diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-03-12 06:16:57 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-03-12 06:16:57 +0000 |
| commit | 42d38bee45a64edfc12641053e58581c20584363 (patch) | |
| tree | 5e1edcd1575af28ed489ae4446563879e4837bc1 | |
| parent | 4a92a0cc2bca6807ea4362797cfe6939bad4889b (diff) | |
| download | open-axiom-42d38bee45a64edfc12641053e58581c20584363.tar.gz | |
* algebra/si.spad.pamphlet (IntegerNumberSystem) [positive?]:
Remove definition.
(SingleInteger): Simplify implementation of random.
* algebra/sf.spad.pamphlet (DoubleFloat): Likewise.
[positive?]: Define.
* algebra/integer.spad.pamphlet (Integer): Tidy.
| -rw-r--r-- | src/ChangeLog | 9 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 35 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 4 | ||||
| -rw-r--r-- | src/interp/lisp-backend.boot | 4 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1343 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9134 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27628 |
11 files changed, 20192 insertions, 20183 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index c303857e..6c279b5e 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,12 @@ +2011-03-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/si.spad.pamphlet (IntegerNumberSystem) [positive?]: + Remove definition. + (SingleInteger): Simplify implementation of random. + * algebra/sf.spad.pamphlet (DoubleFloat): Likewise. + [positive?]: Define. + * algebra/integer.spad.pamphlet (Integer): Tidy. + 2011-03-11 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/catdef.spad.pamphlet (OrderedAbelianGroup): Export diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index 0b70def4..ac09f419 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -86,6 +86,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with import %icst1: % from Foreign Builtin import %ineg: % -> % from Foreign Builtin import %iabs: % -> % from Foreign Builtin + import %irandom: % -> % from Foreign Builtin import %iodd?: % -> Boolean from Foreign Builtin import %hash: % -> SingleInteger from Foreign Builtin import %iadd: (%,%) -> % from Foreign Builtin @@ -161,6 +162,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with dec x == x - 1@% hash x == %hash x negative? x == x < 0@% + positive? x == 0 < x coerce(x):OutputForm == outputForm(x pretend Integer) coerce(m:Integer):% == m pretend % convert(x:%):Integer == x pretend Integer @@ -199,7 +201,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with abs(x) == %iabs x random() == random()$Lisp - random(x) == RANDOM(x)$Lisp + random(x) == %irandom x x = y == %ieq(x,y) x < y == %ilt(x,y) x > y == %igt(x,y) diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 1a6f8266..bfd30d62 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -473,9 +473,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, sign(x) == retract FLOAT_-SIGN(x,1)$Lisp abs x == %fabs x - - - + positive? x == 0 < x manexp(x) == zero? x => [0,0] s := sign x diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 085cc0fe..ad162629 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -84,7 +84,6 @@ IntegerNumberSystem(): Category == characteristic == 0 differentiate x == 0 even? x == not odd? x - positive? x == x > 0 copy x == x bit?(x, i) == odd? shift(x, -i) mask n == dec shift(1, n) @@ -181,10 +180,7 @@ IntegerNumberSystem(): Category == -- Lisp dependencies --- ABSVAL, TIMES, --- QSLESSP, QSGREATERP, QSDIFFERENCE --- QSNOT, QSAND --- QSOR, QSXOR, QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD +-- QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) with @@ -212,6 +208,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w import %icst0: % from Foreign Builtin import %icst1: % from Foreign Builtin + import %icstmin: % from Foreign Builtin + import %icstmax: % from Foreign Builtin import %iadd: (%,%) -> % from Foreign Builtin import %isub: (%,%) -> % from Foreign Builtin import %imul: (%,%) -> % from Foreign Builtin @@ -221,6 +219,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w import %iinc: % -> % from Foreign Builtin import %idec: % -> % from Foreign Builtin import %iabs: % -> % from Foreign Builtin + import %irandom: % -> % from Foreign Builtin import %imax: (%,%) -> % from Foreign Builtin import %imin: (%,%) -> % from Foreign Builtin import %igcd: (%,%) -> % from Foreign Builtin @@ -237,13 +236,6 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w import %bitior: (%,%) -> % from Foreign Builtin import %bitxor: (%,%) -> % from Foreign Builtin - seed : % := %icst1 -- for random() - MAXINT ==> _$ShortMaximum$Lisp - MININT ==> _$ShortMinimum$Lisp - BASE ==> 67108864$Lisp -- 2**26 - MULTIPLIER ==> 314159269$Lisp -- from Knuth's table - MODULUS ==> 2147483647$Lisp -- 2**31-1 - writeOMSingleInt(dev: OpenMathDevice, x: %): Void == if negative? x then OMputApp(dev) @@ -296,8 +288,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w 0 == %icst0 1 == %icst1 base() == per 2 - max() == MAXINT - min() == MININT + max() == %icstmax + min() == %icstmin x = y == %ieq(x,y) ~ x == %bitnot x not(x) == %bitnot x @@ -339,10 +331,10 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w submod(a,b,p) == QSDIFMOD(a,b,p)$Lisp negative?(x) == %ilt(x,%icst0) size() == - (MAXINT - MININT + 1) pretend NonNegativeInteger - index i == per(i + MININT - 1) + (%icstmax - %icstmin + %icst1) pretend NonNegativeInteger + index i == per(i + rep %icstmin - rep %icst1) lookup x == - (x - MININT + 1) pretend PositiveInteger + (x - %icstmin + %icst1) pretend PositiveInteger reducedSystem(m: Matrix %, v: Vector %) == @@ -356,17 +348,14 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,OpenMath) w r coerce(x:Integer):% == per x - - random() == - seed := TIMES(MULTIPLIER,seed)$Lisp rem MODULUS - seed rem BASE - - random(n) == RANDOM(n)$Lisp + random() == random %icstmax + random(n) == %irandom n UCA ==> Record(unit:%,canonical:%,associate:%) unitNormal x == negative? x => [-1@%,-x,-1@%]$UCA [1@%,x,1@%]$UCA + positive? x == 0 < x @ diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index 59cb8363..a2e3a4e8 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -430,9 +430,9 @@ $VMsideEffectFreeOperators == %funcall %nothing %when %false %true %otherwise %2bit %2bool %and %or %not %peq %ieq %ilt %ile %igt %ige %head %tail %integer? %beq %blt %ble %bgt %bge %bitand %bitior %bitxor %bitnot %bcompl - %ilength %ibit %icst0 %icst1 + %ilength %ibit %icst0 %icst1 %icstmin %icstmax %imul %iadd %isub %igcd %ilcm %ipow %imin %imax %ieven? %iodd? %iinc - %irem %iquo %idivide %idec + %irem %iquo %idivide %idec %irandom %feq %flt %fle %fgt %fge %fmul %fadd %fsub %fexp %fmin %fmax %float? %fpowi %fdiv %fneg %i2f %fminval %fmaxval %fbase %fprec %ftrunc %fsqrt %fpowf %flog %flog2 %flog10 %fmanexp diff --git a/src/interp/lisp-backend.boot b/src/interp/lisp-backend.boot index 1899ec39..84638ba4 100644 --- a/src/interp/lisp-backend.boot +++ b/src/interp/lisp-backend.boot @@ -462,6 +462,9 @@ for x in [ ['%beq, :'byteEqual], ['%blt, :'byteLessThan], + -- integer constants + ['%icstmin, :'_$ShortMinimum], + ['%icstmax, :'_$ShortMaximum], -- unary integer operations. ['%iabs, :'ABS], ['%ieven?, :'EVENP], @@ -471,6 +474,7 @@ for x in [ ['%i2s, :'WRITE_-TO_-STRING], ['%ilength, :'INTEGER_-LENGTH], ['%ibit, :'INTEGER_-BIT], + ['%irandom, :'RANDOM], -- binary integer operations. ['%iadd, :"+"], ['%igcd, :'GCD], diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 2dc7e679..786db968 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294709 . 3508838145) +(2294709 . 3508891732) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -4346) +(-32 R -4355) ((|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 -1070) (QUOTE (-560))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -4346 UP UPUP -3043) +(-40 -4355 UP UPUP -3650) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2309 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -4346) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2277 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2277 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2277 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2277 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2277 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2277 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -4355) ((|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 (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4510 . T) (-4511 . T)) -((-2309 (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|))))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|))))))) +((-2277 (-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|))))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-872))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -4346) +(-54 |Base| R -4355) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|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 @@ -171,64 +171,64 @@ 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2187) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2206) ((|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 -2187) +(-62 -2206) ((|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 -2187) +(-63 -2206) ((|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 -2187) +(-64 -2206) ((|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 -2187) +(-65 -2206) ((|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 -2187) +(-66 -2206) ((|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 -2187) +(-67 -2206) ((|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 -2187) +(-68 -2206) ((|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 -2187) +(-69 -2206) ((|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 -2187) +(-70 -2206) ((|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 -2187) +(-71 -2206) ((|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 -2187) +(-72 -2206) ((|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 -2187) +(-73 -2206) ((|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 -2187) +(-74 -2206) ((|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 -2187) +(-75 -2206) ((|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 -2187) +(-78 -2206) ((|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 -2187) +(-79 -2206) ((|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 -2187) +(-80 -2206) ((|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 -2187) +(-81 -2206) ((|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 -2187) +(-82 -2206) ((|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 -2187) +(-83 -2206) ((|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 -2187) +(-84 -2206) ((|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 -2187) +(-85 -2206) ((|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 -2187) +(-86 -2206) ((|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 -2187) +(-87 -2206) ((|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 -2187) +(-88 -2206) ((|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 -2187) +(-89 -2206) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values 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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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 @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2277 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (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 @@ -396,7 +396,7 @@ 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 -4346 UP) +(-117 -4355 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 @@ -407,7 +407,7 @@ 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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-2309 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%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 (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-2277 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%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 (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|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 @@ -423,7 +423,7 @@ 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"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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 @@ -455,7 +455,7 @@ 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."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2309 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-2309 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-2277 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2277 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-2277 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|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 @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4512 "*") . T)) NIL -(-137 |minix| -3061 R) +(-137 |minix| -1808 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| -3061 S T$) +(-138 |minix| -1808 S T$) ((|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 @@ -503,7 +503,7 @@ 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}."))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-2309 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2277 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|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 @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4507 . T)) NIL -(-150 -4346 UP UPUP) +(-150 -4355 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 @@ -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 -4346) +(-160 R -4355) ((|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 @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-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})"))) -((-4503 -2309 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-4437 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 -2277 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-4438 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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}."))) -((-4503 -2309 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-4437 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2277 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2277 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4509)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 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| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -4346) +(-191 R -4355) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -4346 UP UPUP R) +(-219 -4355 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 -4346 FP) +(-220 -4355 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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2277 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -4346) +(-223 R -4355) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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}."))) ((-4507 . T)) NIL -(-228 R -4346) +(-228 R -4355) ((|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.")) (|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}."))) -((-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4432 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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)}.}"))) @@ -855,7 +855,7 @@ 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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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 @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -3061 R) +(-244 S -1808 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 (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -3061 R) +(-245 -1808 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"))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) NIL -(-246 -3061 R) +(-246 -1808 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."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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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 @@ -939,7 +939,7 @@ 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}"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -951,7 +951,7 @@ NIL (-255 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 @@ -1031,7 +1031,7 @@ 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -4346) +(-287 R -4355) ((|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 -4346) +(-288 R -4355) ((|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 @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -2533 -1762 |exactQuo|) +(-301 S R |Mod| -3247 -1379 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) -((-4507 -2309 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) -((|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (|%list| 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2277 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2277 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) (-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 @@ -1159,7 +1159,7 @@ 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|)))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#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 @@ -1172,11 +1172,11 @@ NIL ((|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|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -4346 S) +(-311 -4355 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -4346) +(-312 E -4355) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -4346) +(-322 -4355) ((|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 @@ -1231,11 +1231,11 @@ 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))}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-2309 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| 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(|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-2277 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 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(|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."))) -((-4507 -2309 (-12 (|has| |#1| (-571)) (-2309 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) -((-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE 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(|HasCategory| |#1| (QUOTE (-1081)))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21)))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25)))) (-2277 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-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 -4346) +(-329 R -4355) ((|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 @@ -1255,7 +1255,7 @@ 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ 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."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -4346) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -4355) ((|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 -4346) +(-341 -4355) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -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 -4346 UP UPUP R) +(-346 -4355 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 @@ -1320,11 +1320,11 @@ 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 -4346 UP UPUP R) +(-348 S -4355 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 -4346 UP UPUP R) +(-349 -4355 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 @@ -1343,12 +1343,12 @@ NIL (-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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -4346 UP UPUP) +((-2277 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +(-354 S -4355 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 -4346 UP UPUP) +(-355 -4355 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."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1359,15 +1359,15 @@ 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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-2277 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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 @@ -1384,42 +1384,42 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-364 R UP -4346) +(-364 R UP -4355) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-2277 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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 -4346 GF) +(-370 -4355 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 -4346 FP FPP) +(-371 -4355 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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2277 (|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 @@ -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}."))) -((-4493 . T) (-4501 . T) (-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4493 . T) (-4501 . T) (-4432 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -4346 UP UPUP R) +(-406 -4355 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 @@ -1576,11 +1576,11 @@ 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 -(-412 -2187 |returnType| -4401 |symbols|) +(-412 -2206 |returnType| -4439 |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 -(-413 -4346 UP) +(-413 -4355 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4432 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-419 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."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 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 @@ -1615,7 +1615,7 @@ NIL (-421 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."))) ((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 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 @@ -1636,7 +1636,7 @@ NIL ((|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 -(-427 R -4346 UP A) +(-427 R -4355 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)}."))) ((-4507 . T)) NIL @@ -1644,7 +1644,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-429 R -4346 UP A |ibasis|) +(-429 R -4355 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 -1070) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4507 -2309 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) +((-4507 -2277 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-442 R -4346) +(-442 R -4355) ((|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 @@ -1704,19 +1704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -4346) +(-444 R -4355) ((|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 -(-445 R -4346) +(-445 R -4355) ((|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 -(-446 R -4346) +(-446 R -4355) ((|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)))) -(-447 R -4346) +(-447 R -4355) ((|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 @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-449 R -4346 UP) +(-449 R -4355 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 -1070) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ 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 -(-457 R UP -4346) +(-457 R UP -4355) ((|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 @@ -1803,7 +1803,7 @@ NIL (-468 |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"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 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 @@ -1868,7 +1868,7 @@ 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 -(-485 |lv| -4346 R) +(-485 |lv| -4355 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 @@ -1883,11 +1883,11 @@ NIL (-488 |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.") 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The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4511 . T) (-4510 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |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."))) ((-4510 . T) (-4511 . 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Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. 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 @@ -1911,11 +1911,11 @@ NIL (-495 |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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(-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2277 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-497) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1923,8 +1923,8 @@ NIL (-498 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -4346 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -4355 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2277 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -4346 UP |AlExt| |AlPol|) +(-508 -4355 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 @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -4346) +(-513 R UP -4355) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -4346 |Expon| |VarSet| |DPoly|) +(-518 -4355 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 @@ -2059,15 +2059,15 @@ NIL (-532 |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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2309 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-2277 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 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 @@ -2079,7 +2079,7 @@ NIL (-537 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -4346 |Par|) +(-546 K -4355 |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 @@ -2136,7 +2136,7 @@ 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 -(-552 K -4346 |Par|) +(-552 K -4355 |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 @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) -(-566 R -4346) +((-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|)))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102)))) +(-566 R -4355) ((|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 -(-567 R0 -4346 UP UPUP R) +(-567 R0 -4355 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 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."))) -((-4430 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4432 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-570 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."))) @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-572 R -4346) +(-572 R -4355) ((|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."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -4346 L) +(-575 R -4355 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)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -4346 UP UPUP R) +(-577 -4355 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 -(-578 -4346 UP) +(-578 -4355 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 @@ -2248,15 +2248,15 @@ 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 -(-580 R -4346 L) +(-580 R -4355 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}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -4346) +(-581 R -4355) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -4346 UP) +(-582 -4355 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 @@ -2264,27 +2264,27 @@ 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 -(-584 -4346) +(-584 -4355) ((|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 (-585 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."))) -((-4430 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4432 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-586) ((|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 -(-587 R -4346) +(-587 R -4355) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -4346 UP) +(-588 -4355 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}."))) NIL NIL -(-589 R -4346) +(-589 R -4355) ((|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 @@ -2316,15 +2316,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-597 -4346) +(-597 -4355) ((|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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -4346) +(-598 E -4355) ((|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 -(-599 R -4346) +(-599 R -4355) ((|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 @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2309 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2309 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2277 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2277 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2277 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 @@ -2367,7 +2367,7 @@ NIL (-609 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |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.}"))) (((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -2384,7 +2384,7 @@ 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 -(-614 R -4346 FG) +(-614 R -4355 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 @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4507 -2309 (-2925 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-2309 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -2277 (-2856 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-2277 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-102)))) (-628 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 @@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -4346 UP) +(-634 -4355 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2492,7 +2492,7 @@ NIL ((|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."))) ((-4507 . T)) NIL -(-641 R -4346) +(-641 R -4355) ((|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 @@ -2520,7 +2520,7 @@ NIL ((|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 -(-648 R -4346) +(-648 R -4355) ((|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 @@ -2528,18 +2528,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -4346) +(-650 |lv| -4355) ((|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 (-651) ((|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."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3519) (QUOTE (-51))))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (QUOTE (-1133)))) (-652 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4507 -2309 (-2925 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-2309 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -2277 (-2856 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-2277 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 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 @@ -2563,7 +2563,7 @@ NIL (-658 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 -((-2912 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2846 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 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}."))) ((-4505 . T) (-4504 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 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."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 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 @@ -2607,7 +2607,7 @@ NIL (-669 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 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 @@ -2628,11 +2628,11 @@ NIL ((|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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -4346 L) +(-675 R -4355 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 -(-676 A -4463) +(-676 A -1588) ((|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}}"))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-681 -4346 UP) +(-681 -4355 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)))) @@ -2684,11 +2684,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4511 . T) (-4510 . T)) NIL -(-689 -4346 |Row| |Col| M) +(-689 -4355 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -4346) +(-690 -4355) ((|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}."))) NIL NIL @@ -2699,7 +2699,7 @@ NIL (-692 |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."))) ((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2309 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2277 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|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 @@ -2775,7 +2775,7 @@ NIL (-711 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."))) ((-4510 . T) (-4511 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 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 @@ -2784,7 +2784,7 @@ 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 -(-714 S -4346 FLAF FLAS) +(-714 S -4355 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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T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4432 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-722 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."))) @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -2533 -1762 |exactQuo|) +(-737 R |Mod| -3247 -1379 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4507 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4505 . T) (-4504 . T)) NIL -(-740 -4346) +(-740 -4355) ((|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]]}."))) ((-4507 . T)) NIL @@ -2924,7 +2924,7 @@ 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 -(-749 -4346 UP) +(-749 -4355 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 @@ -2943,7 +2943,7 @@ NIL (-753 |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."))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2277 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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 @@ -3076,11 +3076,11 @@ 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 -(-787 -4346) +(-787 -4355) ((|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 -(-788 P -4346) +(-788 P -4355) ((|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 @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -4346) +(-790 UP -4355) ((|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 @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4512 "*") . T)) NIL -(-794 R -4346) +(-794 R -4355) ((|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 @@ -3124,7 +3124,7 @@ 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 -(-799 -4346 |ExtF| |SUEx| |ExtP| |n|) +(-799 -4355 |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 @@ -3139,11 +3139,11 @@ NIL (-802 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|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)}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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(|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 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 @@ -3219,8 +3219,8 @@ NIL (-822 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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2309 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-823 -2309 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2277 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2277 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-823 -2277 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 @@ -3228,11 +3228,11 @@ 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 -(-825 R -4346 L) +(-825 R -4355 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 -(-826 R -4346) +(-826 R -4355) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3240,7 +3240,7 @@ NIL ((|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 -(-828 R -4346) +(-828 R -4355) ((|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 @@ -3248,11 +3248,11 @@ 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 -(-830 -4346 UP UPUP R) +(-830 -4355 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 -(-831 -4346 UP L LQ) +(-831 -4355 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 @@ -3260,38 +3260,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-833 -4346 UP L LQ) +(-833 -4355 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 -(-834 -4346 UP) +(-834 -4355 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."))) NIL NIL -(-835 -4346 L UP A LO) +(-835 -4355 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 -(-836 -4346 UP) +(-836 -4355 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)))) -(-837 -4346 LO) +(-837 -4355 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 -(-838 -4346 LODO) +(-838 -4355 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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(|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-840 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-841 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4512 "*") |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 . T) (-4505 . T) (-4504 . T)) @@ -3355,7 +3355,7 @@ NIL (-856 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."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2277 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2277 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-857 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 @@ -3395,7 +3395,7 @@ NIL (-866 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2277 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2277 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-867 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -3061 S) +(-869 -1808 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 @@ -3444,11 +3444,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\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 (-571)))) -(-879 R |sigma| -3286) +(-879 R |sigma| -2659) ((|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."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -3286) +(-880 |x| R |sigma| -2659) ((|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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3515,15 +3515,15 @@ NIL (-896 |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)."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-2309 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-2277 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-897 |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)}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-2309 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-2277 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-898 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 (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-899) ((|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 @@ -3583,7 +3583,7 @@ NIL (-913 |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 (-2912 (|HasCategory| |#2| (QUOTE (-1081)))) (-2912 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2912 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) +((-12 (-2846 (|HasCategory| |#2| (QUOTE (-1081)))) (-2846 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2846 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-914 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 @@ -3596,7 +3596,7 @@ NIL ((|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 -(-917 R -3095) +(-917 R -3052) ((|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 @@ -3624,7 +3624,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-924 UP -4346) +(-924 UP -4355) ((|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 @@ -3655,11 +3655,11 @@ NIL (-931 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 (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-932 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4507 . T)) -((-2309 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) +((-2277 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (-933 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 @@ -3692,7 +3692,7 @@ NIL ((|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}."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-941 R0 -4346 UP UPUP R) +(-941 R0 -4355 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 @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik'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 -(-948 -4346) +(-948 -4355) ((|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 @@ -3736,11 +3736,11 @@ NIL ((|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)}"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-952 |xx| -4346) +(-952 |xx| -4355) ((|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 -(-953 -4346 P) +(-953 -4355 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|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 -(-960 R -4346) +(-960 R -4355) ((|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 @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-962 S R -4346) +(-962 S R -4355) ((|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 @@ -3796,11 +3796,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) -(-967 -3095) +(-967 -3052) ((|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 -(-968 R -4346 -3095) +(-968 R -4355 -3052) ((|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 @@ -3823,7 +3823,7 @@ NIL (-973 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-974 |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 @@ -3835,7 +3835,7 @@ NIL (-976 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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-977 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 @@ -3852,7 +3852,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the 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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) NIL -(-981 E V R P -4346) +(-981 E V R P -4355) ((|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 @@ -3860,7 +3860,7 @@ NIL ((|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 -(-983 E V R P -4346) +(-983 E V R P -4355) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3875,7 +3875,7 @@ NIL (-986 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) (-987 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 @@ -3883,7 +3883,7 @@ NIL (-988 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"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-989 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 @@ -3892,7 +3892,7 @@ NIL ((|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 -(-991 -4346) +(-991 -4355) ((|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 @@ -3907,7 +3907,7 @@ NIL (-994 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"))) ((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2309 (-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 (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2309 (-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 (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2277 (-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 (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2277 (-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 (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-995) ((|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 @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1017 K R UP -4346) +(-1017 K R UP -4355) ((|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 @@ -4043,7 +4043,7 @@ NIL (-1028 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.}"))) ((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|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 -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) (-1029 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4059,7 +4059,7 @@ NIL (-1032 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1033 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4068,14 +4068,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1035 -4346 UP UPUP |radicnd| |n|) +(-1035 -4355 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2309 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2277 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2277 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2277 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2277 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2277 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2277 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1036 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2277 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1037) ((|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 @@ -4108,19 +4108,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (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}}"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) NIL -(-1045 R -4346) +(-1045 R -4355) ((|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 -(-1046 R -4346) +(-1046 R -4355) ((|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 -(-1047 -4346 UP) +(-1047 -4355 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 -(-1048 -4346 UP) +(-1048 -4355 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 @@ -4155,8 +4155,8 @@ NIL (-1056 |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"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) -((-2309 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -4346 L) +((-2277 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-1057 -4355 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 @@ -4192,14 +4192,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1066 -4346 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -4355 |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"))) (((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-1067) ((|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.}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3519) (QUOTE (-51))))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102)))) (-1068) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4256,7 +4256,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4507 . T)) NIL -(-1082 |xx| -4346) +(-1082 |xx| -4355) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4275,7 +4275,7 @@ NIL (-1086 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4510 . T) (-4505 . T) (-4504 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2309 (-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 (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2277 (-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 (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) (-1087 |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 @@ -4311,7 +4311,7 @@ NIL (-1095) ((|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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3519) (QUOTE (-51))))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (QUOTE (-102)))) (-1096 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 @@ -4356,7 +4356,7 @@ NIL ((|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 -(-1107 |Base| R -4346) +(-1107 |Base| R -4355) ((|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 @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -4346) +(-1109 |Base| R -4355) ((|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 @@ -4375,7 +4375,7 @@ NIL (-1111 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."))) ((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-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 -928) (QUOTE (-1209)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-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 -928) (QUOTE (-1209)))))) (-1112 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 @@ -4407,7 +4407,7 @@ NIL (-1119 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1120 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 @@ -4447,7 +4447,7 @@ NIL (-1129 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)}}"))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1130 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 @@ -4511,7 +4511,7 @@ NIL (-1145 |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}."))) ((-4504 |has| |#3| (-1081)) (-4505 |has| |#3| (-1081)) (-4507 |has| |#3| (-6 -4507)) (-4510 . 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(|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1146 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 @@ -4524,7 +4524,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `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 -(-1149 R -4346) +(-1149 R -4355) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4559,16 +4559,16 @@ NIL (-1157 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1159 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}"))) ((-4511 . T) (-4510 . T)) NIL -(-1160 UP -4346) +(-1160 UP -4355) ((|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 @@ -4623,11 +4623,11 @@ NIL (-1173 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-2309 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-2309 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-2277 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-2277 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) (-1174 |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}."))) ((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-2309 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2277 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-2277 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1175 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4651,7 +4651,7 @@ NIL (-1180 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1181 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4663,7 +4663,7 @@ NIL (-1183 |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."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|)))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133)))) (-1184) ((|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 @@ -4679,7 +4679,7 @@ NIL (-1187 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."))) ((-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1188 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 @@ -4695,11 +4695,11 @@ NIL (-1191) ((|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"))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2309 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2309 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2277 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2277 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2277 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1192 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#1|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#1|)))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (QUOTE (-102)))) (-1193 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 @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4743,7 +4743,7 @@ NIL (-1203 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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| (((|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 @@ -4755,11 +4755,11 @@ NIL (-1206 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1207 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1208) ((|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 @@ -4775,7 +4775,7 @@ NIL (-1211 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2277 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) (-1212) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4815,7 +4815,7 @@ NIL (-1221 |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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1966) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3519) (|devaluate| |#2|)))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2277 (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (QUOTE (-102)))) (-1222 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 @@ -4875,7 +4875,7 @@ NIL (-1236 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4511 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1237 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -4346) +(-1239 R -4355) ((|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 @@ -4892,14 +4892,14 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1241 R -4346) +(-1241 R -4355) ((|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 -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) (-1242 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 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 @@ -4920,7 +4920,7 @@ NIL ((|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 (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -4346) +(-1248 -4355) ((|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 @@ -4966,8 +4966,8 @@ NIL NIL (-1259 |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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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -5003,7 +5003,7 @@ NIL (-1268 |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}"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4506 |has| |#2| (-376)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2277 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1269 |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 @@ -5039,7 +5039,7 @@ NIL (-1277 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 -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) (-1278 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5051,7 +5051,7 @@ NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |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 @@ -5071,11 +5071,11 @@ NIL (-1285 |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)}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2277 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 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))}."))) (((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-2309 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-2277 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) (-1287 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2277 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3831) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2277 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1290 |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 @@ -5095,7 +5095,7 @@ NIL (-1291 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 (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -2698) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3626) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5104,7 +5104,7 @@ NIL ((|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 -(-1294 -4346 UP L UTS) +(-1294 -4355 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 (-571)))) @@ -5127,7 +5127,7 @@ NIL (-1299 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."))) ((-4511 . T) (-4510 . T)) -((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2277 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2277 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2277 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2277 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1300 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 @@ -5164,7 +5164,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*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 -(-1309 K R UP -4346) +(-1309 K R UP -4355) ((|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 @@ -5196,11 +5196,11 @@ NIL ((|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 -(-1317 S -4346) +(-1317 S -4355) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -4346) +(-1318 -4355) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 3c47c0ae..80299f4a 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3508838151) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) #0#) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|))))) -((((-560)) . T) (($) -2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3508891738) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) #0#) |has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-321 (-2 (|:| -1966 |#1|) (|:| -3519 |#2|))))) +((((-560)) . T) (($) -2277 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -2309 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -2309 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-940)) ((((-888)) . T)) ((((-888)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1191)) . T) (((-229)) . T) (((-391)) . T) (((-916 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-888)) . T)) -(-2309 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-2309 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) +(-2277 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2277 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-871))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-2309 (|has| |#1| (-844)) (|has| |#1| (-872))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-871))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-2277 (|has| |#1| (-844)) (|has| |#1| (-872))) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-871)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-894 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-888)) . T)) ((((-1214)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1214)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -(-2309 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(((|#2| (-496 (-3819 |#1|) (-793))) . T)) -((((-1209)) -2309 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +(-2277 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(((|#2| (-496 (-3782 |#1|) (-793))) . T)) +((((-1209)) -2277 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1| (-545 (-1209))) . T)) ((((-1191)) . T) (((-988 (-130))) . T) (((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2309 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -2081 |#1|) (|:| -2909 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2277 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -2113 |#1|) (|:| -1704 |#2|))) . T)) ((($) . T)) ((((-888)) |has| |#1| (-632 (-888))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-560)) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1209)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-888)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2309 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2277 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (|has| |#1| (-1133)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((((-118 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) @@ -116,14 +116,14 @@ ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2309 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2277 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2309 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2277 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -241,13 +241,13 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -((($ $) -2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) (((|#1| (-1003)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1184)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . 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T)) -((($) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-888)) . T)) (|has| (-1280 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (((|#1|) . T)) ((($) . T)) ((((-560) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . 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T)) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) (((|#1|) |has| |#1| (-175))) (|has| $ (-149)) (|has| $ (-149)) ((((-1214)) . T)) (((|#1|) |has| |#1| (-175))) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-888)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) ((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|))) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1209)) . T)) (|has| |#1| (-571)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-3819 |#1|) (-793)) (-889 |#1|)) . T)) +(((|#2| (-246 (-3782 |#1|) (-793)) (-889 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2309 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2277 (|has| |#1| (-363)) (|has| |#1| (-381))) ((((-1174 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) -(((|#2|) . T) (((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (|has| |#3| (-817)) (|has| |#3| (-817)) ((((-888)) . T)) @@ -1176,18 +1176,18 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) -((((-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (((-1114)) . T)) +((((-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (((-1114)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-630 $)) . T)) (((|#1| (-421 (-560))) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((($ (-1296 |#2|)) . T) (($ (-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) -((((-560)) -2309 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) +((((-560)) -2277 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1195,15 +1195,15 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|))))) -(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) |has| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (-321 (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) |has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-321 (-2 (|:| -1966 |#1|) (|:| -3519 |#2|))))) +(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) |has| (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|)) (-321 (-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))))) ((((-888)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-1209) (-51)) . T)) -((((-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((((-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-889 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-845)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) -(((|#2| |#2|) -2309 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) -(((|#2|) -2309 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2309 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2| |#2|) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) ((((-560)) . T)) ((((-1214)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1214)) . T)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (|has| |#2| (-1184)) -(((#0=(-51)) . T) (((-2 (|:| -1919 (-1209)) (|:| -3529 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1966 (-1209)) (|:| -3519 #0#))) . T)) (((|#1| |#2|) . T)) (((|#1| (-657 |#2|)) . T)) (|has| |#3| (-1081)) @@ -1269,10 +1269,10 @@ (((|#1| (-560) (-1114)) . T)) (((|#1| (-421 (-560)) (-1114)) . T)) ((((-1209)) . T)) -((($) -2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2309 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2277 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2277 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-888)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1209) $) |has| |#1| (-528 (-1209) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|))) ((((-1209)) |has| |#1| (-928 (-1209)))) -(-2309 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2277 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#2|) . T) (((-888)) . T)) ((((-888)) . T)) (((|#2|) . T)) ((((-936 |#1|)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-894 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2277 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (|has| |#2| (-1081)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1235)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2277 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) -((($) -2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) -(-2309 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2277 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2309 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2277 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1191) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . 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T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-3819 |#1|) (-793)) (-889 |#1|)) . T)) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-3782 |#1|) (-793)) (-889 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1209)) (-1209)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((((-1209) (-51)) . 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T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) (|has| |#1| (-872)) (|has| |#1| (-872)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#3|) -2309 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2309 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-940))) -((($) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . 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T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) -(-2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-871)) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T)) (|has| |#1| (-871)) -(((#0=(-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) #0#) |has| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (-321 (-2 (|:| -1919 (-1191)) (|:| -3529 (-51)))))) +(((#0=(-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) #0#) |has| (-2 (|:| -1966 (-1191)) (|:| -3519 (-51))) (-321 (-2 (|:| -1966 (-1191)) (|:| -3519 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#1| (-1133)) ((((-888)) . T) (((-1214)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1114)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -2309 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -2277 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) ((((-694 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1975,7 +1975,7 @@ ((((-888)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-888)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((((-1214)) . T)) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#3|) . T) (((-560)) . T) (((-630 $)) . T)) @@ -1983,12 +1983,12 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#2|) . 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T)) +((($) -2277 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((((-1003)) . T)) ((((-1003)) . T) (((-888)) . T)) @@ -2058,7 +2058,7 @@ ((($) . T)) (((|#1|) . T)) ((((-114)) . T)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) (((|#1| (-560)) . T)) ((($) . T)) @@ -2081,7 +2081,7 @@ (((|#1| (-1259 |#1| |#2| |#3|)) . T)) ((((-888)) . T)) (|has| |#1| (-1133)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#1| (-793)) . T)) ((((-1191) |#1|) . T)) (((|#1|) . T)) @@ -2102,20 +2102,20 @@ ((((-560)) . T)) ((((-560)) . T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-363))) ((((-888)) . T)) (|has| |#1| (-149)) (((|#3|) . 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T)) (((|#3|) |has| |#3| (-1081))) @@ -2362,7 +2362,7 @@ ((((-1209)) |has| |#2| (-928 (-1209)))) (|has| |#1| (-872)) ((((-888)) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (|has| |#1| (-814)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -((($) -2309 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +((($) -2277 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-888)) . T)) (((|#2|) . T) (((-888)) . T)) -((($ (-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-872)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) |has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-321 (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2309 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2277 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-872)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-888)) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1209)) -2309 (-12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081))) (-12 (|has| |#3| (-930 (-1209))) (|has| |#3| (-1081))))) +((((-1209)) -2277 (-12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081))) (-12 (|has| |#3| (-930 (-1209))) (|has| |#3| (-1081))))) ((((-663 (-802 |#1| (-889 |#2|)))) . T) (((-888)) . T)) ((((-549)) |has| (-802 |#1| (-889 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1133)))) (((|#1|) |has| |#1| (-175))) ((((-888)) . T)) -(-2309 (|has| |#2| (-466)) (|has| |#2| (-940))) +(-2277 (|has| |#2| (-466)) (|has| |#2| (-940))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2309 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T) (($ $) -2309 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) +(((|#1| |#1|) . T) (($ $) -2277 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) ((((-976 |#1|)) . T)) -((((-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((($) . T)) ((((-560) |#1|) . T)) ((((-1209)) |has| (-421 |#2|) (-928 (-1209)))) -(((|#1|) . T) (($) -2309 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2277 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) ((((-549)) |has| |#2| (-633 (-549)))) ((((-711 |#2|)) . T) (((-888)) . T)) (((|#1|) . T)) @@ -2518,24 +2518,24 @@ (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) ((((-894 |#1|)) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2309 (|has| |#2| (-844)) (|has| |#2| (-872))) +(-2277 (|has| |#2| (-844)) (|has| |#2| (-872))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T)) -(-2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560))))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-2309 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-2277 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -2832,7 +2832,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1209)) -2309 (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))))) +((($ (-1209)) -2277 (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))))) ((((-888)) . T)) (((|#1| (-545 (-1209))) . T)) ((($ $) . T)) @@ -2842,29 +2842,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#2|) . 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T) (((-560)) . T)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2309 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2277 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-871)) @@ -2880,7 +2880,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-186)) . T) (((-888)) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-872)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) -((($) -2309 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) +((((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) +((($) -2277 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) ((((-888)) . T)) (((|#2|) |has| |#2| (-376))) ((((-888)) . T)) @@ -2913,19 +2913,19 @@ (|has| |#3| (-1081)) (|has| |#1| (-1133)) ((((-1209) (-51)) . T)) -(-2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (|has| |#1| (-844)) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-871)) -((((-1236 |#1|)) . T) (((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-1236 |#1|)) . T) (((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-888)) . T)) (|has| |#1| (-1133)) (((|#1|) . T)) -(((|#1|) -2309 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -2309 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2277 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2277 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (|has| |#1| (-872)) (|has| |#2| (-240)) ((((-889 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1133)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2309 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2277 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1052)) ((($) . T)) (|has| |#1| (-940)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-936 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(-2309 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) +(-2277 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-3819 |#1|) (-793))) . T)) +(((|#2| (-246 (-3782 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((((-1191)) . T) (((-888)) . T)) -(((#0=(-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) #0#) |has| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (-321 (-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))))) +(((#0=(-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) #0#) |has| (-2 (|:| -1966 (-1209)) (|:| -3519 (-51))) (-321 (-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))))) ((((-1191)) . T)) (|has| |#1| (-940)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-845))) ((((-888)) . T)) (|has| |#1| (-376)) -((((-1209)) -2309 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) +((((-1209)) -2277 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) (|has| |#1| (-376)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T)) -(-2309 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2277 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2309 (|has| |#4| (-817)) (|has| |#4| (-872))) -(-2309 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-2277 (|has| |#4| (-817)) (|has| |#4| (-872))) +(-2277 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-872)) ((((-888)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1191)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1081)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1070 (-560))) (((-560)) |has| |#2| (-1070 (-560))) (((-1209)) |has| |#2| (-1070 (-1209))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2309 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-888)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +((((-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) (|has| |#1| (-814)) (|has| |#1| (-814)) ((((-888)) . T)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-888)) . T)) ((((-888)) . T)) -(-2309 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) +(-2277 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-888)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1209)) -2309 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((((-1209)) -2277 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) ((((-888)) . T)) ((((-560)) . T)) -(-2309 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2277 (|has| |#2| (-817)) (|has| |#2| (-872))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-888)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) (|has| |#1| (-1184)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2309 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2277 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-888)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-888)) . T)) -((((-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1209) |#1|) . T)) -(((|#1|) -2309 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2277 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1209)) . T)) -(((|#1|) -2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) +(((|#1|) -2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1133)) ((((-802 |#1| (-889 |#2|))) |has| (-802 |#1| (-889 |#2|)) (-321 (-802 |#1| (-889 |#2|))))) -(-2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1120 (-1209)))) . T)) -((($) -2309 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) +((($) -2277 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 (-51)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-560)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#2| (-376)) ((((-888)) . T)) ((((-888)) . T)) -(-2309 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-2277 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-888)) . T)) ((((-1152)) . T) (((-888)) . T)) ((((-549)) . T) (((-888)) . T)) @@ -3353,14 +3353,14 @@ ((((-560)) . T)) (((|#3|) . T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-560)) . 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T) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) +((((-1157 |#1| |#2|)) . T) ((|#2|) . T) (($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-560)) . T)) +((((-1203 |#1|)) . T) (((-560)) . T) (($) -2277 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1114)) . T) ((|#1|) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) +(-2277 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) (((#0=(-595 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) -((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-1120 (-1209))) . T) (($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-1120 (-1209))) . T) (($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1299 |#1|) (-1299 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-888)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2309 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2277 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2309 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2277 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-940)) (|has| |#1| (-940)) -((($) -2309 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -1919 (-1191)) (|:| -3529 |#1|))) . T)) +((((-2 (|:| -1966 (-1191)) (|:| -3519 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2309 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2277 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1209)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) (((|#1|) . T)) (((|#1|) . T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-549)) . T)) ((((-888)) . T)) -((($) -2309 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081))))) +((($) -2277 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081))))) (|has| |#1| (-872)) ((((-888)) . T)) ((((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) @@ -3443,21 +3443,21 @@ ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -((($) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2309 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((($) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2277 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#2|) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2309 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2277 (|has| |#1| (-175)) (|has| |#1| (-571)))) (|has| |#1| (-571)) (((|#1|) |has| |#1| (-376))) ((((-560)) . T)) ((((-1209) #0=(-118 |#1|)) |has| #0# (-528 (-1209) #0#)) ((#0# #0#) |has| #0# (-321 #0#))) (|has| |#1| (-814)) (|has| |#1| (-814)) -((((-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((((-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) ((((-1114)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-844)) (|has| |#2| (-844)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((($) -2309 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -2309 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2277 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-560)) |has| |#1| (-912 (-560))) (((-391)) |has| |#1| (-912 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-940))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#2|) -2309 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2277 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1209)) . T)) ((((-894 |#1|)) . T)) -(-2309 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) -(-2309 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-817)) (|has| |#3| (-1081))) +(-2277 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) +(-2277 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-817)) (|has| |#3| (-1081))) ((((-888)) . T)) (((|#1|) . T)) -(-2309 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-2309 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) +(-2277 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2277 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) ((((-894 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-381)) @@ -3533,7 +3533,7 @@ (((|#1|) . T)) ((((-888)) . T)) ((($) . T) ((|#2|) . T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-888)) . T)) (|has| |#2| (-940)) -((((-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560))))) ((((-888)) . T)) ((((-888)) . T)) @@ -3553,7 +3553,7 @@ ((((-1203 |#1|)) . T) (((-888)) . T)) ((((-888)) . T)) ((((-421 (-560))) |has| |#2| (-1070 (-421 (-560)))) (((-560)) |has| |#2| (-1070 (-560))) ((|#2|) . T) (((-889 |#1|)) . T)) -((((-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) +((((-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T) (((-1209)) . T)) ((((-888)) . T)) @@ -3573,10 +3573,10 @@ ((((-663 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((($) . T) (((-560)) . T) (((-1286 |#1| |#2| |#3| |#4|)) . T) (((-421 (-560))) . 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T)) @@ -3591,16 +3591,16 @@ ((((-421 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-3819 |#1|) (-793))) . T)) +(-2277 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-3782 |#1|) (-793))) . T)) ((((-560) |#1|) . T)) ((((-1191)) . T) (((-888)) . T)) (((|#2| |#2|) . T)) (((|#1| (-545 (-1209))) . T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-560)) . T)) (((|#2|) . T)) -((($) -2309 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) +((($) -2277 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) (((|#2|) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) @@ -3609,9 +3609,9 @@ ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . T)) -(-2309 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T)) -((($) -2309 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-560))) . T)) @@ -3620,7 +3620,7 @@ ((((-888)) . T)) (((|#1|) . T)) (|has| |#1| (-1184)) -((($ (-1209)) -2309 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((($ (-1209)) -2277 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1|) . T)) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . 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T) (($ $) -2277 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2277 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) (|has| |#2| (-240)) (|has| $ (-149)) ((((-888)) . T)) -((($) . T) (((-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) +((($) . T) (((-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((((-888)) . T)) (|has| |#1| (-871)) ((((-130)) . T)) @@ -3823,7 +3823,7 @@ ((((-421 (-560))) . T) (((-721)) . T) (($) . T) (((-560)) . T)) (((|#1|) . T)) ((((-130)) . T)) -((($ (-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) ((((-888)) . T)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (((|#2| (-694 |#1|)) . T)) @@ -3832,24 +3832,24 @@ ((((-888)) |has| |#1| (-1133))) (((|#4|) . 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T)) -(-2309 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) -(-2309 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-817)) (|has| |#2| (-817)))) +(-2277 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2277 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-817)) (|has| |#2| (-817)))) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-894 |#1|)) . T) (((-421 (-560))) . T)) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) @@ -3858,15 +3858,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3886,7 +3886,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-2309 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2277 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) ((((-888)) . T)) @@ -3895,21 +3895,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . 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T)) -((($) -2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-940)) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-888)) . T)) @@ -3925,9 +3925,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-1214)) . T)) -(-2309 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2277 (|has| |#2| (-817)) (|has| |#2| (-872))) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) (((|#1| |#1|) . T)) @@ -3940,19 +3940,19 @@ (((|#1| (-560)) . T)) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) -((($ (-1209)) -2309 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (($ (-1114)) . T)) +((($ (-1209)) -2277 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (($ (-1114)) . T)) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1214)) . T)) ((((-1214)) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -(-2309 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-175)) (|has| |#1| (-571))) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1| (-793)) . T)) @@ -3960,24 +3960,24 @@ (((|#1| (-545 |#2|) |#2|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . 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T)) ((((-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) (|has| |#2| (-1081)) -(-2309 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2277 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-2309 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2277 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1133)) (((-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) -(-2309 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2277 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-940)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1214)) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#2|) . T)) -(-2309 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2277 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-888)) -2309 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) +((((-888)) -2277 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2309 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-2277 (|has| |#3| (-817)) (|has| |#3| (-872))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1214)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1209)) -2309 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +((((-1209)) -2277 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1172 |#1| |#2|)) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) -((((-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1052)) -(((|#2|) . T) (((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) ((($) . T)) ((((-888)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560)))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-391)) . #0=(|has| |#2| (-1052))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1209)) -2309 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2277 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) ((((-888)) . T)) (((|#2|) . T)) ((((-888)) . T)) @@ -4106,15 +4106,15 @@ ((((-1207 |#1| |#2| |#3|)) . T)) ((((-1207 |#1| |#2| |#3|)) . T) (((-1200 |#1| |#2| |#3|)) . T)) ((((-888)) . T)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2309 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) -(((|#2|) . T) ((|#3|) -2309 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2277 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) +(((|#2|) . T) ((|#3|) -2277 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-888)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) ((($ (-1209)) |has| |#1| (-1081))) -(-2309 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2277 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -1919 (-1209)) (|:| -3529 (-51)))) . T)) +((((-2 (|:| -1966 (-1209)) (|:| -3519 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) -(-2309 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2309 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2277 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2277 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((($) . T)) (((|#2| (-545 (-889 |#1|))) . T)) ((((-1214)) . T)) @@ -4174,7 +4174,7 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-888)) -2309 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2277 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1191) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T)) +((((-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . T)) (((|#2| $) |has| |#2| (-298 |#2| |#2|))) (((|#1| (-663 |#1|)) |has| |#1| (-871))) -(-2309 (|has| |#1| (-240)) (|has| |#1| (-363))) -(-2309 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-240)) (|has| |#1| (-363))) +(-2277 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1296 |#1|)) . T) (((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (|has| |#1| (-1133)) (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) -((((-1296 |#1|)) . T) (((-560)) . T) (($) -2309 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -2309 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) -((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -2309 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -2309 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) +((((-1296 |#1|)) . T) (((-560)) . T) (($) -2277 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -2277 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) +((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -2277 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -2277 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -4216,11 +4216,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1172 |#1| |#2|) #0#) |has| (-1172 |#1| |#2|) (-321 (-1172 |#1| |#2|)))) (((|#1|) . 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196913) ((-1203 . -670) 196802) ((-1157 . -670) 196691) ((-879 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1321 . -23) T) ((-716 . -930) NIL) ((-1320 . -23) T) ((-505 . -1133) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1066 . -1081) T) ((-890 . -102) T) ((-1221 . -298) 196558) ((-171 . -381) 196509) ((-1036 . -1249) T) ((-1003 . -1249) T) ((-944 . -1249) T) ((-858 . -635) 196463) ((-852 . -635) 196418) ((-44 . -23) T) ((-1329 . -102) T) ((-493 . -298) 196397) ((-597 . -1133) T) ((-1178 . -1141) 196366) ((-443 . -1249) T) ((-1135 . -1136) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1144) T) ((-1242 . -739) 196215) ((-1229 . -1133) T) ((-1036 . -910) 196197) ((-1036 . -912) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1036 . -1070) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1081) T) ((-227 . -1089) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1035 . -239) 194419) ((-931 . -102) 194369) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1133) T) ((-802 . -1097) 194290) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194265) ((-671 . -1133) T) ((-1289 . -47) 194242) ((-1286 . -102) T) ((-1280 . -47) 194212) ((-1259 . -47) 194189) ((-1242 . -175) 194140) ((-1206 . -319) 194119) ((-1200 . -319) 194098) ((-1128 . -635) 194079) ((-1123 . -635) 194060) ((-1111 . -571) 194011) ((-1111 . -1254) 193962) ((-1105 . -635) 193943) ((-1036 . -928) NIL) ((-1098 . -635) 193924) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193905) ((-1051 . -635) 193886) ((-736 . -1088) 193856) ((-734 . -922) 193759) ((-721 . -668) 193709) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193693) ((-50 . -1133) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1133) T) ((-532 . -1133) T) ((-501 . -844) T) ((-501 . -951) T) ((-372 . -1254) T) ((-367 . -1254) T) ((-359 . -1254) T) ((-331 . -1144) T) ((-326 . -1083) 193545) ((-325 . -1083) 193474) ((-108 . -1254) T) ((-645 . -635) 193455) ((-372 . -571) T) ((-221 . -951) T) ((-221 . -844) T) ((-326 . -662) 193365) ((-325 . -662) 193294) ((-367 . -571) T) ((-359 . -571) T) ((-659 . -111) 193273) ((-497 . -635) 193254) ((-108 . -571) T) ((-1200 . -1052) NIL) ((-676 . -739) 193224) ((-496 . -875) 193175) ((-222 . -635) 193156) ((-331 . -23) T) ((-67 . -1249) T) ((-1032 . -632) 193088) ((-1329 . -1184) T) ((-716 . -274) 193070) ((-716 . -234) 193052) ((-1324 . -21) T) ((-736 . -111) 193017) ((-1324 . -25) T) ((-663 . -34) T) ((-252 . -503) 193001) ((-1321 . -133) T) ((-1320 . -133) T) ((-1313 . -102) T) ((-1296 . -632) 192967) ((-1129 . -1131) 192951) ((-174 . -1133) T) ((-1289 . -1249) T) ((-1280 . -1249) T) ((-1280 . -1070) 192886) ((-1259 . -1249) T) ((-1259 . -912) NIL) ((-976 . -940) 192865) ((-1259 . -910) 192817) ((-1259 . -1070) 192783) ((-1242 . -528) 192750) ((-529 . -635) 192734) ((-1221 . -633) NIL) ((-1221 . -632) 192716) ((-1174 . -1155) 192661) ((-495 . -940) 192640) ((-1119 . -739) 192489) ((-1094 . -670) 192461) ((-976 . -670) 192350) ((-842 . -875) T) ((-803 . -739) 192179) ((-611 . -504) 192160) ((-600 . -504) 192141) ((-611 . -632) 192107) ((-600 . -632) 192073) ((-549 . -632) 192055) ((-593 . -1249) T) ((-549 . -633) 192036) ((-802 . -739) 191885) ((-1109 . -102) T) ((-642 . -668) 191857) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191746) ((-475 . -739) 191717) ((-468 . -739) 191566) ((-1018 . -102) T) ((-1078 . -1244) 191495) ((-931 . -321) 191433) ((-758 . -102) T) ((-659 . -635) 191410) ((-119 . -668) 191340) ((-901 . -93) T) ((-736 . -635) 191294) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191276) ((-667 . -504) 191257) ((-667 . -632) 191210) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1249) T) ((-609 . -1249) T) ((-357 . -1089) T) ((-301 . -1144) T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190662) ((-1152 . -662) 190649) ((-1152 . -1083) 190636) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190487) ((-936 . -633) 190469) ((-400 . -748) T) ((-897 . -1088) 190421) ((-897 . -111) 190359) ((-736 . -1081) T) ((-734 . -1275) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190236) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1111 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189637) ((-896 . -670) 189582) ((-1259 . -390) 189534) ((-994 . -133) 189389) ((-839 . -133) 189260) ((-45 . -875) NIL) ((-988 . -673) 189244) ((-1258 . -684) T) ((-1119 . -175) 189155) ((-988 . -385) 189139) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-840 . -47) 188801) ((-1094 . -748) T) ((-339 . -503) 188785) ((-976 . -748) T) ((-1313 . -321) 188723) ((-1289 . -928) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1285 . -1088) 188334) ((-1280 . -928) 188240) ((-1264 . -1088) 188048) ((-495 . -748) T) ((-1259 . -928) 187881) ((-1242 . -302) 187860) ((-1219 . -1249) T) ((-1216 . -381) T) ((-1215 . -381) T) ((-1178 . -153) 187844) ((-1152 . -102) T) ((-1147 . -1133) T) ((-1111 . -23) T) ((-1111 . -1144) T) ((-1108 . -102) T) ((-1090 . -632) 187811) ((-1035 . -424) 187783) ((-955 . -985) T) ((-758 . -321) 187721) ((-76 . -1249) T) ((-686 . -397) 187693) ((-171 . -940) 187646) ((-30 . -985) T) ((-114 . -868) T) ((-1 . -632) 187628) ((-1028 . -922) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -928) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-897 . -1081) T) ((-856 . -872) 187324) ((-81 . -1249) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1144) T) ((-367 . -1144) T) ((-359 . -1144) T) ((-1036 . -319) T) ((-944 . -319) T) ((-897 . -250) T) ((-108 . -1144) T) ((-897 . -240) 187123) ((-1285 . -111) 186944) ((-1264 . -111) 186733) ((-252 . -1288) 186717) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1083) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1133) T) ((-678 . -662) 186541) ((-1286 . -38) 186433) ((-1268 . -940) 186412) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186301) ((-896 . -818) NIL) ((-880 . -670) 186275) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-840 . -1070) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1285 . -635) 185618) ((-1264 . -635) 185366) ((-60 . -1249) T) ((-638 . -872) 185345) ((-514 . -684) T) ((-1178 . -1008) 185314) ((-1056 . -668) 185251) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) ((-488 . -1088) 185086) ((-514 . -113) T) ((-357 . -1133) T) ((-325 . -1184) NIL) ((-301 . -133) T) ((-407 . -1133) T) ((-894 . -1089) T) ((-716 . -383) 185053) ((-353 . -668) 184983) ((-227 . -640) 184960) ((-339 . -298) 184912) ((-488 . -111) 184733) ((-1285 . -1081) T) ((-1264 . -1081) T) ((-840 . -390) 184717) ((-850 . -1249) T) ((-171 . -748) T) ((-1315 . -1249) T) ((-678 . -102) T) ((-1285 . -250) 184696) ((-1285 . -240) 184648) ((-1264 . -240) 184553) ((-1264 . -250) 184532) ((-1035 . -416) NIL) ((-692 . -660) 184480) ((-326 . -38) 184390) ((-325 . -38) 184319) ((-69 . -632) 184301) ((-331 . -507) 184267) ((-48 . -668) 184217) ((-1221 . -300) 184196) ((-1258 . -872) T) ((-1145 . -1144) 184174) ((-84 . -1249) T) ((-62 . -632) 184156) ((-889 . -875) T) ((-493 . -300) 184135) ((-1315 . -1070) 184112) ((-1197 . -1133) T) ((-1145 . -23) 183964) ((-840 . -928) 183900) ((-1268 . -748) T) ((-1129 . -1249) T) ((-488 . -635) 183726) ((-365 . -239) T) ((-1119 . -302) 183657) ((-996 . -1133) T) ((-919 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1067 . -321) 183173) ((-901 . -504) 183154) ((-901 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182524) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1152 . -1184) T) ((-1280 . -319) 182433) ((-734 . -1083) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1249) T) ((-734 . -662) 181995) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181974) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181953) ((-663 . -1042) 181937) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181869) ((-1121 . -632) 181836) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181820) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181772) ((-366 . -1088) 181724) ((-358 . -1088) 181676) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181519) ((-255 . -1088) 181362) ((-686 . -111) 181341) ((-841 . -1254) 181320) ((-562 . -868) T) ((-326 . -930) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -930) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180693) ((-130 . -684) T) ((-839 . -660) 180599) ((-841 . -571) 180578) ((-501 . -875) T) ((-260 . -1070) 180405) ((-259 . -1070) 180232) ((-128 . -121) 180216) ((-221 . -875) T) ((-936 . -1088) 180181) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-936 . -111) 179984) ((-40 . -739) 179929) ((-894 . -1133) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1133) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1249) T) ((-1264 . -816) 179062) ((-1264 . -821) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-564 . -875) T) ((-678 . -38) 178923) ((-627 . -34) T) ((-496 . -1144) 178901) ((-489 . -34) T) ((-1145 . -133) 178772) ((-994 . -25) 178583) ((-936 . -635) 178533) ((-899 . -632) 178515) ((-218 . -868) T) ((-994 . -21) 178470) ((-839 . -25) 178303) ((-839 . -21) 178214) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178193) ((-1203 . -47) 178170) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 178022) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177994) ((-119 . -1089) T) ((-1066 . -670) 177968) ((-988 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-366 . -240) 177926) ((-366 . -250) T) ((-358 . -240) 177905) ((-358 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1187 . -153) 177797) ((-260 . -928) 177729) ((-259 . -928) 177661) ((-1174 . -922) 177582) ((-1114 . -872) T) ((-1266 . -1249) 177560) ((-429 . -1144) T) ((-1242 . -1034) 177526) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1206 . -951) 177432) ((-1200 . -951) 177411) ((-1200 . -844) NIL) ((-1028 . -1083) 177307) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177286) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177264) ((-123 . -1133) 177242) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1028 . -662) 177155) ((-894 . -739) 177142) ((-1329 . -668) 177114) ((-1078 . -153) 177079) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-858 . -670) 177008) ((-852 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176938) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176719) ((-130 . -872) T) ((-1203 . -1070) 176599) ((-1157 . -1070) 176482) ((-187 . -632) 176464) ((-879 . -1070) 176360) ((-803 . -298) 176287) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176216) ((-616 . -673) 176200) ((-1035 . -922) 176107) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176085) ((-716 . -1089) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176051) ((-1203 . -390) 176035) ((-1157 . -390) 176019) ((-1056 . -426) 175981) ((-143 . -233) 175963) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1299 . -1298) 175758) ((-365 . -416) T) ((-1299 . -1133) 175708) ((-1223 . -1133) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1286 . -668) 175537) ((-326 . -649) 175516) ((-858 . -748) T) 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T) ((-901 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1254) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1254) T) ((-421 . -922) 174525) ((-229 . -1070) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1249) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173800) ((-1094 . -912) 173782) ((-976 . -912) 173707) ((-677 . -1144) T) ((-642 . -739) 173694) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173678) ((-1094 . -1070) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-976 . -1070) 173522) ((-119 . -739) 173467) ((-734 . -930) 173374) ((-677 . -23) T) ((-495 . -1070) 173250) ((-1119 . -633) NIL) ((-1119 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1145 . -660) 172647) ((-822 . -875) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1067 . -233) 172397) ((-897 . -940) 172376) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1318) 172342) ((-366 . -1318) 172326) ((-358 . -1318) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-976 . -390) 171946) ((-894 . -302) T) ((-50 . -632) 171928) ((-1152 . -668) 171900) ((-1028 . -38) 171848) ((-626 . -1133) T) ((-621 . -1133) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-936 . -1318) 171765) ((-896 . -1249) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1311 . -1249) T) ((-1310 . -1249) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1323 . -1314) 171652) ((-896 . -910) 171629) ((-896 . -912) NIL) ((-994 . -872) 171528) ((-839 . -872) 171479) ((-1257 . -102) T) ((-678 . -680) 171463) ((-1236 . -34) T) ((-174 . -632) 171445) ((-1145 . -25) 171278) ((-1145 . -21) 171189) ((-896 . -1070) 171166) ((-976 . -928) 171147) ((-1268 . -47) 171124) ((-936 . -381) T) ((-607 . -875) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -928) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1249) T) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1324 . -1319) 169581) ((-699 . -1070) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169520) ((-880 . -1249) T) ((-678 . -668) 169479) ((-48 . -1133) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169429) ((-402 . -1133) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1268 . -1070) 169277) ((-880 . -1070) 169173) ((-1174 . -102) T) ((-1028 . -930) 169096) ((-677 . -133) T) ((-674 . -816) 169075) ((-674 . -821) 169054) ((-119 . -528) 168962) ((-585 . -1070) 168944) ((-305 . -1307) 168914) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168893) ((-1242 . -1088) 168776) ((-1035 . -1083) 168721) ((-496 . -660) 168627) ((-935 . -1133) T) ((-1056 . -739) 168564) ((-733 . -1088) 168529) ((-1035 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -928) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1329 . -1089) T) ((-1268 . -390) 168084) ((-419 . -1254) 168062) ((-1147 . -632) 168044) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167997) ((-1264 . -818) 167950) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167915) ((-229 . -1052) T) ((-1286 . -426) 167881) ((-1268 . -928) 167824) ((-365 . -1307) 167801) ((-1242 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -875) 167644) ((-1145 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1323 . -1083) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1323 . -662) 167115) ((-642 . -302) T) ((-597 . -1088) 167090) 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-1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166423) ((-1120 . -1249) T) ((-1119 . -1088) 166266) ((-1107 . -1249) T) ((-275 . -940) 166245) ((-255 . -940) 166224) ((-803 . -1088) 166047) ((-802 . -1088) 165890) ((-627 . -1249) T) ((-1197 . -632) 165872) ((-1119 . -111) 165701) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165672) ((-468 . -1088) 165515) ((-686 . -670) 165499) ((-896 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1191 . -872) T) ((-1120 . -1070) 164755) ((-1107 . -1070) 164732) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1003 . -875) T) ((-996 . -632) 164504) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164488) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164406) ((-1299 . -503) 164390) ((-1217 . -1249) T) ((-1216 . -1249) T) ((-1174 . -38) 164350) ((-986 . -23) T) ((-936 . -670) 164315) ((-890 . -1133) T) ((-866 . -102) T) ((-841 . -21) T) ((-652 . -1083) 164299) ((-620 . -1083) 164283) ((-841 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1088) 164216) ((-532 . -1088) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1215 . -1249) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-891 . -38) 164089) ((-1119 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1144) T) ((-326 . -1089) 163600) ((-325 . -1089) T) ((-132 . -1249) T) ((-131 . -1249) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1081) T) ((-1329 . -1133) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1023) 162778) ((-118 . -895) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) ((-1236 . -1042) 162696) ((-1214 . -632) 162663) ((-1221 . -34) T) ((-984 . -632) 162629) ((-949 . -632) 162611) ((-1145 . -872) 162562) ((-793 . -632) 162544) ((-694 . -632) 162526) ((-531 . -1249) T) ((-1268 . -319) 162505) ((-1187 . -321) 162443) ((-1173 . -34) T) ((-493 . -34) T) ((-1124 . -1249) T) ((-491 . -466) T) ((-1066 . -1249) T) ((-1119 . -1081) T) ((-50 . -635) 162412) ((-803 . -1081) T) ((-802 . -1081) T) ((-669 . -242) 162396) ((-651 . -242) 162342) ((-1211 . -21) T) ((-595 . -635) 162292) ((-532 . -635) 162222) ((-496 . -236) 162113) ((-1211 . -25) T) ((-1119 . -338) 162074) ((-468 . -1081) T) ((-1119 . -240) 162053) ((-803 . -338) 162030) ((-803 . -240) T) ((-802 . -338) 162002) ((-753 . -1254) 161981) ((-533 . -34) T) ((-339 . -673) 161965) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161944) ((-339 . -385) 161928) ((-374 . -1249) T) ((-334 . -1249) T) ((-1035 . -1184) NIL) ((-753 . -571) 161859) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1249) T) ((-1312 . -21) T) ((-1078 . -321) 161767) ((-1312 . -25) T) ((-931 . -1133) 161745) ((-842 . -236) 161732) ((-50 . -1081) T) ((-1207 . -571) 161711) ((-1206 . -1254) 161690) ((-1206 . -571) 161641) ((-1200 . -1254) 161620) ((-1200 . -571) 161571) ((-1056 . -302) T) ((-595 . -1081) T) ((-532 . -1081) T) ((-1035 . -38) 161516) ((-374 . -1070) 161500) ((-334 . -1070) 161484) ((-1028 . -668) 161407) ((-391 . -912) 161389) ((-858 . -1249) T) ((-852 . -1249) T) ((-849 . -1249) T) ((-822 . -1144) T) ((-936 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1158 . -571) 161368) ((-353 . -302) T) ((-669 . -717) 161352) ((-391 . -1070) 161312) ((-305 . -1083) 161233) ((-352 . -922) 161212) ((-1152 . -1089) T) ((-103 . -127) 161196) ((-305 . -662) 161138) ((-822 . -23) T) ((-1321 . -1319) 161114) ((-1320 . -1319) 161093) ((-1299 . -298) 161045) ((-1286 . -1133) T) ((-421 . -321) 161010) ((-1174 . -930) 160933) ((-894 . -632) 160915) ((-858 . -1070) 160884) ((-661 . -1088) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -872) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160696) ((-119 . -298) 160647) ((-1299 . -19) 160631) ((-1259 . -875) NIL) ((-1299 . -618) 160608) ((-1313 . -1133) T) ((-365 . -1083) 160553) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160540) ((-758 . -1133) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -817) T) ((-526 . -818) T) ((-467 . -133) T) ((-421 . -1184) 160463) ((-227 . -1081) T) ((-305 . -102) 160245) ((-143 . -1133) T) ((-721 . -1034) T) ((-1137 . -298) 160201) ((-91 . -1249) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1329 . -175) T) ((-1206 . -376) 160026) ((-1200 . -376) 160005) ((-326 . -1133) T) ((-419 . -133) T) ((-325 . -1133) T) ((-421 . -38) 159957) ((-1165 . -102) T) ((-1286 . -739) 159849) ((-1167 . -1295) T) ((-1128 . -1249) T) ((-1123 . -1249) T) ((-678 . -1089) T) ((-1105 . -1249) T) ((-1098 . -1249) T) ((-1068 . -1249) T) ((-1051 . -1249) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1133) T) ((-137 . -1133) T) ((-115 . -1133) T) ((-883 . -102) T) ((-645 . -1249) T) ((-497 . -1249) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1249) T) ((-496 . -872) 159548) ((-501 . -660) 159530) ((-995 . -632) 159512) ((-1035 . -930) 159421) ((-221 . -660) 159403) ((-229 . -418) T) ((-674 . -670) 159387) ((-55 . -632) 159369) ((-1203 . -951) 159348) ((-753 . -1144) T) ((-657 . -102) T) ((-529 . -1249) T) ((-525 . -1249) T) ((-522 . -1249) T) ((-365 . -102) T) ((-1250 . -1115) T) ((-1152 . -868) T) ((-842 . -872) T) ((-753 . -23) T) ((-357 . -1088) 159293) ((-1180 . -107) 159277) ((-1302 . -632) 159259) ((-1207 . -23) T) ((-1207 . -1144) T) ((-1206 . -1144) T) ((-659 . -1249) T) ((-1206 . -23) T) ((-1200 . -1144) T) ((-1200 . -23) T) ((-1174 . -274) 159243) ((-529 . -1070) 159227) ((-1174 . -234) 159211) ((-1158 . -1144) T) ((-357 . -111) 159140) ((-1036 . -1254) T) ((-128 . -1249) T) ((-944 . -1254) T) ((-1158 . -23) T) ((-1108 . -1133) T) ((-716 . -298) NIL) ((-736 . -1249) T) ((-1036 . -571) T) ((-944 . -571) T) ((-839 . -239) 159037) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1249) T) ((-186 . -1249) T) ((-163 . -1249) T) ((-159 . -1249) T) ((-256 . -632) 159019) ((-622 . -684) T) ((-822 . -133) T) 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. -240) T) ((-1313 . -503) 151456) ((-1296 . -1249) T) ((-1183 . -242) 151406) ((-1119 . -940) 151385) ((-118 . -38) 151372) ((-212 . -824) T) ((-211 . -824) T) ((-210 . -824) T) ((-209 . -824) T) ((-897 . -1052) 151350) ((-686 . -1249) T) ((-667 . -1249) T) ((-803 . -940) 151329) ((-802 . -940) 151308) ((-1221 . -1249) T) ((-368 . -1249) T) ((-366 . -1249) T) ((-358 . -1249) T) ((-275 . -1249) T) ((-255 . -1249) T) ((-468 . -940) 151287) ((-758 . -503) 151271) ((-1119 . -670) 151160) ((-721 . -635) 151095) ((-803 . -670) 150984) ((-642 . -1088) 150971) ((-493 . -1249) T) ((-357 . -381) T) ((-143 . -503) 150953) ((-802 . -670) 150842) ((-1173 . -1249) T) ((-564 . -872) T) ((-475 . -670) 150813) ((-275 . -912) 150672) ((-255 . -912) NIL) ((-119 . -1088) 150617) ((-468 . -670) 150506) ((-686 . -1070) 150483) ((-642 . -111) 150468) ((-404 . -1083) 150452) ((-368 . -1070) 150436) ((-366 . -1070) 150420) ((-358 . -1070) 150404) ((-275 . -1070) 150248) ((-255 . -1070) 150124) ((-936 . -1249) 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. -1083) 148993) ((-1200 . -660) 148945) ((-491 . -662) 148910) ((-663 . -875) 148889) ((-499 . -25) T) ((-499 . -21) T) ((-1264 . -1052) 148841) ((-1090 . -1249) T) ((-1 . -1249) T) ((-642 . -1081) T) ((-391 . -418) T) ((-404 . -102) T) ((-1137 . -637) 148756) ((-275 . -928) 148702) ((-255 . -928) 148679) ((-119 . -1081) T) ((-1119 . -748) T) ((-840 . -1144) T) ((-843 . -875) T) ((-642 . -240) 148658) ((-638 . -102) T) ((-526 . -1249) T) ((-521 . -1249) T) ((-803 . -748) T) ((-802 . -748) T) ((-1255 . -872) T) ((-427 . -1144) T) ((-119 . -250) T) ((-40 . -381) NIL) ((-119 . -240) NIL) ((-400 . -875) 148637) ((-468 . -748) T) ((-840 . -23) T) ((-753 . -25) T) ((-753 . -21) T) ((-692 . -922) 148558) ((-1109 . -298) 148537) ((-75 . -411) T) ((-75 . -410) T) ((-547 . -789) 148519) ((-229 . -875) T) ((-716 . -1088) 148469) ((-1325 . -102) T) ((-1289 . -133) T) ((-1280 . -133) T) ((-1259 . -133) T) ((-1207 . -25) T) ((-1174 . -426) 148453) ((-652 . -380) 148385) ((-620 . -380) 148317) 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-1133) 146013) ((-1257 . -868) T) ((-331 . -1005) 145975) ((-105 . -102) T) ((-48 . -1088) 145940) ((-896 . -875) NIL) ((-1324 . -102) T) ((-395 . -102) T) ((-1286 . -632) 145922) ((-1165 . -1166) 145906) ((-1036 . -660) 145888) ((-901 . -1249) T) ((-48 . -111) 145844) ((-703 . -1249) T) ((-698 . -1249) T) ((-674 . -1249) T) ((-839 . -922) 145711) ((-492 . -1249) T) ((-252 . -1249) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1307) 145695) ((-140 . -1249) T) ((-139 . -1249) T) ((-135 . -1249) T) ((-1250 . -102) T) ((-1056 . -635) 145632) ((-841 . -239) T) ((-1203 . -1254) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1157 . -1254) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1203 . -571) 145127) ((-1157 . -571) 145058) ((-1257 . -1133) T) ((-561 . -875) T) ((-1067 . -298) 145033) ((-1199 . -1115) T) ((-1026 . -1115) T) ((-840 . -133) T) ((-119 . -821) NIL) ((-119 . -816) NIL) ((-368 . -319) T) 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143042) ((-1221 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1226) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1152 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1152 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1259 . -660) 142704) ((-493 . -107) 142654) ((-1025 . -23) T) ((-1324 . -38) 142624) ((-1203 . -1144) T) ((-1157 . -1144) T) ((-1094 . -1254) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-879 . -1144) T) ((-976 . -1254) 142494) ((-495 . -1254) 142473) ((-1094 . -571) T) ((-976 . -571) 142404) ((-1203 . -23) T) ((-1185 . -1115) T) ((-1157 . -23) T) ((-879 . -23) T) ((-495 . -571) 142335) ((-1174 . -739) 142267) ((-692 . -1083) 142251) ((-1178 . -528) 142184) ((-692 . -662) 142168) ((-1067 . -633) NIL) ((-1067 . -632) 142150) ((-96 . -1115) T) ((-1329 . -1088) 142137) ((-891 . -739) 142107) ((-1329 . -111) 142092) ((-1242 . -47) 142061) ((-1200 . -872) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142043) ((-1111 . -922) 141912) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141899) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141883) ((-1036 . -236) 141870) ((-897 . -844) 141849) ((-897 . -951) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141537) ((-1320 . -1083) 141521) ((-1321 . -662) 141491) ((-1187 . -1133) 141469) ((-896 . -1254) T) ((-1320 . -662) 141439) ((-1120 . -875) T) ((-678 . -632) 141421) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141405) ((-1329 . -635) 141387) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141371) ((-367 . -1307) 141355) ((-44 . -662) 141339) ((-359 . -1307) 141323) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141302) ((-733 . -1249) T) ((-988 . -875) 141281) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141260) ((-154 . -1083) 141244) ((-1078 . -1103) 141173) ((-1059 . -1008) 141142) ((-843 . -1144) T) ((-1035 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1144) T) ((-490 . -1008) 141040) ((-477 . -1008) 141009) ((-1216 . -875) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-919 . -632) 140955) ((-1215 . -875) T) ((-1111 . -746) 140934) ((-1329 . -1081) T) ((-840 . -660) 140882) ((-305 . -1089) 140824) ((-171 . -1254) 140729) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140681) ((-1286 . -1088) 140586) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140565) ((-1285 . -951) 140544) ((-1264 . -951) 140523) ((-894 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1133) T) ((-270 . -1133) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1264 . -844) 140278) ((-1321 . -102) T) ((-505 . -1249) T) ((-353 . -1318) 140255) ((-1320 . -102) T) ((-1286 . -111) 140147) ((-1145 . -922) 140014) ((-839 . -1083) 139915) ((-839 . -662) 139837) ((-146 . -632) 139819) ((-1025 . -133) T) ((-44 . -102) T) ((-246 . -872) 139770) ((-597 . -1249) T) ((-1268 . -1254) 139749) ((-103 . -503) 139733) ((-1323 . -739) 139703) ((-1119 . -47) 139664) ((-1094 . -1144) T) ((-976 . -1144) T) ((-129 . -34) T) ((-123 . -34) T) ((-1268 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1229 . -1249) T) ((-1203 . -133) T) ((-353 . -381) T) ((-495 . -1144) T) ((-1157 . -133) T) ((-896 . -376) T) ((-468 . -47) 139503) ((-879 . -133) T) ((-334 . -875) 139482) ((-154 . -102) T) ((-1094 . -23) T) ((-976 . -23) T) ((-585 . -571) T) ((-840 . -25) T) ((-840 . -21) T) 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137363) ((-1119 . -1249) T) ((-1067 . -300) 137338) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137289) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137273) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137249) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137228) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137087) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137065) ((-1138 . -410) T) ((-642 . -670) 137052) ((-468 . -912) NIL) ((-697 . -102) 137002) ((-1119 . -1070) 136829) ((-896 . -23) T) ((-803 . -1070) 136688) ((-802 . -1070) 136545) ((-119 . -670) 136490) ((-468 . -1070) 136366) ((-286 . -1249) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1249) T) ((-404 . -668) 135782) ((-671 . -1070) 135766) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135750) ((-1299 . -34) T) ((-638 . -668) 135709) ((-301 . -1083) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1152 . -1088) 135582) ((-86 . -632) 135564) ((-50 . -1070) 135548) ((-1119 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135478) ((-595 . -1070) 135465) ((-532 . -1070) 135442) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135332) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1036 . -1023) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134993) ((-229 . -133) T) ((-1152 . -111) 134978) ((-171 . -23) T) ((-822 . -149) 134957) ((-822 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1187 . -528) 134647) ((-491 . -668) 134597) ((-657 . -868) T) ((-496 . -922) 134464) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134402) ((-1119 . -928) 134337) ((-803 . -928) 134280) ((-802 . -928) 134264) ((-1321 . -38) 134234) ((-1320 . -38) 134204) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134181) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134153) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134098) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133999) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133798) ((-1035 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133600) ((-496 . -1307) 133570) ((-1152 . -1081) 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131166) ((-1191 . -102) T) ((-1268 . -133) T) ((-1264 . -875) 131065) ((-1203 . -25) T) ((-1203 . -21) T) ((-1192 . -321) 130860) ((-357 . -1249) T) ((-1157 . -25) T) ((-880 . -133) T) ((-407 . -1249) T) ((-1157 . -21) T) ((-879 . -25) T) ((-879 . -21) T) ((-803 . -319) 130839) ((-1187 . -503) 130823) ((-1183 . -153) 130773) ((-1178 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1178 . -633) 130646) ((-585 . -133) T) ((-638 . -871) 130625) ((-1056 . -814) T) ((-1056 . -818) T) ((-1056 . -748) T) ((-839 . -930) 130494) ((-734 . -1088) 130317) ((-616 . -875) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1070) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-734 . -111) 129759) ((-353 . -748) T) ((-692 . -274) 129743) ((-692 . -234) 129727) ((-595 . -319) T) ((-532 . -319) T) ((-305 . -528) 129676) ((-1197 . -1249) T) ((-108 . -321) NIL) ((-72 . -410) T) ((-1145 . -102) 129408) ((-856 . -426) 129392) ((-1152 . -821) T) ((-1152 . -816) T) ((-723 . -1133) T) ((-592 . -632) 129374) ((-391 . -376) T) ((-171 . -507) 129352) ((-226 . -632) 129284) ((-136 . -1133) T) ((-118 . -1133) T) ((-996 . -1249) T) ((-48 . -748) T) ((-1078 . -503) 129249) ((-143 . -440) 129231) ((-143 . -381) T) ((-1059 . -102) T) ((-524 . -523) 129210) ((-734 . -635) 128966) ((-1257 . -632) 128948) ((-1214 . -1249) T) ((-1214 . -1070) 128884) ((-1207 . -239) 128843) ((-490 . -102) T) ((-477 . -102) T) ((-1206 . -239) 128795) ((-1200 . -239) 128618) ((-1066 . -1144) T) ((-331 . -930) 128524) ((-1209 . -875) T) ((-1207 . -35) 128490) ((-1207 . -95) 128456) ((-1207 . -1238) 128422) ((-1207 . -1235) 128388) ((-1206 . -1235) 128354) ((-1206 . -1238) 128320) ((-1206 . -95) 128286) ((-1206 . -35) 128252) ((-1200 . -1235) 128218) ((-1200 . -1238) 128184) ((-1191 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1111 . -1184) 128163) ((-40 . -1249) T) ((-1200 . -95) 128129) ((-1066 . -23) T) ((-1200 . -35) 128095) ((-585 . -507) T) ((-1158 . -35) 128061) ((-1158 . -95) 128027) ((-1158 . -1238) 127993) ((-1158 . -1235) 127959) ((-374 . -1144) T) ((-372 . -1184) 127938) ((-367 . -1184) 127917) ((-359 . -1184) 127896) ((-1135 . -298) 127852) ((-984 . -1249) T) ((-949 . -1249) T) ((-108 . -1184) T) ((-856 . -1089) 127831) ((-793 . -1249) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1249) T) ((-734 . -1081) T) ((-1094 . -660) 127602) ((-1111 . -38) 127470) ((-976 . -660) 127418) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-391 . -1144) T) ((-336 . -25) T) ((-334 . -23) T) ((-973 . -872) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1070) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1133) T) ((-177 . -1133) T) ((-343 . -872) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-858 . -1144) T) ((-108 . -38) 126992) ((-852 . -1144) T) ((-795 . -1133) T) ((-118 . -739) 126979) ((-694 . -1070) 126963) ((-630 . -102) T) ((-858 . -23) T) ((-852 . -23) T) ((-1187 . -298) 126915) ((-1145 . -321) 126853) ((-496 . -1083) 126754) ((-1129 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1185 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -877) 126621) ((-1203 . -236) 126608) ((-1167 . -1115) T) ((-1094 . -21) T) ((-1094 . -25) T) ((-1086 . -1083) 126592) ((-839 . -274) 126561) ((-839 . -234) 126530) ((-976 . -25) T) ((-976 . -21) T) ((-1152 . -381) T) ((-1086 . -662) 126472) ((-638 . -1089) T) ((-1059 . -321) 126410) ((-914 . -632) 126392) ((-692 . -668) 126351) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1083) 126335) ((-911 . -632) 126317) ((-894 . -1249) T) ((-537 . -528) 126250) ((-260 . -872) 126201) ((-259 . -872) 126152) ((-394 . -662) 126122) ((-896 . -660) 126099) ((-490 . -321) 126037) ((-562 . -1249) T) ((-477 . -321) 125975) ((-365 . -302) T) ((-1187 . -1288) 125959) ((-1174 . -632) 125921) ((-1174 . -633) 125882) ((-1172 . -102) T) ((-1028 . -1088) 125778) ((-40 . -928) 125730) ((-1187 . -618) 125707) ((-1329 . -670) 125694) ((-1095 . -153) 125640) ((-501 . -922) NIL) ((-891 . -504) 125617) ((-1028 . -111) 125499) ((-897 . -1254) T) ((-221 . -922) NIL) ((-352 . -739) 125483) ((-891 . -632) 125445) ((-177 . -739) 125377) ((-897 . -571) T) ((-421 . -298) 125335) ((-246 . -239) 125232) ((-108 . -414) 125214) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125196) ((-99 . -748) T) ((-496 . -102) 124928) ((-99 . -487) T) ((-118 . -175) T) ((-1321 . -668) 124887) ((-1320 . -668) 124846) ((-171 . -660) 124794) ((-1111 . -930) 124665) ((-1086 . -102) T) ((-1028 . -635) 124555) ((-896 . -25) T) ((-839 . -245) 124534) ((-896 . -21) T) ((-842 . -102) T) ((-1036 . -239) T) ((-44 . -668) 124477) ((-429 . -102) T) ((-394 . -102) T) ((-110 . -321) NIL) ((-231 . -102) 124427) ((-218 . -1249) T) ((-129 . -1249) T) ((-123 . -1249) T) ((-108 . -930) NIL) ((-841 . -1083) 124378) ((-58 . -875) 124357) ((-841 . -662) 124299) ((-530 . -875) 124278) ((-510 . -875) 124257) ((-1066 . -133) T) ((-692 . -380) 124241) ((-154 . -668) 124200) ((-1329 . -748) T) ((-652 . -298) 124158) ((-620 . -298) 124116) ((-1289 . -147) 124095) ((-1268 . -660) 124043) ((-1028 . -1081) T) ((-1135 . -632) 124025) ((-1035 . -632) 124007) ((-594 . -1249) T) ((-560 . -1249) T) ((-509 . -1249) T) ((-529 . -23) T) ((-525 . -23) T) ((-357 . -319) T) ((-522 . -23) T) ((-334 . -133) T) ((-3 . -1133) T) ((-1035 . -633) 123991) ((-1028 . -250) 123970) ((-1028 . -240) 123949) ((-1289 . -149) 123928) ((-1285 . -1254) 123907) ((-856 . -1133) T) ((-1280 . -149) 123886) ((-1280 . -147) 123865) ((-1264 . -1254) 123844) ((-1259 . -147) 123751) ((-1259 . -149) 123658) ((-391 . -133) T) ((-229 . -236) 123645) ((-177 . -175) T) ((-560 . -912) 123627) ((0 . -1133) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1249) T) ((-49 . -1133) T) ((-1286 . -670) 123532) ((-1285 . -571) 123483) ((-1264 . -571) 123434) ((-736 . -1144) T) ((-659 . -23) T) ((-560 . -1070) 123416) ((-609 . -149) 123395) ((-609 . -147) 123374) ((-509 . -1070) 123317) ((-1167 . -1169) T) ((-88 . -398) T) ((-88 . -410) T) ((-897 . -376) T) ((-858 . -133) T) ((-852 . -133) T) ((-994 . -668) 123261) ((-736 . -23) T) ((-520 . -632) 123211) ((-516 . -632) 123193) ((-839 . -668) 122972) ((-1324 . -1089) T) ((-391 . -1092) T) ((-1058 . -1133) 122950) ((-55 . -1070) 122932) ((-931 . -34) T) ((-496 . -321) 122870) ((-606 . -102) T) ((-1187 . -633) 122831) ((-1187 . -632) 122763) 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T) ((-48 . -1052) T) ((-1264 . -660) 110176) ((-711 . -102) 110126) ((-44 . -739) 110110) ((-565 . -102) T) ((-305 . -635) 110041) ((-67 . -396) T) ((-501 . -930) NIL) ((-67 . -410) T) ((-286 . -875) T) ((-221 . -930) NIL) ((-674 . -23) T) ((-841 . -668) 109977) ((-692 . -783) T) ((-1247 . -1133) 109955) ((-365 . -1088) 109900) ((-697 . -1133) 109878) ((-1094 . -149) T) ((-976 . -149) 109857) ((-976 . -147) 109836) ((-822 . -102) T) ((-154 . -739) 109820) ((-495 . -149) 109799) ((-495 . -147) 109778) ((-365 . -111) 109707) ((-1111 . -1089) T) ((-334 . -872) 109686) ((-1289 . -1005) 109655) ((-1286 . -1249) T) ((-646 . -1133) T) ((-1280 . -1005) 109617) ((-526 . -133) T) ((-521 . -133) T) ((-307 . -233) 109567) ((-372 . -1089) T) ((-367 . -1089) T) ((-359 . -1089) T) ((-305 . -1081) 109509) ((-1259 . -1005) 109478) ((-391 . -872) T) ((-108 . -1089) T) ((-1028 . -748) T) ((-894 . -951) T) ((-866 . -821) 109457) ((-866 . -816) 109436) ((-419 . -321) 109375) ((-482 . -102) T) ((-609 . 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. |RecordCategory|) T) ((-1145 . -1089) 105417) ((-856 . -632) 105399) ((-1094 . -239) T) ((-594 . -951) T) ((-560 . -844) T) ((-560 . -951) T) ((-509 . -951) T) ((-137 . -1070) 105383) ((-229 . -95) T) ((-171 . -149) 105362) ((-76 . -455) T) ((0 . -632) 105344) ((-76 . -410) T) ((-171 . -147) 105295) ((-229 . -35) T) ((-49 . -632) 105277) ((-491 . -1089) T) ((-501 . -274) 105259) ((-501 . -234) 105241) ((-498 . -1000) 105225) ((-221 . -274) 105207) ((-221 . -234) 105189) ((-81 . -455) T) ((-81 . -410) T) ((-1178 . -34) T) ((-753 . -102) T) ((-677 . -668) 105148) ((-1058 . -632) 105115) ((-514 . -298) 105065) ((-326 . -390) 105034) ((-325 . -390) 104995) ((-325 . -351) 104956) ((-1117 . -632) 104938) ((-840 . -980) 104885) ((-674 . -133) T) ((-1268 . -147) 104864) ((-1268 . -149) 104843) ((-1207 . -102) T) ((-1206 . -102) T) ((-1200 . -102) T) ((-1192 . -1133) T) ((-1158 . -102) T) ((-1108 . -1249) T) ((-226 . -34) T) ((-301 . -739) 104830) ((-1289 . -1292) 104814) ((-1192 . -629) 104790) ((-607 . -321) NIL) ((-1289 . -1278) 104767) ((-1183 . -233) 104717) ((-498 . -1133) 104695) ((-452 . -1249) T) ((-404 . -632) 104677) ((-525 . -872) T) ((-1152 . -1249) T) ((-1280 . -1284) 104638) ((-1280 . -1278) 104608) ((-1280 . -1282) 104592) ((-1259 . -1263) 104553) ((-1259 . -1278) 104530) ((-1259 . -1261) 104514) ((-1207 . -296) 104480) ((-638 . -632) 104462) ((-1206 . -296) 104428) ((-721 . -951) T) ((-1200 . -296) 104394) ((-1158 . -296) 104360) ((-1152 . -912) 104342) ((-1111 . -1133) T) ((-1093 . -1133) T) ((-48 . -310) T) ((-326 . -928) 104308) ((-325 . -928) NIL) ((-1093 . -1100) 104287) ((-822 . -38) 104271) ((-275 . -660) 104219) ((-114 . -875) T) ((-255 . -660) 104167) ((-723 . -1088) 104154) ((-609 . -1278) 104131) ((-1152 . -1070) 104113) ((-331 . -175) 104044) ((-372 . -1133) T) ((-367 . -1133) T) ((-359 . -1133) T) ((-514 . -19) 104026) ((-1129 . -153) 104010) ((-896 . -239) NIL) ((-108 . -1133) T) ((-118 . -1088) 103997) ((-733 . -376) T) ((-514 . -618) 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. -47) 98886) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-365 . -1318) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-359 . -175) T) ((-177 . -250) T) ((-1264 . -872) 98637) ((-108 . -175) T) ((-897 . -1023) 98621) ((-676 . -1144) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-326 . -319) 98564) ((-325 . -319) T) ((-616 . -872) 98543) ((-1145 . -739) 98485) ((-623 . -1249) T) ((-534 . -294) 98469) ((-676 . -23) T) ((-419 . -234) 98453) ((-419 . -274) 98437) ((-325 . -1052) NIL) ((-346 . -23) T) ((-103 . -1042) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-630 . -1133) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98338) ((-1119 . -1144) T) ((-1323 . -670) 98312) ((-803 . -1144) T) ((-802 . -1144) T) ((-1211 . -426) 98296) ((-468 . -1144) T) ((-1094 . -466) T) ((-1185 . -1133) T) ((-976 . -466) 98247) ((-1148 . -1115) T) ((-110 . -1133) T) ((-1119 . -23) T) ((-1192 . -528) 98030) 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T) ((-560 . -1254) T) ((-509 . -1254) T) ((-1036 . -274) 86649) ((-331 . -632) 86631) ((-1036 . -234) 86613) ((-171 . -168) 86597) ((-594 . -571) T) ((-560 . -571) T) ((-509 . -571) T) ((-793 . -23) T) ((-1285 . -149) 86576) ((-1285 . -147) 86555) ((-1192 . -618) 86531) ((-1264 . -147) 86456) ((-1059 . -503) 86440) ((-1257 . -1249) T) ((-1264 . -149) 86365) ((-1315 . -1322) 86344) ((-896 . -922) NIL) ((-490 . -503) 86328) ((-477 . -503) 86312) ((-537 . -34) T) ((-677 . -739) 86282) ((-1289 . -930) 86195) ((-1280 . -930) 86101) ((-1259 . -930) 85862) ((-114 . -999) T) ((-1211 . -175) 85813) ((-674 . -872) 85792) ((-377 . -102) T) ((-609 . -930) 85705) ((-246 . -245) 85684) ((-260 . -102) T) ((-259 . -102) T) ((-1268 . -980) 85653) ((-252 . -872) 85632) ((-1056 . -875) T) ((-840 . -38) 85481) ((-45 . -528) 85273) ((-1191 . -298) 85223) ((-217 . -1133) T) ((-1183 . -1133) T) ((-897 . -239) 85174) ((-1183 . -629) 85153) ((-597 . -25) T) ((-597 . -21) T) ((-1129 . -321) 85091) ((-986 . -426) 85075) ((-721 . -1254) T) ((-651 . -298) 85028) ((-1119 . -660) 84976) ((-932 . -1133) T) ((-803 . -660) 84924) ((-802 . -660) 84872) ((-357 . -133) T) ((-301 . -632) 84854) ((-894 . -1144) T) ((-721 . -571) T) ((-130 . -635) 84836) ((-468 . -660) 84784) ((-171 . -922) 84705) ((-932 . -934) 84689) ((-391 . -466) T) ((-501 . -1133) T) ((-973 . -321) 84627) ((-723 . -670) 84599) ((-564 . -868) T) ((-221 . -1133) T) ((-326 . -951) 84578) ((-325 . -951) T) ((-325 . -844) NIL) ((-404 . -742) T) ((-894 . -23) T) ((-118 . -670) 84565) ((-488 . -147) 84544) ((-419 . -426) 84528) ((-488 . -149) 84507) ((-110 . -503) 84489) ((-324 . -635) 84470) ((-2 . -632) 84452) ((-190 . -102) T) ((-1191 . -19) 84434) ((-1191 . -618) 84409) ((-676 . -21) T) ((-676 . -25) T) ((-607 . -1176) T) ((-1145 . -298) 84386) ((-346 . -25) T) ((-346 . -21) T) ((-914 . -1249) T) ((-911 . -1249) T) ((-1321 . -1088) 84370) ((-246 . -668) 84149) ((-509 . -376) T) ((-1320 . -1088) 84133) ((-1315 . -38) 84103) ((-1285 . 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. -1089) T) ((-1242 . -149) 63676) ((-334 . -1083) 63658) ((-1242 . -147) 63637) ((-1217 . -102) T) ((-1216 . -102) T) ((-1215 . -102) T) ((-1207 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1249) T) ((-1206 . -175) 63501) ((-1200 . -175) 63432) ((-1185 . -635) 63413) ((-1158 . -175) 63364) ((-610 . -1089) T) ((-609 . -1089) T) ((-1036 . -1133) T) ((-1003 . -1133) T) ((-391 . -1083) 63329) ((-136 . -1249) T) ((-118 . -1249) T) ((-944 . -1133) T) ((-896 . -930) NIL) ((-391 . -662) 63294) ((-146 . -875) T) ((-822 . -820) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -912) 63237) ((-443 . -1133) T) ((-326 . -1254) 63216) ((-325 . -1254) T) ((-171 . -414) 63200) ((-858 . -1083) 63170) ((-488 . -1005) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-852 . -1083) 63098) ((-108 . -821) T) ((-108 . -816) T) ((-723 . -1070) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-858 . -662) 63029) ((-852 . -662) 62999) ((-1329 . -23) T) ((-136 . -1070) 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. -951) T) ((-723 . -844) T) ((-443 . -632) 39859) ((-1152 . -21) T) ((-1152 . -25) T) ((-692 . -390) 39843) ((-118 . -951) T) ((-897 . -274) 39827) ((-897 . -234) 39811) ((-44 . -1249) T) ((-75 . -1249) T) ((-128 . -127) 39795) ((-1086 . -34) T) ((-1321 . -1070) 39769) ((-1320 . -1070) 39726) ((-1268 . -1089) T) ((-880 . -1089) T) ((-368 . -1184) 39705) ((-366 . -1184) 39684) ((-358 . -1184) 39663) ((-496 . -818) 39642) ((-496 . -817) 39621) ((-231 . -34) T) ((-496 . -748) 39599) ((-822 . -635) 39445) ((-674 . -1083) 39429) ((-60 . -503) 39413) ((-585 . -1089) T) ((-1203 . -175) 39304) ((-674 . -662) 39288) ((-488 . -930) 39194) ((-154 . -1249) T) ((-1157 . -175) 39105) ((-1094 . -1133) T) ((-1119 . -980) 39050) ((-976 . -1133) T) ((-841 . -670) 39001) ((-803 . -980) 38970) ((-735 . -1133) T) ((-802 . -980) 38937) ((-530 . -294) 38921) ((-692 . -928) 38880) ((-495 . -1133) T) ((-468 . -980) 38847) ((-79 . -1249) T) ((-368 . -38) 38812) ((-366 . -38) 38777) ((-358 . -38) 38742) ((-275 . -38) 38591) ((-255 . -38) 38440) ((-936 . -1184) T) ((-538 . -504) 38421) ((-642 . -149) 38400) ((-642 . -147) 38379) ((-612 . -1249) T) ((-538 . -632) 38345) ((-119 . -149) T) ((-119 . -147) NIL) ((-429 . -748) T) ((-822 . -1081) T) ((-560 . -239) T) ((-509 . -239) T) ((-357 . -466) T) ((-1289 . -1034) 38311) ((-1280 . -1034) 38277) ((-1259 . -1034) 38243) ((-936 . -38) 38208) ((-229 . -739) 38173) ((-1028 . -133) T) ((-659 . -668) 38142) ((-331 . -47) 38112) ((-40 . -424) 38084) ((-142 . -632) 38066) ((-994 . -1249) T) ((-839 . -1249) T) ((-177 . -951) T) ((-564 . -381) T) ((-736 . -668) 38011) ((-619 . -635) 37992) ((-357 . -416) T) ((-693 . -635) 37973) ((-325 . -236) NIL) ((-183 . -635) 37954) ((-164 . -635) 37935) ((-158 . -635) 37916) ((-156 . -635) 37897) ((-534 . -300) 37874) ((-1264 . -234) 37844) ((-1264 . -274) 37814) ((-1247 . -1249) 37792) ((-1211 . -670) 37717) ((-901 . -102) T) ((-839 . -1070) 37544) ((-45 . -34) T) ((-703 . -102) T) ((-698 . -102) T) ((-678 . -21) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index d5d46f0c..a50de2d6 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3508838143) +(30 . 3508891730) (4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -489,673 +489,680 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |e01daf| |postfix| - |jokerMode| |monicRightFactorIfCan| |Si| |mapUnivariateIfCan| |lexico| - |numericIfCan| |leftTrim| |sayLength| |setValue!| |alphanumeric| - |numberOfFactors| |rquo| |ip4Address| |showClipRegion| |d02kef| |kind| - |copyInto!| |physicalLength!| |minRowIndex| |conjugates| |shiftRight| - |makeGraphImage| |redmat| |chineseRemainder| - |resultantReduitEuclidean| |maxPoints| |positiveRemainder| - |safeCeiling| FG2F |OMsend| |positive?| |leftTraceMatrix| - |fractionFreeGauss!| |expenseOfEvaluation| |complementaryBasis| - |graeffe| |asecIfCan| |compactFraction| |pToDmp| |localReal?| |minus!| - |rightScalarTimes!| |rombergo| |representationType| - |viewWriteAvailable| |antiAssociative?| |setProperty| - |isAbsolutelyIrreducible?| |dimensionsOf| - |degreeSubResultantEuclidean| |slex| |zeroSetSplit| |qfactor| - |aromberg| |yCoord| |nil?| |cschIfCan| |anfactor| |leastMonomial| - |jvmPublic| |myDegree| |removeRoughlyRedundantFactorsInPol| - |resultantReduit| |bsolve| |subResultantChain| |mesh| |taylorRep| - |cycleRagits| |binding| |systemSizeIF| |rst| |newTypeLists| |optimize| - |operation| |key?| |transcendentalDecompose| |complexNormalize| - |OMlistSymbols| |algebraic?| |rightZero| |tryFunctionalDecomposition| - |pdct| |shuffle| |union| |associatedSystem| |bubbleSort!| |cCsc| - |indicialEquationAtInfinity| |generalizedContinuumHypothesisAssumed?| - |reducedForm| |e04mbf| |semiResultantReduitEuclidean| - |extendedIntegrate| |clearTheIFTable| |pack!| |rroot| |OMgetInteger| - |lazyPremWithDefault| |constantLeft| |rename| |associatedEquations| - |nextIrreduciblePoly| |denomLODE| |denomRicDE| - |cyclotomicDecomposition| |binomial| |mix| |polygamma| - |stoseIntegralLastSubResultant| |initTable!| |infRittWu?| |shade| - |mainKernel| |OMgetError| |extension| |cCoth| |imagi| - |mainPrimitivePart| |radicalEigenvectors| |initials| |reverse| - |discriminantEuclidean| |startTable!| |expintegrate| |triangSolve| - |frobenius| |leadingCoefficientRicDE| |cLog| |d01ajf| - |differentialVariables| |leastAffineMultiple| |dmp2rfi| |numFunEvals| - |subtractIfCan| |reducedSystem| |mdeg| |SturmHabichtCoefficients| - |hash| |intcompBasis| |froot| |insertBottom!| |mkPrim| - |stoseInvertibleSetsqfreg| |li| |removeRedundantFactorsInContents| - 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|coefficients| |maximumExponent| |endSubProgram| - |arbitrary| |mathieu22| |relativeApprox| |domain| |hcrf| |e02daf| - |apply| |isAnd| |permutationRepresentation| |makeCos| |cAcsch| - |associatorDependence| |intChoose| |getSyntaxFormsFromFile| |lists| - |basisOfMiddleNucleus| |entries| |UnVectorise| |package| |wholePart| - |first| |factorSFBRlcUnit| |linearDependenceOverZ| |series| - |squareFreeLexTriangular| |bumptab| |s17ahf| |OMgetEndObject| - |branchIfCan| |safeFloor| |extractProperty| |binomThmExpt| |rest| - |iteratedInitials| |fibonacci| |stopTable!| |cCos| |atrapezoidal| - |ratPoly| |bezoutResultant| |clipSurface| |decreasePrecision| - |aLinear| |region| |binarySearchTree| |setProperties| - |nextLatticePermutation| |complexNumericIfCan| |odd?| - |sylvesterMatrix| |capacity| |nextsousResultant2| |flexibleArray| - |logIfCan| |rightTrace| |factors| |lowerCase| |lquo| |doubleDisc| - |cyclicSubmodule| |deriv| |writeLine!| |rubiksGroup| |besselI| - |nextsubResultant2| |bag| |rationalPoint?| |prod| |min| - |stiffnessAndStabilityFactor| |figureUnits| |computeCycleEntry| - |Vectorise| |rootProduct| |genericRightTrace| |edf2efi| |iomode| - |f07fef| |selectOrPolynomials| |charthRoot| |pseudoRemainder| - |leftUnits| |epilogue| |realZeros| |normal01| |signatureAst| |prefix| - |toseLastSubResultant| |bezoutMatrix| |outlineRender| |iisec| - |readIfCan!| |arg1| |s18dcf| |monomials| |reflect| |commonDenominator| - |credPol| |optional?| |elementary| |mainVariable?| |vedf2vef| |binary| - |iidprod| |predicate| |arg2| |cyclicParents| |e02ddf| |setref| - |symmetricPower| |denominators| |createZechTable| |redpps| - |parseString| |selectIntegrationRoutines| |FormatArabic| |outputList| - |bfEntry| |kmax| |irCtor| |halfExtendedSubResultantGcd2| |rdHack1| - |solid?| |limitedint| |jvmProtected| |meshPar2Var| |setFieldInfo| - |simplify| |next| |conditions| |rarrow| |hdmpToP| |parametersOf| - |medialSet| |viewDefaults| |shrinkable| |e01bhf| |s19aaf| - |integralRepresents| 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|determinant| |constDsolve| - |balancedBinaryTree| |iiacot| |lazyGintegrate| |elaborateFile| - |coordinates| |debug| |parts| |cCsch| |absolutelyIrreducible?| - |stFunc1| |submod| |genericRightMinimalPolynomial| |minPol| - |pointColor| |clip| D |stFuncN| |mapExponents| |ddFact| - |createLowComplexityNormalBasis| |lcm| |coth2trigh| |f07fdf| - |characteristic| |monicCompleteDecompose| |youngDiagram| |belong?| - |hexDigit| |exteriorDifferential| |aQuadratic| |GospersMethod| - |outputAsScript| |underscore| |minimumExponent| |blue| - |taylorQuoByVar| |append| |d01bbf| |low| |eigenMatrix| - |PollardSmallFactor| |associator| |genericLeftMinimalPolynomial| - |subNodeOf?| |digit| |numer| |upperBound| |antisymmetricTensors| |gcd| - |numberOfChildren| |rootNormalize| |updatF| |quotient| |d03eef| - |pureLex| |countRealRoots| |zero?| |prevPrime| |denom| |var1Steps| - |false| |BumInSepFFE| |polygon| |vark| |solveRetract| - |nativeModuleExtension| |jvmInterfaceMethodConstantTag| |subset?| - |exptMod| |OMputEndError| |clikeUniv| |invertIfCan| |getDatabase| - |jvmPrivate| |LazardQuotient2| |compile| |pushuconst| |pi| - |viewport2D| |s19adf| |ScanFloatIgnoreSpaces| |coercePreimagesImages| - |sequences| |hasPredicate?| |principalAncestors| |voidMode| - |magnitude| |infinity| |getPickedPoints| |inc| |numericalIntegration| - |point?| |adaptive?| |linearElement| |leftRegularRepresentation| - |var1StepsDefault| |associates?| |diagonal?| |minordet| - |fortranComplex| |bezoutDiscriminant| |weights| |clipPointsDefault| - |f02akf| |setAttributeButtonStep| |wrregime| |readInt32!| |print| - |autoReduced?| |interactiveEnv| |rightQuotient| |Ei| |startPolynomial| - |hue| |extract!| |deepCopy| |resolve| |power!| |stirling1| |kernel| - |denominator| |extend| |scalarTypeOf| |iiexp| |e02agf| - |reciprocalPolynomial| |setVariableOrder| |homogeneous?| |groebner?| - |list| |irForm| |triangulate| |tanintegrate| |d01akf| |f01maf| |draw| - |critBonD| |iiasech| |createThreeSpace| |integralMatrix| |setLength!| - |nextNormalPrimitivePoly| |debug3D| |alternating| |subscript| |pow| - |hitherPlane| |f07aef| |lhs| |call| |OMputString| |prindINFO| - |OMgetEndApp| |acoshIfCan| |zeroSquareMatrix| |modularFactor| |center| - |find| |fortranLinkerArgs| |showIntensityFunctions| |rhs| |create| - |purelyAlgebraic?| |member?| |groebnerFactorize| |solveLinear| - |roughBase?| |OMputAtp| |prepareDecompose| |setImagSteps| |normDeriv2| - |ParCondList| |cyclicEqual?| |dioSolve| |makeObject| |sizeLess?| - |width| |getBadValues| |host| |rootPoly| |antiCommutator| |ScanRoman| - |graphImage| |declare| |extractClosed| |coef| |permutation| |e02adf| - |subst| |isConnected?| |antiCommutative?| |lfextlimint| - |palgintegrate| |resultant| |normalElement| |clearTheFTable| |tRange| - |constantCoefficientRicDE| |root| |front| |attributeData| - |screenResolution| |semiSubResultantGcdEuclidean2| |pointPlot| - |limitPlus| |solveLinearPolynomialEquationByRecursion| |delta| - |constantToUnaryFunction| |createMultiplicationTable| |rootSimp| - |cyclePartition| |e02bdf| |initial| |symbolIfCan| |singular?| - |OMUnknownSymbol?| |laplacian| |shift| |bipolarCylindrical| - |leftTrace| |f02aff| |normalForm| |strongGenerators| |quasiMonic?| - |signAround| |unrankImproperPartitions0| |swapRows!| |objects| - |createIrreduciblePoly| |matrixGcd| |unitNormal| |mainVariable| - |sncndn| |packageCall| |sechIfCan| |symmetricSquare| |optional| - |exprHasAlgebraicWeight| |base| |getZechTable| |maxIndex| - |infinityNorm| |squareMatrix| |multiEuclidean| |curveColorPalette| - |s15aef| |acosIfCan| |SturmHabichtMultiple| |imagk| |acothIfCan| - |exponential| |normalized?| |f04mbf| |iipow| |df2st| |divisor| UP2UTS - |logGamma| |drawComplex| |jvmStringConstantTag| |removeConstantTerm| - |lp| |listOfMonoms| |log| |useEisensteinCriterion| |setnext!| - |factorsOfCyclicGroupSize| |lazyPseudoQuotient| |pushdown| - |stronglyReduce| |digits| |monomRDE| |laplace| |saturate| |cSinh| - |subPolSet?| |permutations| |printInfo| |lambda| |hasSolution?| - |c06fqf| |coerceP| |reducedQPowers| |one?| |say| |nthFactor| - |clipBoolean| |traverse| |contains?| |left| |weight| |errorInfo| - |minPoints| |float?| |dmpToP| |multiEuclideanTree| |minimize| - |nthRootIfCan| |presub| |right| |rootKerSimp| |cup| |factorSquareFree| - |point| |mapCoef| |minPoints3D| |alternative?| |linearMatrix| |d01fcf| - |ReduceOrder| |cosSinInfo| |df2ef| |e02dcf| |alternatingGroup| - |pointColorDefault| |cache| |primitiveElement| |badValues| - |deepExpand| |updatD| |putColorInfo| |close| |laurentRep| |arrayStack| - |partialDenominators| |iiasec| |s17aff| |primlimitedint| |isList| - |problemPoints| |leftMult| |c06ecf| |mapDown!| |sinhcosh| - |simplifyPower| |cdr| |patternVariable| |e04jaf| |disjunction| - |distance| |display| |qqq| |cyclic| |range| |leviCivitaSymbol| - |sinh2csch| |wholeRadix| |sumSquares| |rightRegularRepresentation| - |sup| |previous| |elem?| |simpleBounds?| |identification| - |numberOfHues| |doubleComplex?| |ptFunc| |unknown| |roughUnitIdeal?| - |HermiteIntegrate| |pile| |Ci| |unit?| |makeResult| |indices| - |conditionP| |powers| |parents| |invertibleElseSplit?| |s19acf| - |leftFactor| |prolateSpheroidal| |coerceListOfPairs| |htrigs| - |multiset| |particularSolution| |roman| |setFormula!| |exQuo| - |upDateBranches| |hasTopPredicate?| |currentEnv| |totalDifferential| - |pseudoQuotient| |distdfact| |hostPlatform| |probablyZeroDim?| - |d01asf| |e02ahf| |quatern| |eq?| |inspect| |s18acf| - |removeSuperfluousQuasiComponents| |evenlambert| |square?| - |properties| |consnewpol| |charClass| |fixedPointExquo| |hconcat| - |padicallyExpand| |symbol| |quadratic?| |ffactor| |realElementary| - |toseSquareFreePart| |shiftRoots| |translate| |output| |separate| - |critpOrder| |mainValue| |factorials| |insertMatch| |expression| - |trim| |viewport3D| |genericRightNorm| |primaryDecomp| |bandedHessian| - |test| |lexTriangular| |bitTruth| |linear?| |generator| - |extendedResultant| |integer| |changeName| |inverseLaplace| - |physicalLength| |trivialIdeal?| |orbit| |remove| |delay| - |insertRoot!| |symmetricDifference| |ldf2vmf| |functionIsOscillatory| - |tracePowMod| |s13adf| UTS2UP |infLex?| |imagI| |wholeRagits| - |printStats!| |sdf2lst| |complexRoots| |primeFactor| |entry| |dark| - |symmetricRemainder| |expr| |quadratic| |last| |dmpToHdmp| - |commutativeEquality| |c06gsf| |hdmpToDmp| |decimal| |se2rfi| - |tablePow| |complexForm| |traceMatrix| |assoc| |knownInfBasis| - |message| |OMencodingBinary| |complexElementary| |insert!| |pushucoef| - |mainContent| |f04asf| |errorKind| |drawStyle| |changeWeightLevel| - |polyPart| |acscIfCan| |polyRicDE| |aQuartic| |rootDirectory| - |jvmIntegerConstantTag| |tensorProduct| |normal?| - |useEisensteinCriterion?| |pointData| |weierstrass| - |lastSubResultantEuclidean| |alphanumeric?| |horizontalTab| - |jvmClassConstantTag| |transform| |variable| |OMputObject| |polygon?| - |unitCanonical| |explicitEntries?| |diagonal| |iicsch| |partitions| - |coefficient| |iterators| |quartic| |pr2dmp| |setleft!| |refine| - |typeList| |extractSplittingLeaf| |substring?| |getButtonValue| - |hasoln| |cylindrical| |overbar| |radicalSimplify| |OMgetString| - |eulerPhi| |high| |monicDecomposeIfCan| |useSingleFactorBound| - |asinIfCan| |LiePoly| |birth| |readByte!| |generalizedEigenvectors| - |gradient| |rightMult| |mainMonomials| |checkPrecision| |incr| - |iiacoth| |suffix?| |invertibleSet| |top| |nullSpace| |empty| - |reverseLex| |makingStats?| |linearlyDependent?| - |selectFiniteRoutines| |ocf2ocdf| |hi| |continue| |rules| |firstDenom| - |isAtom| |OMgetEndAtp| |tubeRadiusDefault| |bytes| |mathieu23| - |character?| |solveInField| |nthCoef| |numeric| |prefix?| |rightOne| - |internalLastSubResultant| |complexEigenvalues| - |algebraicCoefficients?| |OMgetType| |linearAssociatedOrder| |eof?| - |startTableInvSet!| |radical| |stoseInvertible?| |makeCrit| - |overlabel| |horizConcat| |f02ajf| |positiveSolve| |rightAlternative?| - |mergeDifference| |numberOfImproperPartitions| |setelt!| |algDsolve| - |minimumDegree| |findBinding| |setClosed| |UP2ifCan| - |conditionsForIdempotents| |s17akf| |tube| |extendedSubResultantGcd| - |rightTraceMatrix| |radicalSolve| |linearPart| |isOp| |compdegd| - |irVar| |precision| |noLinearFactor?| |rename!| |integrate| |minIndex| - |triangular?| |readInt8!| |OMlistCDs| |plenaryPower| |ldf2lst| - |noValueMode| |closed?| |setCondition!| |critM| |listYoungTableaus| - |e01sff| |makeViewport3D| |exponents| |identitySquareMatrix| - |removeCosSq| |laurentIfCan| |infix?| |nonSingularModel| - |quadraticNorm| |dflist| |intPatternMatch| |sub| |s17dhf| |mkcomm| - |integral| |e04naf| |nextPrimitiveNormalPoly| |mask| |bothWays| - |ptree| |palgint| |monomialIntegrate| |topPredicate| |OMconnectTCP| - |OMputVariable| |symmetricTensors| |primextendedint| - |fullPartialFraction| |lazyEvaluate| |computePowers| |e02akf| |f07adf| - |deref| |freeOf?| |resize| |chebyshevU| |Lazard| - |stoseLastSubResultant| |iifact| |cons| |dominantTerm| |att2Result| - |decomposeFunc| |raisePolynomial| |setsubMatrix!| - |initializeGroupForWordProblem| |iiacsch| |mindeg| |divideExponents| - |getProperty| |beauzamyBound| |OMgetApp| |c06fuf| |generate| - |inverseIntegralMatrix| |roughBasicSet| |leftZero| |middle| |finite?| - |setright!| |readable?| |radicalEigenvector| |hermiteH| |iiatan| - |fglmIfCan| |e01bgf| |addPointLast| |resultantnaif| |OMgetAttr| |rem| - |encodingDirectory| |incrementBy| |argscript| |mpsode| |associative?| - |s17ajf| |iisin| |euclideanSize| |coerceS| |f02aef| |quo| |varselect| - |expand| |mkIntegral| |getCurve| - |generalizedContinuumHypothesisAssumed| |adaptive3D?| |integral?| - |dimensionOfIrreducibleRepresentation| |source| |nextSublist| - |structuralConstants| |ratDenom| |filterWhile| |B1solve| |monicDivide| - |pushdterm| |s18aef| |blankSeparate| |derivationCoordinates| |space| - |qinterval| |div| |leftLcm| |filterUntil| - |functionIsContinuousAtEndPoints| |lastSubResultantElseSplit| - |bitCoef| |any| |nextPrime| |OMmakeConn| |supDimElseRittWu?| |exquo| - |rightGcd| |select| |singleFactorBound| |arity| |realEigenvectors| - |squareFreeFactors| |directory| |OMsupportsCD?| |target| - |quasiRegular?| |leftScalarTimes!| |phiCoord| ~= |doublyTransitive?| - |fprindINFO| |stoseInvertibleSet| |exists?| |revert| |components| - |back| |internal?| |position| |evenInfiniteProduct| |#| - |inputBinaryFile| |mainForm| |numberOfComponents| |resetVariableOrder| - |connect| |lflimitedint| |lookupFunction| |tanNa| |leftExactQuotient| - |rightDivide| ~ |external?| |isQuotient| |product| |coerce| |ipow| - |increment| |var2Steps| |integralAtInfinity?| |octon| |f01rcf| - |generalLambert| |genericRightTraceForm| |accuracyIF| |curryRight| - |construct| |elRow1!| |real?| |palginfieldint| |putProperty| |sin?| - |nextItem| |basicSet| |zerosOf| |plus!| |showRegion| |iiGamma| - |aspFilename| |setIntersection| |subNode?| |nand| |mkAnswer| |lookup| - |/\\| |c06gbf| |cycleLength| |algSplitSimple| |continuedFraction| - |vectorise| |update| |d02cjf| |primitivePart!| |\\/| |lllp| - |rischNormalize| |jvmUTF8ConstantTag| |quoted?| |matrixConcat3D| - |content| |lfextendedint| |roughSubIdeal?| |bfKeys| |removeSinSq| - |twist| |ignore?| |trapezoidalo| |height| |ceiling| - |algebraicVariables| |graphCurves| |fixedDivisor| |numberOfComposites| - |bigEndian| |Gamma| |any?| |clipWithRanges| |genericRightDiscriminant| - |tubeRadius| |sh| |semiSubResultantGcdEuclidean1| |recur| - |lieAdmissible?| |rowEchLocal| |coordinate| |listConjugateBases| - |s17dlf| |factorPolynomial| |tubePointsDefault| |complexIntegrate| - |moebius| |btwFact| |univariate?| |addBadValue| |completeHensel| - |setTopPredicate| |factorAndSplit| |palgLODE| |returnTypeOf| - |appendPoint| |mantissa| |OMgetEndBVar| |viewWriteDefault| - |padicFraction| |commutator| |create3Space| - |ScanFloatIgnoreSpacesIfCan| |semicolonSeparate| |primlimintfrac| - |stronglyReduced?| |neglist| |imagK| |numberOfDivisors| |bernoulliB| - |conjugate| |max| |extractIfCan| |cfirst| |iisqrt3| |vspace| - |moreAlgebraic?| |closedCurve?| |fortranCarriageReturn| - |outputBinaryFile| |irreducibleFactor| |solve| |bombieriNorm| - |linefeed| |imagj| |isImplies| |internalIntegrate0| |sparsityIF| - |leftQuotient| |irreducibleFactors| |setOfMinN| |isMult| - |OMgetEndBind| |rangePascalTriangle| |yellow| |c05adf| |rCoord| - |atoms| |matrixDimensions| |pade| - |rewriteSetByReducingWithParticularGenerators| |radix| |iprint| - |infix| |randnum| |seriesSolve| |gcdcofact| |length| |infiniteProduct| - |socf2socdf| |quotientByP| |seed| |combineFeatureCompatibility| - |shallowCopy| |leftNorm| |nor| |const| |match?| |scripts| |pastel| - |updateStatus!| |rightUnit| |internalSubPolSet?| |setelt| |invmod| - |jvmFinal| |makeTerm| |sumOfSquares| |bivariatePolynomials| |set| - |thetaCoord| |partialNumerators| |alphabetic| |showTheFTable| - |elliptic?| |pToHdmp| |rectangularMatrix| |jvmDoubleConstantTag| - |connectTo| |ListOfTerms| |depth| |kovacic| |sqfrFactor| - |pascalTriangle| |copy| |nonLinearPart| |swap| |meshFun2Var| - |scalarMatrix| |exactQuotient| |powern| |leftDiscriminant| |spherical| - |principalIdeal| |lyndon| |mappingAst| |iidsum| |datalist| - |integerIfCan| |stirling2| |prologue| |nthExpon| |cAcoth| |nullary| - |autoCoerce| |e01baf| |remainder| |fortranDoubleComplex| - |setLabelValue| |An| |closeComponent| |tail| |isPower| - |basisOfRightNucleus| |cSin| |linearForm| |c06gqf| - |generalizedInverse| |cAsec| |d02bbf| |ode| |bitLength| - |relationsIdeal| |realEigenvalues| |mathieu24| |number?| |ode1| - |lllip| |semiDiscriminantEuclidean| |subResultantsChain| |hspace| - |coleman| |numberOfMonomials| |void| |leftGcd| |companionBlocks| - |leadingBasisTerm| |midpoints| |possiblyInfinite?| |infieldint| - |newSubProgram| |getVariableOrder| |e04gcf| |basisOfCentroid| - |sumOfKthPowerDivisors| |nilFactor| |perfectNthPower?| |exp1| - |interpolate| |retract| |cap| |torsion?| |repeatUntilLoop| |setEmpty!| - |nullity| |KrullNumber| |oblateSpheroidal| |badNum| ** |setfirst!| - |separant| |setleaves!| |leadingTerm| |bringDown| - |stiffnessAndStabilityOfODEIF| |linears| |stoseInvertibleSetreg| - |cAcot| |semiLastSubResultantEuclidean| |leftPower| |decrease| - |jvmNameAndTypeConstantTag| |basisOfCommutingElements| |iiabs| - |cyclicGroup| |totalGroebner| |move| |iiasin| |rightDiscriminant| - |minGbasis| |constantOpIfCan| |internalInfRittWu?| |f02abf| - |univariatePolynomial| |setUnion| |writable?| |powmod| |whileLoop| - |complex?| |HenselLift| |complexSolve| |flatten| - |halfExtendedResultant2| |mapdiv| |approximants| |minimalPolynomial| - |wordInGenerators| |rightNorm| |removeIrreducibleRedundantFactors| - |e01sbf| |zag| |retractable?| |patternMatchTimes| |getMeasure| - |pmComplexintegrate| |maxdeg| |box| |numberOfOperations| - |factorFraction| |shiftLeft| |bindings| |headRemainder| - |rightExtendedGcd| |assign| |unknownEndian| |backspace| |makeFR| - |rischDE| |leftRecip| |retractIfCan| |iitanh| |degree| |setTex!| - |qualifier| |OMcloseConn| |listexp| |po| |empty?| |double| - |deepestTail| |OMputEndBVar| |removeDuplicates| |getProperties| - |jvmNative| |dAndcExp| |s14abf| |contractSolve| |push| - |internalSubQuasiComponent?| |s17adf| |getConstant| |cAcsc| |tan2cot| - |tubePlot| |adjoint| |meatAxe| |fortranDouble| |prinb| |npcoef| - |failed| |youngGroup| |select!| |sech2cosh| |zeroMatrix| |error| - |surface| |splitDenominator| |unprotectedRemoveRedundantFactors| - |lowerBound| |rootOf| |computeInt| |vconcat| |fortranReal| |dec| - |lazyIrreducibleFactors| |scanOneDimSubspaces| |viewpoint| |toroidal| - |mapmult| |schema| |nthr| |constantKernel| |internalZeroSetSplit| - |padecf| |lfinfieldint| |graphStates| |leadingExponent| |coefChoose| - |ramifiedAtInfinity?| |cAsinh| |elements| |outerProduct| |cyclicCopy| - |cTanh| |central?| |factor1| |monomialIntPoly| |atanIfCan| - |putProperties| |prime| |leadingIndex| |diagonalMatrix| |scan| - |biRank| |mightHaveRoots| |check| |factorset| |setStatus!| |declare!| - |basis| |withPredicates| |setErrorBound| |powerAssociative?| - |fortranLogical| |c06ekf| |sortConstraints| |minPoly| |cSech| |s15adf| - |groebnerIdeal| |insert| |linearPolynomials| |sort!| |lex| |byte| - |degreePartition| |puiseux| |pomopo!| |polCase| |ellipticCylindrical| - |setOrder| |OMencodingSGML| |bumptab1| |tanQ| |ricDsolve| |s21bdf| - |stop| |restorePrecision| |open?| |iiacos| |f01mcf| |lintgcd| - |scaleRoots| |OMputApp| |showScalarValues| |lexGroebner| |outputForm| - |inv| |resetAttributeButtons| |superHeight| |clearDenominator| - |LyndonCoordinates| |eval| |satisfy?| F2FG |PDESolve| |inrootof| - |has?| |ground?| |zero| |swapColumns!| |compose| |anticoord| |s18adf| - |d01amf| |showTheSymbolTable| |deleteProperty!| |hclf| |printingInfo?| - |unexpand| |ground| |drawCurves| |quasiRegular| - |characteristicPolynomial| |dot| |moduleSum| |powerSum| |alphabetic?| - |typeForm| |testDim| |presuper| |sqfree| |leadingMonomial| - |computeCycleLength| |And| |expenseOfEvaluationIF| |divideIfCan!| - |SturmHabichtSequence| |segment| |cycle| |reduceBasisAtInfinity| - |identityMatrix| |f01rdf| |mainVariables| |leadingCoefficient| |Or| - |jacobi| |vertConcat| |factorByRecursion| |SFunction| |listBranches| - |primPartElseUnitCanonical!| |int| |child?| |iiacosh| - |primitiveMonomials| |extendIfCan| |Not| |OMunhandledSymbol| - |currentScope| |trailingCoefficient| |getCode| |expextendedint| - |reduced?| |listOfLists| |reductum| |iiatanh| |bounds| |mainMonomial| - |primitivePart| |setScreenResolution3D| |totolex| |matrix| |tanh2coth| - |transcendenceDegree| |prinshINFO| |trapezoidal| |internalAugment| - |carriageReturn| |wordsForStrongGenerators| |style| |byteBuffer| - |contract| F |quote| |cotIfCan| |rk4f| |rowEchelon| |chiSquare| - |chiSquare1| |currentCategoryFrame| |prinpolINFO| |addmod| - |rationalIfCan| |createNormalPrimitivePoly| |duplicates| - |rangeIsFinite| |mathieu11| |solid| |hex| |write!| |idealiserMatrix| - |jvmTransient| |redPol| |even?| |componentUpperBound| - |solveLinearPolynomialEquationByFractions| |outputArgs| |in?| - |overset?| |f04maf| |rightFactorCandidate| |monic?| |open| - |useSingleFactorBound?| |generic| |sincos| |viewZoomDefault| - |leftMinimalPolynomial| |modularGcd| |unmakeSUP| |crest| |setRow!| - |build| |jvmFieldrefConstantTag| |flagFactor| |OMputEndAtp| - |colorFunction| |semiResultantEuclidean1| |OMputError| |rdregime| - |nil| |removeSuperfluousCases| |e02dff| |pseudoDivide| |randomR| - |makeViewport2D| |listLoops| |arguments| |represents| - |partialQuotients| |fractRagits| |size?| |OMgetAtp| |changeBase| - |critMonD1| |concat!| |intensity| |comment| |categoryMode| - |mapMatrixIfCan| |cot2trig| |addiag| |operations| |reify| |primitive?| - |generic?| |makeRecord| |replace| |domainTemplate| |close!| |gbasis| - |linearDependence| |integralBasis| |tree| |node?| |numberOfVariables| - |approximate| |dom| |table| |imports| |setPrologue!| |readUInt16!| - |terms| |complex| |radicalRoots| |members| |setAdaptive| |ODESolve| - |Hausdorff| |addPoint| |parent| |obj| |new| |tValues| - |purelyAlgebraicLeadingMonomial?| |sPol| |interpretString| |limit| - |rootsOf| |numberOfFractionalTerms| |paraboloidal| |innerEigenvectors| - |upperCase?| |leftOne| |position!| |gderiv| |leftRankPolynomial| - |expressIdealMember| |jvmSynchronized| |diff| |part?| GF2FG - |fixPredicate| |op| |maxint| |OMopenString| |formfeed| |approxSqrt| - |selectPolynomials| |constantOperator| |unravel| - |numberOfIrreduciblePoly| |clearCache| |bipolar| |abelianGroup| - |genericLeftTraceForm| |atanhIfCan| |aCubic| |realSolve| |axes| - |ramified?| |multMonom| |solveLinearPolynomialEquation| |rightTrim| - |permanent| |sample| |nextSubsetGray| |nil| |infinite| + |Enumeration| |Mapping| |Record| |Union| |fixedPoint| |c06fpf| + |quickSort| |bitTruth| |e01sbf| |safetyMargin| |readInt32!| |iiperm| + |resetVariableOrder| |op| |isobaric?| |characteristicSet| |d02bhf| + |linear?| |zag| |clearCache| |untab| |autoReduced?| |connect| + |constant?| |ODESolve| |increase| |deleteRoutine!| + |intermediateResultsIF| |extendedResultant| |retractable?| + |interactiveEnv| |ScanArabic| |rightTrim| |lflimitedint| |diag| + |Hausdorff| |constantLeft| |bracket| |isEquiv| |changeName| + |elColumn2!| |patternMatchTimes| |innerint| |rightQuotient| |leftTrim| + |lookupFunction| |allRootsOf| |addPoint| |cCot| |merge| |rename| + |inverseLaplace| |mesh?| |getMeasure| |kind| |factorsOfDegree| |Ei| + |cExp| |tanNa| |parent| |cTan| |nodes| |factorGroebnerBasis| + |physicalLength| |pmComplexintegrate| |startPolynomial| |dimension| + |leftExactQuotient| |expIfCan| |tValues| |elaboration| |simpsono| + |seriesToOutputForm| |trivialIdeal?| |maxdeg| |squareTop| |hue| + |optimize| |d02gbf| |rightDivide| |purelyAlgebraicLeadingMonomial?| + |complexZeros| |approxNthRoot| |orbit| |cyclicEntries| + |numberOfOperations| |extract!| |external?| |squareFreePrim| |rst| + |e02bbf| |sPol| |setPredicates| |supRittWu?| |status| |delay| + |factorFraction| |idealiser| |deepCopy| |stoseInvertible?sqfreg| + |product| |newTypeLists| |interpretString| |roughEqualIdeals?| + |sinhIfCan| |insertRoot!| |mirror| |shiftLeft| |ipow| |power!| + |prime?| |operation| |torsionIfCan| |limit| |numerators| |floor| + |totalDegree| |symmetricDifference| |headRemainder| |stirling1| + |totalLex| |union| |increment| |dual| |rootsOf| |cAcosh| |d03faf| + |integerBound| |ldf2vmf| |rightExtendedGcd| |cyclotomicDecomposition| + |denominator| |oddintegers| |var2Steps| |SturmHabicht| + |numberOfFractionalTerms| |crushedSet| + |standardBasisOfCyclicSubmodule| |functionIsOscillatory| |cAsin| + |assign| |dilog| |palglimint0| |extend| |integralAtInfinity?| + |besselY| |paraboloidal| |variable?| |null?| |tracePowMod| |inf| + |unknownEndian| |sin| |scalarTypeOf| |twoFactor| |octon| |dimensions| + |innerEigenvectors| |outputGeneral| |setchildren!| |s13adf| + |resultantEuclideannaif| |backspace| |reverse| |cos| |iiexp| |c06gcf| + |f01qef| |f01rcf| |upperCase?| |invertible?| |controlPanel| |equality| + UTS2UP |makeFR| |tan| |e02agf| |atom?| |numFunEvals3D| + |generalLambert| |leftOne| |hash| |cAcos| |lazy?| |countable?| + |infLex?| |rischDE| |li| |cot| |reciprocalPolynomial| |OMread| + |genericRightTraceForm| |e02ajf| |count| |position!| |read!| |super| + |f04adf| |rank| |c06frf| |imagI| |leftRecip| |sec| |generators| + |setVariableOrder| |accuracyIF| |stopTableGcd!| |gderiv| |mathieu12| + |antisymmetric?| |f02axf| |wholeRagits| |iitanh| |constructor| |csc| + |homogeneous?| |extractIndex| |curryRight| |OMgetVariable| + |leftRankPolynomial| EQ |orthonormalBasis| |minColIndex| + |functionIsFracPolynomial?| |printStats!| |degree| |category| |asin| + |groebner?| |tanh2trigh| |morphism| |elRow1!| |expressIdealMember| + |rootSplit| |csch2sinh| |sdf2lst| |makeYoungTableau| |setTex!| + |domain| |acos| |irForm| |innerSolve1| |exprHasWeightCosWXorSinWX| + |real?| |jvmSynchronized| |logical?| |closedCurve| |complexRoots| + |expPot| |qualifier| |package| |rotatey| |triangulate| |atan| + |integralLastSubResultant| |point| |palginfieldint| |generator| |diff| + |gensym| |OMbindTCP| |primeFactor| |string?| |OMcloseConn| + |tryFunctionalDecomposition| |acot| |tanintegrate| |toseInvertibleSet| + |putProperty| |normalizedDivide| |part?| |c05nbf| |shade| |lazyPrem| + |useNagFunctions| |dark| |listexp| |dfRange| |apply| |asec| |d01akf| + |pdct| |sin?| |OMgetEndError| |mainKernel| GF2FG |e02bcf| |e04mbf| + |lists| |oddInfiniteProduct| |symmetricRemainder| + |numberOfComputedEntries| |po| |cyclotomicFactorization| |acsc| + |first| |f01maf| |series| |nextItem| |viewPosDefault| |fixPredicate| + |basisOfNucleus| |semiResultantReduitEuclidean| |split!| |OMgetObject| + |quadratic| |empty?| |sinh| |rest| |iicsc| |critBonD| |printHeader| + |basicSet| |maxint| |pdf2ef| |iCompose| |box| |cAsech| |dmpToHdmp| + |deepestTail| |cosh| |iiasech| |shufflein| |zerosOf| |e04fdf| + |OMopenString| |regime| |tab1| |commutativeEquality| |normFactors| + |OMputEndBVar| |tanh| |createThreeSpace| |modifyPointData| + |singularitiesOf| |plus!| |formfeed| |primeFrobenius| |OMreadFile| + |c06gsf| |nodeOf?| |removeDuplicates| |integralMatrix| |coth| + |realRoots| |min| |lyndon?| |showRegion| |approxSqrt| |nlde| + |printTypes| |OMputInteger| |hdmpToDmp| |getProperties| |sech| + |setLength!| |children| |iiGamma| |f04arf| |selectPolynomials| + |comparison| |contours| |decimal| |direction| |jvmNative| |prefix| + |csch| |nextNormalPrimitivePoly| |c02aff| |environment| |aspFilename| + |constantOperator| |makeSin| |arg1| |exponent| |makeMulti| |se2rfi| + |dAndcExp| |setIntersection| |asinh| |c02agf| |debug3D| |rightPower| + |incr| |unravel| |shallowExpand| |predicate| |arg2| |d01aqf| + |tablePow| |lazyPseudoDivide| |s14abf| |alternating| |critMTonD1| + |shuffle| |acosh| |over| |hi| |subNode?| |outputList| + |numberOfIrreduciblePoly| |karatsubaOnce| |scale| |choosemon| + |complexForm| |contractSolve| |associatedSystem| |atanh| |eulerE| + |subscript| |nand| |definingPolynomial| |bipolar| |next| + |jvmLongConstantTag| |d02raf| |conditions| |traceMatrix| |symFunc| + |push| |acoth| |pow| |minset| |basisOfLeftNucleus| |mkAnswer| + |abelianGroup| |fortranCompilerName| |match| |isTimes| |knownInfBasis| + |llprop| |internalSubQuasiComponent?| |asech| |merge!| |hitherPlane| + |lookup| |insertionSort!| |genericLeftTraceForm| |computeBasis| + |f04axf| |tubePoints| |OMencodingBinary| |sn| |s17adf| |getStream| + |f07aef| |c06gbf| |partition| |atanhIfCan| |singularAtInfinity?| + |expandTrigProducts| |OMencodingUnknown| |complexElementary| + |getConstant| |multiple| |OMputString| |lowerCase!| |mergeFactors| + |cycleLength| |pattern| |aCubic| |leadingIdeal| |getRef| + |completeSmith| |insert!| |cAcsc| |graeffe| |applyQuote| |functorData| + |prindINFO| |algSplitSimple| |optpair| |realSolve| |polyRDE| |order| + |getIdentifier| |pushucoef| |tan2cot| |dim| |discreteLog| + |OMgetEndApp| |asecIfCan| |continuedFraction| |mindegTerm| |axes| + |e01saf| |mainContent| |tubePlot| |shanksDiscLogAlgorithm| + |acoshIfCan| |verticalTab| |vectorise| |ramified?| |parameters| + |setFieldInfo| |fracPart| |f04asf| |adjoint| |ravel| + |zeroSquareMatrix| |ruleset| |true| |typeLists| |d02cjf| + |resetBadValues| |multMonom| |simplify| |compiledFunction| |errorKind| + |meatAxe| |modularFactor| |reshape| |isNot| |ridHack1| + |primitivePart!| |solveLinearPolynomialEquation| |rarrow| |corrPoly| + |drawStyle| |fortranDouble| |numberOfCycles| |lllp| |permanent| |map| + |hdmpToP| |f04qaf| |changeWeightLevel| |prinb| |jvmPublic| + |exteriorDifferential| |palgLODE0| |suchThat| |rischNormalize| |push!| + |generate| |sample| |parametersOf| |completeEval| |polyPart| |npcoef| + |OMgetError| |perfectSqrt| |aQuadratic| |jvmUTF8ConstantTag| + |karatsuba| |nextSubsetGray| |resultantReduit| |medialSet| + |highCommonTerms| |extension| |acscIfCan| |myDegree| |youngGroup| + |GospersMethod| |eyeDistance| |clipParametric| |incrementBy| |quoted?| + |bsolve| |viewDefaults| |convert| |select!| |cCoth| + |removeRoughlyRedundantFactorsInPol| |certainlySubVariety?| + |outputAsScript| |matrixConcat3D| |makeFloatFunction| |expand| + |shrinkable| |rightRegularRepresentation| |property| |imagi| + |sech2cosh| |underscore| |cycleEntry| |content| |lazyPquo| + |filterWhile| |e01bhf| |sup| |resultantEuclidean| |zeroMatrix| |log10| + |minimumExponent| |rotate| |branchPointAtInfinity?| |lfextendedint| + |id| |filterUntil| |s19aaf| |elem?| |univariatePolynomialsGcds| + |surface| |bitand| |ParCond| |blue| |lo| |integralRepresents| + |simpleBounds?| |curve?| |splitDenominator| |bitior| |taylorQuoByVar| + |defineProperty| |cPower| |hermiteH| |step| |OMconnOutDevice| + |nthFlag| |identification| |unprotectedRemoveRedundantFactors| |chvar| + |d01bbf| |iiatan| RF2UTS |adaptive| |numberOfHues| + |LagrangeInterpolation| |lowerBound| |second| |perfectNthRoot| |low| + |fglmIfCan| |e04ycf| |prefixRagits| |doubleComplex?| + |subresultantSequence| |third| |genericLeftTrace| |eigenMatrix| + |headAst| |e01bgf| |brillhartTrials| |systemCommand| |stack| |key| + |df2mf| |ptFunc| |possiblyInfinite?| |exprHasLogarithmicWeights| + |PollardSmallFactor| |whatInfinity| |addPointLast| |lyndonIfCan| + |genericPosition| |roughUnitIdeal?| |infieldint| |infieldIntegrate| + |associator| |resultantnaif| |exponential1| |filename| + |euclideanNormalForm| |normal| |HermiteIntegrate| |OMserve| + |newSubProgram| |genericLeftMinimalPolynomial| |d02ejf| |OMgetAttr| + |taylorIfCan| |returnType!| |pile| |subResultantGcd| + |getVariableOrder| |bivariate?| |subNodeOf?| |encodingDirectory| + |LyndonWordsList1| |rightFactorCandidate| |forLoop| |parse| |Ci| + |OMUnknownCD?| |e04gcf| |digit| |numberOfPrimitivePoly| |euler| |eq| + |argscript| |monic?| |dequeue!| |unit?| |routines| |basisOfCentroid| + |sequence| |iter| |upperBound| |transpose| |mpsode| + |useSingleFactorBound?| |normalizeIfCan| |lift| |edf2df| |makeResult| + |sumOfKthPowerDivisors| |antiAssociative?| |isOr| + |antisymmetricTensors| |value| |associative?| |imagE| |generic| + |reduce| |unvectorise| |indices| |collectUpper| |nilFactor| + |setProperty| |replaceKthElement| |numberOfChildren| |s17ajf| + |tanhIfCan| |sincos| |localAbs| |conditionP| |generalInfiniteProduct| + |perfectNthPower?| |rootNormalize| |printCode| |iisin| |uniform| + |viewZoomDefault| |subCase?| |powers| |rightFactorIfCan| |exp1| + |euclideanSize| |updatF| |secIfCan| |inverseColeman| |linear| + |leftMinimalPolynomial| |OMputEndBind| |fillPascalTriangle| + |invertibleElseSplit?| |interpolate| |createPrimitiveElement| + |quotient| |localUnquote| |coerceS| |modularGcd| |resetNew| |s19acf| + |expandPower| |cap| |d03eef| |f01ref| |f02aef| |rule| + |evaluateInverse| |polynomial| |unmakeSUP| Y |e01bef| |lfunc| + |leftFactor| |torsion?| |f04atf| |pureLex| |limitedIntegrate| + |varselect| |crest| |fmecg| |prolateSpheroidal| |setMaxPoints3D| + |repeatUntilLoop| |asechIfCan| |countRealRoots| |mkIntegral| + |changeThreshhold| |setRow!| |balancedFactorisation| + |coerceListOfPairs| |initiallyReduce| |setEmpty!| |OMreadStr| |zero?| + |radPoly| |getCurve| |build| |genericLeftDiscriminant| |index| + |nthFractionalTerm| |htrigs| |nullity| |psolve| |prevPrime| + |generalizedContinuumHypothesisAssumed| |index?| + |jvmFieldrefConstantTag| |units| |s18aff| |multiset| |simplifyExp| + |KrullNumber| |var1Steps| |f02bbf| |generalizedEigenvector| + |adaptive3D?| |flagFactor| |pair| |largest| |palglimint| + |particularSolution| |oblateSpheroidal| |qelt| + |semiResultantEuclideannaif| |BumInSepFFE| |integral?| |solveid| + |OMputEndAtp| |d01gaf| |roman| |argumentListOf| |badNum| |qsetelt| + |generateIrredPoly| |sort| |polygon| + |dimensionOfIrreducibleRepresentation| |tab| |colorFunction| + |selectPDERoutines| |setFormula!| |exprToUPS| |setfirst!| |xRange| + |vark| |stopTableInvSet!| |nextSublist| |removeRedundantFactors| + |semiResultantEuclidean1| |indiceSubResultant| |just| |exQuo| + |separant| |yRange| |random| |solveRetract| |stoseInvertible?reg| + |structuralConstants| |coHeight| |code| |OMputError| |setvalue!| + |makeEq| |upDateBranches| |setleaves!| |zRange| |ratDenom| |rootPower| + |scripts| |nativeModuleExtension| |skewSFunction| |result| |rdregime| + |input| |bernoulli| |finiteBound| |hasTopPredicate?| |leadingTerm| + |map!| |palgRDE| |jvmInterfaceMethodConstantTag| |innerSolve| + |B1solve| |removeSuperfluousCases| |library| |s17acf| + |totalDifferential| |rationalPoints| |bringDown| BY |qsetelt!| |name| + |fill!| |subset?| |power| |monicDivide| |e02dff| |exponentialOrder| + |double?| |pseudoQuotient| |stiffnessAndStabilityOfODEIF| |jvmStrict| + |body| |search| |exptMod| |weakBiRank| |pushdterm| |pseudoDivide| + |reset| |every?| |distdfact| |showTheRoutinesTable| |linears| + |OMputEndError| |monicModulo| |s18aef| |getOperands| |randomR| |rk4a| + |hostPlatform| |transcendent?| |stoseInvertibleSetreg| |branchPoint?| + |extendedIntegrate| |OMclose| |clikeUniv| |blankSeparate| |size| + |makeViewport2D| |write| |calcRanges| |brillhartIrreducible?| + |probablyZeroDim?| |cAcot| |invertIfCan| |clearTheIFTable| + |bubbleSort!| |headReduced?| |testModulus| |derivationCoordinates| + |listLoops| |save| |iicos| |d01asf| |f02bjf| + |semiLastSubResultantEuclidean| |acsch| |linearAssociatedLog| + |getDatabase| |space| |lifting| |represents| NOT |upperCase!| |e02ahf| + |isExpt| |leftPower| |jvmPrivate| |d01gbf| |qinterval| + |definingEquations| |partialQuotients| OR |elliptic| |universe| + |quatern| |decrease| |LazardQuotient2| |lineColorDefault| + |createPrimitivePoly| |leftLcm| |fractRagits| AND + |clearTheSymbolTable| |eq?| |definingInequation| + |jvmNameAndTypeConstantTag| |pushuconst| |constant| + |initiallyReduced?| |goodPoint| |functionIsContinuousAtEndPoints| + |size?| |inspect| |convergents| |inHallBasis?| |subResultantChain| + |basisOfCommutingElements| |port| |f01bsf| |viewport2D| + |separateFactors| |lastSubResultantElseSplit| |OMgetAtp| |log2| + |mapBivariate| |s18acf| |mesh| |iiabs| |s19adf| |expt| |bitCoef| + |deepestInitial| |changeBase| |diophantineSystem| |unparse| + |removeSuperfluousQuasiComponents| |cyclicGroup| |bits| |key?| + |ScanFloatIgnoreSpaces| |basisOfRightAnnihilator| |nextPrime| + |critMonD1| |digamma| |green| |evenlambert| |totalGroebner| |node| |t| + |signature| |transcendentalDecompose| |coercePreimagesImages| + |recoverAfterFail| |numberOfNormalPoly| |OMmakeConn| |concat!| |show| + |rationalPower| |minrank| |square?| |move| |e01daf| |ksec| |sequences| + |readUInt32!| |supDimElseRittWu?| |nothing| |intensity| |iicosh| + |consnewpol| |assert| |poisson| |iiasin| |postfix| |ran| + |hasPredicate?| |listRepresentation| |categories| |rightGcd| + |categoryMode| |trace| |currentSubProgram| |charClass| + |quasiComponent| |rightDiscriminant| |jokerMode| |principalAncestors| + |noncommutativeJordanAlgebra?| |rationalApproximation| + |singleFactorBound| |mapMatrixIfCan| |shellSort| |normalize| + |fixedPointExquo| |minGbasis| |monicRightFactorIfCan| |voidMode| + |curryLeft| |variationOfParameters| |arity| |cot2trig| * |univcase| + |hconcat| |repeating| |constantOpIfCan| |Si| |complexExpand| + |magnitude| |realEigenvectors| |OMputBind| |addiag| + |basisOfLeftAnnihilator| |entry?| |padicallyExpand| + |internalInfRittWu?| |mapUnivariateIfCan| |tower| |outputMeasure| + |getPickedPoints| |goodnessOfFit| |squareFreeFactors| |reify| + |quadratic?| |delete!| |f02abf| |lexico| |createNormalElement| + |numericalIntegration| |OMsupportsCD?| |getGraph| |primitive?| + |nextsubResultant2| |ffactor| |simpson| |univariatePolynomial| + |numericIfCan| |loadNativeModule| |unaryFunction| |point?| |implies| + |quasiRegular?| |generic?| |bag| = |realElementary| + |selectNonFiniteRoutines| |setUnion| |sayLength| |readBytes!| + |adaptive?| |subscriptedVariables| |leftScalarTimes!| + |degreeSubResultantEuclidean| |replace| |rationalPoint?| |OMputFloat| + |toseSquareFreePart| |writable?| |setValue!| |domainTemplate| |times!| + |phiCoord| |prod| |slex| |concat| < |shiftRoots| |dihedralGroup| + |powmod| |alphanumeric| |complexNumeric| |supersub| |noKaratsuba| + |doublyTransitive?| |collect| |close!| |stiffnessAndStabilityFactor| > + |macroExpand| |regularRepresentation| |separate| |whileLoop| + |numberOfFactors| |makeVariable| |UpTriBddDenomInv| |cond| + |fprindINFO| |e04dgf| |equation| |gbasis| |figureUnits| <= + |fortranLiteralLine| |critpOrder| |complex?| |elaborate| |rquo| + |kernels| |lowerPolynomial| |mappingMode| |stoseInvertibleSet| + |linearDependence| |computeCycleEntry| >= |HenselLift| |gcdprim| + |ip4Address| |operator| |more?| |exists?| |legendreP| |integralBasis| + |Vectorise| |clipBoolean| |sin2csc| |categoryFrame| |complexSolve| + |plusInfinity| |varList| |showClipRegion| |univariate| |qroot| + |symbolTable| |gcdPrimitive| |revert| |node?| |zeroSetSplit| + |rootProduct| |traverse| |invmultisect| |rightScalarTimes!| + |halfExtendedResultant2| |d02kef| |minusInfinity| |checkForZero| + |e02gaf| |changeMeasure| |components| |qfactor| |numberOfVariables| + |genericRightTrace| + |repSq| |contains?| |mapdiv| |copyInto!| + |rombergo| |rotate!| |iterationVar| |pushFortranOutputStack| |imports| + |edf2efi| - |weight| |leftRemainder| |approximants| + |jordanAdmissible?| |popFortranOutputStack| |physicalLength!| |factor| + |removeSquaresIfCan| |palgRDE0| |makeViewport3D| |setPrologue!| + |iomode| / |errorInfo| |equiv| |exponents| |minimalPolynomial| + |iExquo| |sqrt| |minRowIndex| |subresultantVector| |title| |f01qdf| + |outputAsFortran| |readUInt16!| |f07fef| |minPoints| |pushNewContour| + |fortran| |wordInGenerators| |explicitlyEmpty?| |conjugates| |real| + |endOfFile?| |identitySquareMatrix| |OMputEndApp| |terms| + |selectOrPolynomials| |fortranLiteral| |float?| |type| |explogs2trigs| + |shiftRight| |imag| |OMgetSymbol| + |removeRoughlyRedundantFactorsInPols| |removeCosSq| |radicalRoots| + |charthRoot| |dmpToP| |color| |rectangularMatrix| |e| |directProduct| + |makeGraphImage| |lfintegrate| |userOrdered?| |gramschmidt| + |laurentIfCan| |members| |pseudoRemainder| |multiEuclideanTree| + |jvmFloatConstantTag| |jvmDoubleConstantTag| |redmat| |derivative| + |asimpson| |nonSingularModel| |augment| |setAdaptive| |leftUnits| + |minimize| |enterPointData| |connectTo| |chineseRemainder| |brace| + |OMReadError?| |monomial?| |quadraticNorm| |characteristicSerie| + |epilogue| |uncouplingMatrices| |nthRootIfCan| |ListOfTerms| |erf| + |plus| |destruct| |resultantReduitEuclidean| |reseed| + |lazyResidueClass| |dflist| |relerror| |SFunction| |char| |realZeros| + |makeop| |presub| |kovacic| |maxPoints| |setEpilogue!| |setrest!| + |intPatternMatch| |e02aef| |listBranches| |normal01| |rootKerSimp| + |writeByte!| |sqfrFactor| |positiveRemainder| |binaryFunction| + |tan2trig| |showFortranOutputStack| |sub| |primPartElseUnitCanonical!| + |signatureAst| |cup| |tableau| |pascalTriangle| |times| |delta| + |extendedint| |modifyPoint| |s17dhf| |viewThetaDefault| |child?| + |toseLastSubResultant| |constantIfCan| |factorSquareFree| + |nonLinearPart| |mkcomm| |s21bcf| |monomial| |sinIfCan| + |lastSubResultant| |vector| |options| |iiacosh| |bezoutMatrix| + |mapCoef| |float| |extensionDegree| |swap| |integralCoordinates| + |jacobiIdentity?| |pack!| |multivariate| |integral| |bat1| + |differentiate| |extendIfCan| |outlineRender| |algintegrate| + |minPoints3D| |meshFun2Var| |irDef| |jvmStatic| |e04naf| |rroot| + |variables| |s21baf| |string| |OMunhandledSymbol| |iisec| + |alternative?| |zCoord| |script| |scalarMatrix| |monom| |conjunction| + |outputAsTex| |nextPrimitiveNormalPoly| |hostByteOrder| |currentScope| + |readIfCan!| |linearMatrix| |lifting1| |exactQuotient| |factorial| + |prepareSubResAlgo| |getMultiplicationTable| |bothWays| + |trailingCoefficient| |s18dcf| |d01fcf| |split| |powern| |mapUp!| + |yCoordinates| |palgint| |completeEchelonBasis| |getCode| |monomials| + |partialFraction| |ReduceOrder| |tex| |leftDiscriminant| |common| + |lambda| |unit| |isPlus| |monomialIntegrate| |writeUInt8!| + |expextendedint| |reflect| |symbolTableOf| |cosSinInfo| |spherical| + |element?| |halfExtendedResultant1| |topPredicate| + |firstUncouplingMatrix| |reduced?| |commonDenominator| |df2ef| + |d03edf| |principalIdeal| |leaves| |irreducible?| |OMconnectTCP| + |setMinPoints| |midpoint| |exp| |level| |listOfLists| |credPol| + |e02dcf| |keys| |showArrayValues| GE |lyndon| |eigenvectors| |s20acf| + |jvmAbstract| |OMputVariable| |iiatanh| |mapUnivariate| |optional?| + |alternatingGroup| GT |mappingAst| |inRadical?| |car| + |symmetricTensors| |sec2cos| |bounds| |elementary| LE |inverse| + |pointColorDefault| |iidsum| |taylorRep| |f2st| |bright| + |primextendedint| |acschIfCan| |mr| |univariateSolve| |mainMonomial| + |label| |mainVariable?| |primitiveElement| + |halfExtendedSubResultantGcd1| LT |integerIfCan| |cycleRagits| + |determinant| |abs| |fullPartialFraction| |musserTrials| + |primitivePart| |vedf2vef| |badValues| |getOperator| |stirling2| + |radicalOfLeftTraceForm| |constDsolve| |lazyEvaluate| |c06ebf| + |setScreenResolution3D| |binary| |deepExpand| |startStats!| |prologue| + |balancedBinaryTree| |prem| |fTable| |computePowers| |totolex| + |parents| |iidprod| |updatD| |cot2tan| |nthExpon| |iiacot| |null| + |acotIfCan| |e02akf| |complete| |tanh2coth| |cyclicParents| + |putColorInfo| |Beta| |cAcoth| |maxRowIndex| |lazyGintegrate| SEGMENT + |not| |f07adf| |squareFreePart| |transcendenceDegree| |e02ddf| + |copies| |laurentRep| |nullary| |elaborateFile| + |semiIndiceSubResultantEuclidean| |and| |pointLists| |deref| + |prinshINFO| |setref| |arrayStack| |iiacsc| |e01baf| |notelem| + |coordinates| |or| |freeOf?| |duplicates?| |trapezoidal| |option| + |partialDenominators| |symmetricPower| |compBound| |OMsend| + |remainder| |cCsch| |hermite| |xor| |reindex| |resize| + |internalAugment| |denominators| |iiasec| |argument| |positive?| + |fortranDoubleComplex| |absolutelyIrreducible?| |lagrange| |case| + |chebyshevU| |geometric| |carriageReturn| |createZechTable| + |LyndonBasis| |s17aff| |setLabelValue| |LazardQuotient| |stFunc1| + |Zero| |squareFreePolynomial| |Lazard| |wordsForStrongGenerators| + |interpret| |redpps| |escape| |primlimitedint| |An| |submod| + |subTriSet?| |One| |s18def| |stoseLastSubResultant| |style| |dequeue| + |parseString| |isList| |complexNormalize| |closeComponent| + |nextPrimitivePoly| |genericRightMinimalPolynomial| |iifact| + |leftDivide| |byteBuffer| |problemPoints| |selectIntegrationRoutines| + |jvmSuper| |OMlistSymbols| |isPower| |lepol| |minPol| + |OMsupportsSymbol?| |dominantTerm| |contract| |leftMult| + |FormatArabic| |makeUnit| |comp| |basisOfRightNucleus| |showSummary| + |pointColor| |copy!| |att2Result| |normalDeriv| |quote| |bfEntry| + |function| |c06ecf| |gcdPolynomial| |cSin| |clip| |s21bbf| + |decomposeFunc| |airyBi| |cotIfCan| |kmax| |mapDown!| |ratpart| + |linearForm| |BasicMethod| |showAttributes| |stFuncN| |elt| + |raisePolynomial| |rational?| |rk4f| |condition| |irCtor| + |mainCharacterization| |sinhcosh| |c06gqf| |polar| |mapExponents| + |harmonic| |setsubMatrix!| |rowEchelon| |halfExtendedSubResultantGcd2| + |simplifyPower| |closed| |generalizedInverse| |ddFact| + |reduceByQuasiMonic| |eigenvalues| |initializeGroupForWordProblem| + |chiSquare| |rdHack1| |cdr| |getOrder| |cAsec| |delete| + |createLowComplexityNormalBasis| |f01qcf| |iiacsch| + |subQuasiComponent?| |chiSquare1| |solid?| |setButtonValue| + |patternVariable| |d02bbf| |rotatez| |e02zaf| |coth2trigh| |sum| + |mindeg| |currentCategoryFrame| |limitedint| |pmintegrate| |e04jaf| + |ode| |f07fdf| |rationalFunction| |numericalOptimization| + |divideExponents| |prinpolINFO| |jvmProtected| |ideal| |disjunction| + |bitLength| |lowerCase?| |characteristic| |getProperty| + |OMputEndObject| |addmod| |meshPar2Var| |f01brf| |distance| + |relationsIdeal| |e01bff| |monicCompleteDecompose| |beauzamyBound| + |multiplyCoefficients| |rationalIfCan| |readLineIfCan!| |qqq| + |realEigenvalues| |createNormalPrimitivePoly| |isOpen?| |youngDiagram| + |complexLimit| |OMgetApp| |debug| |parts| |insert| |mathieu22| + |cyclic| |solve1| |mathieu24| |belong?| |column| |c06fuf| + |interReduce| |duplicates| D |relativeApprox| |range| |lcm| + |OMopenFile| |number?| |hexDigit| |expandLog| |df2fi| + |inverseIntegralMatrix| |rangeIsFinite| |hcrf| |leviCivitaSymbol| + |unitsColorDefault| |ode1| |bottom!| |roughBasicSet| |mathieu11| + |e02daf| |newLine| |append| |sinh2csch| |lllip| |extendedEuclidean| + |sorted?| |leftZero| |baseRDE| |solid| |isAnd| |iroot| |wholeRadix| + |gcd| |semiDiscriminantEuclidean| |wronskianMatrix| |lambert| + |expenseOfEvaluation| |mainPrimitivePart| |middle| |axesColorDefault| + |hex| |permutationRepresentation| |sumSquares| |interval| |false| + |subResultantsChain| |iitan| |groebner| |complementaryBasis| + |radicalEigenvectors| |finite?| |stoseInternalLastSubResultant| + |write!| |makeCos| |hspace| |someBasis| |upperCase| |setright!| + |iiasinh| |initials| |idealiserMatrix| |compile| |cAcsch| + |strongGenerators| |primes| |coleman| |reorder| |coerceL| |readable?| + |mapExpon| |discriminantEuclidean| |jvmTransient| + |associatorDependence| |oneDimensionalArray| |quasiMonic?| |inc| + |numberOfMonomials| |rightRecip| |baseRDEsys| |d02gaf| |startTable!| + |radicalEigenvector| |redPol| |intChoose| |signAround| |s17agf| + |leftGcd| |heap| |indiceSubResultantEuclidean| |expintegrate| |even?| + |print| |getSyntaxFormsFromFile| |complexEigenvectors| + |unrankImproperPartitions0| |companionBlocks| |setPosition| |c05pbf| + |ratDsolve| |isAtom| |triangSolve| |resolve| |componentUpperBound| + |basisOfMiddleNucleus| |multinomial| |swapRows!| |leadingBasisTerm| + |binaryTournament| |cosIfCan| |dn| |OMgetEndAtp| |frobenius| + |solveLinearPolynomialEquationByFractions| |entries| + |pointColorPalette| |createIrreduciblePoly| |midpoints| |block| + |internalIntegrate| |normalizeAtInfinity| |tubeRadiusDefault| + |leadingCoefficientRicDE| |outputArgs| |UnVectorise| + |integralMatrixAtInfinity| |matrixGcd| |cCsc| |lazyIntegrate| |zoom| + |rightRank| |bytes| |cLog| |in?| |hyperelliptic| |wholePart| + |unitNormal| |lhs| |call| |vspace| |s17aef| + |indicialEquationAtInfinity| |oddlambert| |s14baf| |mathieu23| + |d01ajf| |center| |overset?| |nsqfree| |factorSFBRlcUnit| + |mainVariable| |rhs| |moreAlgebraic?| |genericLeftNorm| |legendre| + |character?| |patternMatch| |differentialVariables| |f04maf| + |linearDependenceOverZ| |sncndn| |inconsistent?| |closedCurve?| + |weighted| |viewSizeDefault| |d01alf| |solveInField| + |leastAffineMultiple| |packageCall| |squareFreeLexTriangular| |width| + |solveLinearlyOverQ| |fortranCarriageReturn| |nthCoef| |asinhIfCan| + |difference| |declare| |viewPhiDefault| |OMencodingSGML| |dmp2rfi| + |bumptab| |rk4| |sechIfCan| |subst| |outputBinaryFile| |messagePrint| + |countRealRootsMultiple| |rightOne| |xn| |bumptab1| |numFunEvals| + |s17ahf| |symmetricSquare| |fixedPoints| |irreducibleFactor| + |extractTop!| |explimitedint| |reduction| |internalLastSubResultant| + |subtractIfCan| |tanQ| |OMgetEndObject| |exprHasAlgebraicWeight| + |tanSum| |solve| |setStatus| |composite| |complexEigenvalues| + |subHeight| |reducedSystem| |ricDsolve| |initial| |branchIfCan| + |setprevious!| |getZechTable| |bombieriNorm| |ef2edf| + |createLowComplexityTable| |cAtan| |s21bdf| |algebraicCoefficients?| + |init| |mdeg| |safeFloor| |maxIndex| |maxrank| |linefeed| |objects| + |f02adf| |s20adf| |finiteBasis| |OMgetType| |restorePrecision| + |SturmHabichtCoefficients| |infinityNorm| |extractProperty| |optional| + |simplifyLog| |imagj| |base| |Aleph| |multiple?| |distribute| + |linearAssociatedOrder| |intcompBasis| |open?| |binomThmExpt| + |exprToGenUPS| |squareMatrix| |isImplies| |createNormalPoly| + |quasiAlgebraicSet| |eof?| |bivariateSLPEBR| |iiacos| |froot| + |iteratedInitials| |multiEuclidean| |trunc| |internalIntegrate0| + |createPrimitiveNormalPoly| |palgint0| |lp| + |factorSquareFreePolynomial| |startTableInvSet!| |insertBottom!| + |f01mcf| |log| |fibonacci| |nullary?| |curveColorPalette| |sparsityIF| + |multisect| |Frobenius| |bandedJacobian| |stoseInvertible?| |lintgcd| + |mkPrim| |stopTable!| |scopes| |s15aef| |leftQuotient| |printInfo| + |specialTrigs| |shape| |makeCrit| |rightExactQuotient| |scaleRoots| + |stoseInvertibleSetsqfreg| |say| |insertTop!| |cCos| |acosIfCan| + |close| |irreducibleFactors| |left| |formula| + |integralBasisAtInfinity| |primextintfrac| |overlabel| |LiePolyIfCan| + |OMputApp| |removeRedundantFactorsInContents| |atrapezoidal| + |fractRadix| |SturmHabichtMultiple| |setOfMinN| |right| + |rightMinimalPolynomial| |sizePascalTriangle| + |factorSquareFreeByRecursion| |horizConcat| |binomial| + |jordanAlgebra?| |showScalarValues| |ratPoly| |imagk| |maxColIndex| + |display| |isMult| |rowEch| |f02xef| |perspective| |f02ajf| |cache| + |trueEqual| |lexGroebner| |bezoutResultant| |hypergeometric0F1| + |acothIfCan| |OMgetEndBind| |increasePrecision| |monomRDEsys| + |lazyVariations| |positiveSolve| |polarCoordinates| |outputForm| + |clipSurface| |normalDenom| |exponential| |rangePascalTriangle| + |nrows| |palgextint0| |child| |lieAlgebra?| |rightAlternative?| + |resetAttributeButtons| |henselFact| |decreasePrecision| |expint| + |normalized?| |yellow| |ncols| |iicoth| |csc2sin| |mergeDifference| + |getMatch| |superHeight| |enterInCache| |aLinear| |doubleRank| + |f04mbf| |previous| |c05adf| |d01anf| |sturmSequence| + |numberOfImproperPartitions| |leftFactorIfCan| |clearDenominator| + |stoseSquareFreePart| |region| |iipow| |f02awf| |rCoord| |orbits| + |leaf?| |leftUnit| |setelt!| |leftRank| |LyndonCoordinates| + |binarySearchTree| |curveColor| |df2st| |atoms| |euclideanGroebner| + |shift| |cyclic?| |hMonic| |algDsolve| |clearFortranOutputStack| + |satisfy?| |setProperties| |output| |divisor| |head| + |matrixDimensions| |currentEnv| |module| |univariatePolynomials| + |gcdcofactprim| |minimumDegree| F2FG |ode2| |test| + |nextLatticePermutation| |toScale| UP2UTS |pade| |cn| + |algebraicDecompose| |diagonals| |findBinding| |viewDeltaXDefault| + |rightUnits| |PDESolve| |properties| |complexNumericIfCan| |logGamma| + |linearAssociatedExp| |aromberg| + |rewriteSetByReducingWithParticularGenerators| |symbol| + |indicialEquation| |numerator| |cartesian| |setClosed| |inrootof| + |e02baf| |translate| |odd?| |drawComplex| |gethi| |yCoord| |radix| + |expression| |isAbsolutelyIrreducible?| |splitNodeOf!| |squareFree| + |UP2ifCan| |stosePrepareSubResAlgo| |has?| |e02def| |sylvesterMatrix| + |getlo| |jvmStringConstantTag| |iprint| |integer| |dimensionsOf| + |iisech| |tableForDiscreteLogarithm| |edf2fi| + |conditionsForIdempotents| |swapColumns!| |remove| |capacity| + |message| |integralDerivationMatrix| |removeConstantTerm| |infix| + |infinite?| |exactQuotient!| |rightRankPolynomial| |s17akf| |compose| + |nextsousResultant2| |listOfMonoms| |coth2tanh| |randnum| + |basisOfLeftNucloid| |entry| |splitConstant| |OMgetFloat| |expr| + |tube| |anticoord| |last| |flexibleArray| |useEisensteinCriterion| + |readUInt8!| |seriesSolve| |polyred| |queue| |distFact| + |extendedSubResultantGcd| |s18adf| |assoc| |logIfCan| |setnext!| + |extractPoint| |gcdcofact| |algint| |paren| |overlap| + |rightTraceMatrix| |d01amf| |rightTrace| |factorsOfCyclicGroupSize| + |charpol| |infiniteProduct| |cRationalPower| + |removeRoughlyRedundantFactorsInContents| |radicalSolve| + |localIntegralBasis| |showTheSymbolTable| |factors| |f02agf| + |lazyPseudoQuotient| |socf2socdf| |linearPart| |ranges| + |wordInStrongGenerators| |fractionPart| |variable| |deleteProperty!| + |lowerCase| |s13aaf| |pushdown| |quotientByP| + |reducedContinuedFraction| |findConstructor| |checkRur| |isOp| + |iterators| |hclf| |lquo| |hexDigit?| |stronglyReduce| |seed| + |substring?| |splitLinear| |rur| |compdegd| |support| |printingInfo?| + |doubleDisc| |digits| |algebraicSort| |combineFeatureCompatibility| + |OMputAttr| |clearTable!| |irVar| |f04jgf| |unexpand| |leader| + |cyclicSubmodule| |monomRDE| |diagonalProduct| |checkPrecision| + |shallowCopy| |s17dgf| |suffix?| |top| |fintegrate| |noLinearFactor?| + |RemainderList| |drawCurves| |deriv| |parabolicCylindrical| |laplace| + |leftNorm| |continue| |rules| |measure| |startTableGcd!| |s14aaf| + |rename!| |quasiRegular| |writeLine!| |saturate| |constantRight| |nor| + |numeric| |prefix?| |edf2ef| |compound?| |normalizedAssociate| + |integrate| |characteristicPolynomial| |rubiksGroup| |cSinh| |hessian| + |radical| |const| |zeroDimPrime?| |slash| |minIndex| |iFTable| |dot| + |besselI| |subPolSet?| |root?| |pastel| |printStatement| |qPot| + |triangular?| |red| |moduleSum| |permutations| |printInfo!| + |updateStatus!| |modulus| |makeSUP| |readInt8!| |symmetric?| + |powerSum| |setRealSteps| |precision| |primintegrate| |hasSolution?| + |rightUnit| |factorList| |setScreenResolution| |sizeMultiplication| + |OMlistCDs| |alphabetic?| |lazyPseudoRemainder| |c06fqf| + |rewriteIdealWithQuasiMonicGenerators| |internalSubPolSet?| |s13acf| + |internalDecompose| |plenaryPower| |inR?| |testDim| |d01apf| |coerceP| + |separateDegrees| |invmod| |infix?| |schwerpunkt| |ldf2lst| |presuper| + |bumprow| |reducedQPowers| |decompose| |jvmFinal| |mask| + |rowEchelonLocal| |row| |ptree| |noValueMode| |mapGen| |sqfree| |bit?| + |numer| |sumOfDivisors| |one?| |makeTerm| |laguerre| + |triangularSystems| |processTemplate| |closed?| |computeCycleLength| + |denom| |negative?| |palgextint| |nthFactor| |sumOfSquares| + |makeSketch| |intersect| |divide| |setCondition!| + |expenseOfEvaluationIF| |doubleResultant| |cons| |rem| + |bivariatePolynomials| |inputOutputBinaryFile| |e04ucf| |critM| + |f02fjf| |find| |divideIfCan!| |f02wef| |pi| |returns| |algebraic?| + |quo| |thetaCoord| |mat| |frst| |rightZero| |symbol?| + |listYoungTableaus| |directory| |SturmHabichtSequence| |zeroDim?| + |infinity| |setPoly| |fortranLinkerArgs| |partialNumerators| + |factorOfDegree| |boundOfCauchy| |e01sff| |showAllElements| |cycle| + |less?| |showIntensityFunctions| |pquo| |div| |alphabetic| |randomLC| + |plotPolar| |reduceBasisAtInfinity| |Nul| |radicalEigenvalues| + |create| |polygamma| |exquo| |showTheFTable| |cycles| |uniform01| + |leftAlternative?| |polyRicDE| |zeroDimPrimary?| |kernel| + |identityMatrix| |nextPartition| |source| |purelyAlgebraic?| + |stoseIntegralLastSubResultant| ~= |elliptic?| + |createMultiplicationMatrix| |colorDef| |aQuartic| |externalList| + |f01rdf| |rightCharacteristicPolynomial| |list| |newReduc| |member?| + |#| |pToHdmp| |moduloP| |getGoodPrime| |divisors| |rootDirectory| + |any| |mainVariables| |draw| |besselK| |groebnerFactorize| |ref| ~ + |drawToScale| |graphs| |jvmIntegerConstantTag| |OMconnInDevice| + |jacobi| |subMatrix| |target| |setColumn!| |solveLinear| + |roughSubIdeal?| |curve| |goto| |splitSquarefree| |s01eaf| + |tensorProduct| |vertConcat| |groebSolve| |f04mcf| |roughBase?| + |position| |bfKeys| |maxrow| |cubic| |var2StepsDefault| |normal?| + |OMwrite| |factorByRecursion| |flexible?| |modularGcdPrimitive| + |OMputAtp| |chainSubResultants| |/\\| |removeSinSq| |identity| + |failed?| |isQuotient| |coerce| |useEisensteinCriterion?| |whitePoint| + |makeObject| |\\/| |scripted?| |createGenericMatrix| + |prepareDecompose| |twist| |enqueue!| |parametric?| |rischDEsys| + |construct| |quasiMonicPolynomials| |pointData| |rootOf| |conjug| + |coef| |setImagSteps| |janko2| |ignore?| |critT| |associatedEquations| + |possiblyNewVariety?| |cycleTail| |nextNormalPoly| |weierstrass| + |computeInt| |setMaxPoints| |normDeriv2| |explicitlyFinite?| + |trapezoidalo| |rational| |iilog| |firstNumer| |OMencodingXML| + |lastSubResultantEuclidean| |vconcat| |validExponential| |update| + |commutative?| |ParCondList| |s19abf| |ceiling| |alphanumeric?| + |writeInt8!| |removeRedundantFactorsInPols| |mix| |removeZeroes| + |fortranReal| |reverse!| |latex| |cyclicEqual?| |smith| + |algebraicVariables| |getMultiplicationMatrix| |nextIrreduciblePoly| + |height| |setAdaptive3D| |horizontalTab| |fortranInteger| + |lazyIrreducibleFactors| |before?| |dioSolve| |coord| |lprop| + |graphCurves| |addMatchRestricted| |selectSumOfSquaresRoutines| + |jvmClassConstantTag| |subResultantGcdEuclidean| |scanOneDimSubspaces| + |rewriteSetWithReduction| |sizeLess?| |tanAn| |fixedDivisor| + |selectsecond| |mainDefiningPolynomial| |round| |transform| + |composites| |viewpoint| |rspace| |newline| |getBadValues| + |normInvertible?| |numberOfComposites| |unary?| + |irreducibleRepresentation| |primintfldpoly| |OMputObject| |toroidal| + |mainCoefficients| |topFortranOutputStack| |host| |bigEndian| + |LowTriBddDenomInv| |outputSpacing| |mainExpression| |leastPower| + |polygon?| |mapmult| |cycleElt| |rootPoly| |collectQuasiMonic| + |thenBranch| |Gamma| |FormatRoman| |OMreceive| |unitCanonical| + |argumentList!| |schema| |virtualDegree| |antiCommutator| |Lazard2| + |any?| |cyclotomic| |wreath| |linkToFortran| |changeNameToObjf| + |explicitEntries?| |nthr| |degreeSubResultant| |c06eaf| |ScanRoman| + |clipWithRanges| |findCycle| |generalizedContinuumHypothesisAssumed?| + |zeroDimensional?| |light| |nil?| |unitNormalize| |diagonal| + |constantKernel| |graphImage| |nthRoot| |set| |completeHermite| + |genericRightDiscriminant| |discriminant| |reducedForm| |mantissa| + |cschIfCan| |pair?| |setlast!| |iicsch| |pushup| + |internalZeroSetSplit| |iibinom| |genus| |length| |extractClosed| + |tubeRadius| |measure2Result| |basisOfCenter| |mapSolve| |partitions| + |nonQsign| |padecf| |imagJ| |match?| |permutation| + |rootOfIrreduciblePoly| |outputFloating| |sh| |perfectSquare?| + |exprex| |setelt| |e01sef| |coefficient| |lfinfieldint| |trace2PowMod| + |cAtanh| |e02adf| |OMputBVar| |semiSubResultantGcdEuclidean1| + |jacobian| |putGraph| |coerceImages| |quartic| |graphStates| + |generalPosition| |isConnected?| |monicLeftDivide| |depth| |recur| + |semiResultantEuclidean2| |digit?| |OMputSymbol| |copy| |pleskenSplit| + |pr2dmp| |leadingExponent| |cos2sec| |antiCommutative?| |directSum| + |lieAdmissible?| |evaluate| |eisensteinIrreducible?| |stFunc2| + |setleft!| |norm| |coefChoose| |datalist| |unknown| |removeSinhSq| + |lfextlimint| |e02bef| |stopMusserTrials| |rowEchLocal| + |polynomialZeros| |pol| |autoCoerce| |refine| |cycleSplit!| + |ramifiedAtInfinity?| |dualSignature| |palgintegrate| + |mainSquareFreePart| |tail| |coordinate| |is?| |rightRemainder| + |writeBytes!| |typeList| |sts2stst| |cAsinh| |viewDeltaYDefault| + |leadingSupport| |resultant| |listConjugateBases| |preprocess| + |anfactor| |list?| |linearlyDependentOverZ?| |callForm?| + |extractSplittingLeaf| ** |elements| |iicot| |normalElement| |csubst| + |readInt16!| |s17dlf| |void| |OMputEndAttr| |leastMonomial| |airyAi| + |getButtonValue| |outputFixed| |cyclicCopy| |removeDuplicates!| + |clearTheFTable| |pointSizeDefault| |factorPolynomial| |sign| + |normalise| |quoByVar| |rootBound| |hasoln| |cTanh| |lSpaceBasis| + |retract| |tRange| |incrementKthElement| |getExplanations| + |tubePointsDefault| |representationType| |zeroVector| |backOldPos| + |cylindrical| |firstSubsetGray| |central?| |complement| + |constantCoefficientRicDE| |headReduce| |complexIntegrate| |cross| + |viewWriteAvailable| |moebiusMu| |trigs| |overbar| + |selectODEIVPRoutines| |factor1| |rootRadius| |leftTraceMatrix| + |leftCharacteristicPolynomial| |root| |moebius| + |purelyTranscendental?| |littleEndian| |logpart| |trigs2explogs| + |radicalSimplify| |monomialIntPoly| |fractionFreeGauss!| |lighting| + |omError| |front| |btwFact| |loopPoints| |fi2df| |changeVar| |pdf2df| + |OMgetString| |atanIfCan| |attributeData| |makeSeries| |cardinality| + |flatten| |conical| |univariate?| |modTree| |jvmMethodrefConstantTag| + |eulerPhi| |reduceLODE| |putProperties| |unitVector| + |screenResolution| |points| |addBadValue| |toseInvertible?| + |rewriteIdealWithHeadRemainder| |cothIfCan| |high| |besselJ| |prime| + |bindings| |selectMultiDimensionalRoutines| |jvmInterface| + |semiSubResultantGcdEuclidean2| |completeHensel| |elseBranch| |cSec| + |groebgen| |idealSimplify| |retractIfCan| |monicDecomposeIfCan| + |leadingIndex| |cCosh| |failed| |nary?| |pointPlot| |setTopPredicate| + |createRandomElement| |rotatex| |error| |useSingleFactorBound| + |makeprod| |double| |selectOptimizationRoutines| |diagonalMatrix| + |quadraticForm| |indicialEquations| |limitPlus| |factorAndSplit| + |singRicDE| |nthExponent| |generalSqFr| |chebyshevT| |asinIfCan| + |scan| |collectUnder| |top!| + |solveLinearPolynomialEquationByRecursion| |palgLODE| + |primPartElseUnitCanonical| |redPo| |plot| |LiePoly| |RittWuCompare| + |biRank| |denomLODE| |integer?| |constantToUnaryFunction| + |monicRightDivide| |divisorCascade| |returnTypeOf| |iisinh| + |buildSyntax| |component| |birth| |mightHaveRoots| + |createMultiplicationTable| |showTheIFTable| |dec| |recip| + |appendPoint| |generalTwoFactor| |remove!| |stripCommentsAndBlanks| + |readByte!| |usingTable?| |check| |coefficients| |rootSimp| |addMatch| + |OMgetEndBVar| |cosh2sech| |leftReducedSystem| |truncate| + |generalizedEigenvectors| |expintfldpoly| |factorset| + |maximumExponent| |outerProduct| |cyclePartition| |symmetricGroup| + |reopen!| |viewWriteDefault| |recolor| |drawComplexVectorField| |ord| + |gradient| |setStatus!| |e02bdf| |endSubProgram| |romberg| + |initTable!| |padicFraction| |multiplyExponents| |taylor| + |inverseIntegralMatrixAtInfinity| |OMgetInteger| |rightMult| + |linSolve| |declare!| |graphState| |basis| |arbitrary| |symbolIfCan| + |quotedOperators| |infRittWu?| |operators| |commutator| |laurent| + |dihedral| |lazyPremWithDefault| |option?| |showAll?| |eval| + |mainMonomials| |withPredicates| |byte| |singular?| |superscript| + |kroneckerDelta| |create3Space| |puiseux| |heapSort| + |selectAndPolynomials| |iiacoth| |swap!| |setErrorBound| + |OMUnknownSymbol?| |leftExtendedGcd| |ScanFloatIgnoreSpacesIfCan| + |commaSeparate| |droot| |stop| |s17dcf| |f02aaf| |invertibleSet| + |powerAssociative?| |safeCeiling| |laplacian| |repeating?| |s17def| + |semicolonSeparate| |inv| |OMgetBind| |rewriteIdealWithRemainder| + |nullSpace| |subSet| |fortranLogical| |bipolarCylindrical| + |primlimintfrac| |karatsubaDivide| FG2F |subspace| |ground?| |zero| + |f04faf| |empty| |c06ekf| |leftTrace| |exprToXXP| |f2df| + |stronglyReduced?| |ground| |setClipValue| |maxPoints3D| |reverseLex| + |pole?| |sortConstraints| |typeForm| |f02aff| |OMParseError?| + |neglist| |sylvesterSequence| |linGenPos| |leadingMonomial| + |removeCoshSq| |And| |optAttributes| |makingStats?| |segment| + |minPoly| |permutationGroup| |normalForm| |imagK| LODO2FUN + |extractBottom!| |leadingCoefficient| |meshPar1Var| |Or| |iisqrt2| + |linearlyDependent?| |cSech| |mulmod| |numberOfDivisors| |int| + |tanIfCan| |primitiveMonomials| F |setMinPoints3D| |Not| + |selectFiniteRoutines| |divideIfCan| |s15adf| |linearElement| + |OMsetEncoding| |bernoulliB| |reducedDiscriminant| |reductum| + |integers| |addPoint2| |ocf2ocdf| |substitute| |groebnerIdeal| + |leftRegularRepresentation| |matrix| |OMgetEndAttr| |divergence| + |conjugate| |parabolic| |curry| |firstDenom| + |zeroSetSplitIntoTriangularSystems| |linearPolynomials| |opeval| + |var1StepsDefault| |fullDisplay| |max| |jvmVolatile| + |doubleFloatFormat| |sort!| |denomRicDE| |associates?| |selectfirst| + |rightLcm| |extractIfCan| |basisOfRightNucloid| + |tryFunctionalDecomposition?| |unrankImproperPartitions1| |mainValue| + |select| |lex| |diagonal?| |nextColeman| |nil| |symmetricProduct| + |cfirst| |cscIfCan| |fortranTypeOf| |factorials| |dictionary| + |degreePartition| |LyndonWordsList| |minordet| |iisqrt3| |totalfract| + |localReal?| |open| |mvar| |pop!| |zeroOf| |insertMatch| |pomopo!| + |fortranComplex| |hasHi| |summation| |minus!| |readLine!| |binaryTree| + |trim| |polCase| |bezoutDiscriminant| |principal?| |xCoord| |back| + |approximate| |elRow2!| |removeZero| |sturmVariationsOf| |viewport3D| + |ellipticCylindrical| |complex| |arguments| |weights| |enumerate| + |critB| |internal?| |semiDegreeSubResultantEuclidean| |bat| + |setLegalFortranSourceExtensions| |genericRightNorm| |setOrder| + |comment| |clipPointsDefault| |setDifference| |algebraicOf| + |evenInfiniteProduct| |compactFraction| |operations| |primaryDecomp| + |OMgetBVar| |Is| |makeRecord| |screenResolution3D| |imaginary| + |f02akf| |tree| |inGroundField?| |inputBinaryFile| |pToDmp| |dom| + |table| |laguerreL| |areEquivalent?| |exportedOperators| + |bandedHessian| |rightNorm| |applyRules| |setAttributeButtonStep| + |binding| |eigenvector| |mainForm| |obj| |new| |iflist2Result| + |fortranCharacter| |lexTriangular| |predicates| + |removeIrreducibleRedundantFactors| |systemSizeIF| |wrregime| + |coshIfCan| |rk4qc| |numberOfComponents| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 3cd9c6c9..94e8cf77 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,1210 +1,1210 @@ -(3473074 . 3508838164) -((-1860 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-4235 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3986 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1266 (-560)) |#2|) 44 T ELT)) (-1518 (($ $) 80 T ELT)) (-1995 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3817 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-3086 (((-663 |#2|) $) 13 T ELT)) (-1762 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2173 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-1793 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-4233 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3237 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-1723 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-3034 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1266 (-560))) 66 T ELT)) (-3032 (($ $ (-560)) 76 T ELT) (($ $ (-1266 (-560))) 75 T ELT)) (-1485 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-1352 (($ $ $ (-560)) 69 T ELT)) (-4007 (($ $) 68 T ELT)) (-3845 (($ (-663 |#2|)) 73 T ELT)) (-2465 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-3834 (((-888) $) 92 T ELT)) (-3894 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2478 (((-114) $ $) 95 T ELT)) (-2499 (((-114) $ $) 99 T ELT))) -(((-18 |#1| |#2|) (-10 -8 (-15 -2478 ((-114) |#1| |#1|)) (-15 -3834 ((-888) |#1|)) (-15 -2499 ((-114) |#1| |#1|)) (-15 -4235 (|#1| |#1|)) (-15 -4235 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -1518 (|#1| |#1|)) (-15 -1352 (|#1| |#1| |#1| (-560))) (-15 -1860 ((-114) |#1|)) (-15 -1762 (|#1| |#1| |#1|)) (-15 -3817 ((-560) |#2| |#1| (-560))) (-15 -3817 ((-560) |#2| |#1|)) (-15 -3817 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -1860 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -1762 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -3986 (|#2| |#1| (-1266 (-560)) |#2|)) (-15 -4233 (|#1| |#1| |#1| (-560))) (-15 -4233 (|#1| |#2| |#1| (-560))) (-15 -3032 (|#1| |#1| (-1266 (-560)))) (-15 -3032 (|#1| |#1| (-560))) (-15 -1793 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -2465 (|#1| (-663 |#1|))) (-15 -2465 (|#1| |#1| |#1|)) (-15 -2465 (|#1| |#2| |#1|)) (-15 -2465 (|#1| |#1| |#2|)) (-15 -3034 (|#1| |#1| (-1266 (-560)))) (-15 -3845 (|#1| (-663 |#2|))) (-15 -3237 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3034 (|#2| |#1| (-560))) (-15 -3034 (|#2| |#1| (-560) |#2|)) (-15 -3986 (|#2| |#1| (-560) |#2|)) (-15 -1485 ((-793) |#2| |#1|)) (-15 -3086 ((-663 |#2|) |#1|)) (-15 -1485 ((-793) (-1 (-114) |#2|) |#1|)) (-15 -1723 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -3894 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2173 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1793 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4007 (|#1| |#1|))) (-19 |#2|) (-1249)) (T -18)) +(3472990 . 3508891751) +((-3076 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-4387 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3998 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1266 (-560)) |#2|) 44 T ELT)) (-3881 (($ $) 80 T ELT)) (-2034 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3814 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-3041 (((-663 |#2|) $) 13 T ELT)) (-1379 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2193 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-1853 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-3042 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3721 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-2224 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-2962 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1266 (-560))) 66 T ELT)) (-2989 (($ $ (-560)) 76 T ELT) (($ $ (-1266 (-560))) 75 T ELT)) (-1523 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-2532 (($ $ $ (-560)) 69 T ELT)) (-4020 (($ $) 68 T ELT)) (-3843 (($ (-663 |#2|)) 73 T ELT)) (-2451 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-3831 (((-888) $) 92 T ELT)) (-3946 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2430 (((-114) $ $) 95 T ELT)) (-2452 (((-114) $ $) 99 T ELT))) +(((-18 |#1| |#2|) (-10 -8 (-15 -2430 ((-114) |#1| |#1|)) (-15 -3831 ((-888) |#1|)) (-15 -2452 ((-114) |#1| |#1|)) (-15 -4387 (|#1| |#1|)) (-15 -4387 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -3881 (|#1| |#1|)) (-15 -2532 (|#1| |#1| |#1| (-560))) (-15 -3076 ((-114) |#1|)) (-15 -1379 (|#1| |#1| |#1|)) (-15 -3814 ((-560) |#2| |#1| (-560))) (-15 -3814 ((-560) |#2| |#1|)) (-15 -3814 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -3076 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -1379 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -3998 (|#2| |#1| (-1266 (-560)) |#2|)) (-15 -3042 (|#1| |#1| |#1| (-560))) (-15 -3042 (|#1| |#2| |#1| (-560))) (-15 -2989 (|#1| |#1| (-1266 (-560)))) (-15 -2989 (|#1| |#1| (-560))) (-15 -1853 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -2451 (|#1| (-663 |#1|))) (-15 -2451 (|#1| |#1| |#1|)) (-15 -2451 (|#1| |#2| |#1|)) (-15 -2451 (|#1| |#1| |#2|)) (-15 -2962 (|#1| |#1| (-1266 (-560)))) (-15 -3843 (|#1| (-663 |#2|))) (-15 -3721 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -2034 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2034 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2034 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2962 (|#2| |#1| (-560))) (-15 -2962 (|#2| |#1| (-560) |#2|)) (-15 -3998 (|#2| |#1| (-560) |#2|)) (-15 -1523 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T) ((-107 #0=(-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((-102) -2309 (|has| |#2| (-1133)) (|has| |#2| (-102)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-102))) ((-632 (-888)) -2309 (|has| |#2| (-1133)) (|has| |#2| (-632 (-888))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-632 (-888)))) ((-153 #1=(-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1266 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . T) ((-321 #1#) -12 (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-294 #1#) . T) ((-385 #1#) . T) ((-503 #1#) . T) ((-503 |#2|) . T) ((-618 #2# #1#) . T) ((-618 |#1| |#2|) . T) ((-528 #1# #1#) -12 (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-629 |#1| |#2|) . T) ((-673 #1#) . T) ((-688 #1#) . T) ((-872) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) ((-875) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) ((-1042 #1#) . T) ((-1133) -2309 (|has| |#2| (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872))) ((-1182 #1#) . T) ((-1226 |#1| |#2|) . T) ((-1249) . T) ((-1288 #1#) . 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T) ((-107 #0=(-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T) ((-102) -2277 (|has| |#2| (-1133)) (|has| |#2| (-102)) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-1133)) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-872)) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-102))) ((-632 (-888)) -2277 (|has| |#2| (-1133)) (|has| |#2| (-632 (-888))) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-1133)) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-872)) (|has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-632 (-888)))) ((-153 #1=(-2 (|:| -1966 |#1|) (|:| -3519 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -1966 |#1|) (|:| -3519 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1266 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2309 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -2309 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2309 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2309 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . 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T) ((-922 $ #3=(-1209)) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #3#) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) |has| |#1| (-912 (-391))) ((-912 (-560)) |has| |#1| (-912 (-560))) ((-910 |#1|) . T) ((-940) -12 (|has| |#1| (-319)) (|has| |#1| (-940))) ((-951) -2309 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1034) -12 (|has| |#1| (-1034)) (|has| |#1| (-1235))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #0#) -2309 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #0#) -2309 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1235) |has| |#1| (-1235)) ((-1238) |has| |#1| (-1235)) ((-1249) . 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(-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3882 (((-1191) $) NIL T ELT)) (-1511 (((-1152) $) NIL T ELT)) (-3831 (((-888) $) NIL T ELT)) (-3893 (((-114) $ $) NIL T ELT)) (-2430 (((-114) $ $) NIL T ELT))) (((-198) (-809)) (T -198)) NIL (-809) -((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 63 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 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(-229)))) NIL T ELT)) (-3882 (((-1191) $) NIL T ELT)) (-1511 (((-1152) $) NIL T ELT)) (-3831 (((-888) $) NIL T ELT)) (-3893 (((-114) $ $) NIL T ELT)) (-2430 (((-114) $ $) NIL T ELT))) (((-199) (-809)) (T -199)) NIL (-809) -((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 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$ $) NIL T ELT))) (((-202) (-809)) (T -202)) NIL (-809) -((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 78 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T 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T) ((-102) -2277 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|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|) -2277 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2277 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -2277 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -2277 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . T) ((-236 $) -2277 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-234 |#2|) |has| |#2| (-1081)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1081))) ((-239) -2277 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-274 |#2|) |has| |#2| (-1081)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1081)) ((-426 |#2|) |has| |#2| (-1133)) ((-503 |#2|) . T) ((-618 #1# |#2|) . 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T) ((-175) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -2309 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2309 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2309 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-3808 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-2164 ((|#1| $) 61 T ELT)) (-3612 ((|#1| $) 51 T ELT)) (-4405 (((-114) $ (-793)) 8 T ELT)) (-4489 (($) 7 T CONST)) (-1932 (($ $) 67 T ELT)) (-1518 (($ $) 55 T ELT)) (-2786 ((|#1| |#1| $) 53 T ELT)) (-1750 ((|#1| $) 52 T ELT)) (-3086 (((-663 |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-3050 (((-114) $ (-793)) 9 T ELT)) (-4439 (((-663 |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-3243 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-2173 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4511)) ELT)) (-1793 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-1506 (((-114) $ (-793)) 10 T ELT)) (-3970 (((-793) $) 68 T ELT)) (-2128 (((-1191) $) 25 (|has| |#1| (-1133)) ELT)) (-3471 ((|#1| $) 46 T ELT)) (-2210 ((|#1| |#1| $) 59 T ELT)) (-1476 ((|#1| |#1| $) 58 T ELT)) (-3549 (($ |#1| $) 47 T ELT)) (-3886 (((-793) $) 62 T ELT)) (-1473 (((-1152) $) 24 (|has| |#1| (-1133)) ELT)) (-3279 ((|#1| $) 69 T ELT)) (-3001 ((|#1| $) 57 T ELT)) (-1743 ((|#1| $) 56 T ELT)) (-3194 ((|#1| $) 48 T ELT)) (-1723 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4510)) ELT)) (-4265 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-3470 (((-114) $ $) 14 T ELT)) (-2797 ((|#1| |#1| $) 65 T ELT)) (-4150 (((-114) $) 11 T ELT)) (-3614 (($) 12 T ELT)) (-1702 ((|#1| $) 66 T ELT)) (-2297 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-4003 (((-793) $) 50 T ELT)) (-1485 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-4007 (($ $) 13 T ELT)) (-3834 (((-888) $) 20 (|has| |#1| (-632 (-888))) ELT)) (-2651 ((|#1| $) 60 T ELT)) (-1519 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-1619 (($ (-663 |#1|)) 49 T ELT)) (-3815 ((|#1| $) 70 T ELT)) (-3894 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4510)) ELT)) (-2478 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-3819 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) +((-2470 (*1 *2 *3) (-12 (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-3207 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 *4)))) (-1804 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1804 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1555 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-4440 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-2540 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-4440 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-2540 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1344 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-114)))) (-3593 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-817)) (-4 *2 (-277 *4)))) (-3261 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-2167 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-2470 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-980 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1070 |t#2|) (-10 -8 (-15 -2470 ((-1 $ (-793)) |t#2|)) (-15 -3207 ((-663 |t#2|) $)) (-15 -1804 ((-793) $ |t#2|)) (-15 -1804 ((-793) $)) (-15 -1555 ((-793) $ |t#2|)) (-15 -4440 ((-663 (-793)) $)) (-15 -2540 ((-793) $)) (-15 -4440 ((-663 (-793)) $ |t#2|)) (-15 -2540 ((-793) $ |t#2|)) (-15 -1344 ((-114) $)) (-15 -3593 (|t#3| $)) (-15 -3261 ($ $)) (-15 -2167 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -2470 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2277 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -2277 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2277 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2277 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -2277 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -2277 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) +((-3771 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-4194 ((|#1| $) 61 T ELT)) (-3601 ((|#1| $) 51 T ELT)) (-2297 (((-114) $ (-793)) 8 T ELT)) (-1865 (($) 7 T CONST)) (-2534 (($ $) 67 T ELT)) (-3881 (($ $) 55 T ELT)) (-1863 ((|#1| |#1| $) 53 T ELT)) (-4416 ((|#1| $) 52 T ELT)) (-3041 (((-663 |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-2495 (((-114) $ (-793)) 9 T ELT)) (-2599 (((-663 |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-3781 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-2193 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4511)) ELT)) (-1853 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-3746 (((-114) $ (-793)) 10 T ELT)) (-3981 (((-793) $) 68 T ELT)) (-3882 (((-1191) $) 25 (|has| |#1| (-1133)) ELT)) (-2298 ((|#1| $) 46 T ELT)) (-3340 ((|#1| |#1| $) 59 T ELT)) (-3315 ((|#1| |#1| $) 58 T ELT)) (-1794 (($ |#1| $) 47 T ELT)) (-3888 (((-793) $) 62 T ELT)) (-1511 (((-1152) $) 24 (|has| |#1| (-1133)) ELT)) (-4129 ((|#1| $) 69 T ELT)) (-3245 ((|#1| $) 57 T ELT)) (-4343 ((|#1| $) 56 T ELT)) (-1416 ((|#1| $) 48 T ELT)) (-2224 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4510)) ELT)) (-4271 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-2289 (((-114) $ $) 14 T ELT)) (-3840 ((|#1| |#1| $) 65 T ELT)) (-1636 (((-114) $) 11 T ELT)) (-4314 (($) 12 T ELT)) (-2012 ((|#1| $) 66 T ELT)) (-2914 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-4015 (((-793) $) 50 T ELT)) (-1523 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-4020 (($ $) 13 T ELT)) (-3831 (((-888) $) 20 (|has| |#1| (-632 (-888))) ELT)) (-3067 ((|#1| $) 60 T ELT)) (-3893 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-2429 (($ (-663 |#1|)) 49 T ELT)) (-4431 ((|#1| $) 70 T ELT)) (-3946 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4510)) ELT)) (-2430 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-3782 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) (((-263 |#1|) (-142) (-1249)) (T -263)) -((-2297 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-2297 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-4 *1 (-263 *3)))) (-3886 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1249)) (-5 *2 (-793)))) (-2164 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-2651 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-2210 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1476 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-3001 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1743 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1518 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) -(-13 (-1153 |t#1|) (-1027 |t#1|) (-10 -8 (-15 -2297 ($)) (-15 -2297 ($ (-663 |t#1|))) (-15 -3886 ((-793) $)) (-15 -2164 (|t#1| $)) (-15 -2651 (|t#1| $)) (-15 -2210 (|t#1| |t#1| $)) (-15 -1476 (|t#1| |t#1| $)) (-15 -3001 (|t#1| $)) (-15 -1743 (|t#1| $)) (-15 -1518 ($ $)))) -(((-34) . T) ((-107 |#1|) . T) ((-102) -2309 (|has| |#1| (-1133)) (|has| |#1| (-102))) ((-632 (-888)) -2309 (|has| |#1| (-1133)) (|has| |#1| (-632 (-888)))) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-503 |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-1027 |#1|) . T) ((-1133) |has| |#1| (-1133)) ((-1153 |#1|) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -2277 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -2277 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -2277 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -2277 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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|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| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3054 (-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 -3519 ((-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| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3054 (-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| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) (T -574)) +((-3519 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3054 (-1121 (-866 (-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| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3054 (-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 (-574)))) (-3164 (*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| -1966 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -3519 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity 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|notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3054 (-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 (-574)))) (-2825 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -1966 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -3519 (-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 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T) ((-528 (-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) . T) ((-668 #0#) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) . T) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) . T) ((-739 |#1|) . T) ((-739 $) . T) ((-748) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2309 (|has| |#1| (-571)) (|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)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2277 (|has| |#1| (-571)) (|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)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -2277 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -2277 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -2277 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -2277 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -2277 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2309 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2309 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . 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$)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2277 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2277 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2277 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -2277 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2277 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . 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T) ((-662 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1070 |#2|) . T) ((-1083 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1278 |#1| #0#) . T) ((-1282 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-421 (-560)) (-1144)) ((-302) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-376) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1070 |#2|) . T) ((-1083 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2277 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 $) -2277 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1278 |#1| #0#) . T) ((-1282 |#1|) . 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T) ((-1083 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2277 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-888)) . T) ((-175) -2277 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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NIL NIL) (-1226 3109423 3116189 3116245 "TBAGG" 3116645 NIL TBAGG (NIL T T) -9 NIL 3116856 NIL) (-1225 3104307 3105981 3107735 "TBAGG-" 3107740 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103673 3103798 3103943 "TANEXP" 3104196 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103124 3103448 3103538 "TALGOP" 3103618 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102518 3102635 3102773 "TABLEAU" 3103021 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095532 3102375 3102468 "TABLE" 3102473 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3090062 3091360 3092608 "TABLBUMP" 3094318 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089272 3089431 3089612 "SYSTEM" 3089903 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085677 3086430 3087213 "SYSSOLP" 3088523 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085439 3085632 3085663 "SYSPTR" 3085668 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084278 3084970 3085096 "SYSNNI" 3085282 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085374) (-1215 3083485 3084040 3084119 "SYSINT" 3084179 NIL SYSINT (NIL NIL) -8 NIL NIL 3084224) (-1214 3079583 3080763 3081473 "SYNTAX" 3082797 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076663 3077343 3077975 "SYMTAB" 3078973 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071762 3072814 3073797 "SYMS" 3075702 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068668 3071213 3071446 "SYMPOLY" 3071564 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068173 3068260 3068383 "SYMFUNC" 3068580 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063971 3065485 3066298 "SYMBOL" 3067382 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057444 3059199 3060919 "SWITCH" 3062273 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050205 3056400 3056694 "SUTS" 3057208 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041697 3049587 3049851 "SUPXS" 3049999 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040844 3040983 3041200 "SUPFRACF" 3041565 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040459 3040524 3040637 "SUP2" 3040779 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3031003 3040077 3040203 "SUP" 3040368 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029427 3029725 3030081 "SUMRF" 3030702 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028750 3028828 3029020 "SUMFS" 3029348 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010616 3028062 3028304 "SULS" 3028566 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010164 3010438 3010508 "SUCHTAST" 3010568 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009405 3009689 3009829 "SUCH" 3010072 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3003044 3004311 3005270 "SUBSPACE" 3008493 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002464 3002564 3002728 "SUBRESP" 3002932 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996475 2997757 2998904 "STTFNC" 3001364 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989669 2991140 2992451 "STTF" 2995211 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980786 2982851 2984645 "STTAYLOR" 2987910 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973540 2980650 2980733 "STRTBL" 2980738 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967937 2973249 2973348 "STRING" 2973463 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967441 2967524 2967668 "STREAM3" 2967854 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966405 2966606 2966841 "STREAM2" 2967254 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2966087 2966145 2966238 "STREAM1" 2966347 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958201 2963706 2964317 "STREAM" 2965511 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957193 2957398 2957629 "STINPROD" 2958017 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956308 2956682 2956830 "STEPAST" 2957067 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955804 2956049 2956079 "STEP" 2956173 T STEP (NIL) -9 NIL 2956244 NIL) (-1183 2948860 2955703 2955780 "STBL" 2955785 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943410 2948023 2948066 "STAGG" 2948219 NIL STAGG (NIL T) -9 NIL 2948308 NIL) (-1181 2940962 2941714 2942586 "STAGG-" 2942591 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938934 2940732 2940824 "STACK" 2940905 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938251 2938764 2938794 "SRING" 2938799 T SRING (NIL) -9 NIL 2938819 NIL) (-1178 2930258 2936392 2936848 "SREGSET" 2937881 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922605 2924052 2925565 "SRDCMPK" 2928864 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914905 2919964 2919994 "SRAGG" 2921297 T SRAGG (NIL) -9 NIL 2921905 NIL) (-1175 2913856 2914177 2914556 "SRAGG-" 2914561 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907440 2912803 2913224 "SQMATRIX" 2913482 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900852 2904158 2904885 "SPLTREE" 2906785 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896677 2897508 2898154 "SPLNODE" 2900278 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895652 2895957 2895987 "SPFCAT" 2896431 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894347 2894599 2894863 "SPECOUT" 2895410 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884993 2887311 2887341 "SPADXPT" 2892019 T SPADXPT (NIL) -9 NIL 2894185 NIL) (-1168 2884748 2884794 2884863 "SPADPRSR" 2884946 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882351 2884703 2884734 "SPADAST" 2884739 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873952 2876055 2876098 "SPACEC" 2880471 NIL SPACEC (NIL T) -9 NIL 2882287 NIL) (-1165 2871752 2873884 2873933 "SPACE3" 2873938 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870484 2870675 2870966 "SORTPAK" 2871557 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868546 2868879 2869291 "SOLVETRA" 2870148 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867584 2867818 2868079 "SOLVESER" 2868319 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862816 2863776 2864771 "SOLVERAD" 2866636 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858541 2859240 2859969 "SOLVEFOR" 2862183 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852145 2857889 2857986 "SNTSCAT" 2857991 NIL SNTSCAT (NIL T T T T) -9 NIL 2858061 NIL) (-1158 2845696 2850468 2850859 "SMTS" 2851835 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839418 2845584 2845661 "SMP" 2845666 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837547 2837878 2838276 "SMITH" 2839115 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2829072 2834126 2834229 "SMATCAT" 2835580 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836130 NIL) (-1154 2825844 2826835 2828013 "SMATCAT-" 2828018 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823313 2825052 2825095 "SKAGG" 2825356 NIL SKAGG (NIL T) -9 NIL 2825491 NIL) (-1152 2818831 2822796 2822973 "SINT" 2823125 T SINT (NIL) -8 NIL NIL 2823280) (-1151 2818597 2818641 2818707 "SIMPAN" 2818787 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817417 2817656 2817931 "SIGNRF" 2818356 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816232 2816401 2816685 "SIGNEF" 2817246 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815472 2815815 2815939 "SIGAST" 2816130 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814697 2815007 2815147 "SIG" 2815354 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812349 2812841 2813347 "SHP" 2814238 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805673 2812250 2812326 "SHDP" 2812331 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805184 2805424 2805454 "SGROUP" 2805547 T SGROUP (NIL) -9 NIL 2805609 NIL) (-1143 2805036 2805068 2805141 "SGROUP-" 2805146 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801755 2802525 2803248 "SGCF" 2804335 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795457 2801201 2801298 "SFRTCAT" 2801303 NIL SFRTCAT (NIL T T T T) -9 NIL 2801342 NIL) (-1140 2788776 2789896 2791032 "SFRGCD" 2794440 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781794 2782975 2784161 "SFQCMPK" 2787709 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781396 2781503 2781614 "SFORT" 2781735 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780322 2781236 2781357 "SEXOF" 2781362 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775911 2776818 2776913 "SEXCAT" 2779535 NIL SEXCAT (NIL T T T T T) -9 NIL 2780095 NIL) (-1135 2774826 2775792 2775860 "SEX" 2775865 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772948 2773539 2773844 "SETMN" 2774567 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772478 2772666 2772696 "SETCAT" 2772813 T SETCAT (NIL) -9 NIL 2772898 NIL) (-1132 2772246 2772310 2772409 "SETCAT-" 2772414 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768349 2770707 2770750 "SETAGG" 2771620 NIL SETAGG (NIL T) -9 NIL 2771960 NIL) (-1130 2767771 2767923 2768160 "SETAGG-" 2768165 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764580 2767705 2767753 "SET" 2767758 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763963 2764276 2764377 "SEQAST" 2764501 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763090 2763456 2763517 "SEGXCAT" 2763803 NIL SEGXCAT (NIL T T) -9 NIL 2763923 NIL) (-1126 2762015 2762283 2762326 "SEGCAT" 2762848 NIL SEGCAT (NIL T) -9 NIL 2763069 NIL) (-1125 2761630 2761695 2761808 "SEGBIND2" 2761950 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760520 2760993 2761201 "SEGBIND" 2761457 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2760039 2760321 2760398 "SEGAST" 2760465 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759248 2759384 2759588 "SEG2" 2759883 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758164 2758914 2759096 "SEG" 2759101 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757397 2758099 2758146 "SDVAR" 2758151 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748755 2757167 2757297 "SDPOL" 2757302 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747324 2747614 2747933 "SCPKG" 2748470 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746446 2746660 2746852 "SCOPE" 2747154 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745642 2745800 2745979 "SCACHE" 2746301 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745226 2745460 2745490 "SASTCAT" 2745495 T SASTCAT (NIL) -9 NIL 2745508 NIL) (-1114 2744629 2745061 2745137 "SAOS" 2745172 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744188 2744229 2744402 "SAERFFC" 2744588 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743775 2743816 2743975 "SAEFACT" 2744147 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736823 2743672 2743752 "SAE" 2743757 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735126 2735458 2735859 "RURPK" 2736489 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733703 2734069 2734374 "RULESET" 2734960 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733273 2733497 2733580 "RULECOLD" 2733655 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730388 2731026 2731484 "RULE" 2732954 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730172 2730206 2730277 "RTVALUE" 2730339 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729583 2729889 2729983 "RSTRCAST" 2730100 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724353 2725226 2726146 "RSETGCD" 2728782 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712917 2718661 2718758 "RSETCAT" 2722877 NIL RSETCAT (NIL T T T T) -9 NIL 2723974 NIL) (-1102 2710736 2711383 2712207 "RSETCAT-" 2712212 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2703044 2704498 2706018 "RSDCMPK" 2709335 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700913 2701476 2701550 "RRCC" 2702636 NIL RRCC (NIL T T) -9 NIL 2702980 NIL) (-1099 2700234 2700438 2700717 "RRCC-" 2700722 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699617 2699930 2700031 "RPTAST" 2700155 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2672003 2682729 2682796 "RPOLCAT" 2693462 NIL RPOLCAT (NIL T T T) -9 NIL 2696622 NIL) (-1096 2662973 2665841 2668963 "RPOLCAT-" 2668968 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653426 2661184 2661666 "ROUTINE" 2662513 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649489 2653052 2653192 "ROMAN" 2653308 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647601 2648349 2648609 "ROIRC" 2649294 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643321 2646090 2646120 "RNS" 2646424 T RNS (NIL) -9 NIL 2646698 NIL) (-1091 2641728 2642213 2642747 "RNS-" 2642822 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640689 2641093 2641295 "RNGBIND" 2641579 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639982 2640486 2640516 "RNG" 2640521 T RNG (NIL) -9 NIL 2640542 NIL) (-1088 2639277 2639755 2639798 "RMODULE" 2639803 NIL RMODULE (NIL T) -9 NIL 2639830 NIL) (-1087 2638101 2638207 2638543 "RMCAT2" 2639178 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634603 2637447 2637744 "RMATRIX" 2637863 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627102 2629690 2629805 "RMATCAT" 2633164 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634146 NIL) (-1084 2626441 2626624 2626931 "RMATCAT-" 2626936 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2626014 2626228 2626271 "RLINSET" 2626333 NIL RLINSET (NIL T) -9 NIL 2626377 NIL) (-1082 2625575 2625656 2625784 "RINTERP" 2625933 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624499 2625173 2625203 "RING" 2625259 T RING (NIL) -9 NIL 2625351 NIL) (-1080 2624279 2624335 2624432 "RING-" 2624437 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623090 2623357 2623615 "RIDIST" 2624043 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613715 2622558 2622764 "RGCHAIN" 2622938 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612973 2613457 2613498 "RGBCSPC" 2613556 NIL RGBCSPC (NIL T) -9 NIL 2613608 NIL) (-1076 2612039 2612498 2612539 "RGBCMDL" 2612771 NIL RGBCMDL (NIL T) -9 NIL 2612885 NIL) (-1075 2611679 2611748 2611851 "RFFACTOR" 2611970 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611398 2611439 2611536 "RFFACT" 2611638 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609449 2609879 2610261 "RFDIST" 2611038 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606389 2607057 2607727 "RF" 2608813 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605836 2605934 2606097 "RETSOL" 2606291 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605454 2605552 2605595 "RETRACT" 2605728 NIL RETRACT (NIL T) -9 NIL 2605815 NIL) (-1069 2605297 2605328 2605415 "RETRACT-" 2605420 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604845 2605119 2605189 "RETAST" 2605249 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597195 2604498 2604625 "RESULT" 2604740 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595630 2596464 2596663 "RESRING" 2597098 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595254 2595315 2595413 "RESLATC" 2595567 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594953 2594994 2595101 "REPSQ" 2595213 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594644 2594685 2594796 "REPDB" 2594912 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588476 2589933 2591156 "REP2" 2593456 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584779 2585534 2586342 "REP1" 2587703 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582159 2582781 2583383 "REP" 2584199 T REP (NIL) -7 NIL NIL NIL) (-1059 2574167 2580300 2580756 "REGSET" 2581789 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572876 2573315 2573565 "REF" 2573952 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572241 2572356 2572523 "REDORDER" 2572760 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567612 2571454 2571681 "RECLOS" 2572069 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566646 2566845 2567060 "REALSOLV" 2567419 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563093 2563931 2564815 "REAL0Q" 2565811 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558646 2559682 2560743 "REAL0" 2562074 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558480 2558533 2558563 "REAL" 2558568 T REAL (NIL) -9 NIL 2558603 NIL) (-1051 2557891 2558197 2558291 "RDUCEAST" 2558408 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557290 2557368 2557575 "RDIV" 2557813 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556340 2556532 2556745 "RDIST" 2557112 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554925 2555224 2555596 "RDETRS" 2556048 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552719 2553191 2553729 "RDETR" 2554467 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551338 2551622 2552019 "RDEEFS" 2552435 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549841 2550153 2550578 "RDEEF" 2551026 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543320 2546795 2546825 "RCFIELD" 2548120 T RCFIELD (NIL) -9 NIL 2548851 NIL) (-1043 2541276 2541888 2542584 "RCFIELD-" 2542659 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537328 2539349 2539392 "RCAGG" 2540476 NIL RCAGG (NIL T) -9 NIL 2540941 NIL) (-1041 2536938 2537050 2537213 "RCAGG-" 2537218 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536255 2536385 2536550 "RATRET" 2536822 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535796 2535875 2535996 "RATFACT" 2536183 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2535074 2535224 2535376 "RANDSRC" 2535666 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534802 2534852 2534925 "RADUTIL" 2535023 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526947 2533633 2533944 "RADIX" 2534525 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516562 2526789 2526919 "RADFF" 2526924 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516191 2516284 2516314 "RADCAT" 2516474 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515961 2516021 2516121 "RADCAT-" 2516126 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513872 2515731 2515823 "QUEUE" 2515904 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513497 2513546 2513677 "QUATCT2" 2513823 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505875 2509920 2509962 "QUATCAT" 2510753 NIL QUATCAT (NIL T) -9 NIL 2511519 NIL) (-1029 2501756 2503051 2504441 "QUATCAT-" 2504537 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497602 2501689 2501737 "QUAT" 2501742 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494858 2496650 2496693 "QUAGG" 2497074 NIL QUAGG (NIL T) -9 NIL 2497249 NIL) (-1026 2494406 2494680 2494750 "QQUTAST" 2494810 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493317 2493919 2494084 "QFORM" 2494287 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492942 2492991 2493122 "QFCAT2" 2493268 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482639 2488789 2488831 "QFCAT" 2489499 NIL QFCAT (NIL T) -9 NIL 2490500 NIL) (-1022 2477973 2479421 2481008 "QFCAT-" 2481104 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477404 2477538 2477670 "QEQUAT" 2477863 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470422 2471603 2472789 "QCMPACK" 2476337 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469651 2469833 2470069 "QALGSET2" 2470240 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467101 2467637 2468067 "QALGSET" 2469306 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465768 2466010 2466329 "PWFFINTB" 2466874 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463913 2464111 2464467 "PUSHVAR" 2465582 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459640 2460856 2460899 "PTRANFN" 2462810 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457977 2458322 2458646 "PTPACK" 2459351 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457600 2457663 2457774 "PTFUNC2" 2457914 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451516 2456389 2456432 "PTCAT" 2456732 NIL PTCAT (NIL T) -9 NIL 2456885 NIL) (-1011 2451165 2451206 2451332 "PSQFR" 2451475 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449737 2450053 2450389 "PSEUDLIN" 2450863 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436257 2438832 2441158 "PSETPK" 2447497 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428965 2431993 2432091 "PSETCAT" 2435132 NIL PSETCAT (NIL T T T T) -9 NIL 2435946 NIL) (-1007 2426690 2427432 2428256 "PSETCAT-" 2428261 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2426003 2426198 2426228 "PSCURVE" 2426500 T PSCURVE (NIL) -9 NIL 2426667 NIL) (-1005 2421726 2423493 2423560 "PSCAT" 2424412 NIL PSCAT (NIL T T T) -9 NIL 2424652 NIL) (-1004 2420720 2421002 2421405 "PSCAT-" 2421410 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418888 2419779 2420044 "PRTITION" 2420477 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418299 2418605 2418699 "PRTDAST" 2418816 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407143 2409565 2411755 "PRS" 2416161 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404758 2406460 2406502 "PRQAGG" 2406688 NIL PRQAGG (NIL T) -9 NIL 2406790 NIL) (-999 2403937 2404386 2404414 "PROPLOG" 2404553 T PROPLOG (NIL) -9 NIL 2404668 NIL) (-998 2403535 2403598 2403721 "PROPFUN2" 2403860 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402832 2402971 2403143 "PROPFUN1" 2403396 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400813 2401579 2401876 "PROPFRML" 2402568 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400258 2400389 2400517 "PROPERTY" 2400705 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2394071 2398424 2399244 "PRODUCT" 2399484 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393861 2393899 2393958 "PRINT" 2394032 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393177 2393318 2393470 "PRIMES" 2393741 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391224 2391643 2392109 "PRIMELT" 2392756 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390941 2391002 2391030 "PRIMCAT" 2391154 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389930 2390126 2390354 "PRIMARR2" 2390759 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385652 2389868 2389913 "PRIMARR" 2389918 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385289 2385351 2385462 "PREASSOC" 2385590 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382254 2384747 2384981 "PR" 2385100 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381705 2381862 2381890 "PPCURVE" 2382095 T PPCURVE (NIL) -9 NIL 2382231 NIL) (-984 2381252 2381500 2381583 "PORTNUM" 2381642 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378589 2379010 2379602 "POLYROOT" 2380833 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377966 2378030 2378264 "POLYLIFT" 2378525 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374187 2374690 2375319 "POLYCATQ" 2377511 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359835 2365934 2365999 "POLYCAT" 2369513 NIL POLYCAT (NIL T T T) -9 NIL 2371391 NIL) (-979 2352975 2355160 2357537 "POLYCAT-" 2357542 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352556 2352630 2352750 "POLY2UP" 2352901 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352182 2352245 2352354 "POLY2" 2352493 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345397 2351786 2351946 "POLY" 2352055 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2344058 2344321 2344597 "POLUTIL" 2345171 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342377 2342690 2343021 "POLTOPOL" 2343780 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337373 2342311 2342358 "POINT" 2342363 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335506 2335917 2336292 "PNTHEORY" 2337018 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333952 2334261 2334660 "PMTOOLS" 2335204 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333539 2333623 2333740 "PMSYM" 2333868 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2333041 2333116 2333291 "PMQFCAT" 2333464 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332422 2332520 2332682 "PMPREDFS" 2332942 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331765 2331887 2332043 "PMPRED" 2332299 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330419 2330637 2331015 "PMPLCAT" 2331527 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329945 2330030 2330182 "PMLSAGG" 2330334 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329412 2329494 2329676 "PMKERNEL" 2329863 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2329023 2329104 2329217 "PMINS" 2329331 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328459 2328534 2328743 "PMFS" 2328948 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327675 2327805 2328010 "PMDOWN" 2328336 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326924 2327058 2327221 "PMASSFS" 2327562 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2326067 2326249 2326430 "PMASS" 2326763 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325716 2325790 2325884 "PLOTTOOL" 2325993 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321368 2322562 2323484 "PLOT3D" 2324814 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320256 2320457 2320692 "PLOT1" 2321172 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314677 2316067 2317215 "PLOT" 2319128 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289852 2294743 2299594 "PLEQN" 2309943 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289539 2289592 2289695 "PINTERPA" 2289799 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288845 2288979 2289159 "PINTERP" 2289404 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286929 2288095 2288123 "PID" 2288320 T PID (NIL) -9 NIL 2288447 NIL) (-950 2286674 2286717 2286792 "PICOERCE" 2286886 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285770 2286438 2286525 "PI" 2286565 T PI (NIL) -8 NIL NIL 2286632) (-948 2285078 2285229 2285405 "PGROEB" 2285626 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280517 2281476 2282382 "PGE" 2284192 T PGE (NIL) -7 NIL NIL NIL) (-946 2278598 2278887 2279253 "PGCD" 2280234 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277924 2278039 2278200 "PFRPAC" 2278482 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274182 2276472 2276825 "PFR" 2277603 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272535 2272815 2273140 "PFOTOOLS" 2273929 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2271050 2271307 2271658 "PFOQ" 2272292 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269533 2269763 2270119 "PFO" 2270834 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266617 2268123 2268151 "PFECAT" 2268744 T PFECAT (NIL) -9 NIL 2269121 NIL) (-939 2266065 2266230 2266437 "PFECAT-" 2266442 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264638 2264920 2265221 "PFBRU" 2265814 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262467 2262856 2263288 "PFBR" 2264289 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258413 2262356 2262425 "PF" 2262430 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253467 2254620 2255490 "PERMGRP" 2257576 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251379 2252491 2252532 "PERMCAT" 2252932 NIL PERMCAT (NIL T) -9 NIL 2253230 NIL) (-933 2251026 2251073 2251197 "PERMAN" 2251332 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246828 2248535 2249183 "PERM" 2250411 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2244069 2246493 2246615 "PENDTREE" 2246739 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242950 2243213 2243254 "PDSPC" 2243787 NIL PDSPC (NIL T) -9 NIL 2244032 NIL) (-929 2242005 2242271 2242633 "PDSPC-" 2242638 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240719 2241655 2241696 "PDRING" 2241701 NIL PDRING (NIL T) -9 NIL 2241729 NIL) (-927 2239462 2240224 2240278 "PDMOD" 2240283 NIL PDMOD (NIL T T) -9 NIL 2240387 NIL) (-926 2236629 2237455 2238123 "PDEPROB" 2238814 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234138 2234678 2235233 "PDEPACK" 2236094 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2233026 2233240 2233491 "PDECOMP" 2233937 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230543 2231434 2231462 "PDECAT" 2232249 T PDECAT (NIL) -9 NIL 2232962 NIL) (-922 2230160 2230227 2230281 "PDDOM" 2230446 NIL PDDOM (NIL T T) -9 NIL 2230526 NIL) (-921 2229973 2230009 2230116 "PDDOM-" 2230121 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229718 2229757 2229847 "PCOMP" 2229934 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227758 2228519 2228816 "PBWLB" 2229447 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227384 2227447 2227556 "PATTERN2" 2227695 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225093 2225529 2225986 "PATTERN1" 2226973 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217272 2219166 2220504 "PATTERN" 2223776 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216830 2216903 2217035 "PATRES2" 2217199 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214096 2214779 2215260 "PATRES" 2216395 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211949 2212384 2212791 "PATMATCH" 2213763 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211403 2211654 2211695 "PATMAB" 2211802 NIL PATMAB (NIL T) -9 NIL 2211885 NIL) (-911 2209849 2210257 2210515 "PATLRES" 2211208 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209387 2209518 2209559 "PATAB" 2209564 NIL PATAB (NIL T) -9 NIL 2209736 NIL) (-909 2207527 2207964 2208387 "PARTPERM" 2208984 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207136 2207211 2207313 "PARSURF" 2207458 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206762 2206825 2206934 "PARSU2" 2207073 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206520 2206566 2206633 "PARSER" 2206715 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206129 2206204 2206306 "PARSCURV" 2206451 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205755 2205818 2205927 "PARSC2" 2206066 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205382 2205452 2205549 "PARPCURV" 2205691 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2205008 2205071 2205180 "PARPC2" 2205319 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203997 2204381 2204563 "PARAMAST" 2204846 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203505 2203603 2203722 "PAN2EXPR" 2203898 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202198 2202626 2202854 "PALETTE" 2203297 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200543 2201203 2201563 "PAIR" 2201884 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193476 2199800 2199995 "PADICRC" 2200397 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185733 2192820 2193005 "PADICRAT" 2193323 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182530 2184393 2184433 "PADICCT" 2185014 NIL PADICCT (NIL NIL) -9 NIL 2185296 NIL) (-894 2180546 2182467 2182512 "PADIC" 2182517 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179491 2179703 2179971 "PADEPAC" 2180333 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178691 2178836 2179042 "PADE" 2179353 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176924 2177899 2178179 "OWP" 2178495 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176369 2176630 2176727 "OVERSET" 2176847 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175289 2175974 2176146 "OVAR" 2176237 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163525 2166398 2168598 "OUTFORM" 2173109 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162807 2163122 2163249 "OUTBFILE" 2163418 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2162084 2162279 2162307 "OUTBCON" 2162625 T OUTBCON (NIL) -9 NIL 2162791 NIL) (-885 2161667 2161797 2161954 "OUTBCON-" 2161959 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160907 2161052 2161213 "OUT" 2161526 T OUT (NIL) -7 NIL NIL NIL) (-883 2160203 2160636 2160725 "OSI" 2160838 T OSI (NIL) -8 NIL NIL NIL) (-882 2159622 2160044 2160072 "OSGROUP" 2160077 T OSGROUP (NIL) -9 NIL 2160099 NIL) (-881 2158333 2158594 2158879 "ORTHPOL" 2159369 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155584 2158168 2158289 "OREUP" 2158294 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152687 2155275 2155402 "ORESUP" 2155526 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150187 2150715 2151276 "OREPCTO" 2152176 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143565 2146060 2146101 "OREPCAT" 2148449 NIL OREPCAT (NIL T) -9 NIL 2149553 NIL) (-876 2140538 2141494 2142552 "OREPCAT-" 2142557 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139730 2140008 2140036 "ORDTYPE" 2140345 T ORDTYPE (NIL) -9 NIL 2140508 NIL) (-874 2139031 2139247 2139502 "ORDTYPE-" 2139507 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138387 2138770 2138928 "ORDSTRCT" 2138933 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137885 2138255 2138283 "ORDSET" 2138288 T ORDSET (NIL) -9 NIL 2138310 NIL) (-871 2136536 2137507 2137535 "ORDRING" 2137540 T ORDRING (NIL) -9 NIL 2137569 NIL) (-870 2135787 2136352 2136380 "ORDMON" 2136385 T ORDMON (NIL) -9 NIL 2136406 NIL) (-869 2134931 2135096 2135291 "ORDFUNS" 2135636 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134146 2134661 2134689 "ORDFIN" 2134754 T ORDFIN (NIL) -9 NIL 2134828 NIL) (-867 2133400 2133539 2133725 "ORDCOMP2" 2134006 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129747 2131986 2132395 "ORDCOMP" 2133024 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126268 2127238 2128052 "OPTPROB" 2128953 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2123010 2123709 2124413 "OPTPACK" 2125584 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120623 2121449 2121477 "OPTCAT" 2122296 T OPTCAT (NIL) -9 NIL 2122946 NIL) (-862 2119941 2120300 2120405 "OPSIG" 2120538 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119703 2119748 2119814 "OPQUERY" 2119895 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2119009 2119289 2119330 "OPERCAT" 2119542 NIL OPERCAT (NIL T) -9 NIL 2119639 NIL) (-859 2118752 2118820 2118937 "OPERCAT-" 2118942 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115668 2117063 2117567 "OP" 2118281 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114961 2115088 2115262 "ONECOMP2" 2115540 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111574 2113758 2114127 "ONECOMP" 2114625 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110975 2111099 2111229 "OMSERVER" 2111464 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107487 2110413 2110453 "OMSAGG" 2110514 NIL OMSAGG (NIL T) -9 NIL 2110579 NIL) (-853 2106062 2106373 2106655 "OMPKG" 2107225 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104409 2105611 2105780 "OMLO" 2105943 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103345 2103516 2103736 "OMEXPR" 2104235 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102430 2102766 2102926 "OMERRK" 2103205 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101667 2101976 2102112 "OMERR" 2102314 T OMERR (NIL) -8 NIL NIL NIL) (-848 2101058 2101344 2101452 "OMENC" 2101579 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094695 2096138 2097309 "OMDEV" 2099907 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093728 2093935 2094129 "OMCONN" 2094521 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093134 2093261 2093289 "OM" 2093588 T OM (NIL) -9 NIL NIL NIL) (-844 2091412 2092604 2092632 "OINTDOM" 2092637 T OINTDOM (NIL) -9 NIL 2092658 NIL) (-843 2088487 2090100 2090437 "OFMONOID" 2091107 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087721 2088424 2088469 "ODVAR" 2088474 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084865 2087466 2087621 "ODR" 2087626 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076277 2084641 2084767 "ODPOL" 2084772 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069571 2076149 2076254 "ODP" 2076259 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068313 2068552 2068827 "ODETOOLS" 2069345 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065256 2065938 2066654 "ODESYS" 2067646 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2060086 2061046 2062071 "ODERTRIC" 2064331 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059506 2059594 2059788 "ODERED" 2059998 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056358 2056942 2057619 "ODERAT" 2058929 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053274 2053782 2054379 "ODEPRRIC" 2055887 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051169 2051813 2052299 "ODEPROB" 2052808 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047635 2048174 2048821 "ODEPRIM" 2050648 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046878 2046986 2047246 "ODEPAL" 2047527 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042980 2043831 2044695 "ODEPACK" 2046034 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2042023 2042148 2042370 "ODEINT" 2042869 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036088 2037549 2038996 "ODEIFTBL" 2040596 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031438 2032272 2033224 "ODEEF" 2035247 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030781 2030876 2031099 "ODECONST" 2031343 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028844 2029553 2029581 "ODECAT" 2030186 T ODECAT (NIL) -9 NIL 2030717 NIL) (-823 2028476 2028525 2028652 "OCTCT2" 2028795 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024976 2028181 2028303 "OCT" 2028386 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024169 2024769 2024797 "OCAMON" 2024802 T OCAMON (NIL) -9 NIL 2024823 NIL) (-820 2018440 2021212 2021252 "OC" 2022349 NIL OC (NIL T) -9 NIL 2023207 NIL) (-819 2015475 2016415 2017405 "OC-" 2017499 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014895 2015320 2015348 "OASGP" 2015353 T OASGP (NIL) -9 NIL 2015373 NIL) (-817 2013991 2014618 2014646 "OAMONS" 2014686 T OAMONS (NIL) -9 NIL 2014729 NIL) (-816 2013167 2013726 2013754 "OAMON" 2013812 T OAMON (NIL) -9 NIL 2013864 NIL) (-815 2013025 2013058 2013126 "OAMON-" 2013131 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011806 2012559 2012587 "OAGROUP" 2012734 T OAGROUP (NIL) -9 NIL 2012827 NIL) (-813 2011509 2011597 2011715 "OAGROUP-" 2011720 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011191 2011247 2011336 "NUMTUBE" 2011453 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004710 2006282 2007818 "NUMQUAD" 2009675 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000390 2001424 2002459 "NUMODE" 2003695 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997671 1998611 1998639 "NUMINT" 1999562 T NUMINT (NIL) -9 NIL 2000326 NIL) (-808 1996583 1996816 1997034 "NUMFMT" 1997473 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982766 1985887 1988419 "NUMERIC" 1994090 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976470 1982214 1982309 "NTSCAT" 1982314 NIL NTSCAT (NIL T T T T) -9 NIL 1982353 NIL) (-805 1975650 1975829 1976022 "NTPOLFN" 1976309 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975276 1975339 1975448 "NSUP2" 1975587 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962058 1972101 1972913 "NSUP" 1974497 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950901 1961832 1961965 "NSMP" 1961970 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949309 1949634 1949991 "NREP" 1950589 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947888 1948152 1948510 "NPCOEF" 1949052 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946936 1947069 1947285 "NORMRETR" 1947769 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944947 1945267 1945676 "NORMPK" 1946644 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944626 1944660 1944784 "NORMMA" 1944913 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944409 1944444 1944513 "NONE1" 1944590 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944173 1944366 1944395 "NONE" 1944400 T NONE (NIL) -8 NIL NIL NIL) (-794 1943664 1943732 1943911 "NODE1" 1944105 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941725 1942787 1943042 "NNI" 1943389 T NNI (NIL) -8 NIL NIL 1943624) (-792 1940121 1940458 1940822 "NLINSOL" 1941393 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936302 1937357 1938256 "NIPROB" 1939242 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935041 1935293 1935595 "NFINTBAS" 1936064 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934125 1934691 1934732 "NETCLT" 1934904 NIL NETCLT (NIL T) -9 NIL 1934986 NIL) (-788 1932797 1933064 1933345 "NCODIV" 1933893 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932553 1932596 1932671 "NCNTFRAC" 1932754 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930709 1931097 1931517 "NCEP" 1932178 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929372 1930319 1930347 "NASRING" 1930457 T NASRING (NIL) -9 NIL 1930537 NIL) (-784 1929155 1929211 1929305 "NASRING-" 1929310 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928122 1928773 1928801 "NARNG" 1928918 T NARNG (NIL) -9 NIL 1929009 NIL) (-782 1927796 1927881 1928015 "NARNG-" 1928020 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926633 1926882 1927117 "NAGSP" 1927581 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917677 1919589 1921262 "NAGS" 1924980 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916201 1916533 1916864 "NAGF07" 1917366 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910673 1912030 1913337 "NAGF04" 1914914 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903545 1905255 1906888 "NAGF02" 1909060 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898709 1899869 1900986 "NAGF01" 1902448 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892289 1893903 1895488 "NAGE04" 1897144 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883350 1885579 1887709 "NAGE02" 1890179 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879243 1880250 1881214 "NAGE01" 1882406 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877020 1877572 1878130 "NAGD03" 1878705 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868716 1870698 1872652 "NAGD02" 1875086 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862455 1863952 1865392 "NAGD01" 1867296 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858592 1859486 1860323 "NAGC06" 1861638 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857039 1857389 1857745 "NAGC05" 1858256 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856403 1856534 1856678 "NAGC02" 1856915 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855204 1855931 1855971 "NAALG" 1856050 NIL NAALG (NIL T) -9 NIL 1856111 NIL) (-765 1855033 1855068 1855158 "NAALG-" 1855163 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848905 1850091 1851278 "MULTSQFR" 1853929 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848212 1848299 1848483 "MULTFACT" 1848817 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840357 1844795 1844848 "MTSCAT" 1845918 NIL MTSCAT (NIL T T) -9 NIL 1846434 NIL) (-761 1840063 1840123 1840215 "MTHING" 1840297 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839849 1839888 1839948 "MSYSCMD" 1840023 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836594 1839410 1839451 "MSETAGG" 1839456 NIL MSETAGG (NIL T) -9 NIL 1839490 NIL) (-758 1832308 1835349 1835669 "MSET" 1836307 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827907 1829687 1830432 "MRING" 1831608 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827467 1827540 1827671 "MRF2" 1827834 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827079 1827120 1827264 "MRATFAC" 1827426 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824649 1824986 1825417 "MPRFF" 1826784 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817983 1824503 1824600 "MPOLY" 1824605 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817467 1817508 1817716 "MPCPF" 1817942 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816975 1817024 1817208 "MPC3" 1817418 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816158 1816251 1816472 "MPC2" 1816890 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814435 1814796 1815186 "MONOTOOL" 1815818 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813580 1813963 1813991 "MONOID" 1814210 T MONOID (NIL) -9 NIL 1814357 NIL) (-747 1813096 1813245 1813426 "MONOID-" 1813431 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802069 1808916 1808975 "MONOGEN" 1809649 NIL MONOGEN (NIL T T) -9 NIL 1810105 NIL) (-745 1799119 1800022 1801022 "MONOGEN-" 1801141 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797836 1798384 1798412 "MONADWU" 1798804 T MONADWU (NIL) -9 NIL 1799042 NIL) (-743 1797166 1797367 1797615 "MONADWU-" 1797620 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796451 1796755 1796783 "MONAD" 1796990 T MONAD (NIL) -9 NIL 1797102 NIL) (-741 1796118 1796214 1796346 "MONAD-" 1796351 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794257 1795031 1795310 "MOEBIUS" 1795871 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793425 1793925 1793965 "MODULE" 1793970 NIL MODULE (NIL T) -9 NIL 1794009 NIL) (-738 1792963 1793089 1793279 "MODULE-" 1793284 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790493 1791327 1791654 "MODRING" 1792787 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787222 1788598 1789119 "MODOP" 1790022 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785708 1786289 1786566 "MODMONOM" 1787085 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774469 1783999 1784413 "MODMON" 1785345 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771302 1773313 1773589 "MODFIELD" 1774344 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770213 1770583 1770773 "MMLFORM" 1771132 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769733 1769782 1769961 "MMAP" 1770164 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767626 1768565 1768606 "MLO" 1769029 NIL MLO (NIL T) -9 NIL 1769271 NIL) (-729 1764974 1765508 1766110 "MLIFT" 1767107 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764353 1764449 1764603 "MKUCFUNC" 1764885 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763946 1764022 1764145 "MKRECORD" 1764276 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762969 1763155 1763383 "MKFUNC" 1763757 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762345 1762461 1762617 "MKFLCFN" 1762852 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761610 1761724 1761909 "MKBCFUNC" 1762238 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757607 1761164 1761300 "MINT" 1761494 T MINT (NIL) -8 NIL NIL NIL) (-722 1756389 1756662 1756939 "MHROWRED" 1757362 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751140 1754924 1755329 "MFLOAT" 1756004 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750485 1750573 1750744 "MFINFACT" 1751052 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746764 1747648 1748532 "MESH" 1749621 T MESH (NIL) -7 NIL NIL NIL) (-718 1745118 1745466 1745819 "MDDFACT" 1746451 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741654 1744249 1744290 "MDAGG" 1744545 NIL MDAGG (NIL T) -9 NIL 1744688 NIL) (-716 1729377 1740947 1741154 "MCMPLX" 1741467 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728496 1728660 1728861 "MCDEN" 1729226 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726344 1726656 1727036 "MCALCFN" 1728226 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725221 1725509 1725742 "MAYBE" 1726150 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722779 1723356 1723918 "MATSTOR" 1724692 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718201 1722151 1722399 "MATRIX" 1722564 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713901 1714674 1715410 "MATLIN" 1717558 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712477 1712648 1712981 "MATCAT2" 1713736 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701816 1705534 1705611 "MATCAT" 1710643 NIL MATCAT (NIL T T T) -9 NIL 1712115 NIL) (-707 1697769 1699079 1700492 "MATCAT-" 1700497 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695845 1696205 1696589 "MAPPKG3" 1697444 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694802 1694999 1695221 "MAPPKG2" 1695669 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693259 1693585 1693912 "MAPPKG1" 1694508 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692260 1692665 1692842 "MAPPAST" 1693102 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691865 1691929 1692052 "MAPHACK3" 1692196 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691445 1691518 1691632 "MAPHACK2" 1691797 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690871 1690986 1691128 "MAPHACK1" 1691336 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688794 1689571 1689875 "MAGMA" 1690599 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688213 1688518 1688609 "MACROAST" 1688723 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684456 1686452 1686913 "M3D" 1687785 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677928 1682767 1682808 "LZSTAGG" 1683590 NIL LZSTAGG (NIL T) -9 NIL 1683885 NIL) (-695 1673610 1675059 1676516 "LZSTAGG-" 1676521 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670523 1671501 1671988 "LWORD" 1673155 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670045 1670327 1670402 "LSTAST" 1670468 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661973 1669816 1669950 "LSQM" 1669955 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661191 1661336 1661564 "LSPP" 1661828 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657928 1658644 1659374 "LSMP1" 1660493 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655710 1656041 1656497 "LSMP" 1657617 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648838 1654800 1654841 "LSAGG" 1654903 NIL LSAGG (NIL T) -9 NIL 1654981 NIL) (-687 1645347 1646457 1647670 "LSAGG-" 1647675 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642642 1644491 1644740 "LPOLY" 1645142 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642218 1642309 1642432 "LPEFRAC" 1642551 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641901 1641980 1642008 "LOGIC" 1642119 T LOGIC (NIL) -9 NIL 1642201 NIL) (-683 1641757 1641786 1641857 "LOGIC-" 1641862 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640932 1641090 1641283 "LODOOPS" 1641613 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639456 1639705 1640058 "LODOF" 1640679 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635332 1638091 1638132 "LODOCAT" 1638570 NIL LODOCAT (NIL T) -9 NIL 1638781 NIL) (-679 1635047 1635123 1635250 "LODOCAT-" 1635255 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632033 1634888 1635006 "LODO2" 1635011 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629140 1631970 1632015 "LODO1" 1632020 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626235 1629056 1629122 "LODO" 1629127 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625104 1625281 1625586 "LODEEF" 1626058 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623090 1624198 1624451 "LO" 1624936 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618062 1621256 1621297 "LNAGG" 1622159 NIL LNAGG (NIL T) -9 NIL 1622594 NIL) (-672 1617155 1617423 1617765 "LNAGG-" 1617770 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613135 1614080 1614719 "LMOPS" 1616570 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612434 1612912 1612953 "LMODULE" 1612958 NIL LMODULE (NIL T) -9 NIL 1612984 NIL) (-669 1609389 1612079 1612202 "LMDICT" 1612344 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608965 1609179 1609220 "LLINSET" 1609281 NIL LLINSET (NIL T) -9 NIL 1609325 NIL) (-667 1608610 1608873 1608933 "LITERAL" 1608938 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608129 1608209 1608348 "LIST3" 1608530 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606227 1606575 1606974 "LIST2MAP" 1607776 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605216 1605412 1605640 "LIST2" 1606045 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597670 1604150 1604454 "LIST" 1604945 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597253 1597489 1597530 "LINSET" 1597535 NIL LINSET (NIL T) -9 NIL 1597569 NIL) (-661 1596067 1596761 1596928 "LINFORM" 1597138 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594366 1595094 1595135 "LINEXP" 1595625 NIL LINEXP (NIL T) -9 NIL 1595898 NIL) (-659 1592942 1593846 1594027 "LINELT" 1594237 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591499 1591779 1592090 "LINDEP" 1592694 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590635 1591231 1591341 "LINBASIS" 1591429 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587372 1588121 1588898 "LIMITRF" 1589890 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585657 1585971 1586380 "LIMITPS" 1587067 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584485 1585060 1585100 "LIECAT" 1585240 NIL LIECAT (NIL T) -9 NIL 1585391 NIL) (-653 1584320 1584353 1584441 "LIECAT-" 1584446 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578340 1583831 1584059 "LIE" 1584141 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570525 1577880 1578036 "LIB" 1578204 T LIB (NIL) -8 NIL NIL NIL) (-650 1566094 1567043 1567978 "LGROBP" 1569642 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564718 1565626 1565654 "LFCAT" 1565861 T LFCAT (NIL) -9 NIL 1566000 NIL) (-648 1562656 1562990 1563340 "LF" 1564439 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559516 1560188 1560876 "LEXTRIPK" 1562020 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556104 1557086 1557589 "LEXP" 1559096 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555520 1555825 1555917 "LETAST" 1556032 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553906 1554231 1554632 "LEADCDET" 1555202 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553084 1553170 1553399 "LAZM3PK" 1553827 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547609 1551161 1551699 "LAUPOL" 1552596 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547182 1547232 1547393 "LAPLACE" 1547559 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546030 1546746 1546787 "LALG" 1546849 NIL LALG (NIL T) -9 NIL 1546908 NIL) (-639 1545726 1545803 1545939 "LALG-" 1545944 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543463 1544827 1545078 "LA" 1545559 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543292 1543322 1543363 "KVTFROM" 1543425 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542049 1542659 1542844 "KTVLOGIC" 1543127 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541878 1541908 1541949 "KRCFROM" 1542011 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540770 1540969 1541268 "KOVACIC" 1541678 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540599 1540629 1540670 "KONVERT" 1540732 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540428 1540458 1540499 "KOERCE" 1540561 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539912 1540005 1540137 "KERNEL2" 1540342 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537599 1538505 1538882 "KERNEL" 1539568 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531070 1536076 1536130 "KDAGG" 1536507 NIL KDAGG (NIL T T) -9 NIL 1536713 NIL) (-628 1530581 1530723 1530928 "KDAGG-" 1530933 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523281 1530242 1530397 "KAFILE" 1530459 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522885 1523170 1523233 "JVMOP" 1523238 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521621 1522125 1522374 "JVMMDACC" 1522656 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520557 1521011 1521216 "JVMFDACC" 1521436 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519138 1519633 1519933 "JVMCSTTG" 1520277 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518274 1518678 1518839 "JVMCFACC" 1518997 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517952 1518191 1518240 "JVMBCODE" 1518245 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511971 1517463 1517691 "JORDAN" 1517773 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511284 1511620 1511741 "JOINAST" 1511870 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507319 1509461 1509515 "IXAGG" 1510444 NIL IXAGG (NIL T T) -9 NIL 1510903 NIL) (-617 1506172 1506544 1506963 "IXAGG-" 1506968 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501261 1506094 1506153 "IVECTOR" 1506158 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499986 1500264 1500530 "ITUPLE" 1501028 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498458 1498665 1498960 "ITRIGMNP" 1499808 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497185 1497407 1497690 "ITFUN3" 1498234 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496783 1496846 1496969 "ITFUN2" 1497108 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495888 1496263 1496437 "ITFORM" 1496629 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493657 1494908 1495186 "ITAYLOR" 1495643 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482061 1487794 1488957 "ISUPS" 1492527 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481153 1481305 1481541 "ISUMP" 1481908 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476003 1481098 1481139 "ISTRING" 1481144 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475419 1475724 1475816 "ISAST" 1475931 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474616 1474710 1474926 "IRURPK" 1475333 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473528 1473753 1473993 "IRSN" 1474396 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471573 1471954 1472383 "IRRF2F" 1473166 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471314 1471358 1471434 "IRREDFFX" 1471529 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469887 1470188 1470487 "IROOT" 1471047 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469026 1469380 1469531 "IRFORM" 1469756 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468108 1468239 1468453 "IR2F" 1468909 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465697 1466216 1466782 "IR2" 1467586 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462137 1463381 1464073 "IR" 1465037 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461922 1461962 1462022 "IPRNTPK" 1462097 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457896 1461811 1461880 "IPF" 1461885 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455924 1457821 1457878 "IPADIC" 1457883 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455182 1455484 1455614 "IP4ADDR" 1455814 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454520 1454811 1454943 "IOMODE" 1455070 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453491 1454117 1454244 "IOBFILE" 1454413 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452901 1453395 1453423 "IOBCON" 1453428 T IOBCON (NIL) -9 NIL 1453449 NIL) (-589 1452406 1452470 1452653 "INVLAPLA" 1452837 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441976 1444408 1446794 "INTTR" 1450070 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438269 1439053 1439918 "INTTOOLS" 1441161 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437849 1437946 1438063 "INTSLPE" 1438172 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435316 1437772 1437831 "INTRVL" 1437836 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432894 1433430 1434005 "INTRF" 1434801 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432287 1432402 1432544 "INTRET" 1432792 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430260 1430673 1431143 "INTRAT" 1431895 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427505 1428106 1428725 "INTPM" 1429745 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424222 1424849 1425587 "INTPAF" 1426891 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419323 1420363 1421414 "INTPACK" 1423191 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418569 1418727 1418935 "INTHERTR" 1419165 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418002 1418088 1418276 "INTHERAL" 1418483 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415770 1416291 1416748 "INTHEORY" 1417565 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407102 1408797 1410569 "INTG0" 1414122 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387627 1392465 1397275 "INTFTBL" 1402312 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386852 1387014 1387187 "INTFACT" 1387486 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384249 1384725 1385282 "INTEF" 1386406 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382446 1383341 1383369 "INTDOM" 1383670 T INTDOM (NIL) -9 NIL 1383877 NIL) (-570 1381785 1381989 1382231 "INTDOM-" 1382236 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377653 1380074 1380128 "INTCAT" 1380927 NIL INTCAT (NIL T) -9 NIL 1381248 NIL) (-568 1377107 1377228 1377356 "INTBIT" 1377545 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375788 1375960 1376267 "INTALG" 1376952 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375265 1375361 1375518 "INTAF" 1375692 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368232 1375075 1375215 "INTABL" 1375220 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367473 1368035 1368100 "INT8" 1368134 T INT8 (NIL) -8 NIL NIL 1368179) (-563 1366713 1367275 1367340 "INT64" 1367374 T INT64 (NIL) -8 NIL NIL 1367419) (-562 1365953 1366515 1366580 "INT32" 1366614 T INT32 (NIL) -8 NIL NIL 1366659) (-561 1365193 1365755 1365820 "INT16" 1365854 T INT16 (NIL) -8 NIL NIL 1365899) (-560 1361395 1364990 1365099 "INT" 1365104 T INT (NIL) -8 NIL NIL NIL) (-559 1355504 1358943 1358971 "INS" 1359905 T INS (NIL) -9 NIL 1360570 NIL) (-558 1352579 1353529 1354496 "INS-" 1354569 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330936 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329790 1330113 1330141 "INBCON" 1330654 T INBCON (NIL) -9 NIL 1330920 NIL) (-540 1329000 1329265 1329541 "INBCON-" 1329546 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328419 1328724 1328815 "INAST" 1328929 T INAST (NIL) -8 NIL NIL NIL) (-538 1327786 1328098 1328204 "IMPTAST" 1328333 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323707 1327630 1327734 "IMATRIX" 1327739 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322399 1322538 1322854 "IMATQF" 1323563 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320579 1320846 1321183 "IMATLIN" 1322155 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314494 1320503 1320561 "ILIST" 1320566 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312160 1314354 1314467 "IIARRAY2" 1314472 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306981 1312071 1312135 "IFF" 1312140 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306262 1306598 1306714 "IFAST" 1306885 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300774 1305554 1305742 "IFARRAY" 1306119 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299812 1300678 1300751 "IFAMON" 1300756 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299384 1299461 1299515 "IEVALAB" 1299722 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299047 1299127 1299287 "IEVALAB-" 1299292 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298080 1298936 1299011 "IDPOAMS" 1299016 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297182 1297969 1298044 "IDPOAM" 1298049 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296563 1297097 1297159 "IDPO" 1297164 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295043 1295570 1295622 "IDPC" 1296134 NIL IDPC (NIL T T) -9 NIL 1296415 NIL) (-522 1294375 1294935 1295008 "IDPAM" 1295013 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293590 1294267 1294340 "IDPAG" 1294345 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293134 1293396 1293486 "IDENT" 1293520 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289353 1290237 1291132 "IDECOMP" 1292291 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281988 1283276 1284323 "IDEAL" 1288389 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281130 1281260 1281460 "ICDEN" 1281872 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280105 1280610 1280757 "ICARD" 1281003 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278135 1278478 1278883 "IBPTOOLS" 1279782 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273250 1277755 1277868 "IBITS" 1278054 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269925 1270549 1271244 "IBATOOL" 1272667 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267686 1268166 1268699 "IBACHIN" 1269460 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265276 1267532 1267635 "IARRAY2" 1267640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260989 1265202 1265259 "IARRAY1" 1265264 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254006 1259401 1259882 "IAN" 1260528 T IAN (NIL) -8 NIL NIL NIL) (-508 1253511 1253574 1253747 "IALGFACT" 1253943 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253003 1253152 1253180 "HYPCAT" 1253387 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252505 1252658 1252844 "HYPCAT-" 1252849 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252052 1252300 1252383 "HOSTNAME" 1252442 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251885 1251934 1251975 "HOMOTOP" 1251980 NIL HOMOTOP (NIL T) -9 NIL 1252013 NIL) (-503 1248318 1249817 1249858 "HOAGG" 1250839 NIL HOAGG (NIL T) -9 NIL 1251568 NIL) (-502 1246834 1247311 1247837 "HOAGG-" 1247842 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239891 1246427 1246577 "HEXADEC" 1246704 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238603 1238861 1239124 "HEUGCD" 1239668 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237535 1238440 1238570 "HELLFDIV" 1238575 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235543 1237310 1237399 "HEAP" 1237478 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234740 1235095 1235229 "HEADAST" 1235429 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228078 1234655 1234717 "HDP" 1234722 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221097 1227713 1227865 "HDMP" 1227979 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220403 1220561 1220725 "HB" 1220953 T HB (NIL) -7 NIL NIL NIL) (-493 1213413 1220249 1220353 "HASHTBL" 1220358 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212829 1213134 1213226 "HASAST" 1213341 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210242 1212451 1212633 "HACKPI" 1212667 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205414 1210095 1210208 "GTSET" 1210213 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198453 1205292 1205390 "GSTBL" 1205395 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190216 1197618 1197874 "GSERIES" 1198253 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189247 1189760 1189788 "GROUP" 1189991 T GROUP (NIL) -9 NIL 1190125 NIL) (-486 1188571 1188772 1189023 "GROUP-" 1189028 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186920 1187259 1187646 "GROEBSOL" 1188248 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185748 1186108 1186159 "GRMOD" 1186688 NIL GRMOD (NIL T T) -9 NIL 1186856 NIL) (-483 1185504 1185552 1185680 "GRMOD-" 1185685 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180644 1181858 1182858 "GRIMAGE" 1184524 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179038 1179371 1179695 "GRDEF" 1180340 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178470 1178598 1178739 "GRAY" 1178917 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177547 1178049 1178100 "GRALG" 1178253 NIL GRALG (NIL T T) -9 NIL 1178346 NIL) (-478 1177184 1177281 1177444 "GRALG-" 1177449 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173665 1176767 1176946 "GPOLSET" 1177090 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173013 1173076 1173334 "GOSPER" 1173602 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168583 1169451 1169977 "GMODPOL" 1172712 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167570 1167772 1168010 "GHENSEL" 1168395 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161642 1162569 1163589 "GENUPS" 1166654 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161333 1161390 1161479 "GENUFACT" 1161585 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160733 1160822 1160987 "GENPGCD" 1161251 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160201 1160242 1160455 "GENMFACT" 1160692 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158737 1159024 1159331 "GENEEZ" 1159944 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151916 1158348 1158510 "GDMP" 1158660 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140654 1145687 1146793 "GCNAALG" 1150899 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138781 1139829 1139857 "GCDDOM" 1140112 T GCDDOM (NIL) -9 NIL 1140269 NIL) (-465 1138221 1138378 1138593 "GCDDOM-" 1138598 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126693 1129167 1131559 "GBINTERN" 1135912 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124494 1124822 1125243 "GBF" 1126368 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123251 1123440 1123707 "GBEUCLID" 1124310 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121901 1122108 1122412 "GB" 1123030 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121232 1121375 1121524 "GAUSSFAC" 1121772 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119553 1119901 1120215 "GALUTIL" 1120951 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117813 1118135 1118459 "GALPOLYU" 1119280 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115112 1115468 1115875 "GALFACTU" 1117510 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106726 1108417 1110025 "GALFACT" 1113544 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104012 1104772 1104800 "FVFUN" 1105956 T FVFUN (NIL) -9 NIL 1106676 NIL) (-454 1103242 1103460 1103488 "FVC" 1103779 T FVC (NIL) -9 NIL 1103962 NIL) (-453 1102843 1103067 1103135 "FUNDESC" 1103194 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102416 1102640 1102721 "FUNCTION" 1102795 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101093 1101717 1101920 "FTEM" 1102233 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098723 1099415 1099881 "FT" 1100647 T FT (NIL) -8 NIL NIL NIL) (-449 1096992 1097303 1097700 "FSUPFACT" 1098414 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095311 1095678 1096010 "FST" 1096680 T FST (NIL) -8 NIL NIL NIL) (-447 1094492 1094616 1094804 "FSRED" 1095193 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093181 1093447 1093794 "FSPRMELT" 1094207 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090391 1090925 1091411 "FSPECF" 1092744 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089913 1089973 1090143 "FSINT" 1090332 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088049 1088906 1089209 "FSERIES" 1089692 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087073 1087207 1087431 "FSCINT" 1087929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086097 1086258 1086485 "FSAGG2" 1086926 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081961 1085041 1085082 "FSAGG" 1085452 NIL FSAGG (NIL T) -9 NIL 1085711 NIL) (-439 1079561 1080324 1081120 "FSAGG-" 1081215 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077221 1077519 1078067 "FS2UPS" 1079279 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076087 1076270 1076572 "FS2EXPXP" 1077046 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075715 1075764 1075893 "FS2" 1076038 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055953 1065489 1065530 "FS" 1069414 NIL FS (NIL T) -9 NIL 1071703 NIL) (-434 1044014 1047589 1051646 "FS-" 1051946 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043428 1043555 1043707 "FRUTIL" 1043894 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037939 1041117 1041157 "FRNAALG" 1042477 NIL FRNAALG (NIL T) -9 NIL 1043075 NIL) (-431 1033420 1034688 1035963 "FRNAALG-" 1036713 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033052 1033101 1033228 "FRNAAF2" 1033371 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031339 1031901 1032197 "FRMOD" 1032864 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030524 1030617 1030908 "FRIDEAL2" 1031246 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028129 1028899 1029217 "FRIDEAL" 1030315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027220 1027676 1027717 "FRETRCT" 1027722 NIL FRETRCT (NIL T) -9 NIL 1027898 NIL) (-425 1026278 1026563 1026914 "FRETRCT-" 1026919 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023099 1024562 1024621 "FRAMALG" 1025503 NIL FRAMALG (NIL T T) -9 NIL 1025795 NIL) (-423 1021137 1021688 1022318 "FRAMALG-" 1022541 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020767 1020830 1020937 "FRAC2" 1021074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013759 1020240 1020517 "FRAC" 1020522 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013389 1013452 1013559 "FR2" 1013696 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004306 1008884 1010242 "FR" 1012063 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998225 1001685 1001713 "FPS" 1002832 T FPS (NIL) -9 NIL 1003389 NIL) (-417 997650 997783 997947 "FPS-" 998093 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994616 996607 996635 "FPC" 996860 T FPC (NIL) -9 NIL 997002 NIL) (-415 994397 994449 994546 "FPC-" 994551 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993155 993885 993926 "FPATMAB" 993931 NIL FPATMAB (NIL T) -9 NIL 994083 NIL) (-413 991298 991897 992244 "FPARFRAC" 992871 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986590 987190 987872 "FORTRAN" 990730 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984164 984828 984856 "FORTFN" 985916 T FORTFN (NIL) -9 NIL 986540 NIL) (-410 983916 983978 984006 "FORTCAT" 984065 T FORTCAT (NIL) -9 NIL 984127 NIL) (-409 981602 982132 982671 "FORT" 983397 T FORT (NIL) -7 NIL NIL NIL) (-408 981384 981420 981489 "FORMULA1" 981566 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979388 980000 980390 "FORMULA" 981014 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978905 978963 979136 "FORDER" 979330 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977965 978165 978358 "FOP" 978732 T FOP (NIL) -7 NIL NIL NIL) (-404 976378 977245 977419 "FNLA" 977847 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974997 975508 975536 "FNCAT" 975996 T FNCAT (NIL) -9 NIL 976256 NIL) (-402 974440 974956 974984 "FNAME" 974989 T FNAME (NIL) -8 NIL NIL NIL) (-401 972766 973939 973967 "FMTC" 973972 T FMTC (NIL) -9 NIL 974008 NIL) (-400 971315 972702 972748 "FMONOID" 972753 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967904 969270 969311 "FMONCAT" 970528 NIL FMONCAT (NIL T) -9 NIL 971133 NIL) (-398 965226 965974 966002 "FMFUN" 967146 T FMFUN (NIL) -9 NIL 967854 NIL) (-397 962099 963151 963205 "FMCAT" 964400 NIL FMCAT (NIL T T) -9 NIL 964895 NIL) (-396 961332 961549 961577 "FMC" 961867 T FMC (NIL) -9 NIL 962049 NIL) (-395 960000 961098 961198 "FM1" 961277 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959018 959742 959891 "FM" 959896 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956756 957208 957702 "FLOATRP" 958569 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954158 954694 955272 "FLOATCP" 956223 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946821 951887 952508 "FLOAT" 953557 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945339 946413 946454 "FLINEXP" 946459 NIL FLINEXP (NIL T) -9 NIL 946552 NIL) (-389 944469 944728 945056 "FLINEXP-" 945061 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943527 943689 943913 "FLASORT" 944321 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940445 941497 941549 "FLALG" 942776 NIL FLALG (NIL T T) -9 NIL 943243 NIL) (-386 939469 939630 939857 "FLAGG2" 940298 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932724 936878 936919 "FLAGG" 938181 NIL FLAGG (NIL T) -9 NIL 938833 NIL) (-384 931378 931789 932279 "FLAGG-" 932284 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928016 929223 929282 "FINRALG" 930410 NIL FINRALG (NIL T T) -9 NIL 930918 NIL) (-382 927140 927405 927744 "FINRALG-" 927749 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926446 926745 926773 "FINITE" 926969 T FINITE (NIL) -9 NIL 927076 NIL) (-380 918397 920976 921016 "FINAALG" 924683 NIL FINAALG (NIL T) -9 NIL 926136 NIL) (-379 913513 914779 915923 "FINAALG-" 917302 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912073 912495 912549 "FILECAT" 913233 NIL FILECAT (NIL T T) -9 NIL 913449 NIL) (-377 911351 911828 911931 "FILE" 912003 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908754 910581 910609 "FIELD" 910649 T FIELD (NIL) -9 NIL 910729 NIL) (-375 907296 907759 908270 "FIELD-" 908275 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904979 905931 906278 "FGROUP" 906982 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904051 904233 904453 "FGLMICPK" 904811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899306 903976 904033 "FFX" 904038 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898901 898968 899103 "FFSLPE" 899239 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898399 898441 898650 "FFPOLY2" 898859 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894275 895171 895967 "FFPOLY" 897635 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889544 894194 894257 "FFP" 894262 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884075 888887 889077 "FFNBX" 889398 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878408 883210 883468 "FFNBP" 883929 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872446 877692 877903 "FFNB" 878241 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871266 871476 871791 "FFINTBAS" 872243 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866859 869513 869541 "FFIELDC" 870161 T FFIELDC (NIL) -9 NIL 870537 NIL) (-362 865479 865920 866403 "FFIELDC-" 866408 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865036 865094 865218 "FFHOM" 865421 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862695 863218 863735 "FFF" 864551 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857730 862437 862538 "FFCGX" 862638 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852769 857462 857569 "FFCGP" 857673 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847369 852496 852604 "FFCG" 852705 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846774 846823 847058 "FFCAT2" 847320 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825456 836506 836592 "FFCAT" 841757 NIL FFCAT (NIL T T T) -9 NIL 843208 NIL) (-354 820467 821701 823015 "FFCAT-" 824245 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815288 820378 820442 "FF" 820447 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803941 808260 809480 "FEXPR" 814140 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802869 803338 803379 "FEVALAB" 803463 NIL FEVALAB (NIL T) -9 NIL 803724 NIL) (-350 801986 802238 802576 "FEVALAB-" 802581 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798848 799733 799848 "FDIVCAT" 801416 NIL FDIVCAT (NIL T T T T) -9 NIL 801853 NIL) (-348 798604 798637 798807 "FDIVCAT-" 798812 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797818 797911 798188 "FDIV2" 798511 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796228 797201 797404 "FDIV" 797717 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795136 795523 795725 "FCTRDATA" 796046 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793792 794081 794370 "FCPAK1" 794867 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792795 793292 793433 "FCOMP" 793683 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776109 779945 783483 "FC" 789277 T FC (NIL) -8 NIL NIL NIL) (-341 767818 772430 772470 "FAXF" 774272 NIL FAXF (NIL T) -9 NIL 774964 NIL) (-340 764959 765766 766584 "FAXF-" 767049 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759528 764335 764511 "FARRAY" 764816 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754093 756475 756528 "FAMR" 757551 NIL FAMR (NIL T T) -9 NIL 758011 NIL) (-337 752917 753285 753720 "FAMR-" 753725 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751944 752839 752892 "FAMONOID" 752897 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749574 750426 750479 "FAMONC" 751420 NIL FAMONC (NIL T T) -9 NIL 751806 NIL) (-334 748048 749328 749465 "FAGROUP" 749470 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745801 746162 746565 "FACUTIL" 747729 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744888 745085 745307 "FACTFUNC" 745611 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736629 744191 744390 "EXPUPXS" 744744 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734082 734652 735238 "EXPRTUBE" 736063 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730293 730945 731675 "EXPRODE" 733421 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724727 725434 726240 "EXPR2UPS" 729591 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724353 724416 724525 "EXPR2" 724664 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708661 723002 723431 "EXPR" 723957 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698999 707812 708103 "EXPEXPAN" 708497 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698419 698723 698814 "EXITAST" 698928 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698183 698376 698405 "EXIT" 698410 T EXIT (NIL) -8 NIL NIL NIL) (-322 697804 697872 697985 "EVALCYC" 698115 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697321 697463 697504 "EVALAB" 697674 NIL EVALAB (NIL T) -9 NIL 697778 NIL) (-320 696778 696924 697145 "EVALAB-" 697150 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693893 695434 695462 "EUCDOM" 696017 T EUCDOM (NIL) -9 NIL 696367 NIL) (-318 692253 692754 693337 "EUCDOM-" 693342 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691879 691942 692051 "ESTOOLS2" 692190 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691624 691672 691752 "ESTOOLS1" 691831 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678941 681922 684672 "ESTOOLS" 688894 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678680 678718 678800 "ESCONT1" 678903 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674988 675815 676595 "ESCONT" 677920 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674657 674713 674813 "ES2" 674932 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674281 674345 674454 "ES1" 674593 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667982 669912 669940 "ES" 672708 T ES (NIL) -9 NIL 674118 NIL) (-309 662659 664216 666033 "ES-" 666197 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661851 662004 662180 "ERROR" 662503 T ERROR (NIL) -7 NIL NIL NIL) (-307 654867 661710 661801 "EQTBL" 661806 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654493 654556 654665 "EQ2" 654804 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646752 649807 651256 "EQ" 653077 NIL -1539 (NIL T) -8 NIL NIL NIL) (-304 641995 643090 644183 "EP" 645691 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640535 640886 641192 "ENV" 641709 T ENV (NIL) -8 NIL NIL NIL) (-302 639495 640169 640197 "ENTIRER" 640202 T ENTIRER (NIL) -9 NIL 640248 NIL) (-301 635914 637677 638038 "EMR" 639303 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635018 635229 635283 "ELTAGG" 635663 NIL ELTAGG (NIL T T) -9 NIL 635874 NIL) (-299 634725 634799 634940 "ELTAGG-" 634945 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634483 634518 634572 "ELTAB" 634656 NIL ELTAB (NIL T T) -9 NIL 634708 NIL) (-297 633585 633755 633954 "ELFUTS" 634334 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633309 633383 633411 "ELEMFUN" 633516 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633173 633200 633268 "ELEMFUN-" 633273 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627584 631215 631256 "ELAGG" 632196 NIL ELAGG (NIL T) -9 NIL 632659 NIL) (-293 625761 626303 626966 "ELAGG-" 626971 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625043 625210 625366 "ELABOR" 625625 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623649 623983 624277 "ELABEXPR" 624769 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616161 618286 619115 "EFUPXS" 622924 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609287 611410 612221 "EFULS" 615436 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606724 607130 607602 "EFSTRUC" 608919 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596161 598081 599629 "EF" 605239 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595139 595646 595795 "EAB" 596032 T EAB (NIL) -8 NIL NIL NIL) (-285 594261 595098 595126 "E04UCFA" 595131 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593383 594220 594248 "E04NAFA" 594253 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592505 593342 593370 "E04MBFA" 593375 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591627 592464 592492 "E04JAFA" 592497 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590751 591586 591614 "E04GCFA" 591619 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589875 590710 590738 "E04FDFA" 590743 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588997 589834 589862 "E04DGFA" 589867 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583074 584522 585886 "E04AGNT" 587653 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581694 582375 582415 "DVARCAT" 582756 NIL DVARCAT (NIL T) -9 NIL 582919 NIL) (-276 580844 581110 581424 "DVARCAT-" 581429 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572812 580643 580772 "DSMP" 580777 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571163 571954 571995 "DSEXT" 572358 NIL DSEXT (NIL T) -9 NIL 572652 NIL) (-273 569352 569876 570542 "DSEXT-" 570547 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569011 569076 569174 "DROPT1" 569287 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564030 565252 566389 "DROPT0" 567894 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558613 559975 561043 "DROPT" 562982 T DROPT (NIL) -8 NIL NIL NIL) (-269 556922 557283 557669 "DRAWPT" 558247 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556549 556608 556726 "DRAWHACK" 556863 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555250 555549 555840 "DRAWCX" 556278 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554759 554834 554985 "DRAWCURV" 555176 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545077 547189 549304 "DRAWCFUN" 552664 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539568 540587 541666 "DRAW" 544051 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536039 538233 538274 "DQAGG" 538903 NIL DQAGG (NIL T) -9 NIL 539177 NIL) (-262 522622 530250 530333 "DPOLCAT" 532185 NIL DPOLCAT (NIL T T T T) -9 NIL 532730 NIL) (-261 517141 518807 520765 "DPOLCAT-" 520770 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509949 517002 517100 "DPMO" 517105 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502654 509729 509896 "DPMM" 509901 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502176 502438 502527 "DOMTMPLT" 502585 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501525 501978 502058 "DOMCTOR" 502116 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500677 501005 501156 "DOMAIN" 501394 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493696 500312 500464 "DMP" 500578 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491473 492763 492804 "DMEXT" 492809 NIL DMEXT (NIL T) -9 NIL 492985 NIL) (-253 491067 491129 491273 "DLP" 491411 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484190 490394 490584 "DLIST" 490909 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480728 483015 483056 "DLAGG" 483606 NIL DLAGG (NIL T) -9 NIL 483836 NIL) (-250 479240 480054 480082 "DIVRING" 480174 T DIVRING (NIL) -9 NIL 480257 NIL) (-249 478423 478667 478967 "DIVRING-" 478972 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476465 476882 477288 "DISPLAY" 478037 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475295 475516 475781 "DIRPROD2" 476258 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468653 475209 475272 "DIRPROD" 475277 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456816 463364 463417 "DIRPCAT" 463675 NIL DIRPCAT (NIL NIL T) -9 NIL 464550 NIL) (-244 454016 454784 455665 "DIRPCAT-" 456002 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453297 453463 453649 "DIOSP" 453850 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449711 452181 452222 "DIOPS" 452656 NIL DIOPS (NIL T) -9 NIL 452885 NIL) (-241 449230 449374 449565 "DIOPS-" 449570 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448137 448909 448937 "DIFRING" 448942 T DIFRING (NIL) -9 NIL 448964 NIL) (-239 447785 447883 447911 "DIFFSPC" 448030 T DIFFSPC (NIL) -9 NIL 448105 NIL) (-238 447406 447508 447660 "DIFFSPC-" 447665 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446342 446940 446981 "DIFFMOD" 446986 NIL DIFFMOD (NIL T) -9 NIL 447084 NIL) (-236 446038 446095 446136 "DIFFDOM" 446257 NIL DIFFDOM (NIL T) -9 NIL 446325 NIL) (-235 445885 445915 445999 "DIFFDOM-" 446004 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443625 445089 445130 "DIFEXT" 445135 NIL DIFEXT (NIL T) -9 NIL 445288 NIL) (-233 440659 443129 443170 "DIAGG" 443175 NIL DIAGG (NIL T) -9 NIL 443195 NIL) (-232 440007 440200 440452 "DIAGG-" 440457 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434857 438966 439243 "DHMATRIX" 439776 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430325 431378 432388 "DFSFUN" 433867 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424566 429256 429568 "DFLOAT" 430033 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422805 423110 423499 "DFINTTLS" 424274 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419624 420826 421226 "DERHAM" 422471 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417160 419399 419488 "DEQUEUE" 419568 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416402 416547 416730 "DEGRED" 417022 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412808 413577 414423 "DEFINTRF" 415630 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410345 410832 411424 "DEFINTEF" 412327 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409629 409965 410080 "DEFAST" 410250 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402686 409222 409372 "DECIMAL" 409499 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400144 400656 401162 "DDFACT" 402230 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399734 399783 399934 "DBLRESP" 400095 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398935 399504 399595 "DBASIS" 399683 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396719 397165 397526 "DBASE" 398701 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395907 396199 396345 "DATAARY" 396618 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394965 395866 395894 "D03FAFA" 395899 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394024 394924 394952 "D03EEFA" 394957 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391950 392440 392929 "D03AGNT" 393555 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391191 391909 391937 "D02EJFA" 391942 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390432 391150 391178 "D02CJFA" 391183 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389673 390391 390419 "D02BHFA" 390424 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388914 389632 389660 "D02BBFA" 389665 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382045 383700 385306 "D02AGNT" 387328 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379795 380336 380882 "D01WGTS" 381519 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378802 379754 379782 "D01TRNS" 379787 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377810 378761 378789 "D01GBFA" 378794 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376818 377769 377797 "D01FCFA" 377802 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375826 376777 376805 "D01ASFA" 376810 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374834 375785 375813 "D01AQFA" 375818 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373842 374793 374821 "D01APFA" 374826 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372850 373801 373829 "D01ANFA" 373834 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371858 372809 372837 "D01AMFA" 372842 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370866 371817 371845 "D01ALFA" 371850 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369874 370825 370853 "D01AKFA" 370858 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368882 369833 369861 "D01AJFA" 369866 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362105 363730 365291 "D01AGNT" 367341 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361424 361570 361722 "CYCLOTOM" 361973 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358079 358872 359599 "CYCLES" 360717 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357379 357525 357696 "CVMP" 357940 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355166 355478 355847 "CTRIGMNP" 357107 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354639 354897 354998 "CTORKIND" 355085 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353844 354232 354260 "CTORCAT" 354442 T CTORCAT (NIL) -9 NIL 354555 NIL) (-188 353418 353553 353712 "CTORCAT-" 353717 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352832 353092 353200 "CTORCALL" 353342 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352190 352626 352699 "CTOR" 352779 T CTOR (NIL) -8 NIL NIL NIL) (-185 351546 351663 351816 "CSTTOOLS" 352087 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347243 348002 348760 "CRFP" 350858 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346658 346964 347056 "CRCEAST" 347171 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345681 345890 346118 "CRAPACK" 346462 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345061 345166 345370 "CPMATCH" 345557 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344780 344814 344920 "CPIMA" 345027 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341038 341800 342519 "COORDSYS" 344115 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340426 340571 340713 "CONTOUR" 340916 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335898 338429 338921 "CONTFRAC" 339966 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335772 335799 335827 "CONDUIT" 335864 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334726 335400 335428 "COMRING" 335433 T COMRING (NIL) -9 NIL 335485 NIL) (-174 333708 334084 334268 "COMPPROP" 334562 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333363 333404 333532 "COMPLPAT" 333667 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332993 333056 333163 "COMPLEX2" 333300 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321397 332802 332911 "COMPLEX" 332916 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320718 320857 321017 "COMPILER" 321257 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320430 320471 320569 "COMPFACT" 320677 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301824 314134 314174 "COMPCAT" 315178 NIL COMPCAT (NIL T) -9 NIL 316526 NIL) (-167 290712 294263 297890 "COMPCAT-" 298246 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290435 290469 290572 "COMMUPC" 290678 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290223 290263 290322 "COMMONOP" 290396 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289745 290027 290102 "COMMAAST" 290168 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289252 289496 289583 "COMM" 289678 T COMM (NIL) -8 NIL NIL NIL) (-162 288447 288695 288723 "COMBOPC" 289061 T COMBOPC (NIL) -9 NIL 289236 NIL) (-161 287301 287553 287795 "COMBINAT" 288237 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283644 284332 284959 "COMBF" 286723 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282306 282760 282995 "COLOR" 283429 T COLOR (NIL) -8 NIL NIL NIL) (-158 281722 282027 282119 "COLONAST" 282234 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281356 281409 281534 "CMPLXRT" 281669 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280744 281056 281155 "CLLCTAST" 281277 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276203 277274 278354 "CLIP" 279684 T CLIP (NIL) -7 NIL NIL NIL) (-154 274376 275304 275544 "CLIF" 276030 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270358 272494 272535 "CLAGG" 273464 NIL CLAGG (NIL T) -9 NIL 274000 NIL) (-152 268702 269237 269820 "CLAGG-" 269825 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268240 268331 268471 "CINTSLPE" 268611 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265705 266212 266760 "CHVAR" 267768 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264745 265419 265447 "CHARZ" 265452 T CHARZ (NIL) -9 NIL 265467 NIL) (-148 264493 264539 264617 "CHARPOL" 264699 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263411 264117 264145 "CHARNZ" 264206 T CHARNZ (NIL) -9 NIL 264255 NIL) (-146 260355 261465 261994 "CHAR" 262902 T CHAR (NIL) -8 NIL NIL NIL) (-145 260063 260142 260170 "CFCAT" 260281 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259286 259415 259598 "CDEN" 259947 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254883 258439 258719 "CCLASS" 259026 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254104 254291 254468 "CATEGORY" 254726 T -10 (NIL) -8 NIL NIL NIL) (-141 253599 254023 254071 "CATCTOR" 254076 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252990 253302 253400 "CATAST" 253521 T CATAST (NIL) -8 NIL NIL NIL) (-139 252406 252711 252803 "CASEAST" 252918 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251502 251662 251883 "CARTEN2" 252253 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247659 248403 "CARTEN" 250814 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3472975 3472980 3472985 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472960 3472965 3472970 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472945 3472950 3472955 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472930 3472935 3472940 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3471923 3472805 3472882 "ZMOD" 3472887 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3470959 3471141 3471364 "ZLINDEP" 3471755 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3460121 3462027 3463999 "ZDSOLVE" 3469089 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3459355 3459508 3459697 "YSTREAM" 3459967 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3458715 3459024 3459139 "YDIAGRAM" 3459262 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3456163 3458016 3458220 "XRPOLY" 3458558 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3452430 3454034 3454609 "XPR" 3455635 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3449761 3451437 3451492 "XPOLYC" 3451780 NIL XPOLYC (NIL T T) -9 NIL 3451893 NIL) (-1321 3447156 3449092 3449296 "XPOLY" 3449592 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3443102 3445673 3446061 "XPBWPOLY" 3446814 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3437994 3439573 3439628 "XFALG" 3441800 NIL XFALG (NIL T T) -9 NIL 3442589 NIL) (-1318 3433270 3435970 3436012 "XF" 3436633 NIL XF (NIL T) -9 NIL 3437033 NIL) (-1317 3432867 3432979 3433148 "XF-" 3433153 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3431982 3432104 3432309 "XEXPPKG" 3432759 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3429723 3431832 3431928 "XDPOLY" 3431933 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3428378 3429116 3429159 "XALG" 3429164 NIL XALG (NIL T) -9 NIL 3429275 NIL) (-1313 3421288 3426355 3426849 "WUTSET" 3427970 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3419390 3420340 3420663 "WP" 3421099 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3418938 3419212 3419282 "WHILEAST" 3419342 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418350 3418655 3418749 "WHEREAST" 3418866 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417224 3417434 3417729 "WFFINTBS" 3418147 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415092 3415555 3416017 "WEIER" 3416796 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3414016 3414574 3414616 "VSPACE" 3414752 NIL VSPACE (NIL T) -9 NIL 3414826 NIL) (-1306 3413848 3413881 3413972 "VSPACE-" 3413977 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413645 3413699 3413767 "VOID" 3413802 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409913 3410708 3411445 "VIEWDEF" 3412930 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398857 3401461 3403634 "VIEW3D" 3407762 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390874 3392768 3394347 "VIEW2D" 3397300 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388974 3389369 3389775 "VIEW" 3390490 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387527 3387810 3388128 "VECTOR2" 3388704 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382433 3387297 3387389 "VECTOR" 3387470 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375378 3380137 3380180 "VECTCAT" 3381175 NIL VECTCAT (NIL T) -9 NIL 3381762 NIL) (-1297 3374320 3374646 3375036 "VECTCAT-" 3375041 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373726 3373971 3374091 "VARIABLE" 3374235 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373659 3373664 3373694 "UTYPE" 3373699 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372467 3372643 3372905 "UTSODETL" 3373485 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369859 3370367 3370891 "UTSODE" 3372008 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359869 3365792 3365835 "UTSCAT" 3366947 NIL UTSCAT (NIL T) -9 NIL 3367705 NIL) (-1291 3356995 3357939 3358928 "UTSCAT-" 3358933 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356616 3356665 3356798 "UTS2" 3356946 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347933 3354377 3354857 "UTS" 3356194 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341800 3344743 3344786 "URAGG" 3346856 NIL URAGG (NIL T) -9 NIL 3347579 NIL) (-1287 3338523 3339602 3340725 "URAGG-" 3340730 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333899 3337158 3337623 "UPXSSING" 3338187 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326328 3333803 3333875 "UPXSCONS" 3333880 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315086 3322530 3322592 "UPXSCCA" 3323166 NIL UPXSCCA (NIL T T) -9 NIL 3323399 NIL) (-1283 3314706 3314809 3314983 "UPXSCCA-" 3314988 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303364 3310533 3310576 "UPXSCAT" 3311224 NIL UPXSCAT (NIL T) -9 NIL 3311833 NIL) (-1281 3302788 3302873 3303052 "UPXS2" 3303279 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294280 3302170 3302434 "UPXS" 3302582 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292916 3293187 3293538 "UPSQFREE" 3294023 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285747 3289182 3289237 "UPSCAT" 3290317 NIL UPSCAT (NIL T T) -9 NIL 3291083 NIL) (-1277 3284903 3285158 3285485 "UPSCAT-" 3285490 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284524 3284573 3284706 "UPOLYC2" 3284854 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268672 3277651 3277694 "UPOLYC" 3279795 NIL UPOLYC (NIL T) -9 NIL 3281016 NIL) (-1274 3259541 3262440 3265580 "UPOLYC-" 3265585 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258862 3258987 3259151 "UPMP" 3259430 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258409 3258496 3258635 "UPDIVP" 3258775 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256947 3257226 3257542 "UPDECOMP" 3258158 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256160 3256290 3256476 "UPCDEN" 3256831 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255673 3255748 3255897 "UP2" 3256085 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246269 3255356 3255485 "UP" 3255592 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245474 3245611 3245816 "UNISEG2" 3246112 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243827 3244678 3244955 "UNISEG" 3245232 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242869 3243067 3243293 "UNIFACT" 3243643 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229600 3242773 3242845 "ULSCONS" 3242850 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209417 3222680 3222742 "ULSCCAT" 3223380 NIL ULSCCAT (NIL T T) -9 NIL 3223669 NIL) (-1262 3208413 3208712 3209100 "ULSCCAT-" 3209105 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196868 3203959 3204002 "ULSCAT" 3204865 NIL ULSCAT (NIL T) -9 NIL 3205596 NIL) (-1260 3196292 3196377 3196556 "ULS2" 3196783 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178123 3195604 3195846 "ULS" 3196108 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3177042 3177742 3177856 "UINT8" 3177967 T UINT8 (NIL) -8 NIL NIL 3178059) (-1257 3175960 3176660 3176774 "UINT64" 3176885 T UINT64 (NIL) -8 NIL NIL 3176977) (-1256 3174878 3175578 3175692 "UINT32" 3175803 T UINT32 (NIL) -8 NIL NIL 3175895) (-1255 3173796 3174496 3174610 "UINT16" 3174721 T UINT16 (NIL) -8 NIL NIL 3174813) (-1254 3171875 3173042 3173072 "UFD" 3173284 T UFD (NIL) -9 NIL 3173398 NIL) (-1253 3171657 3171715 3171810 "UFD-" 3171815 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170715 3170922 3171138 "UDVO" 3171463 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168481 3168940 3169411 "UDPO" 3170279 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168193 3168436 3168467 "TYPEAST" 3168472 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168126 3168131 3168161 "TYPE" 3168166 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167079 3167299 3167539 "TWOFACT" 3167920 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3166054 3166488 3166723 "TUPLE" 3166879 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163691 3164264 3164803 "TUBETOOL" 3165537 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162497 3162738 3162980 "TUBE" 3163484 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150632 3155254 3155351 "TSETCAT" 3160620 NIL TSETCAT (NIL T T T T) -9 NIL 3162152 NIL) (-1243 3145100 3146964 3148855 "TSETCAT-" 3148860 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139286 3144072 3144355 "TS" 3144852 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133759 3134772 3135701 "TRMANIP" 3138422 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133188 3133263 3133426 "TRIMAT" 3133691 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3131000 3131291 3131648 "TRIGMNIP" 3132937 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130484 3130633 3130663 "TRIGCAT" 3130876 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130129 3130232 3130373 "TRIGCAT-" 3130378 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126743 3128987 3129268 "TREE" 3129883 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125849 3126545 3126575 "TRANFUN" 3126610 T TRANFUN (NIL) -9 NIL 3126676 NIL) (-1234 3125068 3125319 3125599 "TRANFUN-" 3125604 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124866 3124904 3124965 "TOPSP" 3125029 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124196 3124329 3124483 "TOOLSIGN" 3124747 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122710 3123373 3123612 "TEXTFILE" 3123979 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122485 3122522 3122594 "TEX1" 3122673 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120289 3120938 3121367 "TEX" 3122078 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119925 3120000 3120090 "TEMUTL" 3120221 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3118019 3118359 3118684 "TBCMPPK" 3119648 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109339 3116105 3116161 "TBAGG" 3116561 NIL TBAGG (NIL T T) -9 NIL 3116772 NIL) (-1225 3104223 3105897 3107651 "TBAGG-" 3107656 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103589 3103714 3103859 "TANEXP" 3104112 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103040 3103364 3103454 "TALGOP" 3103534 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102434 3102551 3102689 "TABLEAU" 3102937 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095448 3102291 3102384 "TABLE" 3102389 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089978 3091276 3092524 "TABLBUMP" 3094234 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089188 3089347 3089528 "SYSTEM" 3089819 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085593 3086346 3087129 "SYSSOLP" 3088439 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085355 3085548 3085579 "SYSPTR" 3085584 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084194 3084886 3085012 "SYSNNI" 3085198 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085290) (-1215 3083401 3083956 3084035 "SYSINT" 3084095 NIL SYSINT (NIL NIL) -8 NIL NIL 3084140) (-1214 3079499 3080679 3081389 "SYNTAX" 3082713 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076579 3077259 3077891 "SYMTAB" 3078889 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071678 3072730 3073713 "SYMS" 3075618 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068584 3071129 3071362 "SYMPOLY" 3071480 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068089 3068176 3068299 "SYMFUNC" 3068496 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063887 3065401 3066214 "SYMBOL" 3067298 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057360 3059115 3060835 "SWITCH" 3062189 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050121 3056316 3056610 "SUTS" 3057124 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041613 3049503 3049767 "SUPXS" 3049915 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040760 3040899 3041116 "SUPFRACF" 3041481 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040375 3040440 3040553 "SUP2" 3040695 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030919 3039993 3040119 "SUP" 3040284 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029343 3029641 3029997 "SUMRF" 3030618 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028666 3028744 3028936 "SUMFS" 3029264 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010532 3027978 3028220 "SULS" 3028482 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010080 3010354 3010424 "SUCHTAST" 3010484 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009321 3009605 3009745 "SUCH" 3009988 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002960 3004227 3005186 "SUBSPACE" 3008409 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002380 3002480 3002644 "SUBRESP" 3002848 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996391 2997673 2998820 "STTFNC" 3001280 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989585 2991056 2992367 "STTF" 2995127 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980702 2982767 2984561 "STTAYLOR" 2987826 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973456 2980566 2980649 "STRTBL" 2980654 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967853 2973165 2973264 "STRING" 2973379 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967357 2967440 2967584 "STREAM3" 2967770 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966321 2966522 2966757 "STREAM2" 2967170 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2966003 2966061 2966154 "STREAM1" 2966263 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958117 2963622 2964233 "STREAM" 2965427 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957109 2957314 2957545 "STINPROD" 2957933 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956224 2956598 2956746 "STEPAST" 2956983 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955720 2955965 2955995 "STEP" 2956089 T STEP (NIL) -9 NIL 2956160 NIL) (-1183 2948776 2955619 2955696 "STBL" 2955701 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943326 2947939 2947982 "STAGG" 2948135 NIL STAGG (NIL T) -9 NIL 2948224 NIL) (-1181 2940878 2941630 2942502 "STAGG-" 2942507 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938850 2940648 2940740 "STACK" 2940821 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938167 2938680 2938710 "SRING" 2938715 T SRING (NIL) -9 NIL 2938735 NIL) (-1178 2930174 2936308 2936764 "SREGSET" 2937797 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922521 2923968 2925481 "SRDCMPK" 2928780 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914821 2919880 2919910 "SRAGG" 2921213 T SRAGG (NIL) -9 NIL 2921821 NIL) (-1175 2913772 2914093 2914472 "SRAGG-" 2914477 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907356 2912719 2913140 "SQMATRIX" 2913398 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900768 2904074 2904801 "SPLTREE" 2906701 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896593 2897424 2898070 "SPLNODE" 2900194 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895568 2895873 2895903 "SPFCAT" 2896347 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894263 2894515 2894779 "SPECOUT" 2895326 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884909 2887227 2887257 "SPADXPT" 2891935 T SPADXPT (NIL) -9 NIL 2894101 NIL) (-1168 2884664 2884710 2884779 "SPADPRSR" 2884862 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882267 2884619 2884650 "SPADAST" 2884655 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873868 2875971 2876014 "SPACEC" 2880387 NIL SPACEC (NIL T) -9 NIL 2882203 NIL) (-1165 2871668 2873800 2873849 "SPACE3" 2873854 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870400 2870591 2870882 "SORTPAK" 2871473 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868462 2868795 2869207 "SOLVETRA" 2870064 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867500 2867734 2867995 "SOLVESER" 2868235 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862732 2863692 2864687 "SOLVERAD" 2866552 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858457 2859156 2859885 "SOLVEFOR" 2862099 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852061 2857805 2857902 "SNTSCAT" 2857907 NIL SNTSCAT (NIL T T T T) -9 NIL 2857977 NIL) (-1158 2845612 2850384 2850775 "SMTS" 2851751 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839334 2845500 2845577 "SMP" 2845582 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837463 2837794 2838192 "SMITH" 2839031 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828988 2834042 2834145 "SMATCAT" 2835496 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836046 NIL) (-1154 2825760 2826751 2827929 "SMATCAT-" 2827934 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823229 2824968 2825011 "SKAGG" 2825272 NIL SKAGG (NIL T) -9 NIL 2825407 NIL) (-1152 2818748 2822712 2822889 "SINT" 2823041 T SINT (NIL) -8 NIL NIL 2823196) (-1151 2818514 2818558 2818624 "SIMPAN" 2818704 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817334 2817573 2817848 "SIGNRF" 2818273 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816149 2816318 2816602 "SIGNEF" 2817163 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815389 2815732 2815856 "SIGAST" 2816047 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814614 2814924 2815064 "SIG" 2815271 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812266 2812758 2813264 "SHP" 2814155 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805590 2812167 2812243 "SHDP" 2812248 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805101 2805341 2805371 "SGROUP" 2805464 T SGROUP (NIL) -9 NIL 2805526 NIL) (-1143 2804953 2804985 2805058 "SGROUP-" 2805063 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801672 2802442 2803165 "SGCF" 2804252 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795374 2801118 2801215 "SFRTCAT" 2801220 NIL SFRTCAT (NIL T T T T) -9 NIL 2801259 NIL) (-1140 2788693 2789813 2790949 "SFRGCD" 2794357 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781711 2782892 2784078 "SFQCMPK" 2787626 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781313 2781420 2781531 "SFORT" 2781652 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780239 2781153 2781274 "SEXOF" 2781279 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775828 2776735 2776830 "SEXCAT" 2779452 NIL SEXCAT (NIL T T T T T) -9 NIL 2780012 NIL) (-1135 2774743 2775709 2775777 "SEX" 2775782 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772865 2773456 2773761 "SETMN" 2774484 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772395 2772583 2772613 "SETCAT" 2772730 T SETCAT (NIL) -9 NIL 2772815 NIL) (-1132 2772163 2772227 2772326 "SETCAT-" 2772331 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768266 2770624 2770667 "SETAGG" 2771537 NIL SETAGG (NIL T) -9 NIL 2771877 NIL) (-1130 2767688 2767840 2768077 "SETAGG-" 2768082 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764497 2767622 2767670 "SET" 2767675 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763880 2764193 2764294 "SEQAST" 2764418 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763007 2763373 2763434 "SEGXCAT" 2763720 NIL SEGXCAT (NIL T T) -9 NIL 2763840 NIL) (-1126 2761932 2762200 2762243 "SEGCAT" 2762765 NIL SEGCAT (NIL T) -9 NIL 2762986 NIL) (-1125 2761547 2761612 2761725 "SEGBIND2" 2761867 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760437 2760910 2761118 "SEGBIND" 2761374 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759956 2760238 2760315 "SEGAST" 2760382 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759165 2759301 2759505 "SEG2" 2759800 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758081 2758831 2759013 "SEG" 2759018 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757314 2758016 2758063 "SDVAR" 2758068 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748672 2757084 2757214 "SDPOL" 2757219 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747241 2747531 2747850 "SCPKG" 2748387 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746363 2746577 2746769 "SCOPE" 2747071 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745559 2745717 2745896 "SCACHE" 2746218 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745143 2745377 2745407 "SASTCAT" 2745412 T SASTCAT (NIL) -9 NIL 2745425 NIL) (-1114 2744546 2744978 2745054 "SAOS" 2745089 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744105 2744146 2744319 "SAERFFC" 2744505 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743692 2743733 2743892 "SAEFACT" 2744064 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736740 2743589 2743669 "SAE" 2743674 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735043 2735375 2735776 "RURPK" 2736406 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733620 2733986 2734291 "RULESET" 2734877 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733190 2733414 2733497 "RULECOLD" 2733572 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730305 2730943 2731401 "RULE" 2732871 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730089 2730123 2730194 "RTVALUE" 2730256 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729500 2729806 2729900 "RSTRCAST" 2730017 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724270 2725143 2726063 "RSETGCD" 2728699 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712834 2718578 2718675 "RSETCAT" 2722794 NIL RSETCAT (NIL T T T T) -9 NIL 2723891 NIL) (-1102 2710653 2711300 2712124 "RSETCAT-" 2712129 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702961 2704415 2705935 "RSDCMPK" 2709252 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700830 2701393 2701467 "RRCC" 2702553 NIL RRCC (NIL T T) -9 NIL 2702897 NIL) (-1099 2700151 2700355 2700634 "RRCC-" 2700639 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699534 2699847 2699948 "RPTAST" 2700072 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671920 2682646 2682713 "RPOLCAT" 2693379 NIL RPOLCAT (NIL T T T) -9 NIL 2696539 NIL) (-1096 2662890 2665758 2668880 "RPOLCAT-" 2668885 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653343 2661101 2661583 "ROUTINE" 2662430 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649406 2652969 2653109 "ROMAN" 2653225 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647518 2648266 2648526 "ROIRC" 2649211 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643238 2646007 2646037 "RNS" 2646341 T RNS (NIL) -9 NIL 2646615 NIL) (-1091 2641645 2642130 2642664 "RNS-" 2642739 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640606 2641010 2641212 "RNGBIND" 2641496 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639899 2640403 2640433 "RNG" 2640438 T RNG (NIL) -9 NIL 2640459 NIL) (-1088 2639194 2639672 2639715 "RMODULE" 2639720 NIL RMODULE (NIL T) -9 NIL 2639747 NIL) (-1087 2638018 2638124 2638460 "RMCAT2" 2639095 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634520 2637364 2637661 "RMATRIX" 2637780 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627019 2629607 2629722 "RMATCAT" 2633081 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634063 NIL) (-1084 2626358 2626541 2626848 "RMATCAT-" 2626853 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625931 2626145 2626188 "RLINSET" 2626250 NIL RLINSET (NIL T) -9 NIL 2626294 NIL) (-1082 2625492 2625573 2625701 "RINTERP" 2625850 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624416 2625090 2625120 "RING" 2625176 T RING (NIL) -9 NIL 2625268 NIL) (-1080 2624196 2624252 2624349 "RING-" 2624354 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623007 2623274 2623532 "RIDIST" 2623960 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613632 2622475 2622681 "RGCHAIN" 2622855 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612890 2613374 2613415 "RGBCSPC" 2613473 NIL RGBCSPC (NIL T) -9 NIL 2613525 NIL) (-1076 2611956 2612415 2612456 "RGBCMDL" 2612688 NIL RGBCMDL (NIL T) -9 NIL 2612802 NIL) (-1075 2611596 2611665 2611768 "RFFACTOR" 2611887 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611315 2611356 2611453 "RFFACT" 2611555 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609366 2609796 2610178 "RFDIST" 2610955 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606306 2606974 2607644 "RF" 2608730 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605753 2605851 2606014 "RETSOL" 2606208 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605371 2605469 2605512 "RETRACT" 2605645 NIL RETRACT (NIL T) -9 NIL 2605732 NIL) (-1069 2605214 2605245 2605332 "RETRACT-" 2605337 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604762 2605036 2605106 "RETAST" 2605166 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597112 2604415 2604542 "RESULT" 2604657 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595547 2596381 2596580 "RESRING" 2597015 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595171 2595232 2595330 "RESLATC" 2595484 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594870 2594911 2595018 "REPSQ" 2595130 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594561 2594602 2594713 "REPDB" 2594829 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588393 2589850 2591073 "REP2" 2593373 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584696 2585451 2586259 "REP1" 2587620 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582076 2582698 2583300 "REP" 2584116 T REP (NIL) -7 NIL NIL NIL) (-1059 2574084 2580217 2580673 "REGSET" 2581706 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572793 2573232 2573482 "REF" 2573869 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572158 2572273 2572440 "REDORDER" 2572677 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567529 2571371 2571598 "RECLOS" 2571986 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566563 2566762 2566977 "REALSOLV" 2567336 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563010 2563848 2564732 "REAL0Q" 2565728 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558563 2559599 2560660 "REAL0" 2561991 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558397 2558450 2558480 "REAL" 2558485 T REAL (NIL) -9 NIL 2558520 NIL) (-1051 2557808 2558114 2558208 "RDUCEAST" 2558325 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557207 2557285 2557492 "RDIV" 2557730 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556257 2556449 2556662 "RDIST" 2557029 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554842 2555141 2555513 "RDETRS" 2555965 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552636 2553108 2553646 "RDETR" 2554384 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551255 2551539 2551936 "RDEEFS" 2552352 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549758 2550070 2550495 "RDEEF" 2550943 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543237 2546712 2546742 "RCFIELD" 2548037 T RCFIELD (NIL) -9 NIL 2548768 NIL) (-1043 2541193 2541805 2542501 "RCFIELD-" 2542576 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537245 2539266 2539309 "RCAGG" 2540393 NIL RCAGG (NIL T) -9 NIL 2540858 NIL) (-1041 2536855 2536967 2537130 "RCAGG-" 2537135 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536172 2536302 2536467 "RATRET" 2536739 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535713 2535792 2535913 "RATFACT" 2536100 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534991 2535141 2535293 "RANDSRC" 2535583 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534719 2534769 2534842 "RADUTIL" 2534940 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526864 2533550 2533861 "RADIX" 2534442 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516479 2526706 2526836 "RADFF" 2526841 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516108 2516201 2516231 "RADCAT" 2516391 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515878 2515938 2516038 "RADCAT-" 2516043 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513789 2515648 2515740 "QUEUE" 2515821 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513414 2513463 2513594 "QUATCT2" 2513740 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505792 2509837 2509879 "QUATCAT" 2510670 NIL QUATCAT (NIL T) -9 NIL 2511436 NIL) (-1029 2501673 2502968 2504358 "QUATCAT-" 2504454 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497519 2501606 2501654 "QUAT" 2501659 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494775 2496567 2496610 "QUAGG" 2496991 NIL QUAGG (NIL T) -9 NIL 2497166 NIL) (-1026 2494323 2494597 2494667 "QQUTAST" 2494727 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493234 2493836 2494001 "QFORM" 2494204 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492859 2492908 2493039 "QFCAT2" 2493185 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482556 2488706 2488748 "QFCAT" 2489416 NIL QFCAT (NIL T) -9 NIL 2490417 NIL) (-1022 2477890 2479338 2480925 "QFCAT-" 2481021 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477321 2477455 2477587 "QEQUAT" 2477780 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470339 2471520 2472706 "QCMPACK" 2476254 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469568 2469750 2469986 "QALGSET2" 2470157 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467018 2467554 2467984 "QALGSET" 2469223 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465685 2465927 2466246 "PWFFINTB" 2466791 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463830 2464028 2464384 "PUSHVAR" 2465499 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459557 2460773 2460816 "PTRANFN" 2462727 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457894 2458239 2458563 "PTPACK" 2459268 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457517 2457580 2457691 "PTFUNC2" 2457831 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451433 2456306 2456349 "PTCAT" 2456649 NIL PTCAT (NIL T) -9 NIL 2456802 NIL) (-1011 2451082 2451123 2451249 "PSQFR" 2451392 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449654 2449970 2450306 "PSEUDLIN" 2450780 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436174 2438749 2441075 "PSETPK" 2447414 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428882 2431910 2432008 "PSETCAT" 2435049 NIL PSETCAT (NIL T T T T) -9 NIL 2435863 NIL) (-1007 2426607 2427349 2428173 "PSETCAT-" 2428178 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425920 2426115 2426145 "PSCURVE" 2426417 T PSCURVE (NIL) -9 NIL 2426584 NIL) (-1005 2421643 2423410 2423477 "PSCAT" 2424329 NIL PSCAT (NIL T T T) -9 NIL 2424569 NIL) (-1004 2420637 2420919 2421322 "PSCAT-" 2421327 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418805 2419696 2419961 "PRTITION" 2420394 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418216 2418522 2418616 "PRTDAST" 2418733 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407060 2409482 2411672 "PRS" 2416078 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404675 2406377 2406419 "PRQAGG" 2406605 NIL PRQAGG (NIL T) -9 NIL 2406707 NIL) (-999 2403854 2404303 2404331 "PROPLOG" 2404470 T PROPLOG (NIL) -9 NIL 2404585 NIL) (-998 2403452 2403515 2403638 "PROPFUN2" 2403777 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402749 2402888 2403060 "PROPFUN1" 2403313 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400730 2401496 2401793 "PROPFRML" 2402485 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400175 2400306 2400434 "PROPERTY" 2400622 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393988 2398341 2399161 "PRODUCT" 2399401 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393778 2393816 2393875 "PRINT" 2393949 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393094 2393235 2393387 "PRIMES" 2393658 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391141 2391560 2392026 "PRIMELT" 2392673 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390858 2390919 2390947 "PRIMCAT" 2391071 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389847 2390043 2390271 "PRIMARR2" 2390676 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385569 2389785 2389830 "PRIMARR" 2389835 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385206 2385268 2385379 "PREASSOC" 2385507 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382171 2384664 2384898 "PR" 2385017 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381622 2381779 2381807 "PPCURVE" 2382012 T PPCURVE (NIL) -9 NIL 2382148 NIL) (-984 2381169 2381417 2381500 "PORTNUM" 2381559 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378506 2378927 2379519 "POLYROOT" 2380750 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377883 2377947 2378181 "POLYLIFT" 2378442 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374104 2374607 2375236 "POLYCATQ" 2377428 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359752 2365851 2365916 "POLYCAT" 2369430 NIL POLYCAT (NIL T T T) -9 NIL 2371308 NIL) (-979 2352892 2355077 2357454 "POLYCAT-" 2357459 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352473 2352547 2352667 "POLY2UP" 2352818 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352099 2352162 2352271 "POLY2" 2352410 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345314 2351703 2351863 "POLY" 2351972 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343975 2344238 2344514 "POLUTIL" 2345088 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342294 2342607 2342938 "POLTOPOL" 2343697 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337290 2342228 2342275 "POINT" 2342280 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335423 2335834 2336209 "PNTHEORY" 2336935 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333869 2334178 2334577 "PMTOOLS" 2335121 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333456 2333540 2333657 "PMSYM" 2333785 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332958 2333033 2333208 "PMQFCAT" 2333381 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332339 2332437 2332599 "PMPREDFS" 2332859 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331682 2331804 2331960 "PMPRED" 2332216 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330336 2330554 2330932 "PMPLCAT" 2331444 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329862 2329947 2330099 "PMLSAGG" 2330251 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329329 2329411 2329593 "PMKERNEL" 2329780 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328940 2329021 2329134 "PMINS" 2329248 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328376 2328451 2328660 "PMFS" 2328865 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327592 2327722 2327927 "PMDOWN" 2328253 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326841 2326975 2327138 "PMASSFS" 2327479 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325984 2326166 2326347 "PMASS" 2326680 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325633 2325707 2325801 "PLOTTOOL" 2325910 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321285 2322479 2323401 "PLOT3D" 2324731 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320173 2320374 2320609 "PLOT1" 2321089 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314594 2315984 2317132 "PLOT" 2319045 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289769 2294660 2299511 "PLEQN" 2309860 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289456 2289509 2289612 "PINTERPA" 2289716 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288762 2288896 2289076 "PINTERP" 2289321 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286846 2288012 2288040 "PID" 2288237 T PID (NIL) -9 NIL 2288364 NIL) (-950 2286591 2286634 2286709 "PICOERCE" 2286803 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285687 2286355 2286442 "PI" 2286482 T PI (NIL) -8 NIL NIL 2286549) (-948 2284995 2285146 2285322 "PGROEB" 2285543 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280434 2281393 2282299 "PGE" 2284109 T PGE (NIL) -7 NIL NIL NIL) (-946 2278515 2278804 2279170 "PGCD" 2280151 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277841 2277956 2278117 "PFRPAC" 2278399 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274099 2276389 2276742 "PFR" 2277520 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272452 2272732 2273057 "PFOTOOLS" 2273846 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270967 2271224 2271575 "PFOQ" 2272209 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269450 2269680 2270036 "PFO" 2270751 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266534 2268040 2268068 "PFECAT" 2268661 T PFECAT (NIL) -9 NIL 2269038 NIL) (-939 2265982 2266147 2266354 "PFECAT-" 2266359 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264555 2264837 2265138 "PFBRU" 2265731 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262384 2262773 2263205 "PFBR" 2264206 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258330 2262273 2262342 "PF" 2262347 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253384 2254537 2255407 "PERMGRP" 2257493 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251296 2252408 2252449 "PERMCAT" 2252849 NIL PERMCAT (NIL T) -9 NIL 2253147 NIL) (-933 2250943 2250990 2251114 "PERMAN" 2251249 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246745 2248452 2249100 "PERM" 2250328 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243986 2246410 2246532 "PENDTREE" 2246656 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242867 2243130 2243171 "PDSPC" 2243704 NIL PDSPC (NIL T) -9 NIL 2243949 NIL) (-929 2241922 2242188 2242550 "PDSPC-" 2242555 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240636 2241572 2241613 "PDRING" 2241618 NIL PDRING (NIL T) -9 NIL 2241646 NIL) (-927 2239379 2240141 2240195 "PDMOD" 2240200 NIL PDMOD (NIL T T) -9 NIL 2240304 NIL) (-926 2236546 2237372 2238040 "PDEPROB" 2238731 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234055 2234595 2235150 "PDEPACK" 2236011 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232943 2233157 2233408 "PDECOMP" 2233854 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230460 2231351 2231379 "PDECAT" 2232166 T PDECAT (NIL) -9 NIL 2232879 NIL) (-922 2230077 2230144 2230198 "PDDOM" 2230363 NIL PDDOM (NIL T T) -9 NIL 2230443 NIL) (-921 2229890 2229926 2230033 "PDDOM-" 2230038 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229635 2229674 2229764 "PCOMP" 2229851 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227675 2228436 2228733 "PBWLB" 2229364 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227301 2227364 2227473 "PATTERN2" 2227612 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225010 2225446 2225903 "PATTERN1" 2226890 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217189 2219083 2220421 "PATTERN" 2223693 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216747 2216820 2216952 "PATRES2" 2217116 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214013 2214696 2215177 "PATRES" 2216312 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211866 2212301 2212708 "PATMATCH" 2213680 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211320 2211571 2211612 "PATMAB" 2211719 NIL PATMAB (NIL T) -9 NIL 2211802 NIL) (-911 2209766 2210174 2210432 "PATLRES" 2211125 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209304 2209435 2209476 "PATAB" 2209481 NIL PATAB (NIL T) -9 NIL 2209653 NIL) (-909 2207444 2207881 2208304 "PARTPERM" 2208901 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207053 2207128 2207230 "PARSURF" 2207375 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206679 2206742 2206851 "PARSU2" 2206990 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206437 2206483 2206550 "PARSER" 2206632 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206046 2206121 2206223 "PARSCURV" 2206368 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205672 2205735 2205844 "PARSC2" 2205983 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205299 2205369 2205466 "PARPCURV" 2205608 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204925 2204988 2205097 "PARPC2" 2205236 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203914 2204298 2204480 "PARAMAST" 2204763 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203422 2203520 2203639 "PAN2EXPR" 2203815 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202115 2202543 2202771 "PALETTE" 2203214 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200460 2201120 2201480 "PAIR" 2201801 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193393 2199717 2199912 "PADICRC" 2200314 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185650 2192737 2192922 "PADICRAT" 2193240 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182447 2184310 2184350 "PADICCT" 2184931 NIL PADICCT (NIL NIL) -9 NIL 2185213 NIL) (-894 2180463 2182384 2182429 "PADIC" 2182434 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179408 2179620 2179888 "PADEPAC" 2180250 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178608 2178753 2178959 "PADE" 2179270 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176841 2177816 2178096 "OWP" 2178412 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176286 2176547 2176644 "OVERSET" 2176764 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175206 2175891 2176063 "OVAR" 2176154 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163442 2166315 2168515 "OUTFORM" 2173026 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162724 2163039 2163166 "OUTBFILE" 2163335 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2162001 2162196 2162224 "OUTBCON" 2162542 T OUTBCON (NIL) -9 NIL 2162708 NIL) (-885 2161584 2161714 2161871 "OUTBCON-" 2161876 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160824 2160969 2161130 "OUT" 2161443 T OUT (NIL) -7 NIL NIL NIL) (-883 2160120 2160553 2160642 "OSI" 2160755 T OSI (NIL) -8 NIL NIL NIL) (-882 2159539 2159961 2159989 "OSGROUP" 2159994 T OSGROUP (NIL) -9 NIL 2160016 NIL) (-881 2158250 2158511 2158796 "ORTHPOL" 2159286 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155501 2158085 2158206 "OREUP" 2158211 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152604 2155192 2155319 "ORESUP" 2155443 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150104 2150632 2151193 "OREPCTO" 2152093 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143482 2145977 2146018 "OREPCAT" 2148366 NIL OREPCAT (NIL T) -9 NIL 2149470 NIL) (-876 2140455 2141411 2142469 "OREPCAT-" 2142474 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139647 2139925 2139953 "ORDTYPE" 2140262 T ORDTYPE (NIL) -9 NIL 2140425 NIL) (-874 2138948 2139164 2139419 "ORDTYPE-" 2139424 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138304 2138687 2138845 "ORDSTRCT" 2138850 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137802 2138172 2138200 "ORDSET" 2138205 T ORDSET (NIL) -9 NIL 2138227 NIL) (-871 2136453 2137424 2137452 "ORDRING" 2137457 T ORDRING (NIL) -9 NIL 2137486 NIL) (-870 2135704 2136269 2136297 "ORDMON" 2136302 T ORDMON (NIL) -9 NIL 2136323 NIL) (-869 2134848 2135013 2135208 "ORDFUNS" 2135553 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134063 2134578 2134606 "ORDFIN" 2134671 T ORDFIN (NIL) -9 NIL 2134745 NIL) (-867 2133317 2133456 2133642 "ORDCOMP2" 2133923 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129664 2131903 2132312 "ORDCOMP" 2132941 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126185 2127155 2127969 "OPTPROB" 2128870 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122927 2123626 2124330 "OPTPACK" 2125501 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120540 2121366 2121394 "OPTCAT" 2122213 T OPTCAT (NIL) -9 NIL 2122863 NIL) (-862 2119858 2120217 2120322 "OPSIG" 2120455 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119620 2119665 2119731 "OPQUERY" 2119812 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118926 2119206 2119247 "OPERCAT" 2119459 NIL OPERCAT (NIL T) -9 NIL 2119556 NIL) (-859 2118669 2118737 2118854 "OPERCAT-" 2118859 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115585 2116980 2117484 "OP" 2118198 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114878 2115005 2115179 "ONECOMP2" 2115457 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111491 2113675 2114044 "ONECOMP" 2114542 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110892 2111016 2111146 "OMSERVER" 2111381 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107404 2110330 2110370 "OMSAGG" 2110431 NIL OMSAGG (NIL T) -9 NIL 2110496 NIL) (-853 2105979 2106290 2106572 "OMPKG" 2107142 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104326 2105528 2105697 "OMLO" 2105860 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103262 2103433 2103653 "OMEXPR" 2104152 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102347 2102683 2102843 "OMERRK" 2103122 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101584 2101893 2102029 "OMERR" 2102231 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100975 2101261 2101369 "OMENC" 2101496 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094612 2096055 2097226 "OMDEV" 2099824 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093645 2093852 2094046 "OMCONN" 2094438 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093051 2093178 2093206 "OM" 2093505 T OM (NIL) -9 NIL NIL NIL) (-844 2091329 2092521 2092549 "OINTDOM" 2092554 T OINTDOM (NIL) -9 NIL 2092575 NIL) (-843 2088404 2090017 2090354 "OFMONOID" 2091024 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087638 2088341 2088386 "ODVAR" 2088391 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084782 2087383 2087538 "ODR" 2087543 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076194 2084558 2084684 "ODPOL" 2084689 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069488 2076066 2076171 "ODP" 2076176 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068230 2068469 2068744 "ODETOOLS" 2069262 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065173 2065855 2066571 "ODESYS" 2067563 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2060003 2060963 2061988 "ODERTRIC" 2064248 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059423 2059511 2059705 "ODERED" 2059915 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056275 2056859 2057536 "ODERAT" 2058846 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053191 2053699 2054296 "ODEPRRIC" 2055804 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051086 2051730 2052216 "ODEPROB" 2052725 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047552 2048091 2048738 "ODEPRIM" 2050565 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046795 2046903 2047163 "ODEPAL" 2047444 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042897 2043748 2044612 "ODEPACK" 2045951 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041940 2042065 2042287 "ODEINT" 2042786 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036005 2037466 2038913 "ODEIFTBL" 2040513 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031355 2032189 2033141 "ODEEF" 2035164 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030698 2030793 2031016 "ODECONST" 2031260 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028761 2029470 2029498 "ODECAT" 2030103 T ODECAT (NIL) -9 NIL 2030634 NIL) (-823 2028393 2028442 2028569 "OCTCT2" 2028712 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024893 2028098 2028220 "OCT" 2028303 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024086 2024686 2024714 "OCAMON" 2024719 T OCAMON (NIL) -9 NIL 2024740 NIL) (-820 2018357 2021129 2021169 "OC" 2022266 NIL OC (NIL T) -9 NIL 2023124 NIL) (-819 2015392 2016332 2017322 "OC-" 2017416 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014812 2015237 2015265 "OASGP" 2015270 T OASGP (NIL) -9 NIL 2015290 NIL) (-817 2013908 2014535 2014563 "OAMONS" 2014603 T OAMONS (NIL) -9 NIL 2014646 NIL) (-816 2013084 2013643 2013671 "OAMON" 2013729 T OAMON (NIL) -9 NIL 2013781 NIL) (-815 2012942 2012975 2013043 "OAMON-" 2013048 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011723 2012476 2012504 "OAGROUP" 2012651 T OAGROUP (NIL) -9 NIL 2012744 NIL) (-813 2011426 2011514 2011632 "OAGROUP-" 2011637 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011108 2011164 2011253 "NUMTUBE" 2011370 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004627 2006199 2007735 "NUMQUAD" 2009592 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000307 2001341 2002376 "NUMODE" 2003612 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997588 1998528 1998556 "NUMINT" 1999479 T NUMINT (NIL) -9 NIL 2000243 NIL) (-808 1996500 1996733 1996951 "NUMFMT" 1997390 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982683 1985804 1988336 "NUMERIC" 1994007 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976387 1982131 1982226 "NTSCAT" 1982231 NIL NTSCAT (NIL T T T T) -9 NIL 1982270 NIL) (-805 1975567 1975746 1975939 "NTPOLFN" 1976226 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975193 1975256 1975365 "NSUP2" 1975504 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961975 1972018 1972830 "NSUP" 1974414 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950818 1961749 1961882 "NSMP" 1961887 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949226 1949551 1949908 "NREP" 1950506 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947805 1948069 1948427 "NPCOEF" 1948969 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946853 1946986 1947202 "NORMRETR" 1947686 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944864 1945184 1945593 "NORMPK" 1946561 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944543 1944577 1944701 "NORMMA" 1944830 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944326 1944361 1944430 "NONE1" 1944507 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944090 1944283 1944312 "NONE" 1944317 T NONE (NIL) -8 NIL NIL NIL) (-794 1943581 1943649 1943828 "NODE1" 1944022 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941642 1942704 1942959 "NNI" 1943306 T NNI (NIL) -8 NIL NIL 1943541) (-792 1940038 1940375 1940739 "NLINSOL" 1941310 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936219 1937274 1938173 "NIPROB" 1939159 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934958 1935210 1935512 "NFINTBAS" 1935981 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934042 1934608 1934649 "NETCLT" 1934821 NIL NETCLT (NIL T) -9 NIL 1934903 NIL) (-788 1932714 1932981 1933262 "NCODIV" 1933810 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932470 1932513 1932588 "NCNTFRAC" 1932671 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930626 1931014 1931434 "NCEP" 1932095 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929289 1930236 1930264 "NASRING" 1930374 T NASRING (NIL) -9 NIL 1930454 NIL) (-784 1929072 1929128 1929222 "NASRING-" 1929227 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928039 1928690 1928718 "NARNG" 1928835 T NARNG (NIL) -9 NIL 1928926 NIL) (-782 1927713 1927798 1927932 "NARNG-" 1927937 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926550 1926799 1927034 "NAGSP" 1927498 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917594 1919506 1921179 "NAGS" 1924897 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916118 1916450 1916781 "NAGF07" 1917283 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910590 1911947 1913254 "NAGF04" 1914831 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903462 1905172 1906805 "NAGF02" 1908977 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898626 1899786 1900903 "NAGF01" 1902365 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892206 1893820 1895405 "NAGE04" 1897061 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883267 1885496 1887626 "NAGE02" 1890096 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879160 1880167 1881131 "NAGE01" 1882323 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876937 1877489 1878047 "NAGD03" 1878622 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868633 1870615 1872569 "NAGD02" 1875003 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862372 1863869 1865309 "NAGD01" 1867213 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858509 1859403 1860240 "NAGC06" 1861555 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856956 1857306 1857662 "NAGC05" 1858173 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856320 1856451 1856595 "NAGC02" 1856832 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855121 1855848 1855888 "NAALG" 1855967 NIL NAALG (NIL T) -9 NIL 1856028 NIL) (-765 1854950 1854985 1855075 "NAALG-" 1855080 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848822 1850008 1851195 "MULTSQFR" 1853846 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848129 1848216 1848400 "MULTFACT" 1848734 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840274 1844712 1844765 "MTSCAT" 1845835 NIL MTSCAT (NIL T T) -9 NIL 1846351 NIL) (-761 1839980 1840040 1840132 "MTHING" 1840214 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839766 1839805 1839865 "MSYSCMD" 1839940 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836511 1839327 1839368 "MSETAGG" 1839373 NIL MSETAGG (NIL T) -9 NIL 1839407 NIL) (-758 1832225 1835266 1835586 "MSET" 1836224 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827824 1829604 1830349 "MRING" 1831525 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827384 1827457 1827588 "MRF2" 1827751 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826996 1827037 1827181 "MRATFAC" 1827343 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824566 1824903 1825334 "MPRFF" 1826701 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817900 1824420 1824517 "MPOLY" 1824522 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817384 1817425 1817633 "MPCPF" 1817859 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816892 1816941 1817125 "MPC3" 1817335 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816075 1816168 1816389 "MPC2" 1816807 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814352 1814713 1815103 "MONOTOOL" 1815735 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813497 1813880 1813908 "MONOID" 1814127 T MONOID (NIL) -9 NIL 1814274 NIL) (-747 1813013 1813162 1813343 "MONOID-" 1813348 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801986 1808833 1808892 "MONOGEN" 1809566 NIL MONOGEN (NIL T T) -9 NIL 1810022 NIL) (-745 1799036 1799939 1800939 "MONOGEN-" 1801058 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797753 1798301 1798329 "MONADWU" 1798721 T MONADWU (NIL) -9 NIL 1798959 NIL) (-743 1797083 1797284 1797532 "MONADWU-" 1797537 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796368 1796672 1796700 "MONAD" 1796907 T MONAD (NIL) -9 NIL 1797019 NIL) (-741 1796035 1796131 1796263 "MONAD-" 1796268 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794174 1794948 1795227 "MOEBIUS" 1795788 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793342 1793842 1793882 "MODULE" 1793887 NIL MODULE (NIL T) -9 NIL 1793926 NIL) (-738 1792880 1793006 1793196 "MODULE-" 1793201 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790410 1791244 1791571 "MODRING" 1792704 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787139 1788515 1789036 "MODOP" 1789939 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785625 1786206 1786483 "MODMONOM" 1787002 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774386 1783916 1784330 "MODMON" 1785262 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771219 1773230 1773506 "MODFIELD" 1774261 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770130 1770500 1770690 "MMLFORM" 1771049 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769650 1769699 1769878 "MMAP" 1770081 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767543 1768482 1768523 "MLO" 1768946 NIL MLO (NIL T) -9 NIL 1769188 NIL) (-729 1764891 1765425 1766027 "MLIFT" 1767024 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764270 1764366 1764520 "MKUCFUNC" 1764802 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763863 1763939 1764062 "MKRECORD" 1764193 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762886 1763072 1763300 "MKFUNC" 1763674 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762262 1762378 1762534 "MKFLCFN" 1762769 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761527 1761641 1761826 "MKBCFUNC" 1762155 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757524 1761081 1761217 "MINT" 1761411 T MINT (NIL) -8 NIL NIL NIL) (-722 1756306 1756579 1756856 "MHROWRED" 1757279 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751057 1754841 1755246 "MFLOAT" 1755921 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750402 1750490 1750661 "MFINFACT" 1750969 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746681 1747565 1748449 "MESH" 1749538 T MESH (NIL) -7 NIL NIL NIL) (-718 1745035 1745383 1745736 "MDDFACT" 1746368 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741571 1744166 1744207 "MDAGG" 1744462 NIL MDAGG (NIL T) -9 NIL 1744605 NIL) (-716 1729294 1740864 1741071 "MCMPLX" 1741384 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728413 1728577 1728778 "MCDEN" 1729143 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726261 1726573 1726953 "MCALCFN" 1728143 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725138 1725426 1725659 "MAYBE" 1726067 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722696 1723273 1723835 "MATSTOR" 1724609 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718118 1722068 1722316 "MATRIX" 1722481 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713818 1714591 1715327 "MATLIN" 1717475 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712394 1712565 1712898 "MATCAT2" 1713653 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701733 1705451 1705528 "MATCAT" 1710560 NIL MATCAT (NIL T T T) -9 NIL 1712032 NIL) (-707 1697686 1698996 1700409 "MATCAT-" 1700414 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695762 1696122 1696506 "MAPPKG3" 1697361 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694719 1694916 1695138 "MAPPKG2" 1695586 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693176 1693502 1693829 "MAPPKG1" 1694425 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692177 1692582 1692759 "MAPPAST" 1693019 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691782 1691846 1691969 "MAPHACK3" 1692113 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691362 1691435 1691549 "MAPHACK2" 1691714 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690788 1690903 1691045 "MAPHACK1" 1691253 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688711 1689488 1689792 "MAGMA" 1690516 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688130 1688435 1688526 "MACROAST" 1688640 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684373 1686369 1686830 "M3D" 1687702 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677845 1682684 1682725 "LZSTAGG" 1683507 NIL LZSTAGG (NIL T) -9 NIL 1683802 NIL) (-695 1673527 1674976 1676433 "LZSTAGG-" 1676438 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670440 1671418 1671905 "LWORD" 1673072 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669962 1670244 1670319 "LSTAST" 1670385 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661890 1669733 1669867 "LSQM" 1669872 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661108 1661253 1661481 "LSPP" 1661745 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657845 1658561 1659291 "LSMP1" 1660410 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655627 1655958 1656414 "LSMP" 1657534 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648755 1654717 1654758 "LSAGG" 1654820 NIL LSAGG (NIL T) -9 NIL 1654898 NIL) (-687 1645264 1646374 1647587 "LSAGG-" 1647592 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642559 1644408 1644657 "LPOLY" 1645059 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642135 1642226 1642349 "LPEFRAC" 1642468 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641818 1641897 1641925 "LOGIC" 1642036 T LOGIC (NIL) -9 NIL 1642118 NIL) (-683 1641674 1641703 1641774 "LOGIC-" 1641779 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640849 1641007 1641200 "LODOOPS" 1641530 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639373 1639622 1639975 "LODOF" 1640596 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635249 1638008 1638049 "LODOCAT" 1638487 NIL LODOCAT (NIL T) -9 NIL 1638698 NIL) (-679 1634964 1635040 1635167 "LODOCAT-" 1635172 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631950 1634805 1634923 "LODO2" 1634928 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629057 1631887 1631932 "LODO1" 1631937 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626152 1628973 1629039 "LODO" 1629044 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625021 1625198 1625503 "LODEEF" 1625975 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623007 1624115 1624368 "LO" 1624853 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617979 1621173 1621214 "LNAGG" 1622076 NIL LNAGG (NIL T) -9 NIL 1622511 NIL) (-672 1617072 1617340 1617682 "LNAGG-" 1617687 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613052 1613997 1614636 "LMOPS" 1616487 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612351 1612829 1612870 "LMODULE" 1612875 NIL LMODULE (NIL T) -9 NIL 1612901 NIL) (-669 1609306 1611996 1612119 "LMDICT" 1612261 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608882 1609096 1609137 "LLINSET" 1609198 NIL LLINSET (NIL T) -9 NIL 1609242 NIL) (-667 1608527 1608790 1608850 "LITERAL" 1608855 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608046 1608126 1608265 "LIST3" 1608447 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606144 1606492 1606891 "LIST2MAP" 1607693 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605133 1605329 1605557 "LIST2" 1605962 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597587 1604067 1604371 "LIST" 1604862 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597170 1597406 1597447 "LINSET" 1597452 NIL LINSET (NIL T) -9 NIL 1597486 NIL) (-661 1595984 1596678 1596845 "LINFORM" 1597055 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594283 1595011 1595052 "LINEXP" 1595542 NIL LINEXP (NIL T) -9 NIL 1595815 NIL) (-659 1592859 1593763 1593944 "LINELT" 1594154 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591416 1591696 1592007 "LINDEP" 1592611 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590552 1591148 1591258 "LINBASIS" 1591346 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587289 1588038 1588815 "LIMITRF" 1589807 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585574 1585888 1586297 "LIMITPS" 1586984 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584402 1584977 1585017 "LIECAT" 1585157 NIL LIECAT (NIL T) -9 NIL 1585308 NIL) (-653 1584237 1584270 1584358 "LIECAT-" 1584363 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578257 1583748 1583976 "LIE" 1584058 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570442 1577797 1577953 "LIB" 1578121 T LIB (NIL) -8 NIL NIL NIL) (-650 1566011 1566960 1567895 "LGROBP" 1569559 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564635 1565543 1565571 "LFCAT" 1565778 T LFCAT (NIL) -9 NIL 1565917 NIL) (-648 1562573 1562907 1563257 "LF" 1564356 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559433 1560105 1560793 "LEXTRIPK" 1561937 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556021 1557003 1557506 "LEXP" 1559013 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555437 1555742 1555834 "LETAST" 1555949 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553823 1554148 1554549 "LEADCDET" 1555119 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553001 1553087 1553316 "LAZM3PK" 1553744 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547526 1551078 1551616 "LAUPOL" 1552513 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547099 1547149 1547310 "LAPLACE" 1547476 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545947 1546663 1546704 "LALG" 1546766 NIL LALG (NIL T) -9 NIL 1546825 NIL) (-639 1545643 1545720 1545856 "LALG-" 1545861 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543380 1544744 1544995 "LA" 1545476 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543209 1543239 1543280 "KVTFROM" 1543342 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541966 1542576 1542761 "KTVLOGIC" 1543044 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541795 1541825 1541866 "KRCFROM" 1541928 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540687 1540886 1541185 "KOVACIC" 1541595 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540516 1540546 1540587 "KONVERT" 1540649 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540345 1540375 1540416 "KOERCE" 1540478 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539829 1539922 1540054 "KERNEL2" 1540259 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537516 1538422 1538799 "KERNEL" 1539485 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530987 1535993 1536047 "KDAGG" 1536424 NIL KDAGG (NIL T T) -9 NIL 1536630 NIL) (-628 1530498 1530640 1530845 "KDAGG-" 1530850 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523198 1530159 1530314 "KAFILE" 1530376 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522802 1523087 1523150 "JVMOP" 1523155 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521538 1522042 1522291 "JVMMDACC" 1522573 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520474 1520928 1521133 "JVMFDACC" 1521353 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519055 1519550 1519850 "JVMCSTTG" 1520194 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518191 1518595 1518756 "JVMCFACC" 1518914 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517869 1518108 1518157 "JVMBCODE" 1518162 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511888 1517380 1517608 "JORDAN" 1517690 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511201 1511537 1511658 "JOINAST" 1511787 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507236 1509378 1509432 "IXAGG" 1510361 NIL IXAGG (NIL T T) -9 NIL 1510820 NIL) (-617 1506089 1506461 1506880 "IXAGG-" 1506885 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501178 1506011 1506070 "IVECTOR" 1506075 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499903 1500181 1500447 "ITUPLE" 1500945 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498375 1498582 1498877 "ITRIGMNP" 1499725 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497102 1497324 1497607 "ITFUN3" 1498151 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496700 1496763 1496886 "ITFUN2" 1497025 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495805 1496180 1496354 "ITFORM" 1496546 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493574 1494825 1495103 "ITAYLOR" 1495560 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481978 1487711 1488874 "ISUPS" 1492444 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481070 1481222 1481458 "ISUMP" 1481825 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475920 1481015 1481056 "ISTRING" 1481061 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475336 1475641 1475733 "ISAST" 1475848 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474533 1474627 1474843 "IRURPK" 1475250 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473445 1473670 1473910 "IRSN" 1474313 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471490 1471871 1472300 "IRRF2F" 1473083 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471231 1471275 1471351 "IRREDFFX" 1471446 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469804 1470105 1470404 "IROOT" 1470964 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468943 1469297 1469448 "IRFORM" 1469673 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468025 1468156 1468370 "IR2F" 1468826 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465614 1466133 1466699 "IR2" 1467503 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462054 1463298 1463990 "IR" 1464954 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461839 1461879 1461939 "IPRNTPK" 1462014 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457813 1461728 1461797 "IPF" 1461802 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455841 1457738 1457795 "IPADIC" 1457800 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455099 1455401 1455531 "IP4ADDR" 1455731 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454437 1454728 1454860 "IOMODE" 1454987 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453408 1454034 1454161 "IOBFILE" 1454330 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452818 1453312 1453340 "IOBCON" 1453345 T IOBCON (NIL) -9 NIL 1453366 NIL) (-589 1452323 1452387 1452570 "INVLAPLA" 1452754 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441893 1444325 1446711 "INTTR" 1449987 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438186 1438970 1439835 "INTTOOLS" 1441078 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437766 1437863 1437980 "INTSLPE" 1438089 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435233 1437689 1437748 "INTRVL" 1437753 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432811 1433347 1433922 "INTRF" 1434718 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432204 1432319 1432461 "INTRET" 1432709 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430177 1430590 1431060 "INTRAT" 1431812 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427422 1428023 1428642 "INTPM" 1429662 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424139 1424766 1425504 "INTPAF" 1426808 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419240 1420280 1421331 "INTPACK" 1423108 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418486 1418644 1418852 "INTHERTR" 1419082 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417919 1418005 1418193 "INTHERAL" 1418400 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415687 1416208 1416665 "INTHEORY" 1417482 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407019 1408714 1410486 "INTG0" 1414039 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387544 1392382 1397192 "INTFTBL" 1402229 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386769 1386931 1387104 "INTFACT" 1387403 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384166 1384642 1385199 "INTEF" 1386323 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382363 1383258 1383286 "INTDOM" 1383587 T INTDOM (NIL) -9 NIL 1383794 NIL) (-570 1381702 1381906 1382148 "INTDOM-" 1382153 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377570 1379991 1380045 "INTCAT" 1380844 NIL INTCAT (NIL T) -9 NIL 1381165 NIL) (-568 1377024 1377145 1377273 "INTBIT" 1377462 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375705 1375877 1376184 "INTALG" 1376869 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375182 1375278 1375435 "INTAF" 1375609 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368149 1374992 1375132 "INTABL" 1375137 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367390 1367952 1368017 "INT8" 1368051 T INT8 (NIL) -8 NIL NIL 1368096) (-563 1366630 1367192 1367257 "INT64" 1367291 T INT64 (NIL) -8 NIL NIL 1367336) (-562 1365870 1366432 1366497 "INT32" 1366531 T INT32 (NIL) -8 NIL NIL 1366576) (-561 1365110 1365672 1365737 "INT16" 1365771 T INT16 (NIL) -8 NIL NIL 1365816) (-560 1361313 1364907 1365016 "INT" 1365021 T INT (NIL) -8 NIL NIL NIL) (-559 1355422 1358861 1358889 "INS" 1359823 T INS (NIL) -9 NIL 1360488 NIL) (-558 1352579 1353499 1354440 "INS-" 1354513 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330936 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329790 1330113 1330141 "INBCON" 1330654 T INBCON (NIL) -9 NIL 1330920 NIL) (-540 1329000 1329265 1329541 "INBCON-" 1329546 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328419 1328724 1328815 "INAST" 1328929 T INAST (NIL) -8 NIL NIL NIL) (-538 1327786 1328098 1328204 "IMPTAST" 1328333 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323707 1327630 1327734 "IMATRIX" 1327739 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322399 1322538 1322854 "IMATQF" 1323563 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320579 1320846 1321183 "IMATLIN" 1322155 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314494 1320503 1320561 "ILIST" 1320566 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312160 1314354 1314467 "IIARRAY2" 1314472 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306981 1312071 1312135 "IFF" 1312140 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306262 1306598 1306714 "IFAST" 1306885 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300774 1305554 1305742 "IFARRAY" 1306119 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299812 1300678 1300751 "IFAMON" 1300756 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299384 1299461 1299515 "IEVALAB" 1299722 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299047 1299127 1299287 "IEVALAB-" 1299292 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298080 1298936 1299011 "IDPOAMS" 1299016 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297182 1297969 1298044 "IDPOAM" 1298049 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296563 1297097 1297159 "IDPO" 1297164 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295043 1295570 1295622 "IDPC" 1296134 NIL IDPC (NIL T T) -9 NIL 1296415 NIL) (-522 1294375 1294935 1295008 "IDPAM" 1295013 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293590 1294267 1294340 "IDPAG" 1294345 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293134 1293396 1293486 "IDENT" 1293520 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289353 1290237 1291132 "IDECOMP" 1292291 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281988 1283276 1284323 "IDEAL" 1288389 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281130 1281260 1281460 "ICDEN" 1281872 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280105 1280610 1280757 "ICARD" 1281003 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278135 1278478 1278883 "IBPTOOLS" 1279782 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273250 1277755 1277868 "IBITS" 1278054 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269925 1270549 1271244 "IBATOOL" 1272667 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267686 1268166 1268699 "IBACHIN" 1269460 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265276 1267532 1267635 "IARRAY2" 1267640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260989 1265202 1265259 "IARRAY1" 1265264 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254006 1259401 1259882 "IAN" 1260528 T IAN (NIL) -8 NIL NIL NIL) (-508 1253511 1253574 1253747 "IALGFACT" 1253943 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253003 1253152 1253180 "HYPCAT" 1253387 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252505 1252658 1252844 "HYPCAT-" 1252849 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252052 1252300 1252383 "HOSTNAME" 1252442 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251885 1251934 1251975 "HOMOTOP" 1251980 NIL HOMOTOP (NIL T) -9 NIL 1252013 NIL) (-503 1248318 1249817 1249858 "HOAGG" 1250839 NIL HOAGG (NIL T) -9 NIL 1251568 NIL) (-502 1246834 1247311 1247837 "HOAGG-" 1247842 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239891 1246427 1246577 "HEXADEC" 1246704 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238603 1238861 1239124 "HEUGCD" 1239668 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237535 1238440 1238570 "HELLFDIV" 1238575 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235543 1237310 1237399 "HEAP" 1237478 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234740 1235095 1235229 "HEADAST" 1235429 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228078 1234655 1234717 "HDP" 1234722 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221097 1227713 1227865 "HDMP" 1227979 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220403 1220561 1220725 "HB" 1220953 T HB (NIL) -7 NIL NIL NIL) (-493 1213413 1220249 1220353 "HASHTBL" 1220358 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212829 1213134 1213226 "HASAST" 1213341 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210242 1212451 1212633 "HACKPI" 1212667 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205414 1210095 1210208 "GTSET" 1210213 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198453 1205292 1205390 "GSTBL" 1205395 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190216 1197618 1197874 "GSERIES" 1198253 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189247 1189760 1189788 "GROUP" 1189991 T GROUP (NIL) -9 NIL 1190125 NIL) (-486 1188571 1188772 1189023 "GROUP-" 1189028 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186920 1187259 1187646 "GROEBSOL" 1188248 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185748 1186108 1186159 "GRMOD" 1186688 NIL GRMOD (NIL T T) -9 NIL 1186856 NIL) (-483 1185504 1185552 1185680 "GRMOD-" 1185685 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180644 1181858 1182858 "GRIMAGE" 1184524 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179038 1179371 1179695 "GRDEF" 1180340 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178470 1178598 1178739 "GRAY" 1178917 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177547 1178049 1178100 "GRALG" 1178253 NIL GRALG (NIL T T) -9 NIL 1178346 NIL) (-478 1177184 1177281 1177444 "GRALG-" 1177449 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173665 1176767 1176946 "GPOLSET" 1177090 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173013 1173076 1173334 "GOSPER" 1173602 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168583 1169451 1169977 "GMODPOL" 1172712 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167570 1167772 1168010 "GHENSEL" 1168395 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161642 1162569 1163589 "GENUPS" 1166654 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161333 1161390 1161479 "GENUFACT" 1161585 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160733 1160822 1160987 "GENPGCD" 1161251 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160201 1160242 1160455 "GENMFACT" 1160692 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158737 1159024 1159331 "GENEEZ" 1159944 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151916 1158348 1158510 "GDMP" 1158660 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140654 1145687 1146793 "GCNAALG" 1150899 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138781 1139829 1139857 "GCDDOM" 1140112 T GCDDOM (NIL) -9 NIL 1140269 NIL) (-465 1138221 1138378 1138593 "GCDDOM-" 1138598 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126693 1129167 1131559 "GBINTERN" 1135912 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124494 1124822 1125243 "GBF" 1126368 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123251 1123440 1123707 "GBEUCLID" 1124310 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121901 1122108 1122412 "GB" 1123030 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121232 1121375 1121524 "GAUSSFAC" 1121772 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119553 1119901 1120215 "GALUTIL" 1120951 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117813 1118135 1118459 "GALPOLYU" 1119280 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115112 1115468 1115875 "GALFACTU" 1117510 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106726 1108417 1110025 "GALFACT" 1113544 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104012 1104772 1104800 "FVFUN" 1105956 T FVFUN (NIL) -9 NIL 1106676 NIL) (-454 1103242 1103460 1103488 "FVC" 1103779 T FVC (NIL) -9 NIL 1103962 NIL) (-453 1102843 1103067 1103135 "FUNDESC" 1103194 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102416 1102640 1102721 "FUNCTION" 1102795 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101093 1101717 1101920 "FTEM" 1102233 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098723 1099415 1099881 "FT" 1100647 T FT (NIL) -8 NIL NIL NIL) (-449 1096992 1097303 1097700 "FSUPFACT" 1098414 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095311 1095678 1096010 "FST" 1096680 T FST (NIL) -8 NIL NIL NIL) (-447 1094492 1094616 1094804 "FSRED" 1095193 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093181 1093447 1093794 "FSPRMELT" 1094207 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090391 1090925 1091411 "FSPECF" 1092744 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089913 1089973 1090143 "FSINT" 1090332 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088049 1088906 1089209 "FSERIES" 1089692 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087073 1087207 1087431 "FSCINT" 1087929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086097 1086258 1086485 "FSAGG2" 1086926 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081961 1085041 1085082 "FSAGG" 1085452 NIL FSAGG (NIL T) -9 NIL 1085711 NIL) (-439 1079561 1080324 1081120 "FSAGG-" 1081215 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077221 1077519 1078067 "FS2UPS" 1079279 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076087 1076270 1076572 "FS2EXPXP" 1077046 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075715 1075764 1075893 "FS2" 1076038 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055953 1065489 1065530 "FS" 1069414 NIL FS (NIL T) -9 NIL 1071703 NIL) (-434 1044014 1047589 1051646 "FS-" 1051946 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043428 1043555 1043707 "FRUTIL" 1043894 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037939 1041117 1041157 "FRNAALG" 1042477 NIL FRNAALG (NIL T) -9 NIL 1043075 NIL) (-431 1033420 1034688 1035963 "FRNAALG-" 1036713 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033052 1033101 1033228 "FRNAAF2" 1033371 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031339 1031901 1032197 "FRMOD" 1032864 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030524 1030617 1030908 "FRIDEAL2" 1031246 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028129 1028899 1029217 "FRIDEAL" 1030315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027220 1027676 1027717 "FRETRCT" 1027722 NIL FRETRCT (NIL T) -9 NIL 1027898 NIL) (-425 1026278 1026563 1026914 "FRETRCT-" 1026919 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023099 1024562 1024621 "FRAMALG" 1025503 NIL FRAMALG (NIL T T) -9 NIL 1025795 NIL) (-423 1021137 1021688 1022318 "FRAMALG-" 1022541 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020767 1020830 1020937 "FRAC2" 1021074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013759 1020240 1020517 "FRAC" 1020522 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013389 1013452 1013559 "FR2" 1013696 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004306 1008884 1010242 "FR" 1012063 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998225 1001685 1001713 "FPS" 1002832 T FPS (NIL) -9 NIL 1003389 NIL) (-417 997650 997783 997947 "FPS-" 998093 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994616 996607 996635 "FPC" 996860 T FPC (NIL) -9 NIL 997002 NIL) (-415 994397 994449 994546 "FPC-" 994551 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993155 993885 993926 "FPATMAB" 993931 NIL FPATMAB (NIL T) -9 NIL 994083 NIL) (-413 991298 991897 992244 "FPARFRAC" 992871 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986590 987190 987872 "FORTRAN" 990730 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984164 984828 984856 "FORTFN" 985916 T FORTFN (NIL) -9 NIL 986540 NIL) (-410 983916 983978 984006 "FORTCAT" 984065 T FORTCAT (NIL) -9 NIL 984127 NIL) (-409 981602 982132 982671 "FORT" 983397 T FORT (NIL) -7 NIL NIL NIL) (-408 981384 981420 981489 "FORMULA1" 981566 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979388 980000 980390 "FORMULA" 981014 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978905 978963 979136 "FORDER" 979330 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977965 978165 978358 "FOP" 978732 T FOP (NIL) -7 NIL NIL NIL) (-404 976378 977245 977419 "FNLA" 977847 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974997 975508 975536 "FNCAT" 975996 T FNCAT (NIL) -9 NIL 976256 NIL) (-402 974440 974956 974984 "FNAME" 974989 T FNAME (NIL) -8 NIL NIL NIL) (-401 972766 973939 973967 "FMTC" 973972 T FMTC (NIL) -9 NIL 974008 NIL) (-400 971315 972702 972748 "FMONOID" 972753 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967904 969270 969311 "FMONCAT" 970528 NIL FMONCAT (NIL T) -9 NIL 971133 NIL) (-398 965226 965974 966002 "FMFUN" 967146 T FMFUN (NIL) -9 NIL 967854 NIL) (-397 962099 963151 963205 "FMCAT" 964400 NIL FMCAT (NIL T T) -9 NIL 964895 NIL) (-396 961332 961549 961577 "FMC" 961867 T FMC (NIL) -9 NIL 962049 NIL) (-395 960000 961098 961198 "FM1" 961277 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959018 959742 959891 "FM" 959896 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956756 957208 957702 "FLOATRP" 958569 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954158 954694 955272 "FLOATCP" 956223 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946821 951887 952508 "FLOAT" 953557 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945339 946413 946454 "FLINEXP" 946459 NIL FLINEXP (NIL T) -9 NIL 946552 NIL) (-389 944469 944728 945056 "FLINEXP-" 945061 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943527 943689 943913 "FLASORT" 944321 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940445 941497 941549 "FLALG" 942776 NIL FLALG (NIL T T) -9 NIL 943243 NIL) (-386 939469 939630 939857 "FLAGG2" 940298 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932724 936878 936919 "FLAGG" 938181 NIL FLAGG (NIL T) -9 NIL 938833 NIL) (-384 931378 931789 932279 "FLAGG-" 932284 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928016 929223 929282 "FINRALG" 930410 NIL FINRALG (NIL T T) -9 NIL 930918 NIL) (-382 927140 927405 927744 "FINRALG-" 927749 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926446 926745 926773 "FINITE" 926969 T FINITE (NIL) -9 NIL 927076 NIL) (-380 918397 920976 921016 "FINAALG" 924683 NIL FINAALG (NIL T) -9 NIL 926136 NIL) (-379 913513 914779 915923 "FINAALG-" 917302 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912073 912495 912549 "FILECAT" 913233 NIL FILECAT (NIL T T) -9 NIL 913449 NIL) (-377 911351 911828 911931 "FILE" 912003 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908754 910581 910609 "FIELD" 910649 T FIELD (NIL) -9 NIL 910729 NIL) (-375 907296 907759 908270 "FIELD-" 908275 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904979 905931 906278 "FGROUP" 906982 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904051 904233 904453 "FGLMICPK" 904811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899306 903976 904033 "FFX" 904038 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898901 898968 899103 "FFSLPE" 899239 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898399 898441 898650 "FFPOLY2" 898859 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894275 895171 895967 "FFPOLY" 897635 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889544 894194 894257 "FFP" 894262 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884075 888887 889077 "FFNBX" 889398 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878408 883210 883468 "FFNBP" 883929 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872446 877692 877903 "FFNB" 878241 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871266 871476 871791 "FFINTBAS" 872243 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866859 869513 869541 "FFIELDC" 870161 T FFIELDC (NIL) -9 NIL 870537 NIL) (-362 865479 865920 866403 "FFIELDC-" 866408 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865036 865094 865218 "FFHOM" 865421 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862695 863218 863735 "FFF" 864551 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857730 862437 862538 "FFCGX" 862638 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852769 857462 857569 "FFCGP" 857673 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847369 852496 852604 "FFCG" 852705 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846774 846823 847058 "FFCAT2" 847320 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825456 836506 836592 "FFCAT" 841757 NIL FFCAT (NIL T T T) -9 NIL 843208 NIL) (-354 820467 821701 823015 "FFCAT-" 824245 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815288 820378 820442 "FF" 820447 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803941 808260 809480 "FEXPR" 814140 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802869 803338 803379 "FEVALAB" 803463 NIL FEVALAB (NIL T) -9 NIL 803724 NIL) (-350 801986 802238 802576 "FEVALAB-" 802581 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798848 799733 799848 "FDIVCAT" 801416 NIL FDIVCAT (NIL T T T T) -9 NIL 801853 NIL) (-348 798604 798637 798807 "FDIVCAT-" 798812 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797818 797911 798188 "FDIV2" 798511 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796228 797201 797404 "FDIV" 797717 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795136 795523 795725 "FCTRDATA" 796046 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793792 794081 794370 "FCPAK1" 794867 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792795 793292 793433 "FCOMP" 793683 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776109 779945 783483 "FC" 789277 T FC (NIL) -8 NIL NIL NIL) (-341 767818 772430 772470 "FAXF" 774272 NIL FAXF (NIL T) -9 NIL 774964 NIL) (-340 764959 765766 766584 "FAXF-" 767049 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759528 764335 764511 "FARRAY" 764816 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754093 756475 756528 "FAMR" 757551 NIL FAMR (NIL T T) -9 NIL 758011 NIL) (-337 752917 753285 753720 "FAMR-" 753725 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751944 752839 752892 "FAMONOID" 752897 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749574 750426 750479 "FAMONC" 751420 NIL FAMONC (NIL T T) -9 NIL 751806 NIL) (-334 748048 749328 749465 "FAGROUP" 749470 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745801 746162 746565 "FACUTIL" 747729 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744888 745085 745307 "FACTFUNC" 745611 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736629 744191 744390 "EXPUPXS" 744744 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734082 734652 735238 "EXPRTUBE" 736063 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730293 730945 731675 "EXPRODE" 733421 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724727 725434 726240 "EXPR2UPS" 729591 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724353 724416 724525 "EXPR2" 724664 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708661 723002 723431 "EXPR" 723957 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698999 707812 708103 "EXPEXPAN" 708497 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698419 698723 698814 "EXITAST" 698928 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698183 698376 698405 "EXIT" 698410 T EXIT (NIL) -8 NIL NIL NIL) (-322 697804 697872 697985 "EVALCYC" 698115 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697321 697463 697504 "EVALAB" 697674 NIL EVALAB (NIL T) -9 NIL 697778 NIL) (-320 696778 696924 697145 "EVALAB-" 697150 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693893 695434 695462 "EUCDOM" 696017 T EUCDOM (NIL) -9 NIL 696367 NIL) (-318 692253 692754 693337 "EUCDOM-" 693342 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691879 691942 692051 "ESTOOLS2" 692190 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691624 691672 691752 "ESTOOLS1" 691831 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678941 681922 684672 "ESTOOLS" 688894 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678680 678718 678800 "ESCONT1" 678903 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674988 675815 676595 "ESCONT" 677920 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674657 674713 674813 "ES2" 674932 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674281 674345 674454 "ES1" 674593 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667982 669912 669940 "ES" 672708 T ES (NIL) -9 NIL 674118 NIL) (-309 662659 664216 666033 "ES-" 666197 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661851 662004 662180 "ERROR" 662503 T ERROR (NIL) -7 NIL NIL NIL) (-307 654867 661710 661801 "EQTBL" 661806 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654493 654556 654665 "EQ2" 654804 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646752 649807 651256 "EQ" 653077 NIL -1550 (NIL T) -8 NIL NIL NIL) (-304 641995 643090 644183 "EP" 645691 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640535 640886 641192 "ENV" 641709 T ENV (NIL) -8 NIL NIL NIL) (-302 639495 640169 640197 "ENTIRER" 640202 T ENTIRER (NIL) -9 NIL 640248 NIL) (-301 635914 637677 638038 "EMR" 639303 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635018 635229 635283 "ELTAGG" 635663 NIL ELTAGG (NIL T T) -9 NIL 635874 NIL) (-299 634725 634799 634940 "ELTAGG-" 634945 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634483 634518 634572 "ELTAB" 634656 NIL ELTAB (NIL T T) -9 NIL 634708 NIL) (-297 633585 633755 633954 "ELFUTS" 634334 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633309 633383 633411 "ELEMFUN" 633516 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633173 633200 633268 "ELEMFUN-" 633273 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627584 631215 631256 "ELAGG" 632196 NIL ELAGG (NIL T) -9 NIL 632659 NIL) (-293 625761 626303 626966 "ELAGG-" 626971 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625043 625210 625366 "ELABOR" 625625 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623649 623983 624277 "ELABEXPR" 624769 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616161 618286 619115 "EFUPXS" 622924 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609287 611410 612221 "EFULS" 615436 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606724 607130 607602 "EFSTRUC" 608919 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596161 598081 599629 "EF" 605239 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595139 595646 595795 "EAB" 596032 T EAB (NIL) -8 NIL NIL NIL) (-285 594261 595098 595126 "E04UCFA" 595131 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593383 594220 594248 "E04NAFA" 594253 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592505 593342 593370 "E04MBFA" 593375 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591627 592464 592492 "E04JAFA" 592497 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590751 591586 591614 "E04GCFA" 591619 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589875 590710 590738 "E04FDFA" 590743 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588997 589834 589862 "E04DGFA" 589867 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583074 584522 585886 "E04AGNT" 587653 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581694 582375 582415 "DVARCAT" 582756 NIL DVARCAT (NIL T) -9 NIL 582919 NIL) (-276 580844 581110 581424 "DVARCAT-" 581429 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572812 580643 580772 "DSMP" 580777 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571163 571954 571995 "DSEXT" 572358 NIL DSEXT (NIL T) -9 NIL 572652 NIL) (-273 569352 569876 570542 "DSEXT-" 570547 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569011 569076 569174 "DROPT1" 569287 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564030 565252 566389 "DROPT0" 567894 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558613 559975 561043 "DROPT" 562982 T DROPT (NIL) -8 NIL NIL NIL) (-269 556922 557283 557669 "DRAWPT" 558247 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556549 556608 556726 "DRAWHACK" 556863 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555250 555549 555840 "DRAWCX" 556278 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554759 554834 554985 "DRAWCURV" 555176 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545077 547189 549304 "DRAWCFUN" 552664 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539568 540587 541666 "DRAW" 544051 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536039 538233 538274 "DQAGG" 538903 NIL DQAGG (NIL T) -9 NIL 539177 NIL) (-262 522622 530250 530333 "DPOLCAT" 532185 NIL DPOLCAT (NIL T T T T) -9 NIL 532730 NIL) (-261 517141 518807 520765 "DPOLCAT-" 520770 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509949 517002 517100 "DPMO" 517105 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502654 509729 509896 "DPMM" 509901 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502176 502438 502527 "DOMTMPLT" 502585 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501525 501978 502058 "DOMCTOR" 502116 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500677 501005 501156 "DOMAIN" 501394 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493696 500312 500464 "DMP" 500578 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491473 492763 492804 "DMEXT" 492809 NIL DMEXT (NIL T) -9 NIL 492985 NIL) (-253 491067 491129 491273 "DLP" 491411 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484190 490394 490584 "DLIST" 490909 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480728 483015 483056 "DLAGG" 483606 NIL DLAGG (NIL T) -9 NIL 483836 NIL) (-250 479240 480054 480082 "DIVRING" 480174 T DIVRING (NIL) -9 NIL 480257 NIL) (-249 478423 478667 478967 "DIVRING-" 478972 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476465 476882 477288 "DISPLAY" 478037 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475295 475516 475781 "DIRPROD2" 476258 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468653 475209 475272 "DIRPROD" 475277 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456816 463364 463417 "DIRPCAT" 463675 NIL DIRPCAT (NIL NIL T) -9 NIL 464550 NIL) (-244 454016 454784 455665 "DIRPCAT-" 456002 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453297 453463 453649 "DIOSP" 453850 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449711 452181 452222 "DIOPS" 452656 NIL DIOPS (NIL T) -9 NIL 452885 NIL) (-241 449230 449374 449565 "DIOPS-" 449570 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448137 448909 448937 "DIFRING" 448942 T DIFRING (NIL) -9 NIL 448964 NIL) (-239 447785 447883 447911 "DIFFSPC" 448030 T DIFFSPC (NIL) -9 NIL 448105 NIL) (-238 447406 447508 447660 "DIFFSPC-" 447665 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446342 446940 446981 "DIFFMOD" 446986 NIL DIFFMOD (NIL T) -9 NIL 447084 NIL) (-236 446038 446095 446136 "DIFFDOM" 446257 NIL DIFFDOM (NIL T) -9 NIL 446325 NIL) (-235 445885 445915 445999 "DIFFDOM-" 446004 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443625 445089 445130 "DIFEXT" 445135 NIL DIFEXT (NIL T) -9 NIL 445288 NIL) (-233 440659 443129 443170 "DIAGG" 443175 NIL DIAGG (NIL T) -9 NIL 443195 NIL) (-232 440007 440200 440452 "DIAGG-" 440457 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434857 438966 439243 "DHMATRIX" 439776 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430325 431378 432388 "DFSFUN" 433867 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424566 429256 429568 "DFLOAT" 430033 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422805 423110 423499 "DFINTTLS" 424274 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419624 420826 421226 "DERHAM" 422471 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417160 419399 419488 "DEQUEUE" 419568 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416402 416547 416730 "DEGRED" 417022 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412808 413577 414423 "DEFINTRF" 415630 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410345 410832 411424 "DEFINTEF" 412327 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409629 409965 410080 "DEFAST" 410250 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402686 409222 409372 "DECIMAL" 409499 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400144 400656 401162 "DDFACT" 402230 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399734 399783 399934 "DBLRESP" 400095 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398935 399504 399595 "DBASIS" 399683 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396719 397165 397526 "DBASE" 398701 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395907 396199 396345 "DATAARY" 396618 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394965 395866 395894 "D03FAFA" 395899 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394024 394924 394952 "D03EEFA" 394957 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391950 392440 392929 "D03AGNT" 393555 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391191 391909 391937 "D02EJFA" 391942 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390432 391150 391178 "D02CJFA" 391183 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389673 390391 390419 "D02BHFA" 390424 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388914 389632 389660 "D02BBFA" 389665 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382045 383700 385306 "D02AGNT" 387328 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379795 380336 380882 "D01WGTS" 381519 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378802 379754 379782 "D01TRNS" 379787 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377810 378761 378789 "D01GBFA" 378794 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376818 377769 377797 "D01FCFA" 377802 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375826 376777 376805 "D01ASFA" 376810 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374834 375785 375813 "D01AQFA" 375818 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373842 374793 374821 "D01APFA" 374826 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372850 373801 373829 "D01ANFA" 373834 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371858 372809 372837 "D01AMFA" 372842 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370866 371817 371845 "D01ALFA" 371850 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369874 370825 370853 "D01AKFA" 370858 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368882 369833 369861 "D01AJFA" 369866 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362105 363730 365291 "D01AGNT" 367341 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361424 361570 361722 "CYCLOTOM" 361973 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358079 358872 359599 "CYCLES" 360717 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357379 357525 357696 "CVMP" 357940 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355166 355478 355847 "CTRIGMNP" 357107 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354639 354897 354998 "CTORKIND" 355085 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353844 354232 354260 "CTORCAT" 354442 T CTORCAT (NIL) -9 NIL 354555 NIL) (-188 353418 353553 353712 "CTORCAT-" 353717 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352832 353092 353200 "CTORCALL" 353342 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352190 352626 352699 "CTOR" 352779 T CTOR (NIL) -8 NIL NIL NIL) (-185 351546 351663 351816 "CSTTOOLS" 352087 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347243 348002 348760 "CRFP" 350858 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346658 346964 347056 "CRCEAST" 347171 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345681 345890 346118 "CRAPACK" 346462 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345061 345166 345370 "CPMATCH" 345557 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344780 344814 344920 "CPIMA" 345027 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341038 341800 342519 "COORDSYS" 344115 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340426 340571 340713 "CONTOUR" 340916 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335898 338429 338921 "CONTFRAC" 339966 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335772 335799 335827 "CONDUIT" 335864 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334726 335400 335428 "COMRING" 335433 T COMRING (NIL) -9 NIL 335485 NIL) (-174 333708 334084 334268 "COMPPROP" 334562 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333363 333404 333532 "COMPLPAT" 333667 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332993 333056 333163 "COMPLEX2" 333300 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321397 332802 332911 "COMPLEX" 332916 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320718 320857 321017 "COMPILER" 321257 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320430 320471 320569 "COMPFACT" 320677 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301824 314134 314174 "COMPCAT" 315178 NIL COMPCAT (NIL T) -9 NIL 316526 NIL) (-167 290712 294263 297890 "COMPCAT-" 298246 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290435 290469 290572 "COMMUPC" 290678 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290223 290263 290322 "COMMONOP" 290396 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289745 290027 290102 "COMMAAST" 290168 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289252 289496 289583 "COMM" 289678 T COMM (NIL) -8 NIL NIL NIL) (-162 288447 288695 288723 "COMBOPC" 289061 T COMBOPC (NIL) -9 NIL 289236 NIL) (-161 287301 287553 287795 "COMBINAT" 288237 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283644 284332 284959 "COMBF" 286723 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282306 282760 282995 "COLOR" 283429 T COLOR (NIL) -8 NIL NIL NIL) (-158 281722 282027 282119 "COLONAST" 282234 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281356 281409 281534 "CMPLXRT" 281669 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280744 281056 281155 "CLLCTAST" 281277 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276203 277274 278354 "CLIP" 279684 T CLIP (NIL) -7 NIL NIL NIL) (-154 274376 275304 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254023 254071 "CATCTOR" 254076 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252990 253302 253400 "CATAST" 253521 T CATAST (NIL) -8 NIL NIL NIL) (-139 252406 252711 252803 "CASEAST" 252918 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251502 251662 251883 "CARTEN2" 252253 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247659 248403 "CARTEN" 250814 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 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*1) (-4 *1 (-487))) + ((*1 *1 *1) (-12 (-4 *1 (-820 *2)) (-4 *2 (-175)))) + ((*1 *2 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-909)))) + ((*1 *1 *1) (-5 *1 (-1003))) + ((*1 *1 *1) (-12 (-4 *1 (-1030 *2)) (-4 *2 (-175))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1133)) (-4 *2 (-928 *5)) (-5 *1 (-714 *5 *2 *3 *4)) + (-4 *3 (-385 *2)) (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4510))))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-793)) (-5 *3 (-1 *4 (-560) (-560))) (-4 *4 (-1081)) (-4 *1 (-708 *4 *5 *6)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)))) @@ -739,33 +472,22 @@ (-12 (-5 *2 (-663 (-663 *5))) (-4 *5 (-1081)) (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1299 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) + (-5 *2 (-711 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-432 *3)) (-4 *3 (-175)) (-5 *2 (-711 *3))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-376)) + (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6))))) +(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-669 *2)) (-4 *2 (-1133))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 (-495 *4 *5))) (-14 *4 (-663 (-1209))) - (-4 *5 (-466)) (-5 *2 (-663 (-255 *4 *5))) (-5 *1 (-650 *4 *5))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) -(((*1 *1 *1) - (-12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)) - (-4 *2 (-466)))) - ((*1 *1 *1) - (-12 (-4 *1 (-355 *2 *3 *4)) (-4 *2 (-1254)) (-4 *3 (-1275 *2)) - (-4 *4 (-1275 (-421 *3))))) - ((*1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-466)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-980 *3 *4 *2)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *2 (-872)) (-4 *3 (-466)))) - ((*1 *1 *1) - (-12 (-4 *1 (-980 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-466)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-319)) (-4 *3 (-571)) (-5 *1 (-1196 *3 *2)) - (-4 *2 (-1275 *3))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-1167))) (-5 *1 (-1123))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034)))))) + (-12 (-5 *3 (-866 (-391))) (-5 *2 (-866 (-229))) (-5 *1 (-315))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-973 *4)) (-4 *4 (-1081)) (-5 *1 (-1197 *3 *4)) + (-14 *3 (-949))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1187 (-560))) (-5 *1 (-1193 *4)) (-4 *4 (-1081)) + (-5 *3 (-560))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1081)) (-14 *3 (-663 (-1209))))) @@ -776,10 +498,10 @@ (-12 (-4 *1 (-397 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-1133)))) ((*1 *1 *1) (-12 (-14 *2 (-663 (-1209))) (-4 *3 (-175)) - (-4 *5 (-245 (-3819 *2) (-793))) + (-4 *5 (-245 (-3782 *2) (-793))) (-14 *6 - (-1 (-114) (-2 (|:| -2081 *4) (|:| -2909 *5)) - (-2 (|:| -2081 *4) (|:| -2909 *5)))) + (-1 (-114) (-2 (|:| -2113 *4) (|:| -1704 *5)) + (-2 (|:| -2113 *4) (|:| -1704 *5)))) (-5 *1 (-475 *2 *3 *4 *5 *6 *7)) (-4 *4 (-872)) (-4 *7 (-980 *3 *5 (-889 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *2 (-102)) (-4 *3 (-875)))) @@ -795,53 +517,32 @@ (-4 *2 (-872)))) ((*1 *1 *1) (-12 (-5 *1 (-1323 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-870))))) -(((*1 *2 *1) - (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-5 *2 (-663 (-663 *3))))) - ((*1 *2 *1) - (-12 (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *5 (-1081)) - (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-5 *2 (-663 (-663 *5))))) - ((*1 *2 *1) - (-12 (-5 *2 (-663 (-663 *3))) (-5 *1 (-1222 *3)) (-4 *3 (-1133))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-663 *1)) (-4 *1 (-1097 *4 *5 *6)) (-4 *4 (-1081)) - (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1097 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *5 (-872)) (-5 *2 (-114)))) - ((*1 *2 *3 *1 *4) - (-12 (-5 *4 (-1 (-114) *3 *3)) (-4 *1 (-1244 *5 *6 *7 *3)) - (-4 *5 (-571)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-114))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3379 *6) (|:| |sol?| (-114))) (-560) - *6)) - (-4 *6 (-376)) (-4 *7 (-1275 *6)) - (-5 *2 - (-3 (-2 (|:| |answer| (-421 *7)) (|:| |a0| *6)) - (-2 (|:| -2301 (-421 *7)) (|:| |coeff| (-421 *7))) "failed")) - (-5 *1 (-588 *6 *7)) (-5 *3 (-421 *7))))) -(((*1 *2 *1) (-12 (-5 *2 (-1135)) (-5 *1 (-342))))) -(((*1 *2 *1) - (-12 (-4 *2 (-571)) (-5 *1 (-642 *2 *3)) (-4 *3 (-1275 *2))))) -(((*1 *1) (-5 *1 (-1117)))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-323)) (-5 *1 (-853))))) +(((*1 *2 *3) + (-12 (-4 *3 (-1275 *2)) (-4 *2 (-1275 *4)) + (-5 *1 (-1017 *4 *2 *3 *5)) (-4 *4 (-363)) (-4 *5 (-746 *2 *3))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-793)) (-5 *1 (-805 *2)) (-4 *2 (-38 (-421 (-560)))) + (-4 *2 (-175))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-848)) (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-376)) (-5 *1 (-659 *3 *4)) + (-14 *4 (-663 (-1209)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-571)) + (-5 *2 (-2 (|:| -2069 *3) (|:| -2875 *3))) (-5 *1 (-1272 *4 *3)) + (-4 *3 (-1275 *4))))) +(((*1 *1 *1) (-5 *1 (-1095)))) (((*1 *1 *1) (-12 (-5 *1 (-514 *2)) (-14 *2 (-560)))) ((*1 *1 *1) (-5 *1 (-1152)))) -(((*1 *1 *1 *2) - (|partial| -12 (-4 *1 (-1244 *3 *4 *5 *2)) (-4 *3 (-571)) - (-4 *4 (-817)) (-4 *5 (-872)) (-4 *2 (-1097 *3 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-793)) (-5 *2 (-1 (-391))) (-5 *1 (-1073))))) (((*1 *2 *1) (-12 (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-663 *1)) (-4 *1 (-980 *3 *4 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034)))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1042 *3)) (-4 *3 (-1249)) (-4 *3 (-1133)) - (-5 *2 (-114))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1209)) (-4 *4 (-13 (-319) (-1070 (-560)) (-660 (-560)) (-149))) @@ -850,27 +551,22 @@ ((*1 *1 *1) (-5 *1 (-888))) ((*1 *2 *3) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-1193 *3)) (-4 *3 (-1081))))) +(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-576))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-559)))) (((*1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571))))) -(((*1 *2 *1) (-12 (-4 *1 (-985)) (-5 *2 (-663 (-663 (-973 (-229))))))) - ((*1 *2 *1) (-12 (-4 *1 (-1006)) (-5 *2 (-663 (-663 (-973 (-229)))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-949))) (-5 *2 (-1211 (-421 (-560)))) - (-5 *1 (-193))))) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) (((*1 *2 *3) - (-12 (-4 *4 (-940)) (-4 *5 (-817)) (-4 *6 (-872)) - (-4 *7 (-980 *4 *5 *6)) (-5 *2 (-419 (-1203 *7))) - (-5 *1 (-937 *4 *5 *6 *7)) (-5 *3 (-1203 *7)))) - ((*1 *2 *3) - (-12 (-4 *4 (-940)) (-4 *5 (-1275 *4)) (-5 *2 (-419 (-1203 *5))) - (-5 *1 (-938 *4 *5)) (-5 *3 (-1203 *5))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-708 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-385 *2)) - (-4 *4 (-385 *2))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-576))))) + (-12 (-5 *3 (-1299 *5)) (-4 *5 (-13 (-1081) (-660 *4))) + (-4 *4 (-571)) (-5 *2 (-114)) (-5 *1 (-658 *4 *5))))) +(((*1 *2) + (-12 (-4 *2 (-13 (-435 *3) (-1034))) (-5 *1 (-287 *3 *2)) + (-4 *3 (-571))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-514 *2)) (-14 *2 (-560)))) ((*1 *1 *1 *1) (-5 *1 (-1152)))) +(((*1 *2 *3 *3 *3 *4 *5 *6) + (-12 (-5 *3 (-326 (-560))) (-5 *4 (-1 (-229) (-229))) + (-5 *5 (-1121 (-229))) (-5 *6 (-663 (-270))) (-5 *2 (-1165 (-229))) + (-5 *1 (-719))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-816)) (-4 *2 (-1081)))) ((*1 *2 *1) (-12 (-4 *2 (-1081)) (-5 *1 (-50 *2 *3)) (-14 *3 (-663 (-1209))))) @@ -880,10 +576,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-397 *2 *3)) (-4 *3 (-1133)) (-4 *2 (-1081)))) ((*1 *2 *1) - (-12 (-14 *3 (-663 (-1209))) (-4 *5 (-245 (-3819 *3) (-793))) + (-12 (-14 *3 (-663 (-1209))) (-4 *5 (-245 (-3782 *3) (-793))) (-14 *6 - (-1 (-114) (-2 (|:| -2081 *4) (|:| -2909 *5)) - (-2 (|:| -2081 *4) (|:| -2909 *5)))) + (-1 (-114) (-2 (|:| -2113 *4) (|:| -1704 *5)) + (-2 (|:| -2113 *4) (|:| -1704 *5)))) (-4 *2 (-175)) (-5 *1 (-475 *3 *2 *4 *5 *6 *7)) (-4 *4 (-872)) (-4 *7 (-980 *2 *5 (-889 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *3 (-875)) (-4 *2 (-102)))) @@ -900,54 +596,65 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1097 *3 *4 *2)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *2 (-872))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1008 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-663 *5))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1191)) (-5 *4 (-560)) (-5 *5 (-711 (-171 (-229)))) - (-5 *2 (-1067)) (-5 *1 (-776))))) +(((*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1081)) (-4 *5 (-1275 *4)) (-5 *2 (-1 *6 (-663 *6))) + (-5 *1 (-1294 *4 *5 *3 *6)) (-4 *3 (-680 *5)) (-4 *6 (-1292 *4))))) +(((*1 *2 *1) (-12 (-4 *1 (-820 *2)) (-4 *2 (-175)))) + ((*1 *2 *1) (-12 (-4 *1 (-1030 *2)) (-4 *2 (-175))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-663 *2)) (-4 *2 (-980 *4 *5 *6)) (-4 *4 (-376)) + (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) + (-5 *1 (-461 *4 *5 *6 *2)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-376)) + (-5 *2 + (-2 (|:| R (-711 *6)) (|:| A (-711 *6)) (|:| |Ainv| (-711 *6)))) + (-5 *1 (-1010 *6)) (-5 *3 (-711 *6))))) (((*1 *1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-697 *3)) (-4 *3 (-1081)) - (-4 *3 (-1133))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1299 *1)) (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) - (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4)))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-4 *1 (-934 *3))))) + (-12 (-5 *2 (-663 (-932 *3))) (-4 *3 (-1133)) (-5 *1 (-935 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-630 *5)) (-4 *5 (-435 *4)) (-4 *4 (-1070 (-560))) + (-4 *4 (-571)) (-5 *2 (-1203 *5)) (-5 *1 (-32 *4 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-630 *1)) (-4 *1 (-1081)) (-4 *1 (-310)) + (-5 *2 (-1203 *1))))) (((*1 *2 *1) (-12 (-4 *2 (-1126 *3)) (-5 *1 (-1090 *2 *3)) (-4 *3 (-1249)))) ((*1 *2 *1) (-12 (-5 *2 (-1121 *3)) (-5 *1 (-1124 *3)) (-4 *3 (-1249)))) ((*1 *1 *2 *2) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1249)))) ((*1 *1 *2) (-12 (-5 *1 (-1266 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-844)) (-14 *5 (-1209)) (-5 *2 (-663 (-1268 *5 *4))) - (-5 *1 (-1146 *4 *5)) (-5 *3 (-1268 *5 *4))))) -(((*1 *2 *3 *3 *2 *4) - (-12 (-5 *3 (-711 *2)) (-5 *4 (-560)) - (-4 *2 (-13 (-319) (-10 -8 (-15 -1903 ((-419 $) $))))) - (-4 *5 (-1275 *2)) (-5 *1 (-513 *2 *5 *6)) (-4 *6 (-424 *2 *5))))) +(((*1 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-1227 *3 *4)) (-4 *3 (-1133)) + (-4 *4 (-1133))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) - (|:| |fn| (-1299 (-326 (-229)))) (|:| |yinit| (-663 (-229))) - (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) - (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (-5 *2 (-391)) (-5 *1 (-208))))) + (-3 + (|:| |noa| + (-2 (|:| |fn| (-326 (-229))) (|:| -3271 (-663 (-229))) + (|:| |lb| (-663 (-866 (-229)))) + (|:| |cf| (-663 (-326 (-229)))) + (|:| |ub| (-663 (-866 (-229)))))) + (|:| |lsa| + (-2 (|:| |lfn| (-663 (-326 (-229)))) + (|:| -3271 (-663 (-229))))))) + (-5 *2 (-663 (-1191))) (-5 *1 (-278))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-514 *2)) (-14 *2 (-560)))) ((*1 *1 *1 *1) (-5 *1 (-1152)))) -(((*1 *2 *3) - (-12 (-4 *4 (-1249)) (-5 *2 (-793)) (-5 *1 (-185 *4 *3)) - (-4 *3 (-696 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1235)))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)))) ((*1 *2 *1) (-12 (-4 *1 (-397 *3 *2)) (-4 *3 (-1081)) (-4 *2 (-1133)))) ((*1 *2 *1) (-12 (-14 *3 (-663 (-1209))) (-4 *4 (-175)) - (-4 *6 (-245 (-3819 *3) (-793))) + (-4 *6 (-245 (-3782 *3) (-793))) (-14 *7 - (-1 (-114) (-2 (|:| -2081 *5) (|:| -2909 *6)) - (-2 (|:| -2081 *5) (|:| -2909 *6)))) + (-1 (-114) (-2 (|:| -2113 *5) (|:| -1704 *6)) + (-2 (|:| -2113 *5) (|:| -1704 *6)))) (-5 *2 (-735 *5 *6 *7)) (-5 *1 (-475 *3 *4 *5 *6 *7 *8)) (-4 *5 (-872)) (-4 *8 (-980 *4 *6 (-889 *3))))) ((*1 *2 *1) @@ -956,102 +663,71 @@ ((*1 *1 *1) (-12 (-4 *1 (-1005 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-816)) (-4 *4 (-872))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-319) (-149))) (-4 *4 (-13 (-872) (-633 (-1209)))) - (-4 *5 (-817)) (-5 *1 (-954 *3 *4 *5 *2)) (-4 *2 (-980 *3 *5 *4))))) -(((*1 *1 *1 *1) (-5 *1 (-888)))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-495 *4 *5))) (-5 *3 (-663 (-889 *4))) - (-14 *4 (-663 (-1209))) (-4 *5 (-466)) (-5 *1 (-485 *4 *5 *6)) - (-4 *6 (-466))))) -(((*1 *2 *1) (-12 (-5 *2 (-611)) (-5 *1 (-292))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) (((*1 *2 *3) - (-12 (-5 *3 (-949)) (-5 *2 (-1211 (-421 (-560)))) (-5 *1 (-193))))) -(((*1 *2 *2 *2) + (-12 (-5 *3 (-663 (-495 *4 *5))) (-14 *4 (-663 (-1209))) + (-4 *5 (-466)) + (-5 *2 + (-2 (|:| |gblist| (-663 (-255 *4 *5))) + (|:| |gvlist| (-663 (-560))))) + (-5 *1 (-650 *4 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-376)) (-5 *2 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"failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-2 (|:| -3265 *3) (|:| -2724 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -3848 *3) (|:| -2707 *4)))) (-4 *3 (-1081)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -4070,25 +3780,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -3423 (-663 (-1121 (-866 (-229))))) + (|:| -3054 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| -3054 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249)))) @@ -4106,23 +3816,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -2689 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -3271 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -2689 (-663 (-229))))))) + (|:| -3271 (-663 (-229))))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2689 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3271 (-663 (-229))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -2689 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -3271 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (-5 *1 (-865)))) @@ -4223,85 +3933,80 @@ ((*1 *1 *2) (-12 (-5 *2 (-686 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)) (-5 *1 (-1320 *3 *4))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-560)) (-14 *3 (-793)) - (-4 *4 (-175)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-160 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1124 *2)) (-4 *2 (-435 *4)) (-4 *4 (-571)) - (-5 *1 (-160 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1124 *1)) (-4 *1 (-162)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1209)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-479 *2 *3)) (-4 *2 (-175)) (-4 *3 (-23)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-1320 *3 *4)) (-4 *3 (-872)) - (-4 *4 (-175))))) (((*1 *2 *2) (|partial| -12 (-5 *2 (-326 (-229))) (-5 *1 (-315)))) ((*1 *2 *1) (|partial| -12 (-5 *2 (-2 (|:| |num| (-916 *3)) (|:| |den| (-916 *3)))) (-5 *1 (-916 *3)) (-4 *3 (-1133))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 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*3)) (-4 *3 (-435 *6)) + (-4 *6 (-13 (-571) (-633 (-549)))) (-5 *2 (-51)) + (-5 *1 (-329 *6 *3)))) + ((*1 *2 *3 *4 *5 *6) + (-12 (-5 *4 (-115)) (-5 *5 (-305 *3)) (-5 *6 (-663 *3)) + (-4 *3 (-435 *7)) (-4 *7 (-13 (-571) (-633 (-549)))) (-5 *2 (-51)) + (-5 *1 (-329 *7 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1258)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-5 *1 (-339 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-5 *1 (-530 *3 *4)) + (-14 *4 (-560))))) (((*1 *2 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1249)))) ((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1128)))) ((*1 *2 *1) @@ -5750,22 +5758,29 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1288 *3)) (-4 *3 (-1249)))) ((*1 *2 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) - (-5 *2 (-663 *4)) (-5 *1 (-1160 *3 *4)) (-4 *3 (-1275 *4)))) - ((*1 *2 *3 *3 *3) - (-12 (-4 *3 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) - (-5 *2 (-663 *3)) (-5 *1 (-1160 *4 *3)) (-4 *4 (-1275 *3))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-663 *6)) (-5 *4 (-663 (-255 *5 *6))) (-4 *6 (-466)) + (-5 *2 (-255 *5 *6)) (-14 *5 (-663 (-1209))) (-5 *1 (-650 *5 *6))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-229)) (-5 *5 (-560)) (-5 *2 (-1245 *3)) + (-5 *1 (-812 *3)) (-4 *3 (-1006)))) + ((*1 *1 *2 *3 *4) + (-12 (-5 *3 (-663 (-663 (-973 (-229))))) (-5 *4 (-114)) + (-5 *1 (-1245 *2)) (-4 *2 (-1006))))) (((*1 *2 *1) (-12 (-4 *1 (-1136 *3 *4 *5 *6 *2)) (-4 *3 (-1133)) (-4 *4 (-1133)) (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *2 (-1133))))) -(((*1 *1 *1 *1) (-4 *1 (-559)))) -(((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-899))))) +(((*1 *2 *1) (-12 (-5 *2 (-229)) (-5 *1 (-847))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1209)) + (-4 *5 (-13 (-1070 (-560)) (-466) (-660 (-560)))) + (-5 *2 (-2 (|:| -3632 *3) (|:| |nconst| *3))) (-5 *1 (-581 *5 *3)) + (-4 *3 (-13 (-27) (-1235) (-435 *5)))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -5783,7 +5798,7 @@ (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3423 + (|:| -3054 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -5791,52 +5806,54 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-560)) (-5 *1 (-419 *2)) (-4 *2 (-571))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-421 (-976 (-171 (-560))))) (-5 *2 (-663 (-171 *4))) - (-5 *1 (-392 *4)) (-4 *4 (-13 (-376) (-871))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-663 (-421 (-976 (-171 (-560)))))) - (-5 *4 (-663 (-1209))) (-5 *2 (-663 (-663 (-171 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*2 (-252 (-1191))) (-5 *1 (-217 *4)) (-4 *4 (-13 (-872) - (-10 -8 (-15 -3034 ((-1191) $ *3)) (-15 -3420 ((-1305) $)) - (-15 -2854 ((-1305) $))))))) + (-10 -8 (-15 -2962 ((-1191) $ *3)) (-15 -3368 ((-1305) $)) + (-15 -4383 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1021)) (-5 *1 (-217 *3)) (-4 *3 (-13 (-872) - (-10 -8 (-15 -3034 ((-1191) $ (-1209))) (-15 -3420 ((-1305) $)) - (-15 -2854 ((-1305) $))))))) + (-10 -8 (-15 -2962 ((-1191) $ (-1209))) (-15 -3368 ((-1305) $)) + (-15 -4383 ((-1305) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-793)) (-5 *1 (-252 *4)) (-4 *4 (-872)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-252 *3)) (-4 *3 (-872)))) @@ -8337,143 +8694,15 @@ (-12 (-5 *2 "rest") (-4 *1 (-1288 *3)) (-4 *3 (-1249)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-932 *4)) (-4 *4 (-1133)) (-5 *2 (-663 (-793))) - (-5 *1 (-935 *4))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1266 (-560))) (-4 *1 (-673 *3)) (-4 *3 (-1249)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-673 *3)) (-4 *3 (-1249))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-421 (-560))) (-5 *1 (-609 *3)) (-4 *3 (-38 *2)) - (-4 *3 (-1081))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-310)))) - ((*1 *1 *1) (-4 *1 (-310))) - ((*1 *1 *2) (-12 (-5 *2 (-663 (-888))) (-5 *1 (-888)))) - ((*1 *1 *1) (-5 *1 (-888)))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-1032 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-229)) (-5 *1 (-847))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571))))) -(((*1 *2 *1) - (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-872)) - (-4 *5 (-817)) (-4 *2 (-277 *4))))) (((*1 *2 *3) - (-12 (-4 *1 (-363)) (-5 *3 (-560)) (-5 *2 (-1221 (-949) (-793)))))) -(((*1 *1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-1172 *4 *5))) (-5 *3 (-1 (-114) *5 *5)) - (-4 *4 (-13 (-1133) (-34))) (-4 *5 (-13 (-1133) (-34))) - (-5 *1 (-1173 *4 *5)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-663 (-1172 *3 *4))) (-4 *3 (-13 (-1133) (-34))) - (-4 *4 (-13 (-1133) (-34))) (-5 *1 (-1173 *3 *4))))) -(((*1 *2 *3 *4) - (-12 (-4 *2 (-1275 *4)) (-5 *1 (-831 *4 *2 *3 *5)) - (-4 *4 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *3 (-680 *2)) - (-4 *5 (-680 (-421 *2))))) - ((*1 *2 *3 *4) - (-12 (-4 *2 (-1275 *4)) (-5 *1 (-831 *4 *2 *5 *3)) - (-4 *4 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *5 (-680 *2)) - (-4 *3 (-680 (-421 *2)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-114)) (-4 *6 (-466)) (-4 *7 (-817)) (-4 *8 (-872)) - (-4 *3 (-1097 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -2417 *4)))))) - (-5 *1 (-1101 *6 *7 *8 *3 *4)) (-4 *4 (-1103 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -2417 *4)))))) - (-5 *1 (-1177 *5 *6 *7 *3 *4)) (-4 *4 (-1141 *5 *6 *7 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-427 *3 *4 *5 *6)) (-4 *6 (-1070 *4)) (-4 *3 (-319)) - (-4 *4 (-1023 *3)) (-4 *5 (-1275 *4)) (-4 *6 (-424 *4 *5)) - (-14 *7 (-1299 *6)) (-5 *1 (-429 *3 *4 *5 *6 *7)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1299 *6)) (-4 *6 (-424 *4 *5)) (-4 *4 (-1023 *3)) - (-4 *5 (-1275 *4)) (-4 *3 (-319)) (-5 *1 (-429 *3 *4 *5 *6 *7)) - (-14 *7 *2)))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-319)) - (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-462 *3 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-663 *7)) (-5 *3 (-1191)) (-4 *7 (-980 *4 *5 *6)) - (-4 *4 (-319)) (-4 *5 (-817)) (-4 *6 (-872)) - (-5 *1 (-462 *4 *5 *6 *7)))) - ((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-663 *7)) (-5 *3 (-1191)) (-4 *7 (-980 *4 *5 *6)) - (-4 *4 (-319)) (-4 *5 (-817)) (-4 *6 (-872)) - (-5 *1 (-462 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-4 *1 (-1042 *3)) (-4 *3 (-1249)) (-5 *2 (-114)))) - ((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-1197 *3 *4)) (-14 *3 (-949)) - (-4 *4 (-1081))))) -(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) - (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1067)) - (-5 *1 (-770))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1235)))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-1197 *3 *4)) (-14 *3 (-949)) - (-4 *4 (-1081))))) -(((*1 *2 *3 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1275 *5)) - (-4 *5 (-13 (-376) (-149) (-1070 (-560)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-421 *6)) (|:| |h| *6) - (|:| |c1| (-421 *6)) (|:| |c2| (-421 *6)) (|:| -2343 *6))) - (-5 *1 (-1048 *5 *6)) (-5 *3 (-421 *6))))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-114)) (-5 *5 (-711 (-171 (-229)))) - (-5 *2 (-1067)) (-5 *1 (-777))))) -(((*1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-459 *3)) (-4 *3 (-1081))))) -(((*1 *2) - (-12 (-4 *3 (-1254)) (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4))) - (-5 *2 (-1299 *1)) (-4 *1 (-355 *3 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-1003)) (-5 *1 (-1325))))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-1187 *4)) (-5 *3 (-560)) (-4 *4 (-1081)) - (-5 *1 (-1193 *4)))) - ((*1 *1 *2 *2 *1) - (-12 (-5 *2 (-560)) (-5 *1 (-1289 *3 *4 *5)) (-4 *3 (-1081)) - (-14 *4 (-1209)) (-14 *5 *3)))) -(((*1 *2 *3) - (-12 (-5 *3 (-949)) (-5 *2 (-1203 *4)) (-5 *1 (-369 *4)) - (-4 *4 (-363))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-980 *4 *6 *5)) (-4 *4 (-466)) - (-4 *5 (-872)) (-4 *6 (-817)) (-5 *1 (-1018 *4 *5 *6 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-531)))) - ((*1 *2 *1) - (-12 (-4 *2 (-13 (-1133) (-34))) (-5 *1 (-1172 *3 *2)) - (-4 *3 (-13 (-1133) (-34))))) - ((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1311))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-916 *3)) (-4 *3 (-1133))))) -(((*1 *2 *3 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) - (-5 *1 (-777))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-949)) - (-5 *2 (-1299 (-663 (-2 (|:| -1992 *4) (|:| -2081 (-1152)))))) - (-5 *1 (-360 *4)) (-4 *4 (-363))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-3 (-114) "failed")) (-4 *3 (-466)) (-4 *4 (-872)) - (-4 *5 (-817)) (-5 *1 (-1018 *3 *4 *5 *6)) (-4 *6 (-980 *3 *5 *4))))) + (-12 (-5 *3 (-1 *5 (-663 *5))) (-4 *5 (-1292 *4)) + (-4 *4 (-38 (-421 (-560)))) + (-5 *2 (-1 (-1187 *4) (-663 (-1187 *4)))) (-5 *1 (-1293 *4 *5))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3054 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -8491,7 +8720,7 @@ (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3423 + (|:| -3054 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -8499,38 +8728,66 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574))))) -(((*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) +(((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-573 *3)) (-4 *3 (-559))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-376)) (-5 *1 (-661 *3 *4)) + (-14 *4 (-663 (-1209)))))) +(((*1 *2 *1) (-12 (-5 *1 (-597 *2)) (-4 *2 (-376))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 (-663 *2) *2 *2 *2)) (-4 *2 (-1133)) + (-5 *1 (-103 *2)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1133)) (-5 *1 (-103 *2))))) (((*1 *2 *3) - (-12 (-5 *3 (-1268 *5 *4)) (-4 *4 (-466)) (-4 *4 (-844)) - (-14 *5 (-1209)) (-5 *2 (-560)) (-5 *1 (-1146 *4 *5))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1131 *2)) (-4 *2 (-1133)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1131 *2)) (-4 *2 (-1133))))) + (-12 (-5 *3 (-663 (-630 *5))) (-4 *4 (-1133)) (-5 *2 (-630 *5)) + (-5 *1 (-587 *4 *5)) (-4 *5 (-435 *4))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) + ((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) + ((*1 *1 *1) (-4 *1 (-1171)))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-421 (-1203 (-326 *3)))) (-4 *3 (-571)) + (-5 *1 (-1162 *3))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 (-2 (|:| -1992 *4) (|:| -3370 (-560))))) - (-4 *4 (-1133)) (-5 *2 (-1 *4)) (-5 *1 (-1049 *4))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-576)))) + (-12 (-5 *3 (-955)) + (-5 *2 + (-2 (|:| |brans| (-663 (-663 (-973 (-229))))) + (|:| |xValues| (-1121 (-229))) (|:| |yValues| (-1121 (-229))))) + (-5 *1 (-155)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-955)) (-5 *4 (-421 (-560))) + (-5 *2 + (-2 (|:| |brans| (-663 (-663 (-973 (-229))))) + (|:| |xValues| (-1121 (-229))) (|:| |yValues| (-1121 (-229))))) + (-5 *1 (-155)))) ((*1 *2 *3) - (-12 (-5 *2 (-1203 (-421 (-560)))) (-5 *1 (-972)) (-5 *3 (-560))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) -(((*1 *1 *1 *2 *2) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-955)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-955)))) - ((*1 *1 *1 *2 *2 *2) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-957)))) - ((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-391)) (-5 *2 (-1305)) (-5 *1 (-1303)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1305)) (-5 *1 (-1303))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-5 *1 (-342))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-134)) (-5 *3 (-793)) (-5 *2 (-1305))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-793)) (-4 *5 (-571)) + (-12 (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-1001 *5 *3)) (-4 *3 (-1275 *5))))) + (-2 (|:| |brans| (-663 (-663 (-973 (-229))))) + (|:| |xValues| (-1121 (-229))) (|:| |yValues| (-1121 (-229))))) + (-5 *1 (-155)) (-5 *3 (-663 (-973 (-229)))))) + ((*1 *2 *3) + (-12 + (-5 *2 + (-2 (|:| |brans| (-663 (-663 (-973 (-229))))) + (|:| |xValues| (-1121 (-229))) (|:| |yValues| (-1121 (-229))))) + (-5 *1 (-155)) (-5 *3 (-663 (-663 (-973 (-229))))))) + ((*1 *1 *2) (-12 (-5 *2 (-663 (-1121 (-391)))) (-5 *1 (-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270))))) (((*1 *1 *1) - (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-571)))) - ((*1 *1 *1) (|partial| -4 *1 (-744)))) -(((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1191)) (-5 *1 (-732))))) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1203 *1)) (-4 *1 (-466)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1203 *6)) (-4 *6 (-980 *5 *3 *4)) (-4 *3 (-817)) + (-4 *4 (-872)) (-4 *5 (-940)) (-5 *1 (-471 *3 *4 *5 *6)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-1203 *1)) (-4 *1 (-940))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-769))))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-663 (-1209))) (-5 *3 (-1209)) (-5 *1 (-549)))) ((*1 *2 *3 *2) @@ -8542,143 +8799,264 @@ ((*1 *2 *3 *2 *4) (-12 (-5 *4 (-663 (-1209))) (-5 *2 (-1209)) (-5 *1 (-726 *3)) (-4 *3 (-633 (-549)))))) -(((*1 *2) (-12 (-4 *3 (-175)) (-5 *2 (-1299 *1)) (-4 *1 (-380 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1209)) + (-5 *2 + (-2 (|:| |zeros| (-1187 (-229))) (|:| |ones| (-1187 (-229))) + (|:| |singularities| (-1187 (-229))))) + (-5 *1 (-105))))) +(((*1 *1) (-5 *1 (-146))) ((*1 *1 *1) (-5 *1 (-888)))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1203 *7)) (-5 *3 (-560)) (-4 *7 (-980 *6 *4 *5)) + (-4 *4 (-817)) (-4 *5 (-872)) (-4 *6 (-1081)) + (-5 *1 (-333 *4 *5 *6 *7))))) +(((*1 *2 *3) + (-12 + (-5 *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| (-1187 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3054 + (-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 *2 (-1067)) (-5 *1 (-315))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-712 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-899)) (-5 *1 (-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-270))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-256))))) +(((*1 *2) + (-12 (-4 *3 (-571)) (-5 *2 (-663 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-432 *3))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1133)) + (-4 *6 (-1133)) (-4 *2 (-1133)) (-5 *1 (-702 *5 *6 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(-888))) ((*1 *2 *1) (-12 (-4 *1 (-1136 *2 *3 *4 *5 *6)) (-4 *3 (-1133)) (-4 *4 (-1133)) @@ -9999,18 +10044,12 @@ ((*1 *1 *2) (-12 (-5 *2 (-229)) (-5 *1 (-1191)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-1191)))) ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1209))))) -(((*1 *2 *3) (-12 (-5 *3 (-865)) (-5 *2 (-1067)) (-5 *1 (-864)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-326 (-391)))) (-5 *4 (-663 (-391))) - (-5 *2 (-1067)) (-5 *1 (-864))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *5 (-663 *4)) (-4 *4 (-376)) (-5 *2 (-1299 *4)) - (-5 *1 (-838 *4 *3)) (-4 *3 (-680 *4))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2689 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3271 (-663 (-229))))) (-5 *2 (-663 (-1209))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1203 *7)) (-4 *7 (-980 *6 *4 *5)) (-4 *4 (-817)) @@ -10032,7 +10071,7 @@ (-5 *1 (-981 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -3834 ($ *7)) (-15 -3125 (*7 $)) (-15 -3138 (*7 $))))))) + (-10 -8 (-15 -3831 ($ *7)) (-15 -3694 (*7 $)) (-15 -3703 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1005 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-816)) (-4 *5 (-872)) (-5 *2 (-663 *5)))) @@ -10042,36 +10081,36 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1209))) (-5 *1 (-1072 *4))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-421 (-560))) (-5 *1 (-229)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-421 (-560))) (-5 *1 (-229)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-421 (-560))) (-5 *1 (-391)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-5 *2 (-421 (-560))) (-5 *1 (-391))))) -(((*1 *2 *3) - (-12 (-5 *3 (-560)) (-4 *4 (-817)) (-4 *5 (-872)) (-4 *2 (-1081)) - (-5 *1 (-333 *4 *5 *2 *6)) (-4 *6 (-980 *2 *4 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1256)))))) -(((*1 *2 *2) (-12 (-5 *2 (-949)) 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(-872)) - (-4 *6 (-245 (-3819 *4) (-793))) + (-4 *6 (-245 (-3782 *4) (-793))) (-14 *7 - (-1 (-114) (-2 (|:| -2081 *5) (|:| -2909 *6)) - (-2 (|:| -2081 *5) (|:| -2909 *6)))) + (-1 (-114) (-2 (|:| -2113 *5) (|:| -1704 *6)) + (-2 (|:| -2113 *5) (|:| -1704 *6)))) (-14 *4 (-663 (-1209))) (-4 *2 (-175)) (-5 *1 (-475 *4 *2 *5 *6 *7 *8)) (-4 *8 (-980 *2 *6 (-889 *4))))) ((*1 *1 *2 *3) @@ -10274,237 +10270,209 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-1005 *4 *3 *2)) (-4 *4 (-1081)) (-4 *3 (-816)) (-4 *2 (-872))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *5 (-1299 (-663 *3))) (-4 *4 (-319)) - (-5 *2 (-663 *3)) (-5 *1 (-469 *4 *3)) (-4 *3 (-1275 *4))))) -(((*1 *2 *3 *4 *5 *5) - (-12 (-5 *3 (-3 (-421 (-976 *6)) (-1198 (-1209) (-976 *6)))) - (-5 *5 (-793)) (-4 *6 (-466)) (-5 *2 (-663 (-711 (-421 (-976 *6))))) - (-5 *1 (-304 *6)) (-5 *4 (-711 (-421 (-976 *6)))))) - ((*1 *2 *3 *4) - (-12 - (-5 *3 - (-2 (|:| |eigval| (-3 (-421 (-976 *5)) (-1198 (-1209) (-976 *5)))) - (|:| |eigmult| (-793)) (|:| |eigvec| 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\ No newline at end of file |