989767 989795 "FPC" 990020 T FPC (NIL) -9 NIL 990162 NIL) (-413 987557 987609 987706 "FPC-" 987711 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 986315 987045 987086 "FPATMAB" 987091 NIL FPATMAB (NIL T) -9 NIL 987243 NIL) (-411 984458 985057 985404 "FPARFRAC" 986031 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 979750 980350 981032 "FORTRAN" 983890 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 977324 977988 978016 "FORTFN" 979076 T FORTFN (NIL) -9 NIL 979700 NIL) (-408 977076 977138 977166 "FORTCAT" 977225 T FORTCAT (NIL) -9 NIL 977287 NIL) (-407 974762 975292 975831 "FORT" 976557 T FORT (NIL) -7 NIL NIL NIL) (-406 974279 974337 974510 "FORDER" 974704 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 973339 973539 973732 "FOP" 974106 T FOP (NIL) -7 NIL NIL NIL) (-404 971752 972619 972793 "FNLA" 973221 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 970371 970882 970910 "FNCAT" 971370 T FNCAT (NIL) -9 NIL 971630 NIL) (-402 969814 970330 970358 "FNAME" 970363 T FNAME (NIL) -8 NIL NIL NIL) (-401 968140 969313 969341 "FMTC" 969346 T FMTC (NIL) -9 NIL 969382 NIL) (-400 966689 968076 968122 "FMONOID" 968127 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 963278 964644 964685 "FMONCAT" 965902 NIL FMONCAT (NIL T) -9 NIL 966507 NIL) (-398 960600 961348 961376 "FMFUN" 962520 T FMFUN (NIL) -9 NIL 963228 NIL) (-397 957473 958525 958579 "FMCAT" 959774 NIL FMCAT (NIL T T) -9 NIL 960269 NIL) (-396 956706 956923 956951 "FMC" 957241 T FMC (NIL) -9 NIL 957423 NIL) (-395 955374 956472 956572 "FM1" 956651 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 954392 955116 955265 "FM" 955270 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 952130 952582 953076 "FLOATRP" 953943 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949532 950068 950646 "FLOATCP" 951597 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 942195 947261 947882 "FLOAT" 948931 T FLOAT (NIL) -8 NIL NIL NIL) (-390 940713 941787 941828 "FLINEXP" 941833 NIL FLINEXP (NIL T) -9 NIL 941926 NIL) (-389 939843 940102 940430 "FLINEXP-" 940435 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 938901 939063 939287 "FLASORT" 939695 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 935819 936871 936923 "FLALG" 938150 NIL FLALG (NIL T T) -9 NIL 938617 NIL) (-386 934843 935004 935231 "FLAGG2" 935672 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 928212 932252 932293 "FLAGG" 933555 NIL FLAGG (NIL T) -9 NIL 934207 NIL) (-384 926866 927277 927767 "FLAGG-" 927772 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 923504 924711 924770 "FINRALG" 925898 NIL FINRALG (NIL T T) -9 NIL 926406 NIL) (-382 922628 922893 923232 "FINRALG-" 923237 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 921934 922233 922261 "FINITE" 922457 T FINITE (NIL) -9 NIL 922564 NIL) (-380 913885 916464 916504 "FINAALG" 920171 NIL FINAALG (NIL T) -9 NIL 921624 NIL) (-379 909001 910267 911411 "FINAALG-" 912790 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 907561 907983 908037 "FILECAT" 908721 NIL FILECAT (NIL T T) -9 NIL 908937 NIL) (-377 906839 907316 907419 "FILE" 907491 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 904242 906069 906097 "FIELD" 906137 T FIELD (NIL) -9 NIL 906217 NIL) (-375 902784 903247 903758 "FIELD-" 903763 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 900467 901419 901766 "FGROUP" 902470 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 899539 899721 899941 "FGLMICPK" 900299 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 894794 899464 899521 "FFX" 899526 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 894389 894456 894591 "FFSLPE" 894727 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 893887 893929 894138 "FFPOLY2" 894347 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 889763 890659 891455 "FFPOLY" 893123 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 885032 889682 889745 "FFP" 889750 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 879563 884375 884565 "FFNBX" 884886 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 873896 878698 878956 "FFNBP" 879417 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 867934 873180 873391 "FFNB" 873729 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 866754 866964 867279 "FFINTBAS" 867731 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 862347 865001 865029 "FFIELDC" 865649 T FFIELDC (NIL) -9 NIL 866025 NIL) (-362 860967 861408 861891 "FFIELDC-" 861896 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 860524 860582 860706 "FFHOM" 860909 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 858183 858706 859223 "FFF" 860039 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 853218 857925 858026 "FFCGX" 858126 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 848257 852950 853057 "FFCGP" 853161 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 842857 847984 848092 "FFCG" 848193 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 842262 842311 842546 "FFCAT2" 842808 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 820944 831994 832080 "FFCAT" 837245 NIL FFCAT (NIL T T T) -9 NIL 838696 NIL) (-354 815955 817189 818503 "FFCAT-" 819733 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 810776 815866 815930 "FF" 815935 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 799429 803748 804968 "FEXPR" 809628 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 798357 798826 798867 "FEVALAB" 798951 NIL FEVALAB (NIL T) -9 NIL 799212 NIL) (-350 797474 797726 798064 "FEVALAB-" 798069 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 794336 795221 795336 "FDIVCAT" 796904 NIL FDIVCAT (NIL T T T T) -9 NIL 797341 NIL) (-348 794092 794125 794295 "FDIVCAT-" 794300 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 793306 793399 793676 "FDIV2" 793999 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 791716 792689 792892 "FDIV" 793205 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 790624 791011 791213 "FCTRDATA" 791534 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 789280 789569 789858 "FCPAK1" 790355 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 788283 788780 788921 "FCOMP" 789171 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 771597 775433 778971 "FC" 784765 T FC (NIL) -8 NIL NIL NIL) (-341 763306 767918 767958 "FAXF" 769760 NIL FAXF (NIL T) -9 NIL 770452 NIL) (-340 760447 761254 762072 "FAXF-" 762537 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 755130 759823 759999 "FARRAY" 760304 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 749695 752077 752130 "FAMR" 753153 NIL FAMR (NIL T T) -9 NIL 753613 NIL) (-337 748519 748887 749322 "FAMR-" 749327 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 747546 748441 748494 "FAMONOID" 748499 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 745176 746028 746081 "FAMONC" 747022 NIL FAMONC (NIL T T) -9 NIL 747408 NIL) (-334 743650 744930 745067 "FAGROUP" 745072 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 741403 741764 742167 "FACUTIL" 743331 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 740490 740687 740909 "FACTFUNC" 741213 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 732231 739793 739992 "EXPUPXS" 740346 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 729684 730254 730840 "EXPRTUBE" 731665 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 725895 726547 727277 "EXPRODE" 729023 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 720329 721036 721842 "EXPR2UPS" 725193 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 719955 720018 720127 "EXPR2" 720266 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 704263 718604 719033 "EXPR" 719559 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 694601 703414 703705 "EXPEXPAN" 704099 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 694021 694325 694416 "EXITAST" 694530 T EXITAST (NIL) -8 NIL NIL NIL) (-323 693785 693978 694007 "EXIT" 694012 T EXIT (NIL) -8 NIL NIL NIL) (-322 693406 693474 693587 "EVALCYC" 693717 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 692923 693065 693106 "EVALAB" 693276 NIL EVALAB (NIL T) -9 NIL 693380 NIL) (-320 692380 692526 692747 "EVALAB-" 692752 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 689495 691036 691064 "EUCDOM" 691619 T EUCDOM (NIL) -9 NIL 691969 NIL) (-318 687855 688356 688939 "EUCDOM-" 688944 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 687481 687544 687653 "ESTOOLS2" 687792 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 687226 687274 687354 "ESTOOLS1" 687433 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 674543 677524 680274 "ESTOOLS" 684496 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 674282 674320 674402 "ESCONT1" 674505 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 670590 671417 672197 "ESCONT" 673522 T ESCONT (NIL) -7 NIL NIL NIL) (-312 670259 670315 670415 "ES2" 670534 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 669883 669947 670056 "ES1" 670195 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 663584 665514 665542 "ES" 668310 T ES (NIL) -9 NIL 669720 NIL) (-309 658261 659818 661635 "ES-" 661799 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 657453 657606 657782 "ERROR" 658105 T ERROR (NIL) -7 NIL NIL NIL) (-307 650583 657312 657403 "EQTBL" 657408 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 650209 650272 650381 "EQ2" 650520 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 642468 645523 646972 "EQ" 648793 NIL -3372 (NIL T) -8 NIL NIL NIL) (-304 637710 638806 639899 "EP" 641407 NIL EP (NIL T) -7 NIL NIL NIL) (-303 636250 636601 636907 "ENV" 637424 T ENV (NIL) -8 NIL NIL NIL) (-302 635210 635884 635912 "ENTIRER" 635917 T ENTIRER (NIL) -9 NIL 635963 NIL) (-301 631629 633392 633753 "EMR" 635018 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 630733 630944 630998 "ELTAGG" 631378 NIL ELTAGG (NIL T T) -9 NIL 631589 NIL) (-299 630440 630514 630655 "ELTAGG-" 630660 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 630198 630233 630287 "ELTAB" 630371 NIL ELTAB (NIL T T) -9 NIL 630423 NIL) (-297 629300 629470 629669 "ELFUTS" 630049 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 629024 629098 629126 "ELEMFUN" 629231 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 628888 628915 628983 "ELEMFUN-" 628988 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 623413 626930 626971 "ELAGG" 627911 NIL ELAGG (NIL T) -9 NIL 628374 NIL) (-293 621590 622132 622795 "ELAGG-" 622800 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 620872 621039 621195 "ELABOR" 621454 T ELABOR (NIL) -8 NIL NIL NIL) (-291 619478 619812 620106 "ELABEXPR" 620598 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 611990 614115 614944 "EFUPXS" 618753 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 605116 607239 608050 "EFULS" 611265 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 602553 602959 603431 "EFSTRUC" 604748 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 591991 593910 595458 "EF" 601068 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 590969 591476 591625 "EAB" 591862 T EAB (NIL) -8 NIL NIL NIL) (-285 590091 590928 590956 "E04UCFA" 590961 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 589213 590050 590078 "E04NAFA" 590083 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 588335 589172 589200 "E04MBFA" 589205 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 587457 588294 588322 "E04JAFA" 588327 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 586581 587416 587444 "E04GCFA" 587449 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 585705 586540 586568 "E04FDFA" 586573 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 584827 585664 585692 "E04DGFA" 585697 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 578904 580352 581716 "E04AGNT" 583483 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 577524 578205 578245 "DVARCAT" 578586 NIL DVARCAT (NIL T) -9 NIL 578749 NIL) (-276 576674 576940 577254 "DVARCAT-" 577259 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 568642 576473 576602 "DSMP" 576607 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 566993 567784 567825 "DSEXT" 568188 NIL DSEXT (NIL T) -9 NIL 568482 NIL) (-273 565182 565706 566372 "DSEXT-" 566377 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 564841 564906 565004 "DROPT1" 565117 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 559860 561082 562219 "DROPT0" 563724 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 554443 555805 556873 "DROPT" 558812 T DROPT (NIL) -8 NIL NIL NIL) (-269 552752 553113 553499 "DRAWPT" 554077 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 552379 552438 552556 "DRAWHACK" 552693 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 551080 551379 551670 "DRAWCX" 552108 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 550589 550664 550815 "DRAWCURV" 551006 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 540907 543019 545134 "DRAWCFUN" 548494 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 535398 536417 537496 "DRAW" 539881 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 531980 534063 534104 "DQAGG" 534733 NIL DQAGG (NIL T) -9 NIL 535007 NIL) (-262 518563 526191 526274 "DPOLCAT" 528126 NIL DPOLCAT (NIL T T T T) -9 NIL 528671 NIL) (-261 513082 514748 516706 "DPOLCAT-" 516711 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 506004 512943 513041 "DPMO" 513046 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 498823 505784 505951 "DPMM" 505956 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 498345 498607 498696 "DOMTMPLT" 498754 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 497694 498147 498227 "DOMCTOR" 498285 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 496846 497174 497325 "DOMAIN" 497563 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 489865 496481 496633 "DMP" 496747 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 487642 488932 488973 "DMEXT" 488978 NIL DMEXT (NIL T) -9 NIL 489154 NIL) (-253 487236 487298 487442 "DLP" 487580 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 480359 486563 486753 "DLIST" 487078 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 477008 479184 479225 "DLAGG" 479775 NIL DLAGG (NIL T) -9 NIL 480005 NIL) (-250 475520 476334 476362 "DIVRING" 476454 T DIVRING (NIL) -9 NIL 476537 NIL) (-249 474703 474947 475247 "DIVRING-" 475252 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 472745 473162 473568 "DISPLAY" 474317 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 471575 471796 472061 "DIRPROD2" 472538 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 465047 471489 471552 "DIRPROD" 471557 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 453324 459758 459811 "DIRPCAT" 460069 NIL DIRPCAT (NIL NIL T) -9 NIL 460944 NIL) (-244 450524 451292 452173 "DIRPCAT-" 452510 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 449805 449971 450157 "DIOSP" 450358 T DIOSP (NIL) -7 NIL NIL NIL) (-242 446330 448689 448730 "DIOPS" 449164 NIL DIOPS (NIL T) -9 NIL 449393 NIL) (-241 445849 445993 446184 "DIOPS-" 446189 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 444756 445528 445556 "DIFRING" 445561 T DIFRING (NIL) -9 NIL 445583 NIL) (-239 444404 444502 444530 "DIFFSPC" 444649 T DIFFSPC (NIL) -9 NIL 444724 NIL) (-238 444025 444127 444279 "DIFFSPC-" 444284 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442961 443559 443600 "DIFFMOD" 443605 NIL DIFFMOD (NIL T) -9 NIL 443703 NIL) (-236 442657 442714 442755 "DIFFDOM" 442876 NIL DIFFDOM (NIL T) -9 NIL 442944 NIL) (-235 442504 442534 442618 "DIFFDOM-" 442623 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 440244 441708 441749 "DIFEXT" 441754 NIL DIFEXT (NIL T) -9 NIL 441907 NIL) (-233 437389 439748 439789 "DIAGG" 439794 NIL DIAGG (NIL T) -9 NIL 439814 NIL) (-232 436737 436930 437182 "DIAGG-" 437187 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 431701 435696 435973 "DHMATRIX" 436506 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 427169 428222 429232 "DFSFUN" 430711 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 421278 425999 426334 "DFLOAT" 426854 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 419517 419822 420211 "DFINTTLS" 420986 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 416336 417538 417938 "DERHAM" 419183 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 413986 416111 416200 "DEQUEUE" 416280 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 413228 413373 413556 "DEGRED" 413848 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 409634 410403 411249 "DEFINTRF" 412456 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 407171 407658 408250 "DEFINTEF" 409153 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 406455 406791 406906 "DEFAST" 407076 T DEFAST (NIL) -8 NIL NIL NIL) (-221 399512 406048 406198 "DECIMAL" 406325 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 396970 397482 397988 "DDFACT" 399056 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 396560 396609 396760 "DBLRESP" 396921 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395761 396330 396421 "DBASIS" 396509 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 393545 393991 394352 "DBASE" 395527 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392733 393025 393171 "DATAARY" 393444 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391791 392692 392720 "D03FAFA" 392725 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390850 391750 391778 "D03EEFA" 391783 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388776 389266 389755 "D03AGNT" 390381 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 388017 388735 388763 "D02EJFA" 388768 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 387258 387976 388004 "D02CJFA" 388009 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 386499 387217 387245 "D02BHFA" 387250 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385740 386458 386486 "D02BBFA" 386491 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378871 380526 382132 "D02AGNT" 384154 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376621 377162 377708 "D01WGTS" 378345 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375628 376580 376608 "D01TRNS" 376613 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374636 375587 375615 "D01GBFA" 375620 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373644 374595 374623 "D01FCFA" 374628 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372652 373603 373631 "D01ASFA" 373636 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371660 372611 372639 "D01AQFA" 372644 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370668 371619 371647 "D01APFA" 371652 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369676 370627 370655 "D01ANFA" 370660 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368684 369635 369663 "D01AMFA" 369668 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367692 368643 368671 "D01ALFA" 368676 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366700 367651 367679 "D01AKFA" 367684 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365708 366659 366687 "D01AJFA" 366692 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 358931 360556 362117 "D01AGNT" 364167 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 358250 358396 358548 "CYCLOTOM" 358799 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 354905 355698 356425 "CYCLES" 357543 T CYCLES (NIL) -7 NIL NIL NIL) (-192 354205 354351 354522 "CVMP" 354766 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 351992 352304 352673 "CTRIGMNP" 353933 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 351465 351723 351824 "CTORKIND" 351911 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350670 351058 351086 "CTORCAT" 351268 T CTORCAT (NIL) -9 NIL 351381 NIL) (-188 350244 350379 350538 "CTORCAT-" 350543 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349658 349918 350026 "CTORCALL" 350168 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 349016 349452 349525 "CTOR" 349605 T CTOR (NIL) -8 NIL NIL NIL) (-185 348372 348489 348642 "CSTTOOLS" 348913 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 344069 344828 345586 "CRFP" 347684 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 343484 343790 343882 "CRCEAST" 343997 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 342507 342716 342944 "CRAPACK" 343288 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341887 341992 342196 "CPMATCH" 342383 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341606 341640 341746 "CPIMA" 341853 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337864 338626 339345 "COORDSYS" 340941 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 337252 337397 337539 "CONTOUR" 337742 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332723 335255 335747 "CONTFRAC" 336792 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332597 332624 332652 "CONDUIT" 332689 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 331551 332225 332253 "COMRING" 332258 T COMRING (NIL) -9 NIL 332310 NIL) (-174 330533 330909 331093 "COMPPROP" 331387 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 330188 330229 330357 "COMPLPAT" 330492 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329818 329881 329988 "COMPLEX2" 330125 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 318222 329627 329736 "COMPLEX" 329741 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 317543 317682 317842 "COMPILER" 318082 T COMPILER (NIL) -8 NIL NIL NIL) (-169 317255 317296 317394 "COMPFACT" 317502 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298649 310959 310999 "COMPCAT" 312003 NIL COMPCAT (NIL T) -9 NIL 313351 NIL) (-167 287537 291088 294715 "COMPCAT-" 295071 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 287260 287294 287397 "COMMUPC" 287503 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 287048 287088 287147 "COMMONOP" 287221 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286570 286852 286927 "COMMAAST" 286993 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 286077 286321 286408 "COMM" 286503 T COMM (NIL) -8 NIL NIL NIL) (-162 285272 285520 285548 "COMBOPC" 285886 T COMBOPC (NIL) -9 NIL 286061 NIL) (-161 284126 284378 284620 "COMBINAT" 285062 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 280469 281157 281784 "COMBF" 283548 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 279131 279585 279820 "COLOR" 280254 T COLOR (NIL) -8 NIL NIL NIL) (-158 278547 278852 278944 "COLONAST" 279059 T COLONAST (NIL) -8 NIL NIL NIL) (-157 278181 278234 278359 "CMPLXRT" 278494 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277569 277881 277980 "CLLCTAST" 278102 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 273029 274099 275179 "CLIP" 276509 T CLIP (NIL) -7 NIL NIL NIL) (-154 271202 272130 272370 "CLIF" 272856 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 267295 269320 269361 "CLAGG" 270290 NIL CLAGG (NIL T) -9 NIL 270826 NIL) (-152 265639 266174 266757 "CLAGG-" 266762 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 265177 265268 265408 "CINTSLPE" 265548 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262642 263149 263697 "CHVAR" 264705 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261682 262356 262384 "CHARZ" 262389 T CHARZ (NIL) -9 NIL 262404 NIL) (-148 261430 261476 261554 "CHARPOL" 261636 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 260348 261054 261082 "CHARNZ" 261143 T CHARNZ (NIL) -9 NIL 261192 NIL) (-146 257292 258402 258931 "CHAR" 259839 T CHAR (NIL) -8 NIL NIL NIL) (-145 257000 257079 257107 "CFCAT" 257218 T CFCAT (NIL) -9 NIL NIL NIL) (-144 256223 256352 256535 "CDEN" 256884 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 251934 255376 255656 "CCLASS" 255963 T CCLASS (NIL) -8 NIL NIL NIL) (-142 251155 251342 251519 "CATEGORY" 251777 T -10 (NIL) -8 NIL NIL NIL) (-141 250650 251074 251122 "CATCTOR" 251127 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 250041 250353 250451 "CATAST" 250572 T CATAST (NIL) -8 NIL NIL NIL) (-139 249457 249762 249854 "CASEAST" 249969 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248553 248713 248934 "CARTEN2" 249304 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 243450 244710 245454 "CARTEN" 247865 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241580 242600 242857 "CARD" 243213 T CARD (NIL) -8 NIL NIL NIL) (-135 241102 241384 241459 "CAPSLAST" 241525 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240544 240800 240828 "CACHSET" 240960 T CACHSET (NIL) -9 NIL 241038 NIL) (-133 239934 240322 240350 "CABMON" 240400 T CABMON (NIL) -9 NIL 240456 NIL) (-132 239371 239638 239748 "BYTEORD" 239844 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 234412 238876 239048 "BYTEBUF" 239219 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 233243 233955 234090 "BYTE" 234253 T BYTE (NIL) -8 NIL NIL 234368) (-129 230619 232935 233042 "BTREE" 233169 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 227935 230267 230389 "BTOURN" 230529 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 225153 227377 227418 "BTCAT" 227486 NIL BTCAT (NIL T) -9 NIL 227563 NIL) (-126 224802 224900 225049 "BTCAT-" 225054 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219805 224048 224076 "BTAGG" 224190 T BTAGG (NIL) -9 NIL 224300 NIL) (-124 219259 219420 219626 "BTAGG-" 219631 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 216109 218537 218752 "BSTREE" 219076 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 215217 215373 215557 "BRILL" 215965 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211723 213915 213956 "BRAGG" 214605 NIL BRAGG (NIL T) -9 NIL 214863 NIL) (-120 210156 210658 211213 "BRAGG-" 211218 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 202413 209500 209685 "BPADICRT" 210003 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 200429 202350 202395 "BPADIC" 202400 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 200121 200157 200271 "BOUNDZRO" 200393 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197848 198306 198781 "BOP1" 199679 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192878 194308 195206 "BOP" 196970 T BOP (NIL) -8 NIL NIL NIL) (-114 191638 192536 192660 "BOOLEAN" 192774 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 191231 191388 191416 "BOOLE" 191527 T BOOLE (NIL) -9 NIL 191608 NIL) (-112 191099 191126 191192 "BOOLE-" 191197 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 190268 190768 190822 "BMODULE" 190827 NIL BMODULE (NIL T T) -9 NIL 190892 NIL) (-110 185703 190066 190139 "BITS" 190215 T BITS (NIL) -8 NIL NIL NIL) (-109 185100 185243 185383 "BINDING" 185583 T BINDING (NIL) -8 NIL NIL NIL) (-108 178160 184695 184844 "BINARY" 184971 T BINARY (NIL) -8 NIL NIL NIL) (-107 175878 177387 177428 "BGAGG" 177688 NIL BGAGG (NIL T) -9 NIL 177825 NIL) (-106 175703 175741 175832 "BGAGG-" 175837 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174726 175087 175292 "BFUNCT" 175518 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 173396 173594 173882 "BEZOUT" 174550 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169708 172248 172578 "BBTREE" 173099 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 169291 169387 169415 "BASTYPE" 169592 T BASTYPE (NIL) -9 NIL 169691 NIL) (-101 168949 169048 169183 "BASTYPE-" 169188 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 168371 168459 168611 "BALFACT" 168860 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 167107 167786 167972 "AUTOMOR" 168216 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166833 166838 166864 "ATTREG" 166869 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164995 165530 165882 "ATTRBUT" 166499 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 164549 164823 164889 "ATTRAST" 164947 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 164049 164198 164224 "ATRIG" 164425 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163846 163899 163986 "ATRIG-" 163991 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 163429 163663 163689 "ASTCAT" 163694 T ASTCAT (NIL) -9 NIL 163724 NIL) (-92 163138 163215 163334 "ASTCAT-" 163339 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 161226 162914 163002 "ASTACK" 163081 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159715 160028 160393 "ASSOCEQ" 160908 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158639 159374 159498 "ASP9" 159622 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 157399 158244 158386 "ASP80" 158528 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 157127 157347 157386 "ASP8" 157391 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155973 156804 156922 "ASP78" 157040 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154834 155653 155770 "ASP77" 155887 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153638 154472 154603 "ASP74" 154734 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 152430 153273 153405 "ASP73" 153537 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 151220 152065 152197 "ASP7" 152329 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 150216 151046 151146 "ASP6" 151151 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 149055 149893 150011 "ASP55" 150129 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147896 148729 148848 "ASP50" 148967 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146876 147597 147707 "ASP49" 147817 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145552 146415 146583 "ASP42" 146765 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 144221 145085 145255 "ASP41" 145439 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 143201 143922 144032 "ASP4" 144142 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 142043 142878 142996 "ASP35" 143114 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141772 141991 142030 "ASP34" 142035 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141491 141576 141652 "ASP33" 141727 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140277 141126 141258 "ASP31" 141390 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 140006 140225 140264 "ASP30" 140269 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139723 139810 139886 "ASP29" 139961 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139452 139671 139710 "ASP28" 139715 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 139181 139400 139439 "ASP27" 139444 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 138157 138879 138990 "ASP24" 139101 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 137126 137959 138071 "ASP20" 138076 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135961 136800 136919 "ASP19" 137038 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135680 135765 135841 "ASP12" 135916 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134424 135279 135423 "ASP10" 135567 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133404 134125 134235 "ASP1" 134345 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131130 133248 133339 "ARRAY2" 133344 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130144 130335 130556 "ARRAY12" 130953 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125618 129792 129906 "ARRAY1" 130061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119774 121820 121895 "ARR2CAT" 124525 NIL ARR2CAT (NIL T 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NIL NIL NIL) (-43 74445 75105 75712 "ALGPKG" 77435 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73710 73823 74007 "ALGMFACT" 74331 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69693 70324 70918 "ALGMANIP" 73294 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59053 69319 69469 "ALGFF" 69626 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58225 58380 58559 "ALGFACT" 58911 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57014 57752 57790 "ALGEBRA" 57795 NIL ALGEBRA (NIL T) -9 NIL 57836 NIL) (-37 56714 56791 56923 "ALGEBRA-" 56928 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37668 54551 54603 "ALAGG" 54739 NIL ALAGG (NIL T T) -9 NIL 54900 NIL) (-35 37168 37317 37343 "AHYP" 37544 T AHYP (NIL) -9 NIL NIL NIL) (-34 36470 36653 36679 "AGG" 36962 T AGG (NIL) -9 NIL 37151 NIL) (-33 36177 36264 36379 "AGG-" 36384 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33937 34406 34811 "AF" 35819 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33357 33662 33752 "ADDAST" 33865 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32589 32884 33040 "ACPLOT" 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T) ((-23) . T) ((-47 |#1| #1=(-558)) . T) ((-25) . T) ((-38 #2=(-419 (-558))) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 #2# #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-633 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 #3=(-1206)) -12 (|has| |#1| (-376)) (|has| |#2| (-1067 (-1206)))) ((-633 |#1|) |has| |#1| (-175)) ((-633 |#2|) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1141)) ((-302) -4034 (|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 (-1206) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1206) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-666 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 |#2|) |has| |#1| (-376)) ((-666 $) . T) ((-668 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-668 #4=(-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-660 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-660 |#1|) |has| |#1| (-175)) ((-660 |#2|) |has| |#1| (-376)) ((-660 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-658 #4#) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-658 |#2|) |has| |#1| (-376)) ((-737 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-737 |#1|) |has| |#1| (-175)) ((-737 |#2|) |has| |#1| (-376)) ((-737 $) -4034 (|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))) ((-868) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-869) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-869))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-872) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-869))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-919 $ #5=(-1206)) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1206)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-925 (-1206)) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-927 #5#) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1206)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-909 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-909 (-391)))) ((-909 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-909 (-558)))) ((-907 |#2|) |has| |#1| (-376)) ((-937) -12 (|has| |#1| (-376)) (|has| |#2| (-937))) ((-1002 |#1| #1# (-1111)) . 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T) ((-23) . T) ((-47 |#1| #1=(-791)) . T) ((-25) . T) ((-38 #2=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #2#) -4034 (|has| |#1| (-1067 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 #3=(-1111)) . T) ((-633 |#1|) . T) ((-633 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-630 (-885)) . T) ((-175) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-547)) -12 (|has| |#1| (-631 (-547))) (|has| (-1111) (-631 (-547)))) ((-631 (-913 (-391))) -12 (|has| |#1| (-631 (-913 (-391)))) (|has| (-1111) (-631 (-913 (-391))))) ((-631 (-913 (-558))) -12 (|has| |#1| (-631 (-913 (-558)))) (|has| (-1111) (-631 (-913 (-558))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-419 $) (-419 $)) |has| |#1| (-569)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #1#) . T) ((-390 |#1|) . T) ((-424 |#1|) . T) ((-464) -4034 (|has| |#1| (-937)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-526 #3# |#1|) . T) ((-526 #3# $) . T) ((-526 $ $) . T) ((-569) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-666 #2#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #2#) |has| |#1| (-38 (-419 (-558)))) ((-668 #4=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #2#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-658 #4#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #2#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-746) . T) ((-919 $ #3#) . T) ((-919 $ #5=(-1206)) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-925 #3#) . T) ((-925 (-1206)) |has| |#1| (-925 (-1206))) ((-927 #3#) . T) ((-927 #5#) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-909 (-391)) -12 (|has| |#1| (-909 (-391))) (|has| (-1111) (-909 (-391)))) ((-909 (-558)) -12 (|has| |#1| (-909 (-558))) (|has| (-1111) (-909 (-558)))) ((-977 |#1| #1# #3#) . T) ((-937) |has| |#1| (-937)) ((-948) |has| |#1| (-376)) ((-1067 (-419 (-558))) |has| |#1| (-1067 (-419 (-558)))) ((-1067 (-558)) |has| |#1| (-1067 (-558))) ((-1067 #3#) . T) ((-1067 |#1|) . T) ((-1080 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1080 |#1|) . T) ((-1080 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1085 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1085 |#1|) . T) ((-1085 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1181) |has| |#1| (-1181)) ((-1246) . 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"TUBETOOL" 3138915 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1242 3135875 3136116 3136358 "TUBE" 3136862 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1241 3124124 3128632 3128729 "TSETCAT" 3133998 NIL TSETCAT (NIL T T T T) -9 NIL 3135530 NIL) (-1240 3118592 3120456 3122347 "TSETCAT-" 3122352 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3112778 3117564 3117847 "TS" 3118344 NIL TS (NIL T) -8 NIL NIL NIL) (-1238 3107251 3108264 3109193 "TRMANIP" 3111914 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1237 3106680 3106755 3106918 "TRIMAT" 3107183 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1236 3104492 3104783 3105140 "TRIGMNIP" 3106429 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1235 3103976 3104125 3104155 "TRIGCAT" 3104368 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1234 3103621 3103724 3103865 "TRIGCAT-" 3103870 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1233 3100347 3102479 3102760 "TREE" 3103375 NIL TREE (NIL T) -8 NIL NIL NIL) (-1232 3099453 3100149 3100179 "TRANFUN" 3100214 T TRANFUN (NIL) -9 NIL 3100280 NIL) (-1231 3098672 3098923 3099203 "TRANFUN-" 3099208 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1230 3098470 3098508 3098569 "TOPSP" 3098633 T TOPSP (NIL) -7 NIL NIL NIL) (-1229 3097800 3097933 3098087 "TOOLSIGN" 3098351 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1228 3096314 3096977 3097216 "TEXTFILE" 3097583 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1227 3096089 3096126 3096198 "TEX1" 3096277 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3093893 3094542 3094971 "TEX" 3095682 T TEX (NIL) -8 NIL NIL NIL) (-1225 3093529 3093604 3093694 "TEMUTL" 3093825 T TEMUTL (NIL) -7 NIL NIL NIL) (-1224 3091623 3091963 3092288 "TBCMPPK" 3093252 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1223 3083059 3089709 3089765 "TBAGG" 3090165 NIL TBAGG (NIL T T) -9 NIL 3090376 NIL) (-1222 3077943 3079617 3081371 "TBAGG-" 3081376 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1221 3077309 3077434 3077579 "TANEXP" 3077832 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1220 3076760 3077084 3077174 "TALGOP" 3077254 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1219 3076154 3076271 3076409 "TABLEAU" 3076657 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3069284 3076011 3076104 "TABLE" 3076109 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1217 3063814 3065112 3066360 "TABLBUMP" 3068070 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1216 3063024 3063183 3063364 "SYSTEM" 3063655 T SYSTEM (NIL) -8 NIL NIL NIL) (-1215 3059429 3060182 3060965 "SYSSOLP" 3062275 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1214 3059191 3059384 3059415 "SYSPTR" 3059420 T SYSPTR (NIL) -8 NIL NIL NIL) (-1213 3058030 3058722 3058848 "SYSNNI" 3059034 NIL SYSNNI (NIL NIL) -8 NIL NIL 3059126) (-1212 3057237 3057792 3057871 "SYSINT" 3057931 NIL SYSINT (NIL NIL) -8 NIL NIL 3057976) (-1211 3053347 3054515 3055225 "SYNTAX" 3056549 T SYNTAX (NIL) -8 NIL NIL NIL) (-1210 3050427 3051107 3051739 "SYMTAB" 3052737 T SYMTAB (NIL) -8 NIL NIL NIL) (-1209 3045550 3046596 3047573 "SYMS" 3049472 T SYMS (NIL) -8 NIL NIL NIL) (-1208 3042468 3045006 3045239 "SYMPOLY" 3045357 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1207 3041973 3042060 3042183 "SYMFUNC" 3042380 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1206 3037916 3039299 3040105 "SYMBOL" 3041189 T SYMBOL (NIL) -8 NIL NIL NIL) (-1205 3031389 3033144 3034864 "SWITCH" 3036218 T SWITCH (NIL) -8 NIL NIL NIL) (-1204 3024150 3030345 3030639 "SUTS" 3031153 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3015646 3023532 3023796 "SUPXS" 3023944 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1202 3014793 3014932 3015149 "SUPFRACF" 3015514 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3014408 3014473 3014586 "SUP2" 3014728 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3004987 3014026 3014152 "SUP" 3014317 NIL SUP (NIL T) -8 NIL NIL NIL) (-1199 3003411 3003709 3004065 "SUMRF" 3004686 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1198 3002734 3002812 3003004 "SUMFS" 3003332 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1197 2984616 3002046 3002288 "SULS" 3002550 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1196 2984164 2984438 2984508 "SUCHTAST" 2984568 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1195 2983405 2983689 2983829 "SUCH" 2984072 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1194 2977044 2978311 2979270 "SUBSPACE" 2982493 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1193 2976464 2976564 2976728 "SUBRESP" 2976932 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1192 2970475 2971757 2972904 "STTFNC" 2975364 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2963669 2965140 2966451 "STTF" 2969211 NIL STTF (NIL T) -7 NIL NIL NIL) (-1190 2954785 2956851 2958645 "STTAYLOR" 2961910 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1189 2947655 2954649 2954732 "STRTBL" 2954737 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1188 2942308 2947378 2947470 "STRING" 2947585 T STRING (NIL) -8 NIL NIL NIL) (-1187 2941812 2941895 2942039 "STREAM3" 2942225 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2940776 2940977 2941212 "STREAM2" 2941625 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2940458 2940516 2940609 "STREAM1" 2940718 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2932574 2938077 2938688 "STREAM" 2939882 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1183 2931566 2931771 2932002 "STINPROD" 2932390 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1182 2930681 2931055 2931203 "STEPAST" 2931440 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2930177 2930422 2930452 "STEP" 2930546 T STEP (NIL) -9 NIL 2930617 NIL) (-1180 2923349 2930076 2930153 "STBL" 2930158 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1179 2917532 2922143 2922186 "STAGG" 2922618 NIL STAGG (NIL T) -9 NIL 2922797 NIL) (-1178 2915090 2915840 2916710 "STAGG-" 2916715 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1177 2913176 2914860 2914952 "STACK" 2915033 NIL STACK (NIL T) -8 NIL NIL NIL) (-1176 2912493 2913006 2913036 "SRING" 2913041 T SRING (NIL) -9 NIL 2913061 NIL) (-1175 2904642 2910634 2911090 "SREGSET" 2912123 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1174 2896989 2898436 2899949 "SRDCMPK" 2903248 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1173 2889403 2894348 2894378 "SRAGG" 2895681 T SRAGG (NIL) -9 NIL 2896289 NIL) (-1172 2888354 2888675 2889054 "SRAGG-" 2889059 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1171 2882056 2887301 2887722 "SQMATRIX" 2887980 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1170 2875583 2878774 2879501 "SPLTREE" 2881401 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1169 2871408 2872239 2872885 "SPLNODE" 2875009 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1168 2870383 2870688 2870718 "SPFCAT" 2871162 T SPFCAT (NIL) -9 NIL NIL NIL) (-1167 2869078 2869330 2869594 "SPECOUT" 2870141 T SPECOUT (NIL) -7 NIL NIL NIL) (-1166 2859730 2862046 2862076 "SPADXPT" 2866752 T SPADXPT (NIL) -9 NIL 2868916 NIL) (-1165 2859485 2859531 2859600 "SPADPRSR" 2859683 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1164 2857090 2859440 2859471 "SPADAST" 2859476 T SPADAST (NIL) -8 NIL NIL NIL) (-1163 2848691 2850794 2850837 "SPACEC" 2855210 NIL SPACEC (NIL T) -9 NIL 2857026 NIL) (-1162 2846491 2848623 2848672 "SPACE3" 2848677 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1161 2845223 2845414 2845705 "SORTPAK" 2846296 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1160 2843285 2843618 2844030 "SOLVETRA" 2844887 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1159 2842323 2842557 2842818 "SOLVESER" 2843058 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1158 2837555 2838515 2839510 "SOLVERAD" 2841375 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1157 2833280 2833979 2834708 "SOLVEFOR" 2836922 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1156 2827025 2832628 2832725 "SNTSCAT" 2832730 NIL SNTSCAT (NIL T T T T) -9 NIL 2832800 NIL) (-1155 2820576 2825348 2825739 "SMTS" 2826715 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1154 2814324 2820464 2820541 "SMP" 2820546 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1153 2812453 2812784 2813182 "SMITH" 2814021 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1152 2804090 2809026 2809129 "SMATCAT" 2810483 NIL SMATCAT (NIL NIL T T T) -9 NIL 2811033 NIL) (-1151 2800883 2801867 2803038 "SMATCAT-" 2803043 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1150 2798463 2800091 2800134 "SKAGG" 2800395 NIL SKAGG (NIL T) -9 NIL 2800530 NIL) (-1149 2794127 2797960 2798130 "SINT" 2798282 T SINT (NIL) -8 NIL NIL 2798430) (-1148 2793893 2793937 2794003 "SIMPAN" 2794083 T SIMPAN (NIL) -7 NIL NIL NIL) (-1147 2792734 2792966 2793234 "SIGNRF" 2793659 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1146 2791570 2791732 2792009 "SIGNEF" 2792570 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1145 2790810 2791153 2791277 "SIGAST" 2791468 T SIGAST (NIL) -8 NIL NIL NIL) (-1144 2790035 2790345 2790485 "SIG" 2790692 T SIG (NIL) -8 NIL NIL NIL) (-1143 2787687 2788179 2788685 "SHP" 2789576 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1142 2781132 2787588 2787664 "SHDP" 2787669 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1141 2780643 2780883 2780913 "SGROUP" 2781006 T SGROUP (NIL) -9 NIL 2781068 NIL) (-1140 2780495 2780527 2780600 "SGROUP-" 2780605 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1139 2777214 2777984 2778707 "SGCF" 2779794 T SGCF (NIL) -7 NIL NIL NIL) (-1138 2771057 2776660 2776757 "SFRTCAT" 2776762 NIL SFRTCAT (NIL T T T T) -9 NIL 2776801 NIL) (-1137 2764376 2765496 2766632 "SFRGCD" 2770040 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1136 2757394 2758575 2759761 "SFQCMPK" 2763309 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1135 2756996 2757103 2757214 "SFORT" 2757335 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1134 2755922 2756836 2756957 "SEXOF" 2756962 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1133 2751511 2752418 2752513 "SEXCAT" 2755135 NIL SEXCAT (NIL T T T T T) -9 NIL 2755695 NIL) (-1132 2750426 2751392 2751460 "SEX" 2751465 T SEX (NIL) -8 NIL NIL NIL) (-1131 2748554 2749143 2749446 "SETMN" 2750169 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1130 2748084 2748272 2748302 "SETCAT" 2748419 T SETCAT (NIL) -9 NIL 2748504 NIL) (-1129 2747852 2747916 2748015 "SETCAT-" 2748020 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1128 2744066 2746313 2746356 "SETAGG" 2747226 NIL SETAGG (NIL T) -9 NIL 2747566 NIL) (-1127 2743488 2743640 2743877 "SETAGG-" 2743882 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1126 2740411 2743422 2743470 "SET" 2743475 NIL SET (NIL T) -8 NIL NIL NIL) (-1125 2739794 2740107 2740208 "SEQAST" 2740332 T SEQAST (NIL) -8 NIL NIL NIL) (-1124 2738921 2739287 2739348 "SEGXCAT" 2739634 NIL SEGXCAT (NIL T T) -9 NIL 2739754 NIL) (-1123 2737846 2738114 2738157 "SEGCAT" 2738679 NIL SEGCAT (NIL T) -9 NIL 2738900 NIL) (-1122 2737461 2737526 2737639 "SEGBIND2" 2737781 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2736351 2736824 2737032 "SEGBIND" 2737288 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1120 2735870 2736152 2736229 "SEGAST" 2736296 T SEGAST (NIL) -8 NIL NIL NIL) (-1119 2735079 2735215 2735419 "SEG2" 2735714 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1118 2733995 2734745 2734927 "SEG" 2734932 NIL SEG (NIL T) -8 NIL NIL NIL) (-1117 2733228 2733930 2733977 "SDVAR" 2733982 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1116 2724622 2732998 2733128 "SDPOL" 2733133 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1115 2723191 2723481 2723800 "SCPKG" 2724337 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1114 2722313 2722527 2722719 "SCOPE" 2723021 T SCOPE (NIL) -8 NIL NIL NIL) (-1113 2721509 2721667 2721846 "SCACHE" 2722168 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1112 2721093 2721327 2721357 "SASTCAT" 2721362 T SASTCAT (NIL) -9 NIL 2721375 NIL) (-1111 2720496 2720928 2721004 "SAOS" 2721039 T SAOS (NIL) -8 NIL NIL NIL) (-1110 2720055 2720096 2720269 "SAERFFC" 2720455 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1109 2719642 2719683 2719842 "SAEFACT" 2720014 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1108 2712699 2719539 2719619 "SAE" 2719624 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1107 2711002 2711334 2711735 "RURPK" 2712365 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1106 2709579 2709945 2710250 "RULESET" 2710836 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1105 2709149 2709373 2709456 "RULECOLD" 2709531 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1104 2706264 2706902 2707360 "RULE" 2708830 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1103 2706048 2706082 2706153 "RTVALUE" 2706215 T RTVALUE (NIL) -8 NIL NIL NIL) (-1102 2705459 2705765 2705859 "RSTRCAST" 2705976 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1101 2700229 2701102 2702022 "RSETGCD" 2704658 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2688934 2694537 2694634 "RSETCAT" 2698753 NIL RSETCAT (NIL T T T T) -9 NIL 2699850 NIL) (-1099 2686753 2687400 2688224 "RSETCAT-" 2688229 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1098 2679061 2680515 2682035 "RSDCMPK" 2685352 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1097 2676930 2677493 2677567 "RRCC" 2678653 NIL RRCC (NIL T T) -9 NIL 2678997 NIL) (-1096 2676251 2676455 2676734 "RRCC-" 2676739 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1095 2675634 2675947 2676048 "RPTAST" 2676172 T RPTAST (NIL) -8 NIL NIL NIL) (-1094 2648046 2658746 2658813 "RPOLCAT" 2669479 NIL RPOLCAT (NIL T T T) -9 NIL 2672639 NIL) (-1093 2639052 2641908 2645018 "RPOLCAT-" 2645023 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1092 2629621 2637263 2637745 "ROUTINE" 2638592 T ROUTINE (NIL) -8 NIL NIL NIL) (-1091 2625686 2629247 2629387 "ROMAN" 2629503 T ROMAN (NIL) -8 NIL NIL NIL) (-1090 2623800 2624546 2624806 "ROIRC" 2625491 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1089 2619577 2622342 2622372 "RNS" 2622641 T RNS (NIL) -9 NIL 2622897 NIL) (-1088 2617984 2618469 2619003 "RNS-" 2619078 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1087 2616945 2617349 2617551 "RNGBIND" 2617835 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1086 2616238 2616742 2616772 "RNG" 2616777 T RNG (NIL) -9 NIL 2616798 NIL) (-1085 2615533 2616011 2616054 "RMODULE" 2616059 NIL RMODULE (NIL T) -9 NIL 2616086 NIL) (-1084 2614357 2614463 2614799 "RMCAT2" 2615434 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1083 2610973 2613703 2614000 "RMATRIX" 2614119 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1082 2603583 2606060 2606175 "RMATCAT" 2609534 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2610516 NIL) (-1081 2602922 2603105 2603412 "RMATCAT-" 2603417 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1080 2602495 2602709 2602752 "RLINSET" 2602814 NIL RLINSET (NIL T) -9 NIL 2602858 NIL) (-1079 2602056 2602137 2602265 "RINTERP" 2602414 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1078 2600980 2601654 2601684 "RING" 2601740 T RING (NIL) -9 NIL 2601832 NIL) (-1077 2600760 2600816 2600913 "RING-" 2600918 NIL RING- (NIL T) -8 NIL NIL NIL) (-1076 2599571 2599838 2600096 "RIDIST" 2600524 T RIDIST (NIL) -7 NIL NIL NIL) (-1075 2590337 2599039 2599245 "RGCHAIN" 2599419 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1074 2589595 2590079 2590120 "RGBCSPC" 2590178 NIL RGBCSPC (NIL T) -9 NIL 2590230 NIL) (-1073 2588661 2589120 2589161 "RGBCMDL" 2589393 NIL RGBCMDL (NIL T) -9 NIL 2589507 NIL) (-1072 2588301 2588370 2588473 "RFFACTOR" 2588592 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1071 2588020 2588061 2588158 "RFFACT" 2588260 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1070 2586071 2586501 2586883 "RFDIST" 2587660 T RFDIST (NIL) -7 NIL NIL NIL) (-1069 2583011 2583679 2584349 "RF" 2585435 NIL RF (NIL T) -7 NIL NIL NIL) (-1068 2582458 2582556 2582719 "RETSOL" 2582913 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1067 2582076 2582174 2582217 "RETRACT" 2582350 NIL RETRACT (NIL T) -9 NIL 2582437 NIL) (-1066 2581919 2581950 2582037 "RETRACT-" 2582042 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1065 2581467 2581741 2581811 "RETAST" 2581871 T RETAST (NIL) -8 NIL NIL NIL) (-1064 2573933 2581120 2581247 "RESULT" 2581362 T RESULT (NIL) -8 NIL NIL NIL) (-1063 2572368 2573202 2573401 "RESRING" 2573836 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1062 2571992 2572053 2572151 "RESLATC" 2572305 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1061 2571691 2571732 2571839 "REPSQ" 2571951 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1060 2571382 2571423 2571534 "REPDB" 2571650 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1059 2565214 2566671 2567894 "REP2" 2570194 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1058 2561517 2562272 2563080 "REP1" 2564441 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1057 2558897 2559519 2560121 "REP" 2560937 T REP (NIL) -7 NIL NIL NIL) (-1056 2551046 2557038 2557494 "REGSET" 2558527 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1055 2549755 2550194 2550444 "REF" 2550831 NIL REF (NIL T) -8 NIL NIL NIL) (-1054 2549120 2549235 2549402 "REDORDER" 2549639 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1053 2544522 2548333 2548560 "RECLOS" 2548948 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1052 2543556 2543755 2543970 "REALSOLV" 2544329 T REALSOLV (NIL) -7 NIL NIL NIL) (-1051 2540003 2540841 2541725 "REAL0Q" 2542721 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1050 2535556 2536592 2537653 "REAL0" 2538984 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1049 2535390 2535443 2535473 "REAL" 2535478 T REAL (NIL) -9 NIL 2535513 NIL) (-1048 2534801 2535107 2535201 "RDUCEAST" 2535318 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1047 2534200 2534278 2534485 "RDIV" 2534723 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1046 2533250 2533442 2533655 "RDIST" 2534022 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1045 2531835 2532134 2532506 "RDETRS" 2532958 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1044 2529629 2530101 2530639 "RDETR" 2531377 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1043 2528248 2528532 2528929 "RDEEFS" 2529345 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1042 2526751 2527063 2527488 "RDEEF" 2527936 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1041 2520239 2523705 2523735 "RCFIELD" 2525030 T RCFIELD (NIL) -9 NIL 2525761 NIL) (-1040 2518195 2518807 2519503 "RCFIELD-" 2519578 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1039 2514358 2516268 2516311 "RCAGG" 2517395 NIL RCAGG (NIL T) -9 NIL 2517860 NIL) (-1038 2513968 2514080 2514243 "RCAGG-" 2514248 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1037 2513285 2513415 2513580 "RATRET" 2513852 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1036 2512826 2512905 2513026 "RATFACT" 2513213 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1035 2512104 2512254 2512406 "RANDSRC" 2512696 T RANDSRC (NIL) -7 NIL NIL NIL) (-1034 2511832 2511882 2511955 "RADUTIL" 2512053 T RADUTIL (NIL) -7 NIL NIL NIL) (-1033 2503993 2510663 2510974 "RADIX" 2511555 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1032 2493619 2503835 2503965 "RADFF" 2503970 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1031 2493248 2493341 2493371 "RADCAT" 2493531 T RADCAT (NIL) -9 NIL NIL NIL) (-1030 2493018 2493078 2493178 "RADCAT-" 2493183 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1029 2491043 2492788 2492880 "QUEUE" 2492961 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1028 2490668 2490717 2490848 "QUATCT2" 2490994 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1027 2483053 2487091 2487133 "QUATCAT" 2487924 NIL QUATCAT (NIL T) -9 NIL 2488690 NIL) (-1026 2478955 2480243 2481626 "QUATCAT-" 2481722 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1025 2474808 2478888 2478936 "QUAT" 2478941 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1024 2472175 2473856 2473899 "QUAGG" 2474280 NIL QUAGG (NIL T) -9 NIL 2474455 NIL) (-1023 2471723 2471997 2472067 "QQUTAST" 2472127 T QQUTAST (NIL) -8 NIL NIL NIL) (-1022 2470634 2471236 2471401 "QFORM" 2471604 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1021 2470259 2470308 2470439 "QFCAT2" 2470585 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2459972 2466106 2466148 "QFCAT" 2466816 NIL QFCAT (NIL T) -9 NIL 2467817 NIL) (-1019 2455342 2456778 2458353 "QFCAT-" 2458449 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1018 2454773 2454907 2455039 "QEQUAT" 2455232 T QEQUAT (NIL) -8 NIL NIL NIL) (-1017 2447791 2448972 2450158 "QCMPACK" 2453706 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1016 2447020 2447202 2447438 "QALGSET2" 2447609 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1015 2444476 2445010 2445438 "QALGSET" 2446677 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1014 2443143 2443385 2443704 "PWFFINTB" 2444249 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1013 2441305 2441503 2441859 "PUSHVAR" 2442957 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1012 2437032 2438248 2438291 "PTRANFN" 2440202 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1011 2435369 2435714 2436038 "PTPACK" 2436743 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1010 2434992 2435055 2435166 "PTFUNC2" 2435306 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1009 2429022 2433781 2433824 "PTCAT" 2434124 NIL PTCAT (NIL T) -9 NIL 2434277 NIL) (-1008 2428671 2428712 2428838 "PSQFR" 2428981 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1007 2427243 2427559 2427895 "PSEUDLIN" 2428369 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1006 2413763 2416338 2418664 "PSETPK" 2425003 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1005 2406582 2409499 2409597 "PSETCAT" 2412638 NIL PSETCAT (NIL T T T T) -9 NIL 2413452 NIL) (-1004 2404307 2405049 2405873 "PSETCAT-" 2405878 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1003 2403620 2403815 2403845 "PSCURVE" 2404117 T PSCURVE (NIL) -9 NIL 2404284 NIL) (-1002 2399343 2401110 2401177 "PSCAT" 2402029 NIL PSCAT (NIL T T T) -9 NIL 2402269 NIL) (-1001 2398337 2398619 2399022 "PSCAT-" 2399027 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1000 2396505 2397396 2397661 "PRTITION" 2398094 T PRTITION (NIL) -8 NIL NIL NIL) (-999 2395920 2396226 2396318 "PRTDAST" 2396433 T PRTDAST (NIL) -8 NIL NIL NIL) (-998 2384802 2387224 2389412 "PRS" 2393782 NIL PRS (NIL T T) -7 NIL NIL NIL) (-997 2382533 2384124 2384164 "PRQAGG" 2384347 NIL PRQAGG (NIL T) -9 NIL 2384449 NIL) (-996 2381712 2382161 2382189 "PROPLOG" 2382328 T PROPLOG (NIL) -9 NIL 2382443 NIL) (-995 2381310 2381373 2381496 "PROPFUN2" 2381635 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-994 2380607 2380746 2380918 "PROPFUN1" 2381171 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-993 2378588 2379354 2379651 "PROPFRML" 2380343 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-992 2378033 2378164 2378292 "PROPERTY" 2378480 T PROPERTY (NIL) -8 NIL NIL NIL) (-991 2371846 2376199 2377019 "PRODUCT" 2377259 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-990 2371636 2371674 2371733 "PRINT" 2371807 T PRINT (NIL) -7 NIL NIL NIL) (-989 2370952 2371093 2371245 "PRIMES" 2371516 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-988 2368999 2369418 2369884 "PRIMELT" 2370531 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-987 2368716 2368777 2368805 "PRIMCAT" 2368929 T PRIMCAT (NIL) -9 NIL NIL NIL) (-986 2367705 2367901 2368129 "PRIMARR2" 2368534 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2363541 2367643 2367688 "PRIMARR" 2367693 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-984 2363178 2363240 2363351 "PREASSOC" 2363479 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-983 2360150 2362636 2362870 "PR" 2362989 NIL PR (NIL T T) -8 NIL NIL NIL) (-982 2359601 2359758 2359786 "PPCURVE" 2359991 T PPCURVE (NIL) -9 NIL 2360127 NIL) (-981 2359148 2359396 2359479 "PORTNUM" 2359538 T PORTNUM (NIL) -8 NIL NIL NIL) (-980 2356485 2356906 2357498 "POLYROOT" 2358729 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-979 2355862 2355926 2356160 "POLYLIFT" 2356421 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-978 2352083 2352586 2353215 "POLYCATQ" 2355407 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-977 2337745 2343830 2343895 "POLYCAT" 2347409 NIL POLYCAT (NIL T T T) -9 NIL 2349287 NIL) (-976 2330927 2333098 2335461 "POLYCAT-" 2335466 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-975 2330508 2330582 2330702 "POLY2UP" 2330853 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-974 2330134 2330197 2330306 "POLY2" 2330445 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-973 2323375 2329738 2329898 "POLY" 2330007 NIL POLY (NIL T) -8 NIL NIL NIL) (-972 2322036 2322299 2322575 "POLUTIL" 2323149 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-971 2320355 2320668 2320999 "POLTOPOL" 2321758 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-970 2315465 2320289 2320336 "POINT" 2320341 NIL POINT (NIL T) -8 NIL NIL NIL) (-969 2313598 2314009 2314384 "PNTHEORY" 2315110 T PNTHEORY (NIL) -7 NIL NIL NIL) (-968 2312044 2312353 2312752 "PMTOOLS" 2313296 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-967 2311631 2311715 2311832 "PMSYM" 2311960 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-966 2311133 2311208 2311383 "PMQFCAT" 2311556 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-965 2310514 2310612 2310774 "PMPREDFS" 2311034 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-964 2309857 2309979 2310135 "PMPRED" 2310391 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-963 2308511 2308729 2309107 "PMPLCAT" 2309619 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-962 2308037 2308122 2308274 "PMLSAGG" 2308426 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-961 2307504 2307586 2307768 "PMKERNEL" 2307955 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-960 2307115 2307196 2307309 "PMINS" 2307423 NIL PMINS (NIL T) -7 NIL NIL NIL) (-959 2306551 2306626 2306835 "PMFS" 2307040 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-958 2305767 2305897 2306102 "PMDOWN" 2306428 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-957 2305016 2305150 2305313 "PMASSFS" 2305654 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-956 2304159 2304341 2304522 "PMASS" 2304855 T PMASS (NIL) -7 NIL NIL NIL) (-955 2303808 2303882 2303976 "PLOTTOOL" 2304085 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-954 2299460 2300654 2301576 "PLOT3D" 2302906 T PLOT3D (NIL) -8 NIL NIL NIL) (-953 2298348 2298549 2298784 "PLOT1" 2299264 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-952 2292769 2294159 2295307 "PLOT" 2297220 T PLOT (NIL) -8 NIL NIL NIL) (-951 2267944 2272835 2277686 "PLEQN" 2288035 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-950 2267631 2267684 2267787 "PINTERPA" 2267891 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-949 2266937 2267071 2267251 "PINTERP" 2267496 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-948 2265021 2266187 2266215 "PID" 2266412 T PID (NIL) -9 NIL 2266539 NIL) (-947 2264766 2264809 2264884 "PICOERCE" 2264978 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-946 2263862 2264530 2264617 "PI" 2264657 T PI (NIL) -8 NIL NIL 2264724) (-945 2263170 2263321 2263497 "PGROEB" 2263718 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-944 2258609 2259568 2260474 "PGE" 2262284 T PGE (NIL) -7 NIL NIL NIL) (-943 2256690 2256979 2257345 "PGCD" 2258326 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-942 2256016 2256131 2256292 "PFRPAC" 2256574 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-941 2252276 2254564 2254917 "PFR" 2255695 NIL PFR (NIL T) -8 NIL NIL NIL) (-940 2250629 2250909 2251234 "PFOTOOLS" 2252023 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-939 2249144 2249401 2249752 "PFOQ" 2250386 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-938 2247627 2247857 2248213 "PFO" 2248928 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-937 2244711 2246217 2246245 "PFECAT" 2246838 T PFECAT (NIL) -9 NIL 2247215 NIL) (-936 2244159 2244324 2244531 "PFECAT-" 2244536 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-935 2242732 2243014 2243315 "PFBRU" 2243908 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-934 2240561 2240950 2241382 "PFBR" 2242383 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-933 2236509 2240450 2240519 "PF" 2240524 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2231563 2232716 2233586 "PERMGRP" 2235672 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-931 2229475 2230587 2230628 "PERMCAT" 2231028 NIL PERMCAT (NIL T) -9 NIL 2231326 NIL) (-930 2229122 2229169 2229293 "PERMAN" 2229428 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-929 2224924 2226631 2227279 "PERM" 2228507 NIL PERM (NIL T) -8 NIL NIL NIL) (-928 2222281 2224589 2224711 "PENDTREE" 2224835 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-927 2221162 2221425 2221466 "PDSPC" 2221999 NIL PDSPC (NIL T) -9 NIL 2222244 NIL) (-926 2220217 2220483 2220845 "PDSPC-" 2220850 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-925 2218931 2219867 2219908 "PDRING" 2219913 NIL PDRING (NIL T) -9 NIL 2219941 NIL) (-924 2217674 2218436 2218490 "PDMOD" 2218495 NIL PDMOD (NIL T T) -9 NIL 2218599 NIL) (-923 2214841 2215667 2216335 "PDEPROB" 2217026 T PDEPROB (NIL) -8 NIL NIL NIL) (-922 2212350 2212890 2213445 "PDEPACK" 2214306 T PDEPACK (NIL) -7 NIL NIL NIL) (-921 2211238 2211452 2211703 "PDECOMP" 2212149 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-920 2208755 2209646 2209674 "PDECAT" 2210461 T PDECAT (NIL) -9 NIL 2211174 NIL) (-919 2208372 2208439 2208493 "PDDOM" 2208658 NIL PDDOM (NIL T T) -9 NIL 2208738 NIL) (-918 2208185 2208221 2208328 "PDDOM-" 2208333 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-917 2207930 2207969 2208059 "PCOMP" 2208146 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-916 2205970 2206731 2207028 "PBWLB" 2207659 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-915 2205596 2205659 2205768 "PATTERN2" 2205907 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-914 2203305 2203741 2204198 "PATTERN1" 2205185 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-913 2195486 2197378 2198716 "PATTERN" 2201988 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-912 2195044 2195117 2195249 "PATRES2" 2195413 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-911 2192310 2192993 2193474 "PATRES" 2194609 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-910 2190163 2190598 2191005 "PATMATCH" 2191977 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-909 2189617 2189868 2189909 "PATMAB" 2190016 NIL PATMAB (NIL T) -9 NIL 2190099 NIL) (-908 2188063 2188471 2188729 "PATLRES" 2189422 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-907 2187601 2187732 2187773 "PATAB" 2187778 NIL PATAB (NIL T) -9 NIL 2187950 NIL) (-906 2185741 2186178 2186601 "PARTPERM" 2187198 T PARTPERM (NIL) -7 NIL NIL NIL) (-905 2185350 2185425 2185527 "PARSURF" 2185672 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-904 2184976 2185039 2185148 "PARSU2" 2185287 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-903 2184734 2184780 2184847 "PARSER" 2184929 T PARSER (NIL) -7 NIL NIL NIL) (-902 2184343 2184418 2184520 "PARSCURV" 2184665 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-901 2183969 2184032 2184141 "PARSC2" 2184280 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-900 2183596 2183666 2183763 "PARPCURV" 2183905 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-899 2183222 2183285 2183394 "PARPC2" 2183533 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-898 2182211 2182595 2182777 "PARAMAST" 2183060 T PARAMAST (NIL) -8 NIL NIL NIL) (-897 2181719 2181817 2181936 "PAN2EXPR" 2182112 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-896 2180412 2180840 2181068 "PALETTE" 2181511 T PALETTE (NIL) -8 NIL NIL NIL) (-895 2178757 2179417 2179777 "PAIR" 2180098 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-894 2171706 2178014 2178209 "PADICRC" 2178611 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-893 2163979 2171050 2171235 "PADICRAT" 2171553 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-892 2160778 2162639 2162679 "PADICCT" 2163260 NIL PADICCT (NIL NIL) -9 NIL 2163542 NIL) (-891 2158796 2160715 2160760 "PADIC" 2160765 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-890 2157741 2157953 2158221 "PADEPAC" 2158583 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-889 2156941 2157086 2157292 "PADE" 2157603 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-888 2155174 2156149 2156429 "OWP" 2156745 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-887 2154619 2154880 2154977 "OVERSET" 2155097 T OVERSET (NIL) -8 NIL NIL NIL) (-886 2153539 2154224 2154396 "OVAR" 2154487 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-885 2141775 2144648 2146848 "OUTFORM" 2151359 T OUTFORM (NIL) -8 NIL NIL NIL) (-884 2141057 2141372 2141499 "OUTBFILE" 2141668 T OUTBFILE (NIL) -8 NIL NIL NIL) (-883 2140334 2140529 2140557 "OUTBCON" 2140875 T OUTBCON (NIL) -9 NIL 2141041 NIL) (-882 2139917 2140047 2140204 "OUTBCON-" 2140209 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-881 2139157 2139302 2139463 "OUT" 2139776 T OUT (NIL) -7 NIL NIL NIL) (-880 2138453 2138886 2138975 "OSI" 2139088 T OSI (NIL) -8 NIL NIL NIL) (-879 2137872 2138294 2138322 "OSGROUP" 2138327 T OSGROUP (NIL) -9 NIL 2138349 NIL) (-878 2136583 2136844 2137129 "ORTHPOL" 2137619 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-877 2133848 2136418 2136539 "OREUP" 2136544 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-876 2130965 2133539 2133666 "ORESUP" 2133790 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-875 2128465 2128993 2129554 "OREPCTO" 2130454 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-874 2121850 2124338 2124379 "OREPCAT" 2126727 NIL OREPCAT (NIL T) -9 NIL 2127831 NIL) (-873 2118844 2119793 2120844 "OREPCAT-" 2120849 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-872 2118036 2118314 2118342 "ORDTYPE" 2118651 T ORDTYPE (NIL) -9 NIL 2118814 NIL) (-871 2117337 2117553 2117808 "ORDTYPE-" 2117813 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-870 2116693 2117076 2117234 "ORDSTRCT" 2117239 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-869 2116191 2116561 2116589 "ORDSET" 2116594 T ORDSET (NIL) -9 NIL 2116616 NIL) (-868 2114842 2115813 2115841 "ORDRING" 2115846 T ORDRING (NIL) -9 NIL 2115875 NIL) (-867 2114093 2114658 2114686 "ORDMON" 2114691 T ORDMON (NIL) -9 NIL 2114712 NIL) (-866 2113237 2113402 2113597 "ORDFUNS" 2113942 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-865 2112452 2112967 2112995 "ORDFIN" 2113060 T ORDFIN (NIL) -9 NIL 2113134 NIL) (-864 2111706 2111845 2112031 "ORDCOMP2" 2112312 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2108060 2110292 2110701 "ORDCOMP" 2111330 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-862 2104581 2105551 2106365 "OPTPROB" 2107266 T OPTPROB (NIL) -8 NIL NIL NIL) (-861 2101323 2102022 2102726 "OPTPACK" 2103897 T OPTPACK (NIL) -7 NIL NIL NIL) (-860 2098936 2099762 2099790 "OPTCAT" 2100609 T OPTCAT (NIL) -9 NIL 2101259 NIL) (-859 2098254 2098613 2098718 "OPSIG" 2098851 T OPSIG (NIL) -8 NIL NIL NIL) (-858 2098016 2098061 2098127 "OPQUERY" 2098208 T OPQUERY (NIL) -7 NIL NIL NIL) (-857 2097322 2097602 2097643 "OPERCAT" 2097855 NIL OPERCAT (NIL T) -9 NIL 2097952 NIL) (-856 2097065 2097133 2097250 "OPERCAT-" 2097255 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-855 2093983 2095376 2095880 "OP" 2096594 NIL OP (NIL T) -8 NIL NIL NIL) (-854 2093276 2093403 2093577 "ONECOMP2" 2093855 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-853 2089896 2092073 2092442 "ONECOMP" 2092940 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-852 2086521 2089336 2089376 "OMSAGG" 2089437 NIL OMSAGG (NIL T) -9 NIL 2089501 NIL) (-851 2085096 2085407 2085689 "OMPKG" 2086259 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2083443 2084645 2084814 "OMLO" 2084977 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2082379 2082550 2082770 "OMEXPR" 2083269 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2081464 2081800 2081960 "OMERRK" 2082239 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2080701 2081010 2081146 "OMERR" 2081348 T OMERR (NIL) -8 NIL NIL NIL) (-846 2080092 2080378 2080486 "OMENC" 2080613 T OMENC (NIL) -8 NIL NIL NIL) (-845 2073729 2075172 2076343 "OMDEV" 2078941 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2072762 2072969 2073163 "OMCONN" 2073555 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2072168 2072295 2072323 "OM" 2072622 T OM (NIL) -9 NIL NIL NIL) (-842 2070446 2071638 2071666 "OINTDOM" 2071671 T OINTDOM (NIL) -9 NIL 2071692 NIL) (-841 2067528 2069134 2069471 "OFMONOID" 2070141 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2066762 2067465 2067510 "ODVAR" 2067515 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2063908 2066507 2066662 "ODR" 2066667 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2055356 2063684 2063810 "ODPOL" 2063815 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2048771 2055228 2055333 "ODP" 2055338 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2047513 2047752 2048027 "ODETOOLS" 2048545 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2044456 2045138 2045854 "ODESYS" 2046846 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2039286 2040246 2041271 "ODERTRIC" 2043531 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2038706 2038794 2038988 "ODERED" 2039198 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2035566 2036148 2036823 "ODERAT" 2038131 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2032482 2032990 2033587 "ODEPRRIC" 2035095 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2030377 2031021 2031507 "ODEPROB" 2032016 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2026843 2027382 2028029 "ODEPRIM" 2029856 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2026086 2026194 2026454 "ODEPAL" 2026735 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2022188 2023039 2023903 "ODEPACK" 2025242 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2021231 2021356 2021578 "ODEINT" 2022077 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2015296 2016757 2018204 "ODEIFTBL" 2019804 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2010660 2011490 2012438 "ODEEF" 2014459 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2010003 2010098 2010321 "ODECONST" 2010565 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2008066 2008775 2008803 "ODECAT" 2009408 T ODECAT (NIL) -9 NIL 2009939 NIL) (-821 2007698 2007747 2007874 "OCTCT2" 2008017 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2004210 2007403 2007525 "OCT" 2007608 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2003403 2004003 2004031 "OCAMON" 2004036 T OCAMON (NIL) -9 NIL 2004057 NIL) (-818 1997681 2000446 2000486 "OC" 2001583 NIL OC (NIL T) -9 NIL 2002441 NIL) (-817 1994737 1995670 1996653 "OC-" 1996747 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 1994157 1994582 1994610 "OASGP" 1994615 T OASGP (NIL) -9 NIL 1994635 NIL) (-815 1993253 1993880 1993908 "OAMONS" 1993948 T OAMONS (NIL) -9 NIL 1993991 NIL) (-814 1992429 1992988 1993016 "OAMON" 1993074 T OAMON (NIL) -9 NIL 1993126 NIL) (-813 1992287 1992320 1992388 "OAMON-" 1992393 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-812 1991068 1991821 1991849 "OAGROUP" 1991996 T OAGROUP (NIL) -9 NIL 1992089 NIL) (-811 1990771 1990859 1990977 "OAGROUP-" 1990982 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-810 1990453 1990509 1990598 "NUMTUBE" 1990715 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-809 1983972 1985544 1987080 "NUMQUAD" 1988937 T NUMQUAD (NIL) -7 NIL NIL NIL) (-808 1979652 1980686 1981721 "NUMODE" 1982957 T NUMODE (NIL) -7 NIL NIL NIL) (-807 1976933 1977873 1977901 "NUMINT" 1978824 T NUMINT (NIL) -9 NIL 1979588 NIL) (-806 1975845 1976078 1976296 "NUMFMT" 1976735 T NUMFMT (NIL) -7 NIL NIL NIL) (-805 1962028 1965149 1967681 "NUMERIC" 1973352 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-804 1955873 1961476 1961571 "NTSCAT" 1961576 NIL NTSCAT (NIL T T T T) -9 NIL 1961615 NIL) (-803 1955053 1955232 1955425 "NTPOLFN" 1955712 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-802 1954679 1954742 1954851 "NSUP2" 1954990 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1941501 1951504 1952316 "NSUP" 1953900 NIL NSUP (NIL T) -8 NIL NIL NIL) (-800 1930387 1941275 1941408 "NSMP" 1941413 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-799 1928795 1929120 1929477 "NREP" 1930075 NIL NREP (NIL T) -7 NIL NIL NIL) (-798 1927374 1927638 1927996 "NPCOEF" 1928538 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-797 1926422 1926555 1926771 "NORMRETR" 1927255 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-796 1924433 1924753 1925162 "NORMPK" 1926130 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-795 1924112 1924146 1924270 "NORMMA" 1924399 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-794 1923895 1923930 1923999 "NONE1" 1924076 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1923659 1923852 1923881 "NONE" 1923886 T NONE (NIL) -8 NIL NIL NIL) (-792 1923150 1923218 1923397 "NODE1" 1923591 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-791 1921211 1922273 1922528 "NNI" 1922875 T NNI (NIL) -8 NIL NIL 1923110) (-790 1919607 1919944 1920308 "NLINSOL" 1920879 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-789 1915788 1916843 1917742 "NIPROB" 1918728 T NIPROB (NIL) -8 NIL NIL NIL) (-788 1914527 1914779 1915081 "NFINTBAS" 1915550 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-787 1913611 1914177 1914218 "NETCLT" 1914390 NIL NETCLT (NIL T) -9 NIL 1914472 NIL) (-786 1912283 1912550 1912831 "NCODIV" 1913379 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-785 1912039 1912082 1912157 "NCNTFRAC" 1912240 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-784 1910195 1910583 1911003 "NCEP" 1911664 NIL NCEP (NIL T) -7 NIL NIL NIL) (-783 1908865 1909805 1909833 "NASRING" 1909943 T NASRING (NIL) -9 NIL 1910023 NIL) (-782 1908648 1908704 1908798 "NASRING-" 1908803 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-781 1907615 1908266 1908294 "NARNG" 1908411 T NARNG (NIL) -9 NIL 1908502 NIL) (-780 1907289 1907374 1907508 "NARNG-" 1907513 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-779 1906126 1906375 1906610 "NAGSP" 1907074 T NAGSP (NIL) -7 NIL NIL NIL) (-778 1897170 1899082 1900755 "NAGS" 1904473 T NAGS (NIL) -7 NIL NIL NIL) (-777 1895694 1896026 1896357 "NAGF07" 1896859 T NAGF07 (NIL) -7 NIL NIL NIL) (-776 1890166 1891523 1892830 "NAGF04" 1894407 T NAGF04 (NIL) -7 NIL NIL NIL) (-775 1883038 1884748 1886381 "NAGF02" 1888553 T NAGF02 (NIL) -7 NIL NIL NIL) (-774 1878202 1879362 1880479 "NAGF01" 1881941 T NAGF01 (NIL) -7 NIL NIL NIL) (-773 1871782 1873396 1874981 "NAGE04" 1876637 T NAGE04 (NIL) -7 NIL NIL NIL) (-772 1862843 1865072 1867202 "NAGE02" 1869672 T NAGE02 (NIL) -7 NIL NIL NIL) (-771 1858736 1859743 1860707 "NAGE01" 1861899 T NAGE01 (NIL) -7 NIL NIL NIL) (-770 1856513 1857065 1857623 "NAGD03" 1858198 T NAGD03 (NIL) -7 NIL NIL NIL) (-769 1848209 1850191 1852145 "NAGD02" 1854579 T NAGD02 (NIL) -7 NIL NIL NIL) (-768 1841948 1843445 1844885 "NAGD01" 1846789 T NAGD01 (NIL) -7 NIL NIL NIL) (-767 1838085 1838979 1839816 "NAGC06" 1841131 T NAGC06 (NIL) -7 NIL NIL NIL) (-766 1836532 1836882 1837238 "NAGC05" 1837749 T NAGC05 (NIL) -7 NIL NIL NIL) (-765 1835896 1836027 1836171 "NAGC02" 1836408 T NAGC02 (NIL) -7 NIL NIL NIL) (-764 1834697 1835424 1835464 "NAALG" 1835543 NIL NAALG (NIL T) -9 NIL 1835604 NIL) (-763 1834526 1834561 1834651 "NAALG-" 1834656 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-762 1828398 1829584 1830771 "MULTSQFR" 1833422 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-761 1827705 1827792 1827976 "MULTFACT" 1828310 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-760 1819850 1824288 1824341 "MTSCAT" 1825411 NIL MTSCAT (NIL T T) -9 NIL 1825927 NIL) (-759 1819556 1819616 1819708 "MTHING" 1819790 NIL MTHING (NIL T) -7 NIL NIL NIL) (-758 1819342 1819381 1819441 "MSYSCMD" 1819516 T MSYSCMD (NIL) -7 NIL NIL NIL) (-757 1816198 1818903 1818944 "MSETAGG" 1818949 NIL MSETAGG (NIL T) -9 NIL 1818983 NIL) (-756 1812026 1814953 1815273 "MSET" 1815911 NIL MSET (NIL T) -8 NIL NIL NIL) (-755 1807630 1809405 1810150 "MRING" 1811326 NIL MRING (NIL T T) -8 NIL NIL NIL) (-754 1807190 1807263 1807394 "MRF2" 1807557 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-753 1806802 1806843 1806987 "MRATFAC" 1807149 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-752 1804372 1804709 1805140 "MPRFF" 1806507 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-751 1797732 1804226 1804323 "MPOLY" 1804328 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-750 1797216 1797257 1797465 "MPCPF" 1797691 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-749 1796724 1796773 1796957 "MPC3" 1797167 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1795907 1796000 1796221 "MPC2" 1796639 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1794184 1794545 1794935 "MONOTOOL" 1795567 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-746 1793329 1793712 1793740 "MONOID" 1793959 T MONOID (NIL) -9 NIL 1794106 NIL) (-745 1792845 1792994 1793175 "MONOID-" 1793180 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-744 1781827 1788665 1788724 "MONOGEN" 1789398 NIL MONOGEN (NIL T T) -9 NIL 1789854 NIL) (-743 1778898 1779794 1780787 "MONOGEN-" 1780906 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-742 1777615 1778163 1778191 "MONADWU" 1778583 T MONADWU (NIL) -9 NIL 1778821 NIL) (-741 1776945 1777146 1777394 "MONADWU-" 1777399 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-740 1776230 1776534 1776562 "MONAD" 1776769 T MONAD (NIL) -9 NIL 1776881 NIL) (-739 1775897 1775993 1776125 "MONAD-" 1776130 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-738 1774036 1774810 1775089 "MOEBIUS" 1775650 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-737 1773204 1773704 1773744 "MODULE" 1773749 NIL MODULE (NIL T) -9 NIL 1773788 NIL) (-736 1772742 1772868 1773058 "MODULE-" 1773063 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-735 1770316 1771150 1771477 "MODRING" 1772566 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-734 1767047 1768421 1768942 "MODOP" 1769845 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-733 1765533 1766114 1766391 "MODMONOM" 1766910 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-732 1754328 1763824 1764238 "MODMON" 1765170 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-731 1751187 1753196 1753472 "MODFIELD" 1754203 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1750098 1750468 1750658 "MMLFORM" 1751017 T MMLFORM (NIL) -8 NIL NIL NIL) (-729 1749618 1749667 1749846 "MMAP" 1750049 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-728 1747511 1748450 1748491 "MLO" 1748914 NIL MLO (NIL T) -9 NIL 1749156 NIL) (-727 1744859 1745393 1745995 "MLIFT" 1746992 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-726 1744238 1744334 1744488 "MKUCFUNC" 1744770 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-725 1743831 1743907 1744030 "MKRECORD" 1744161 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-724 1742854 1743040 1743268 "MKFUNC" 1743642 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-723 1742230 1742346 1742502 "MKFLCFN" 1742737 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-722 1741495 1741609 1741794 "MKBCFUNC" 1742123 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-721 1737494 1741049 1741185 "MINT" 1741379 T MINT (NIL) -8 NIL NIL NIL) (-720 1736276 1736549 1736826 "MHROWRED" 1737249 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-719 1731036 1734811 1735216 "MFLOAT" 1735891 T MFLOAT (NIL) -8 NIL NIL NIL) (-718 1730381 1730469 1730640 "MFINFACT" 1730948 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-717 1726680 1727559 1728438 "MESH" 1729522 T MESH (NIL) -7 NIL NIL NIL) (-716 1725034 1725382 1725735 "MDDFACT" 1726367 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-715 1721681 1724165 1724206 "MDAGG" 1724461 NIL MDAGG (NIL T) -9 NIL 1724604 NIL) (-714 1709417 1720974 1721181 "MCMPLX" 1721494 T MCMPLX (NIL) -8 NIL NIL NIL) (-713 1708536 1708700 1708901 "MCDEN" 1709266 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-712 1706384 1706696 1707076 "MCALCFN" 1708266 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-711 1705261 1705549 1705782 "MAYBE" 1706190 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-710 1702819 1703396 1703958 "MATSTOR" 1704732 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-709 1698354 1702191 1702439 "MATRIX" 1702604 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-708 1694054 1694827 1695563 "MATLIN" 1697711 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-707 1692630 1692801 1693134 "MATCAT2" 1693889 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1682077 1685684 1685761 "MATCAT" 1690796 NIL MATCAT (NIL T T T) -9 NIL 1692268 NIL) (-705 1678030 1679340 1680753 "MATCAT-" 1680758 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-704 1676106 1676466 1676850 "MAPPKG3" 1677705 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-703 1675063 1675260 1675482 "MAPPKG2" 1675930 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-702 1673520 1673846 1674173 "MAPPKG1" 1674769 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-701 1672521 1672926 1673103 "MAPPAST" 1673363 T MAPPAST (NIL) -8 NIL NIL NIL) (-700 1672126 1672190 1672313 "MAPHACK3" 1672457 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-699 1671706 1671779 1671893 "MAPHACK2" 1672058 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-698 1671132 1671247 1671389 "MAPHACK1" 1671597 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-697 1669055 1669832 1670136 "MAGMA" 1670860 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-696 1668474 1668779 1668870 "MACROAST" 1668984 T MACROAST (NIL) -8 NIL NIL NIL) (-695 1664831 1666713 1667174 "M3D" 1668046 NIL M3D (NIL T) -8 NIL NIL NIL) (-694 1658305 1663142 1663183 "LZSTAGG" 1663965 NIL LZSTAGG (NIL T) -9 NIL 1664260 NIL) (-693 1653987 1655436 1656893 "LZSTAGG-" 1656898 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-692 1650900 1651878 1652365 "LWORD" 1653532 NIL LWORD (NIL T) -8 NIL NIL NIL) (-691 1650422 1650704 1650779 "LSTAST" 1650845 T LSTAST (NIL) -8 NIL NIL NIL) (-690 1642495 1650193 1650327 "LSQM" 1650332 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-689 1641713 1641858 1642086 "LSPP" 1642350 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-688 1638513 1639212 1639925 "LSMP1" 1641032 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1636318 1636642 1637091 "LSMP" 1638209 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-686 1629448 1635408 1635449 "LSAGG" 1635511 NIL LSAGG (NIL T) -9 NIL 1635589 NIL) (-685 1625957 1627067 1628280 "LSAGG-" 1628285 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-684 1623252 1625101 1625350 "LPOLY" 1625752 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-683 1622828 1622919 1623042 "LPEFRAC" 1623161 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-682 1622511 1622590 1622618 "LOGIC" 1622729 T LOGIC (NIL) -9 NIL 1622811 NIL) (-681 1622367 1622396 1622467 "LOGIC-" 1622472 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-680 1621542 1621700 1621893 "LODOOPS" 1622223 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1620066 1620315 1620668 "LODOF" 1621289 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1615956 1618701 1618742 "LODOCAT" 1619180 NIL LODOCAT (NIL T) -9 NIL 1619391 NIL) (-677 1615671 1615747 1615874 "LODOCAT-" 1615879 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1612671 1615512 1615630 "LODO2" 1615635 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1609792 1612608 1612653 "LODO1" 1612658 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1606901 1609708 1609774 "LODO" 1609779 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1605770 1605947 1606252 "LODEEF" 1606724 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1603756 1604864 1605117 "LO" 1605602 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1598839 1601922 1601963 "LNAGG" 1602825 NIL LNAGG (NIL T) -9 NIL 1603260 NIL) (-670 1597932 1598200 1598542 "LNAGG-" 1598547 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-669 1593912 1594857 1595496 "LMOPS" 1597347 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-668 1593211 1593689 1593730 "LMODULE" 1593735 NIL LMODULE (NIL T) -9 NIL 1593761 NIL) (-667 1590280 1592856 1592979 "LMDICT" 1593121 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-666 1589856 1590070 1590111 "LLINSET" 1590172 NIL LLINSET (NIL T) -9 NIL 1590216 NIL) (-665 1589501 1589764 1589824 "LITERAL" 1589829 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-664 1589020 1589100 1589239 "LIST3" 1589421 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1587118 1587466 1587865 "LIST2MAP" 1588667 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1586107 1586303 1586531 "LIST2" 1586936 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-661 1578861 1585139 1585394 "LIST" 1585885 NIL LIST (NIL T) -8 NIL NIL NIL) (-660 1578444 1578680 1578721 "LINSET" 1578726 NIL LINSET (NIL T) -9 NIL 1578760 NIL) (-659 1577258 1577952 1578119 "LINFORM" 1578329 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-658 1575557 1576285 1576326 "LINEXP" 1576816 NIL LINEXP (NIL T) -9 NIL 1577089 NIL) (-657 1574133 1575037 1575218 "LINELT" 1575428 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-656 1572690 1572970 1573281 "LINDEP" 1573885 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-655 1571826 1572422 1572532 "LINBASIS" 1572620 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-654 1568634 1569364 1570122 "LIMITRF" 1571100 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-653 1566942 1567249 1567651 "LIMITPS" 1568336 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-652 1565770 1566345 1566385 "LIECAT" 1566525 NIL LIECAT (NIL T) -9 NIL 1566676 NIL) (-651 1565605 1565638 1565726 "LIECAT-" 1565731 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-650 1559657 1565116 1565344 "LIE" 1565426 NIL LIE (NIL T T) -8 NIL NIL NIL) (-649 1551958 1559197 1559353 "LIB" 1559521 T LIB (NIL) -8 NIL NIL NIL) (-648 1547527 1548476 1549411 "LGROBP" 1551075 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-647 1546151 1547059 1547087 "LFCAT" 1547294 T LFCAT (NIL) -9 NIL 1547433 NIL) (-646 1544089 1544423 1544773 "LF" 1545872 NIL LF (NIL T T) -7 NIL NIL NIL) (-645 1540949 1541621 1542309 "LEXTRIPK" 1543453 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-644 1537537 1538519 1539022 "LEXP" 1540529 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-643 1536953 1537258 1537350 "LETAST" 1537465 T LETAST (NIL) -8 NIL NIL NIL) (-642 1535339 1535664 1536065 "LEADCDET" 1536635 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-641 1534517 1534603 1534832 "LAZM3PK" 1535260 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-640 1529056 1532594 1533132 "LAUPOL" 1534029 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-639 1528629 1528679 1528840 "LAPLACE" 1529006 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-638 1527477 1528193 1528234 "LALG" 1528296 NIL LALG (NIL T) -9 NIL 1528355 NIL) (-637 1527173 1527250 1527386 "LALG-" 1527391 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-636 1524910 1526274 1526525 "LA" 1527006 NIL LA (NIL T T T) -8 NIL NIL NIL) (-635 1524739 1524769 1524810 "KVTFROM" 1524872 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-634 1523496 1524106 1524291 "KTVLOGIC" 1524574 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-633 1523325 1523355 1523396 "KRCFROM" 1523458 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-632 1522217 1522416 1522715 "KOVACIC" 1523125 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-631 1522046 1522076 1522117 "KONVERT" 1522179 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-630 1521875 1521905 1521946 "KOERCE" 1522008 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-629 1521359 1521452 1521584 "KERNEL2" 1521789 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1519046 1519952 1520329 "KERNEL" 1521015 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-627 1512628 1517523 1517577 "KDAGG" 1517954 NIL KDAGG (NIL T T) -9 NIL 1518160 NIL) (-626 1512139 1512281 1512486 "KDAGG-" 1512491 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-625 1504955 1511800 1511955 "KAFILE" 1512017 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-624 1504559 1504844 1504907 "JVMOP" 1504912 T JVMOP (NIL) -8 NIL NIL NIL) (-623 1503295 1503799 1504048 "JVMMDACC" 1504330 T JVMMDACC (NIL) -8 NIL NIL NIL) (-622 1502231 1502685 1502890 "JVMFDACC" 1503110 T JVMFDACC (NIL) -8 NIL NIL NIL) (-621 1500812 1501307 1501607 "JVMCSTTG" 1501951 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-620 1499948 1500352 1500513 "JVMCFACC" 1500671 T JVMCFACC (NIL) -8 NIL NIL NIL) (-619 1499626 1499865 1499914 "JVMBCODE" 1499919 T JVMBCODE (NIL) -8 NIL NIL NIL) (-618 1493677 1499137 1499365 "JORDAN" 1499447 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1492990 1493326 1493447 "JOINAST" 1493576 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1489136 1491167 1491221 "IXAGG" 1492150 NIL IXAGG (NIL T T) -9 NIL 1492609 NIL) (-615 1487989 1488361 1488780 "IXAGG-" 1488785 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1483192 1487911 1487970 "IVECTOR" 1487975 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1481917 1482195 1482461 "ITUPLE" 1482959 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1480389 1480596 1480891 "ITRIGMNP" 1481739 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1479116 1479338 1479621 "ITFUN3" 1480165 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1478714 1478777 1478900 "ITFUN2" 1479039 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-609 1477819 1478194 1478368 "ITFORM" 1478560 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1475588 1476839 1477117 "ITAYLOR" 1477574 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1463992 1469725 1470888 "ISUPS" 1474458 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1463084 1463236 1463472 "ISUMP" 1463839 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1458048 1463029 1463070 "ISTRING" 1463075 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1457464 1457769 1457861 "ISAST" 1457976 T ISAST (NIL) -8 NIL NIL NIL) (-603 1456662 1456755 1456971 "IRURPK" 1457378 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1455574 1455799 1456039 "IRSN" 1456442 T IRSN (NIL) -7 NIL NIL NIL) (-601 1453619 1454000 1454429 "IRRF2F" 1455212 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1453360 1453404 1453480 "IRREDFFX" 1453575 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1451933 1452234 1452533 "IROOT" 1453093 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1451072 1451426 1451577 "IRFORM" 1451802 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1450154 1450285 1450499 "IR2F" 1450955 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1447743 1448262 1448828 "IR2" 1449632 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1444183 1445427 1446119 "IR" 1447083 NIL IR (NIL T) -8 NIL NIL NIL) (-594 1443968 1444008 1444068 "IPRNTPK" 1444143 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1439944 1443857 1443926 "IPF" 1443931 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1437974 1439869 1439926 "IPADIC" 1439931 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1437232 1437534 1437664 "IP4ADDR" 1437864 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1436570 1436861 1436993 "IOMODE" 1437120 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1435541 1436167 1436294 "IOBFILE" 1436463 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1434951 1435445 1435473 "IOBCON" 1435478 T IOBCON (NIL) -9 NIL 1435499 NIL) (-587 1434456 1434520 1434703 "INVLAPLA" 1434887 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1424074 1426494 1428868 "INTTR" 1432132 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1420367 1421151 1422016 "INTTOOLS" 1423259 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1419947 1420044 1420161 "INTSLPE" 1420270 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1417414 1419870 1419929 "INTRVL" 1419934 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1414992 1415528 1416103 "INTRF" 1416899 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1414385 1414500 1414642 "INTRET" 1414890 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1412358 1412771 1413241 "INTRAT" 1413993 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1409603 1410204 1410823 "INTPM" 1411843 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1406343 1406963 1407694 "INTPAF" 1408996 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1401444 1402484 1403535 "INTPACK" 1405312 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1400690 1400848 1401056 "INTHERTR" 1401286 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1400123 1400209 1400397 "INTHERAL" 1400604 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1397891 1398412 1398869 "INTHEORY" 1399686 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1389281 1390958 1392712 "INTG0" 1396261 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1375506 1378919 1382304 "INTFTBL" 1385916 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1374731 1374893 1375066 "INTFACT" 1375365 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1372134 1372608 1373163 "INTEF" 1374287 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1370331 1371226 1371254 "INTDOM" 1371555 T INTDOM (NIL) -9 NIL 1371762 NIL) (-568 1369670 1369874 1370116 "INTDOM-" 1370121 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1365538 1367959 1368013 "INTCAT" 1368812 NIL INTCAT (NIL T) -9 NIL 1369133 NIL) (-566 1364992 1365113 1365241 "INTBIT" 1365430 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1363673 1363845 1364152 "INTALG" 1364837 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1363150 1363246 1363403 "INTAF" 1363577 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1356233 1362960 1363100 "INTABL" 1363105 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1355474 1356036 1356101 "INT8" 1356135 T INT8 (NIL) -8 NIL NIL 1356180) (-561 1354714 1355276 1355341 "INT64" 1355375 T INT64 (NIL) -8 NIL NIL 1355420) (-560 1353954 1354516 1354581 "INT32" 1354615 T INT32 (NIL) -8 NIL NIL 1354660) (-559 1353194 1353756 1353821 "INT16" 1353855 T INT16 (NIL) -8 NIL NIL 1353900) (-558 1349546 1353005 1353107 "INT" 1353112 T INT (NIL) -8 NIL NIL NIL) (-557 1343657 1347094 1347122 "INS" 1348056 T INS (NIL) -9 NIL 1348721 NIL) (-556 1340814 1341734 1342675 "INS-" 1342748 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1339644 1339867 1340143 "INPSIGN" 1340589 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1338738 1338879 1339076 "INPRODPF" 1339524 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1337608 1337749 1337986 "INPRODFF" 1338618 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1336596 1336760 1337020 "INNMFACT" 1337444 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1335775 1335890 1336078 "INMODGCD" 1336495 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1334259 1334528 1334852 "INFSP" 1335520 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1333419 1333560 1333743 "INFPROD0" 1334139 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1333017 1333089 1333187 "INFORM1" 1333354 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1329584 1331082 1331597 "INFORM" 1332510 T INFORM (NIL) -8 NIL NIL NIL) (-546 1329089 1329196 1329310 "INFINITY" 1329490 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1328163 1328809 1328910 "INETCLTS" 1329008 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1326761 1327029 1327350 "INEP" 1327911 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1325791 1326658 1326723 "INDE" 1326728 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1325343 1325423 1325540 "INCRMAPS" 1325718 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1324065 1324612 1324818 "INBFILE" 1325157 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1319245 1320301 1321245 "INBFF" 1323153 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1318099 1318422 1318450 "INBCON" 1318963 T INBCON (NIL) -9 NIL 1319229 NIL) (-538 1317309 1317574 1317850 "INBCON-" 1317855 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1316728 1317033 1317124 "INAST" 1317238 T INAST (NIL) -8 NIL NIL NIL) (-536 1316095 1316407 1316513 "IMPTAST" 1316642 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1312129 1315939 1316043 "IMATRIX" 1316048 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1310821 1310960 1311276 "IMATQF" 1311985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1309001 1309268 1309605 "IMATLIN" 1310577 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1302918 1308925 1308983 "ILIST" 1308988 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1300698 1302778 1302891 "IIARRAY2" 1302896 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1295521 1300609 1300673 "IFF" 1300678 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1294802 1295138 1295254 "IFAST" 1295425 T IFAST (NIL) -8 NIL NIL NIL) (-528 1289428 1294094 1294282 "IFARRAY" 1294659 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1288466 1289332 1289405 "IFAMON" 1289410 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1288038 1288115 1288169 "IEVALAB" 1288376 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1287701 1287781 1287941 "IEVALAB-" 1287946 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1286734 1287590 1287665 "IDPOAMS" 1287670 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1285836 1286623 1286698 "IDPOAM" 1286703 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1285217 1285751 1285813 "IDPO" 1285818 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1283697 1284224 1284276 "IDPC" 1284788 NIL IDPC (NIL T T) -9 NIL 1285069 NIL) (-520 1283029 1283589 1283662 "IDPAM" 1283667 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1282244 1282921 1282994 "IDPAG" 1282999 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1281788 1282050 1282140 "IDENT" 1282174 T IDENT (NIL) -8 NIL NIL NIL) (-517 1278007 1278891 1279786 "IDECOMP" 1280945 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1270642 1271930 1272977 "IDEAL" 1277043 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1269784 1269914 1270114 "ICDEN" 1270526 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1268759 1269264 1269411 "ICARD" 1269657 T ICARD (NIL) -8 NIL NIL NIL) (-513 1266789 1267132 1267537 "IBPTOOLS" 1268436 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1262018 1266409 1266522 "IBITS" 1266708 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1258693 1259317 1260012 "IBATOOL" 1261435 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1256454 1256934 1257467 "IBACHIN" 1258228 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1254158 1256300 1256403 "IARRAY2" 1256408 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1249985 1254084 1254141 "IARRAY1" 1254146 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1243011 1248397 1248878 "IAN" 1249524 T IAN (NIL) -8 NIL NIL NIL) (-506 1242516 1242579 1242752 "IALGFACT" 1242948 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1242008 1242157 1242185 "HYPCAT" 1242392 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1241510 1241663 1241849 "HYPCAT-" 1241854 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1241057 1241305 1241388 "HOSTNAME" 1241447 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1240890 1240939 1240980 "HOMOTOP" 1240985 NIL HOMOTOP (NIL T) -9 NIL 1241018 NIL) (-501 1237434 1238822 1238863 "HOAGG" 1239844 NIL HOAGG (NIL T) -9 NIL 1240573 NIL) (-500 1235950 1236427 1236953 "HOAGG-" 1236958 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1229023 1235543 1235693 "HEXADEC" 1235820 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1227735 1227993 1228256 "HEUGCD" 1228800 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1226667 1227572 1227702 "HELLFDIV" 1227707 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1224791 1226444 1226532 "HEAP" 1226611 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1223988 1224343 1224477 "HEADAST" 1224677 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1217447 1223903 1223965 "HDP" 1223970 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1210492 1217082 1217234 "HDMP" 1217348 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1209798 1209956 1210120 "HB" 1210348 T HB (NIL) -7 NIL NIL NIL) (-491 1202924 1209644 1209748 "HASHTBL" 1209753 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1202340 1202645 1202737 "HASAST" 1202852 T HASAST (NIL) -8 NIL NIL NIL) (-489 1199757 1201962 1202144 "HACKPI" 1202178 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1195070 1199610 1199723 "GTSET" 1199728 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1188225 1194948 1195046 "GSTBL" 1195051 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1179990 1187390 1187646 "GSERIES" 1188025 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1179021 1179534 1179562 "GROUP" 1179765 T GROUP (NIL) -9 NIL 1179899 NIL) (-484 1178345 1178546 1178797 "GROUP-" 1178802 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1176694 1177033 1177420 "GROEBSOL" 1178022 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1175522 1175882 1175933 "GRMOD" 1176462 NIL GRMOD (NIL T T) -9 NIL 1176630 NIL) (-481 1175278 1175326 1175454 "GRMOD-" 1175459 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1170418 1171632 1172632 "GRIMAGE" 1174298 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1168812 1169145 1169469 "GRDEF" 1170114 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1168244 1168372 1168513 "GRAY" 1168691 T GRAY (NIL) -7 NIL NIL NIL) (-477 1167321 1167823 1167874 "GRALG" 1168027 NIL GRALG (NIL T T) -9 NIL 1168120 NIL) (-476 1166958 1167055 1167218 "GRALG-" 1167223 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1163553 1166541 1166720 "GPOLSET" 1166864 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1162901 1162964 1163222 "GOSPER" 1163490 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1158471 1159339 1159865 "GMODPOL" 1162600 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1157458 1157660 1157898 "GHENSEL" 1158283 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1151530 1152457 1153477 "GENUPS" 1156542 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1151221 1151278 1151367 "GENUFACT" 1151473 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1150621 1150710 1150875 "GENPGCD" 1151139 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1150089 1150130 1150343 "GENMFACT" 1150580 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1148626 1148912 1149219 "GENEEZ" 1149832 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1141830 1148237 1148399 "GDMP" 1148549 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1130590 1135601 1136707 "GCNAALG" 1140813 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1128717 1129765 1129793 "GCDDOM" 1130048 T GCDDOM (NIL) -9 NIL 1130205 NIL) (-463 1128157 1128314 1128529 "GCDDOM-" 1128534 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1116629 1119103 1121495 "GBINTERN" 1125848 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1114430 1114758 1115179 "GBF" 1116304 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1113187 1113376 1113643 "GBEUCLID" 1114246 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1111837 1112044 1112348 "GB" 1112966 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1111168 1111311 1111460 "GAUSSFAC" 1111708 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1109489 1109837 1110151 "GALUTIL" 1110887 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1107749 1108071 1108395 "GALPOLYU" 1109216 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1105048 1105404 1105811 "GALFACTU" 1107446 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1096662 1098353 1099961 "GALFACT" 1103480 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1093948 1094708 1094736 "FVFUN" 1095892 T FVFUN (NIL) -9 NIL 1096612 NIL) (-452 1093178 1093396 1093424 "FVC" 1093715 T FVC (NIL) -9 NIL 1093898 NIL) (-451 1092779 1093003 1093071 "FUNDESC" 1093130 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1092352 1092576 1092657 "FUNCTION" 1092731 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1091029 1091653 1091856 "FTEM" 1092169 T FTEM (NIL) -8 NIL NIL NIL) (-448 1088671 1089360 1089823 "FT" 1090586 T FT (NIL) -8 NIL NIL NIL) (-447 1086940 1087251 1087648 "FSUPFACT" 1088362 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1085259 1085626 1085958 "FST" 1086628 T FST (NIL) -8 NIL NIL NIL) (-445 1084440 1084564 1084752 "FSRED" 1085141 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1083129 1083395 1083742 "FSPRMELT" 1084155 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1080339 1080873 1081359 "FSPECF" 1082692 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1079861 1079921 1080091 "FSINT" 1080280 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1077997 1078854 1079157 "FSERIES" 1079640 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1077021 1077155 1077379 "FSCINT" 1077877 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1076045 1076206 1076433 "FSAGG2" 1076874 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 1072020 1074989 1075030 "FSAGG" 1075400 NIL FSAGG (NIL T) -9 NIL 1075659 NIL) (-437 1069620 1070383 1071179 "FSAGG-" 1071274 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1067280 1067578 1068126 "FS2UPS" 1069338 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1066146 1066329 1066631 "FS2EXPXP" 1067105 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 1065774 1065823 1065952 "FS2" 1066097 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1046041 1055548 1055589 "FS" 1059473 NIL FS (NIL T) -9 NIL 1061762 NIL) (-432 1034183 1037731 1041761 "FS-" 1042061 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 1033597 1033724 1033876 "FRUTIL" 1034063 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 1028140 1031286 1031326 "FRNAALG" 1032646 NIL FRNAALG (NIL T) -9 NIL 1033244 NIL) (-429 1023672 1024923 1026181 "FRNAALG-" 1026931 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1023304 1023353 1023480 "FRNAAF2" 1023623 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1021591 1022153 1022449 "FRMOD" 1023116 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1020776 1020869 1021160 "FRIDEAL2" 1021498 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018381 1019151 1019469 "FRIDEAL" 1020567 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 1017479 1017928 1017969 "FRETRCT" 1017974 NIL FRETRCT (NIL T) -9 NIL 1018150 NIL) (-423 1016558 1016836 1017180 "FRETRCT-" 1017185 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1013379 1014842 1014901 "FRAMALG" 1015783 NIL FRAMALG (NIL T T) -9 NIL 1016075 NIL) (-421 1011417 1011968 1012598 "FRAMALG-" 1012821 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1011047 1011110 1011217 "FRAC2" 1011354 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004534 1010692 1010883 "FRAC" 1010888 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 1004164 1004227 1004334 "FR2" 1004471 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 995196 999740 1001071 "FR" 1002865 NIL FR (NIL T) -8 NIL NIL NIL) (-416 989119 992575 992603 "FPS" 993722 T FPS (NIL) -9 NIL 994279 NIL) (-415 988544 988677 988841 "FPS-" 988987 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 985512 987501 987529 "FPC" 987754 T FPC (NIL) -9 NIL 987896 NIL) (-413 985293 985345 985442 "FPC-" 985447 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 984051 984781 984822 "FPATMAB" 984827 NIL FPATMAB (NIL T) -9 NIL 984979 NIL) (-411 982194 982793 983140 "FPARFRAC" 983767 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 977525 978125 978807 "FORTRAN" 981626 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 975099 975763 975791 "FORTFN" 976851 T FORTFN (NIL) -9 NIL 977475 NIL) (-408 974851 974913 974941 "FORTCAT" 975000 T FORTCAT (NIL) -9 NIL 975062 NIL) (-407 972537 973067 973606 "FORT" 974332 T FORT (NIL) -7 NIL NIL NIL) (-406 972054 972112 972285 "FORDER" 972479 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 971114 971314 971507 "FOP" 971881 T FOP (NIL) -7 NIL NIL NIL) (-404 969527 970394 970568 "FNLA" 970996 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 968146 968657 968685 "FNCAT" 969145 T FNCAT (NIL) -9 NIL 969405 NIL) (-402 967589 968105 968133 "FNAME" 968138 T FNAME (NIL) -8 NIL NIL NIL) (-401 965915 967088 967116 "FMTC" 967121 T FMTC (NIL) -9 NIL 967157 NIL) (-400 964471 965851 965897 "FMONOID" 965902 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 961060 962426 962467 "FMONCAT" 963684 NIL FMONCAT (NIL T) -9 NIL 964289 NIL) (-398 958382 959130 959158 "FMFUN" 960302 T FMFUN (NIL) -9 NIL 961010 NIL) (-397 955255 956307 956361 "FMCAT" 957556 NIL FMCAT (NIL T T) -9 NIL 958051 NIL) (-396 954488 954705 954733 "FMC" 955023 T FMC (NIL) -9 NIL 955205 NIL) (-395 953156 954254 954354 "FM1" 954433 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 952174 952898 953047 "FM" 953052 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 949912 950364 950858 "FLOATRP" 951725 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 947314 947850 948428 "FLOATCP" 949379 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 940132 945057 945671 "FLOAT" 946720 T FLOAT (NIL) -8 NIL NIL NIL) (-390 938650 939724 939765 "FLINEXP" 939770 NIL FLINEXP (NIL T) -9 NIL 939863 NIL) (-389 937780 938039 938367 "FLINEXP-" 938372 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 936838 937000 937224 "FLASORT" 937632 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 933756 934808 934860 "FLALG" 936087 NIL FLALG (NIL T T) -9 NIL 936554 NIL) (-386 932780 932941 933168 "FLAGG2" 933609 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 926149 930189 930230 "FLAGG" 931492 NIL FLAGG (NIL T) -9 NIL 932144 NIL) (-384 924803 925214 925704 "FLAGG-" 925709 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 921441 922648 922707 "FINRALG" 923835 NIL FINRALG (NIL T T) -9 NIL 924343 NIL) (-382 920565 920830 921169 "FINRALG-" 921174 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 919871 920170 920198 "FINITE" 920394 T FINITE (NIL) -9 NIL 920501 NIL) (-380 911822 914401 914441 "FINAALG" 918108 NIL FINAALG (NIL T) -9 NIL 919561 NIL) (-379 906938 908204 909348 "FINAALG-" 910727 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 905498 905920 905974 "FILECAT" 906658 NIL FILECAT (NIL T T) -9 NIL 906874 NIL) (-377 904776 905253 905356 "FILE" 905428 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 902181 904006 904034 "FIELD" 904074 T FIELD (NIL) -9 NIL 904154 NIL) (-375 900723 901186 901697 "FIELD-" 901702 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 898406 899358 899705 "FGROUP" 900409 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 897478 897660 897880 "FGLMICPK" 898238 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 892735 897403 897460 "FFX" 897465 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 892330 892397 892532 "FFSLPE" 892668 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 891828 891870 892079 "FFPOLY2" 892288 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 887704 888600 889396 "FFPOLY" 891064 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 882975 887623 887686 "FFP" 887691 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 877508 882318 882508 "FFNBX" 882829 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 871843 876643 876901 "FFNBP" 877362 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 865883 871127 871338 "FFNB" 871676 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 864703 864913 865228 "FFINTBAS" 865680 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 860298 862950 862978 "FFIELDC" 863598 T FFIELDC (NIL) -9 NIL 863974 NIL) (-362 858918 859359 859842 "FFIELDC-" 859847 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 858475 858533 858657 "FFHOM" 858860 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 856134 856657 857174 "FFF" 857990 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 851171 855876 855977 "FFCGX" 856077 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 846212 850903 851010 "FFCGP" 851114 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 840814 845939 846047 "FFCG" 846148 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 840219 840268 840503 "FFCAT2" 840765 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 818910 829951 830037 "FFCAT" 835202 NIL FFCAT (NIL T T T) -9 NIL 836653 NIL) (-354 813921 815155 816469 "FFCAT-" 817699 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 808744 813832 813896 "FF" 813901 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 797399 801716 802936 "FEXPR" 807596 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 796327 796796 796837 "FEVALAB" 796921 NIL FEVALAB (NIL T) -9 NIL 797182 NIL) (-350 795444 795696 796034 "FEVALAB-" 796039 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 792306 793191 793306 "FDIVCAT" 794874 NIL FDIVCAT (NIL T T T T) -9 NIL 795311 NIL) (-348 792062 792095 792265 "FDIVCAT-" 792270 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 791276 791369 791646 "FDIV2" 791969 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 789686 790659 790862 "FDIV" 791175 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 788594 788981 789183 "FCTRDATA" 789504 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 787250 787539 787828 "FCPAK1" 788325 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 786253 786750 786891 "FCOMP" 787141 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 769567 773403 776941 "FC" 782735 T FC (NIL) -8 NIL NIL NIL) (-341 761278 765888 765928 "FAXF" 767730 NIL FAXF (NIL T) -9 NIL 768422 NIL) (-340 758419 759226 760044 "FAXF-" 760509 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 753102 757795 757971 "FARRAY" 758276 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 747674 750049 750102 "FAMR" 751125 NIL FAMR (NIL T T) -9 NIL 751585 NIL) (-337 746498 746866 747301 "FAMR-" 747306 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 745525 746420 746473 "FAMONOID" 746478 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 743155 744007 744060 "FAMONC" 745001 NIL FAMONC (NIL T T) -9 NIL 745387 NIL) (-334 741629 742909 743046 "FAGROUP" 743051 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 739382 739743 740146 "FACUTIL" 741310 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 738469 738666 738888 "FACTFUNC" 739192 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 730212 737772 737971 "EXPUPXS" 738325 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 727665 728235 728821 "EXPRTUBE" 729646 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 723876 724528 725258 "EXPRODE" 727004 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 718310 719017 719823 "EXPR2UPS" 723174 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 717936 717999 718108 "EXPR2" 718247 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 702305 716585 717014 "EXPR" 717540 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 692664 701456 701747 "EXPEXPAN" 702141 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 692084 692388 692479 "EXITAST" 692593 T EXITAST (NIL) -8 NIL NIL NIL) (-323 691848 692041 692070 "EXIT" 692075 T EXIT (NIL) -8 NIL NIL NIL) (-322 691469 691537 691650 "EVALCYC" 691780 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 690986 691128 691169 "EVALAB" 691339 NIL EVALAB (NIL T) -9 NIL 691443 NIL) (-320 690443 690589 690810 "EVALAB-" 690815 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 687558 689099 689127 "EUCDOM" 689682 T EUCDOM (NIL) -9 NIL 690032 NIL) (-318 685918 686419 687002 "EUCDOM-" 687007 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 685544 685607 685716 "ESTOOLS2" 685855 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 685289 685337 685417 "ESTOOLS1" 685496 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 672606 675587 678337 "ESTOOLS" 682559 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 672345 672383 672465 "ESCONT1" 672568 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 668653 669480 670260 "ESCONT" 671585 T ESCONT (NIL) -7 NIL NIL NIL) (-312 668322 668378 668478 "ES2" 668597 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 667946 668010 668119 "ES1" 668258 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 661647 663577 663605 "ES" 666373 T ES (NIL) -9 NIL 667783 NIL) (-309 656324 657881 659698 "ES-" 659862 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 655516 655669 655845 "ERROR" 656168 T ERROR (NIL) -7 NIL NIL NIL) (-307 648648 655375 655466 "EQTBL" 655471 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 648274 648337 648446 "EQ2" 648585 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 640533 643588 645037 "EQ" 646858 NIL -4033 (NIL T) -8 NIL NIL NIL) (-304 635775 636871 637964 "EP" 639472 NIL EP (NIL T) -7 NIL NIL NIL) (-303 634315 634666 634972 "ENV" 635489 T ENV (NIL) -8 NIL NIL NIL) (-302 633275 633949 633977 "ENTIRER" 633982 T ENTIRER (NIL) -9 NIL 634028 NIL) (-301 629740 631501 631862 "EMR" 633083 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 628844 629055 629109 "ELTAGG" 629489 NIL ELTAGG (NIL T T) -9 NIL 629700 NIL) (-299 628551 628625 628766 "ELTAGG-" 628771 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 628309 628344 628398 "ELTAB" 628482 NIL ELTAB (NIL T T) -9 NIL 628534 NIL) (-297 627411 627581 627780 "ELFUTS" 628160 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 627135 627209 627237 "ELEMFUN" 627342 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 626999 627026 627094 "ELEMFUN-" 627099 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 621524 625041 625082 "ELAGG" 626022 NIL ELAGG (NIL T) -9 NIL 626485 NIL) (-293 619701 620243 620906 "ELAGG-" 620911 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 618983 619150 619306 "ELABOR" 619565 T ELABOR (NIL) -8 NIL NIL NIL) (-291 617589 617923 618217 "ELABEXPR" 618709 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 610228 612226 613055 "EFUPXS" 616864 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 603481 605477 606288 "EFULS" 609503 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 600918 601324 601796 "EFSTRUC" 603113 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 590356 592275 593823 "EF" 599433 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 589334 589841 589990 "EAB" 590227 T EAB (NIL) -8 NIL NIL NIL) (-285 588456 589293 589321 "E04UCFA" 589326 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 587578 588415 588443 "E04NAFA" 588448 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 586700 587537 587565 "E04MBFA" 587570 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 585822 586659 586687 "E04JAFA" 586692 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 584946 585781 585809 "E04GCFA" 585814 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 584070 584905 584933 "E04FDFA" 584938 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 583192 584029 584057 "E04DGFA" 584062 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 577269 578717 580081 "E04AGNT" 581848 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 575889 576570 576610 "DVARCAT" 576951 NIL DVARCAT (NIL T) -9 NIL 577114 NIL) (-276 575039 575305 575619 "DVARCAT-" 575624 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 567043 574838 574967 "DSMP" 574972 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 565394 566185 566226 "DSEXT" 566589 NIL DSEXT (NIL T) -9 NIL 566883 NIL) (-273 563583 564107 564773 "DSEXT-" 564778 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563242 563307 563405 "DROPT1" 563518 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 558261 559483 560620 "DROPT0" 562125 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 552844 554206 555274 "DROPT" 557213 T DROPT (NIL) -8 NIL NIL NIL) (-269 551153 551514 551900 "DRAWPT" 552478 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 550780 550839 550957 "DRAWHACK" 551094 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 549481 549780 550071 "DRAWCX" 550509 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 548990 549065 549216 "DRAWCURV" 549407 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 539308 541420 543535 "DRAWCFUN" 546895 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 533799 534818 535897 "DRAW" 538282 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 530381 532464 532505 "DQAGG" 533134 NIL DQAGG (NIL T) -9 NIL 533408 NIL) (-262 516995 524592 524675 "DPOLCAT" 526527 NIL DPOLCAT (NIL T T T T) -9 NIL 527072 NIL) (-261 511565 513214 515155 "DPOLCAT-" 515160 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 504494 511426 511524 "DPMO" 511529 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 497320 504274 504441 "DPMM" 504446 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 496842 497104 497193 "DOMTMPLT" 497251 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 496191 496644 496724 "DOMCTOR" 496782 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 495343 495671 495822 "DOMAIN" 496060 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 488388 494978 495130 "DMP" 495244 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 486165 487455 487496 "DMEXT" 487501 NIL DMEXT (NIL T) -9 NIL 487677 NIL) (-253 485759 485821 485965 "DLP" 486103 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 478884 485086 485276 "DLIST" 485601 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 475534 477709 477750 "DLAGG" 478300 NIL DLAGG (NIL T) -9 NIL 478530 NIL) (-250 474046 474860 474888 "DIVRING" 474980 T DIVRING (NIL) -9 NIL 475063 NIL) (-249 473229 473473 473773 "DIVRING-" 473778 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 471271 471688 472094 "DISPLAY" 472843 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 470101 470322 470587 "DIRPROD2" 471064 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 463580 470015 470078 "DIRPROD" 470083 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 451864 458291 458344 "DIRPCAT" 458602 NIL DIRPCAT (NIL NIL T) -9 NIL 459477 NIL) (-244 449064 449832 450713 "DIRPCAT-" 451050 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 448345 448511 448697 "DIOSP" 448898 T DIOSP (NIL) -7 NIL NIL NIL) (-242 444870 447229 447270 "DIOPS" 447704 NIL DIOPS (NIL T) -9 NIL 447933 NIL) (-241 444389 444533 444724 "DIOPS-" 444729 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 443296 444068 444096 "DIFRING" 444101 T DIFRING (NIL) -9 NIL 444123 NIL) (-239 442944 443042 443070 "DIFFSPC" 443189 T DIFFSPC (NIL) -9 NIL 443264 NIL) (-238 442565 442667 442819 "DIFFSPC-" 442824 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 441501 442099 442140 "DIFFMOD" 442145 NIL DIFFMOD (NIL T) -9 NIL 442243 NIL) (-236 441197 441254 441295 "DIFFDOM" 441416 NIL DIFFDOM (NIL T) -9 NIL 441484 NIL) (-235 441044 441074 441158 "DIFFDOM-" 441163 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 438784 440248 440289 "DIFEXT" 440294 NIL DIFEXT (NIL T) -9 NIL 440447 NIL) (-233 435929 438288 438329 "DIAGG" 438334 NIL DIAGG (NIL T) -9 NIL 438354 NIL) (-232 435277 435470 435722 "DIAGG-" 435727 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 430240 434236 434513 "DHMATRIX" 435046 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 425708 426761 427771 "DFSFUN" 429250 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 419972 424552 424880 "DFLOAT" 425400 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 418211 418516 418905 "DFINTTLS" 419680 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 415030 416232 416632 "DERHAM" 417877 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 412680 414805 414894 "DEQUEUE" 414974 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 411922 412067 412250 "DEGRED" 412542 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 408508 409232 410033 "DEFINTRF" 411195 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 406157 406616 407180 "DEFINTEF" 408055 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 405441 405777 405892 "DEFAST" 406062 T DEFAST (NIL) -8 NIL NIL NIL) (-221 398514 405034 405184 "DECIMAL" 405311 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 395972 396484 396990 "DDFACT" 398058 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 395562 395611 395762 "DBLRESP" 395923 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 394763 395332 395423 "DBASIS" 395511 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 392547 392993 393354 "DBASE" 394529 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 391735 392027 392173 "DATAARY" 392446 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 390793 391694 391722 "D03FAFA" 391727 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 389852 390752 390780 "D03EEFA" 390785 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 387778 388268 388757 "D03AGNT" 389383 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 387019 387737 387765 "D02EJFA" 387770 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 386260 386978 387006 "D02CJFA" 387011 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 385501 386219 386247 "D02BHFA" 386252 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 384742 385460 385488 "D02BBFA" 385493 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 377873 379528 381134 "D02AGNT" 383156 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 375623 376164 376710 "D01WGTS" 377347 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 374630 375582 375610 "D01TRNS" 375615 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 373638 374589 374617 "D01GBFA" 374622 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 372646 373597 373625 "D01FCFA" 373630 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 371654 372605 372633 "D01ASFA" 372638 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 370662 371613 371641 "D01AQFA" 371646 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 369670 370621 370649 "D01APFA" 370654 T D01APFA (NIL) -8 NIL NIL NIL) (-200 368678 369629 369657 "D01ANFA" 369662 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 367686 368637 368665 "D01AMFA" 368670 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 366694 367645 367673 "D01ALFA" 367678 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 365702 366653 366681 "D01AKFA" 366686 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 364710 365661 365689 "D01AJFA" 365694 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 357933 359558 361119 "D01AGNT" 363169 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 357252 357398 357550 "CYCLOTOM" 357801 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 353907 354700 355427 "CYCLES" 356545 T CYCLES (NIL) -7 NIL NIL NIL) (-192 353207 353353 353524 "CVMP" 353768 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 350994 351306 351675 "CTRIGMNP" 352935 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 350467 350725 350826 "CTORKIND" 350913 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 349672 350060 350088 "CTORCAT" 350270 T CTORCAT (NIL) -9 NIL 350383 NIL) (-188 349246 349381 349540 "CTORCAT-" 349545 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 348660 348920 349028 "CTORCALL" 349170 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 348018 348454 348527 "CTOR" 348607 T CTOR (NIL) -8 NIL NIL NIL) (-185 347374 347491 347644 "CSTTOOLS" 347915 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 343071 343830 344588 "CRFP" 346686 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 342486 342792 342884 "CRCEAST" 342999 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 341509 341718 341946 "CRAPACK" 342290 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 340889 340994 341198 "CPMATCH" 341385 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 340608 340642 340748 "CPIMA" 340855 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 336866 337628 338347 "COORDSYS" 339943 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 336254 336399 336541 "CONTOUR" 336744 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 331727 334257 334749 "CONTFRAC" 335794 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 331601 331628 331656 "CONDUIT" 331693 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 330555 331229 331257 "COMRING" 331262 T COMRING (NIL) -9 NIL 331314 NIL) (-174 329537 329913 330097 "COMPPROP" 330391 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 329192 329233 329361 "COMPLPAT" 329496 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 328822 328885 328992 "COMPLEX2" 329129 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 317566 328759 328804 "COMPLEX" 328809 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 316887 317026 317186 "COMPILER" 317426 T COMPILER (NIL) -8 NIL NIL NIL) (-169 316599 316640 316738 "COMPFACT" 316846 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298002 310303 310343 "COMPCAT" 311347 NIL COMPCAT (NIL T) -9 NIL 312695 NIL) (-167 286911 290455 294075 "COMPCAT-" 294431 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 286634 286668 286771 "COMMUPC" 286877 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 286422 286462 286521 "COMMONOP" 286595 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 285944 286226 286301 "COMMAAST" 286367 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 285451 285695 285782 "COMM" 285877 T COMM (NIL) -8 NIL NIL NIL) (-162 284646 284894 284922 "COMBOPC" 285260 T COMBOPC (NIL) -9 NIL 285435 NIL) (-161 283500 283752 283994 "COMBINAT" 284436 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 279843 280531 281158 "COMBF" 282922 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 278505 278959 279194 "COLOR" 279628 T COLOR (NIL) -8 NIL NIL NIL) (-158 277921 278226 278318 "COLONAST" 278433 T COLONAST (NIL) -8 NIL NIL NIL) (-157 277555 277608 277733 "CMPLXRT" 277868 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 276943 277255 277354 "CLLCTAST" 277476 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 272403 273473 274553 "CLIP" 275883 T CLIP (NIL) -7 NIL NIL NIL) (-154 270576 271504 271744 "CLIF" 272230 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 266669 268694 268735 "CLAGG" 269664 NIL CLAGG (NIL T) -9 NIL 270200 NIL) (-152 265013 265548 266131 "CLAGG-" 266136 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 264551 264642 264782 "CINTSLPE" 264922 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262016 262523 263071 "CHVAR" 264079 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261056 261730 261758 "CHARZ" 261763 T CHARZ (NIL) -9 NIL 261778 NIL) (-148 260804 260850 260928 "CHARPOL" 261010 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 259722 260428 260456 "CHARNZ" 260517 T CHARNZ (NIL) -9 NIL 260566 NIL) (-146 256666 257776 258305 "CHAR" 259213 T CHAR (NIL) -8 NIL NIL NIL) (-145 256374 256453 256481 "CFCAT" 256592 T CFCAT (NIL) -9 NIL NIL NIL) (-144 255597 255726 255909 "CDEN" 256258 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 251308 254750 255030 "CCLASS" 255337 T CCLASS (NIL) -8 NIL NIL NIL) (-142 250529 250716 250893 "CATEGORY" 251151 T -10 (NIL) -8 NIL NIL NIL) (-141 250024 250448 250496 "CATCTOR" 250501 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 249415 249727 249825 "CATAST" 249946 T CATAST (NIL) -8 NIL NIL NIL) (-139 248831 249136 249228 "CASEAST" 249343 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247927 248087 248308 "CARTEN2" 248678 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 242824 244084 244828 "CARTEN" 247239 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 240954 241974 242231 "CARD" 242587 T CARD (NIL) -8 NIL NIL NIL) (-135 240476 240758 240833 "CAPSLAST" 240899 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 239918 240174 240202 "CACHSET" 240334 T CACHSET (NIL) -9 NIL 240412 NIL) (-133 239308 239696 239724 "CABMON" 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(-572))))) (((*1 *2 *3) - (-12 (-5 *3 (-1165)) (-5 *2 (-711 (-292))) (-5 *1 (-170))))) -(((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1036))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-1207)) - (-4 *6 (-13 (-319) (-1068 (-558)) (-658 (-558)) (-149))) - (-4 *4 (-13 (-29 *6) (-1233) (-988))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -2565 (-661 *4)))) - (-5 *1 (-823 *6 *4 *3)) (-4 *3 (-678 *4))))) + (|partial| -12 + (-5 *3 + (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) + (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1184 (-229))) + (|:| |notEvaluated| "Internal singularities not yet evaluated"))) + (|:| -1646 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-572))))) (((*1 *1 *2) (-12 (-5 *2 (-661 (-2 - (|:| -4312 - (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -2972 (-1119 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -4367 + (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) + (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (|:| -2065 + (|:| -2294 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -14531,1817 +12361,1823 @@ (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1185 (-229))) + (-3 (|:| |str| (-1184 (-229))) (|:| |notEvaluated| "Internal 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(|:| CF (-326 (-171 (-391)))) (|:| |switch| (-1206)))) - (-5 *1 (-1206))))) -(((*1 *1 *1) (-4 *1 (-1174)))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-791)) (-5 *1 (-879 *2)) (-4 *2 (-175)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1201 (-558))) (-5 *1 (-970)) (-5 *3 (-558))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-558)) (-5 *4 (-709 (-229))) (-5 *2 (-1065)) - (-5 *1 (-767))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1201 *1)) (-5 *4 (-1207)) (-4 *1 (-27)) - (-5 *2 (-661 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-1201 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-974 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1207)) (-4 *4 (-569)) (-5 *2 (-661 *1)) - (-4 *1 (-29 *4)))) - ((*1 *2 *1) (-12 (-4 *3 (-569)) (-5 *2 (-661 *1)) (-4 *1 (-29 *3))))) + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| 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