diff options
author | dos-reis <gdr@axiomatics.org> | 2008-12-27 19:16:40 +0000 |
---|---|---|
committer | dos-reis <gdr@axiomatics.org> | 2008-12-27 19:16:40 +0000 |
commit | e51b2aa30afc0e65cca5bfc32d32dd9471fd65ea (patch) | |
tree | 4d2fd56347cc09adba11747665d1cddcbf7c8ce7 /src/share/algebra/browse.daase | |
parent | fdc64c2abcdf53d9afee4541503d1d17763ee92c (diff) | |
download | open-axiom-e51b2aa30afc0e65cca5bfc32d32dd9471fd65ea.tar.gz |
* algebra/catdef.spad.pamphlet (OrderedFinite): Export `min' and
`max' values.
* algebra/si.spad.pamphlet (SingleInteger): Now satisfies
OrderedFinite. Tidy.
Diffstat (limited to 'src/share/algebra/browse.daase')
-rw-r--r-- | src/share/algebra/browse.daase | 48 |
1 files changed, 24 insertions, 24 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 6c7b2a3f..3f2a3e54 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2276957 . 3439324113) +(2276553 . 3439392485) (-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 @@ -88,7 +88,7 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3215 UP UPUP -4362) +(-40 -3215 UP UPUP -1415) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3998 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3998 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3998 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3998 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) @@ -1080,7 +1080,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-288 S R |Mod| -1966 -1346 |exactQuo|) +(-288 S R |Mod| -4050 -1949 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL @@ -1203,7 +1203,7 @@ NIL (-318 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2656) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2671) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-319 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1819,7 +1819,7 @@ NIL (-472 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2656) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2671) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-473 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4383 . T)) @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-648 A -2610) +(-648 A -1975) ((|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}}"))) ((-4376 . T) (-4377 . T) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) @@ -2716,7 +2716,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-697 S -1867 I) +(-697 S -1866 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-702 R |Mod| -1966 -1346 |exactQuo|) +(-702 R |Mod| -4050 -1949 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL @@ -2752,7 +2752,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-706 R |Mod| -1966 -1346 |exactQuo|) +(-706 R |Mod| -4050 -1949 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4379 . T)) NIL @@ -3269,7 +3269,7 @@ NIL ((-4379 |has| |#1| (-839))) ((|HasCategory| |#1| (QUOTE (-839))) (-3998 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3998 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-835) -((|constructor| (NIL "Ordered finite sets."))) +((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL (-836 -3084 S) @@ -3448,7 +3448,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-880 R -1867) +(-880 R -1866) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3636,11 +3636,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -876) (|devaluate| |#1|)))) -(-927 R -3215 -1867) +(-927 R -3215 -1866) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-928 -1867) +(-928 -1866) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -4357,7 +4357,7 @@ NIL NIL NIL (-1107) -((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) +((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) ((-4370 . T) (-4374 . T) (-4369 . T) (-4380 . T) (-4381 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) NIL (-1108 S) @@ -4547,7 +4547,7 @@ NIL (-1154 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) (((-4384 "*") -3998 (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-171)) (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4375 -3998 (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-550)) (-2084 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3998 (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (QUOTE (-1138))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -285) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -308) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| (-1161 |#1| |#2| |#3|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(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 @@ -4571,11 +4571,11 @@ NIL (-1160 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . 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(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| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) 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integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4851,11 +4851,11 @@ NIL (-1230 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2656) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2671) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3998 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1232 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4384 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4375 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -2671) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2656) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4237) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) (-1237 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) @@ -4883,7 +4883,7 @@ NIL (-1238 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2656) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2671) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3998 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3220) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3998 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -4237) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2670) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1239 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<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 @@ -5044,4 +5044,4 @@ NIL NIL NIL NIL -((-3 NIL 2276937 2276942 2276947 2276952) (-2 NIL 2276917 2276922 2276927 2276932) (-1 NIL 2276897 2276902 2276907 2276912) (0 NIL 2276877 2276882 2276887 2276892) (-1274 "ZMOD.spad" 2276686 2276699 2276815 2276872) (-1273 "ZLINDEP.spad" 2275730 2275741 2276676 2276681) (-1272 "ZDSOLVE.spad" 2265579 2265601 2275720 2275725) (-1271 "YSTREAM.spad" 2265072 2265083 2265569 2265574) (-1270 "XRPOLY.spad" 2264292 2264312 2264928 2264997) (-1269 "XPR.spad" 2262083 2262096 2264010 2264109) (-1268 "XPOLY.spad" 2261638 2261649 2261939 2262008) (-1267 "XPOLYC.spad" 2260955 2260971 2261564 2261633) (-1266 "XPBWPOLY.spad" 2259392 2259412 2260735 2260804) (-1265 "XF.spad" 2257853 2257868 2259294 2259387) (-1264 "XF.spad" 2256294 2256311 2257737 2257742) (-1263 "XFALG.spad" 2253318 2253334 2256220 2256289) (-1262 "XEXPPKG.spad" 2252569 2252595 2253308 2253313) (-1261 "XDPOLY.spad" 2252183 2252199 2252425 2252494) (-1260 "XALG.spad" 2251843 2251854 2252139 2252178) (-1259 "WUTSET.spad" 2247682 2247699 2251489 2251516) (-1258 "WP.spad" 2246881 2246925 2247540 2247607) (-1257 "WHILEAST.spad" 2246679 2246688 2246871 2246876) (-1256 "WHEREAST.spad" 2246350 2246359 2246669 2246674) (-1255 "WFFINTBS.spad" 2243913 2243935 2246340 2246345) (-1254 "WEIER.spad" 2242127 2242138 2243903 2243908) (-1253 "VSPACE.spad" 2241800 2241811 2242095 2242122) (-1252 "VSPACE.spad" 2241493 2241506 2241790 2241795) (-1251 "VOID.spad" 2241170 2241179 2241483 2241488) (-1250 "VIEW.spad" 2238792 2238801 2241160 2241165) (-1249 "VIEWDEF.spad" 2233989 2233998 2238782 2238787) (-1248 "VIEW3D.spad" 2217824 2217833 2233979 2233984) (-1247 "VIEW2D.spad" 2205561 2205570 2217814 2217819) (-1246 "VECTOR.spad" 2204236 2204247 2204487 2204514) (-1245 "VECTOR2.spad" 2202863 2202876 2204226 2204231) (-1244 "VECTCAT.spad" 2200763 2200774 2202831 2202858) (-1243 "VECTCAT.spad" 2198471 2198484 2200541 2200546) (-1242 "VARIABLE.spad" 2198251 2198266 2198461 2198466) (-1241 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2154804 2157085 2157090) (-1222 "UPOLYC.spad" 2149756 2149767 2154620 2154773) (-1221 "UPOLYC.spad" 2144626 2144639 2149492 2149497) (-1220 "UPOLYC2.spad" 2144095 2144114 2144616 2144621) (-1219 "UP.spad" 2141252 2141267 2141645 2141798) (-1218 "UPMP.spad" 2140142 2140155 2141242 2141247) (-1217 "UPDIVP.spad" 2139705 2139719 2140132 2140137) (-1216 "UPDECOMP.spad" 2137942 2137956 2139695 2139700) (-1215 "UPCDEN.spad" 2137149 2137165 2137932 2137937) (-1214 "UP2.spad" 2136511 2136532 2137139 2137144) (-1213 "UNISEG.spad" 2135864 2135875 2136430 2136435) (-1212 "UNISEG2.spad" 2135357 2135370 2135820 2135825) (-1211 "UNIFACT.spad" 2134458 2134470 2135347 2135352) (-1210 "ULS.spad" 2125010 2125038 2126103 2126532) (-1209 "ULSCONS.spad" 2117404 2117424 2117776 2117925) (-1208 "ULSCCAT.spad" 2115133 2115153 2117250 2117399) (-1207 "ULSCCAT.spad" 2112970 2112992 2115089 2115094) (-1206 "ULSCAT.spad" 2111186 2111202 2112816 2112965) (-1205 "ULS2.spad" 2110698 2110751 2111176 2111181) (-1204 "UFD.spad" 2109763 2109772 2110624 2110693) (-1203 "UFD.spad" 2108890 2108901 2109753 2109758) (-1202 "UDVO.spad" 2107737 2107746 2108880 2108885) (-1201 "UDPO.spad" 2105164 2105175 2107693 2107698) (-1200 "TYPE.spad" 2105096 2105105 2105154 2105159) (-1199 "TYPEAST.spad" 2105015 2105024 2105086 2105091) (-1198 "TWOFACT.spad" 2103665 2103680 2105005 2105010) (-1197 "TUPLE.spad" 2103149 2103160 2103564 2103569) (-1196 "TUBETOOL.spad" 2099986 2099995 2103139 2103144) (-1195 "TUBE.spad" 2098627 2098644 2099976 2099981) (-1194 "TS.spad" 2097216 2097232 2098192 2098289) (-1193 "TSETCAT.spad" 2084343 2084360 2097184 2097211) (-1192 "TSETCAT.spad" 2071456 2071475 2084299 2084304) (-1191 "TRMANIP.spad" 2065822 2065839 2071162 2071167) (-1190 "TRIMAT.spad" 2064781 2064806 2065812 2065817) (-1189 "TRIGMNIP.spad" 2063298 2063315 2064771 2064776) (-1188 "TRIGCAT.spad" 2062810 2062819 2063288 2063293) (-1187 "TRIGCAT.spad" 2062320 2062331 2062800 2062805) (-1186 "TREE.spad" 2060891 2060902 2061927 2061954) (-1185 "TRANFUN.spad" 2060722 2060731 2060881 2060886) (-1184 "TRANFUN.spad" 2060551 2060562 2060712 2060717) (-1183 "TOPSP.spad" 2060225 2060234 2060541 2060546) (-1182 "TOOLSIGN.spad" 2059888 2059899 2060215 2060220) (-1181 "TEXTFILE.spad" 2058445 2058454 2059878 2059883) (-1180 "TEX.spad" 2055577 2055586 2058435 2058440) (-1179 "TEX1.spad" 2055133 2055144 2055567 2055572) (-1178 "TEMUTL.spad" 2054688 2054697 2055123 2055128) (-1177 "TBCMPPK.spad" 2052781 2052804 2054678 2054683) (-1176 "TBAGG.spad" 2051817 2051840 2052761 2052776) (-1175 "TBAGG.spad" 2050861 2050886 2051807 2051812) (-1174 "TANEXP.spad" 2050237 2050248 2050851 2050856) (-1173 "TABLE.spad" 2048648 2048671 2048918 2048945) (-1172 "TABLEAU.spad" 2048129 2048140 2048638 2048643) (-1171 "TABLBUMP.spad" 2044912 2044923 2048119 2048124) (-1170 "SYSTEM.spad" 2044186 2044195 2044902 2044907) (-1169 "SYSSOLP.spad" 2041659 2041670 2044176 2044181) (-1168 "SYNTAX.spad" 2037929 2037938 2041649 2041654) (-1167 "SYMTAB.spad" 2035985 2035994 2037919 2037924) (-1166 "SYMS.spad" 2031970 2031979 2035975 2035980) (-1165 "SYMPOLY.spad" 2030977 2030988 2031059 2031186) (-1164 "SYMFUNC.spad" 2030452 2030463 2030967 2030972) (-1163 "SYMBOL.spad" 2027879 2027888 2030442 2030447) (-1162 "SWITCH.spad" 2024636 2024645 2027869 2027874) (-1161 "SUTS.spad" 2021535 2021563 2023103 2023200) (-1160 "SUPXS.spad" 2018670 2018698 2019667 2019816) (-1159 "SUP.spad" 2015439 2015450 2016220 2016373) (-1158 "SUPFRACF.spad" 2014544 2014562 2015429 2015434) (-1157 "SUP2.spad" 2013934 2013947 2014534 2014539) (-1156 "SUMRF.spad" 2012900 2012911 2013924 2013929) (-1155 "SUMFS.spad" 2012533 2012550 2012890 2012895) (-1154 "SULS.spad" 2003072 2003100 2004178 2004607) (-1153 "SUCHTAST.spad" 2002841 2002850 2003062 2003067) (-1152 "SUCH.spad" 2002521 2002536 2002831 2002836) (-1151 "SUBSPACE.spad" 1994528 1994543 2002511 2002516) (-1150 "SUBRESP.spad" 1993688 1993702 1994484 1994489) (-1149 "STTF.spad" 1989787 1989803 1993678 1993683) (-1148 "STTFNC.spad" 1986255 1986271 1989777 1989782) (-1147 "STTAYLOR.spad" 1978653 1978664 1986136 1986141) (-1146 "STRTBL.spad" 1977158 1977175 1977307 1977334) (-1145 "STRING.spad" 1976567 1976576 1976581 1976608) (-1144 "STRICAT.spad" 1976355 1976364 1976535 1976562) (-1143 "STREAM.spad" 1973213 1973224 1975880 1975895) (-1142 "STREAM3.spad" 1972758 1972773 1973203 1973208) (-1141 "STREAM2.spad" 1971826 1971839 1972748 1972753) (-1140 "STREAM1.spad" 1971530 1971541 1971816 1971821) (-1139 "STINPROD.spad" 1970436 1970452 1971520 1971525) (-1138 "STEP.spad" 1969637 1969646 1970426 1970431) (-1137 "STBL.spad" 1968163 1968191 1968330 1968345) (-1136 "STAGG.spad" 1967238 1967249 1968153 1968158) (-1135 "STAGG.spad" 1966311 1966324 1967228 1967233) (-1134 "STACK.spad" 1965662 1965673 1965918 1965945) (-1133 "SREGSET.spad" 1963366 1963383 1965308 1965335) (-1132 "SRDCMPK.spad" 1961911 1961931 1963356 1963361) (-1131 "SRAGG.spad" 1957008 1957017 1961879 1961906) (-1130 "SRAGG.spad" 1952125 1952136 1956998 1957003) (-1129 "SQMATRIX.spad" 1949741 1949759 1950657 1950744) (-1128 "SPLTREE.spad" 1944293 1944306 1949177 1949204) (-1127 "SPLNODE.spad" 1940881 1940894 1944283 1944288) (-1126 "SPFCAT.spad" 1939658 1939667 1940871 1940876) (-1125 "SPECOUT.spad" 1938208 1938217 1939648 1939653) (-1124 "SPADXPT.spad" 1930347 1930356 1938198 1938203) (-1123 "spad-parser.spad" 1929812 1929821 1930337 1930342) (-1122 "SPADAST.spad" 1929513 1929522 1929802 1929807) (-1121 "SPACEC.spad" 1913526 1913537 1929503 1929508) (-1120 "SPACE3.spad" 1913302 1913313 1913516 1913521) (-1119 "SORTPAK.spad" 1912847 1912860 1913258 1913263) (-1118 "SOLVETRA.spad" 1910604 1910615 1912837 1912842) (-1117 "SOLVESER.spad" 1909124 1909135 1910594 1910599) (-1116 "SOLVERAD.spad" 1905134 1905145 1909114 1909119) (-1115 "SOLVEFOR.spad" 1903554 1903572 1905124 1905129) (-1114 "SNTSCAT.spad" 1903154 1903171 1903522 1903549) (-1113 "SMTS.spad" 1901414 1901440 1902719 1902816) (-1112 "SMP.spad" 1898853 1898873 1899243 1899370) (-1111 "SMITH.spad" 1897696 1897721 1898843 1898848) (-1110 "SMATCAT.spad" 1895806 1895836 1897640 1897691) (-1109 "SMATCAT.spad" 1893848 1893880 1895684 1895689) (-1108 "SKAGG.spad" 1892809 1892820 1893816 1893843) (-1107 "SINT.spad" 1891117 1891126 1892675 1892804) (-1106 "SIMPAN.spad" 1890845 1890854 1891107 1891112) (-1105 "SIG.spad" 1890173 1890182 1890835 1890840) (-1104 "SIGNRF.spad" 1889281 1889292 1890163 1890168) (-1103 "SIGNEF.spad" 1888550 1888567 1889271 1889276) (-1102 "SIGAST.spad" 1887931 1887940 1888540 1888545) (-1101 "SHP.spad" 1885849 1885864 1887887 1887892) (-1100 "SHDP.spad" 1875560 1875587 1876069 1876200) (-1099 "SGROUP.spad" 1875168 1875177 1875550 1875555) (-1098 "SGROUP.spad" 1874774 1874785 1875158 1875163) (-1097 "SGCF.spad" 1867655 1867664 1874764 1874769) (-1096 "SFRTCAT.spad" 1866583 1866600 1867623 1867650) (-1095 "SFRGCD.spad" 1865646 1865666 1866573 1866578) (-1094 "SFQCMPK.spad" 1860283 1860303 1865636 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1036109) (-643 "LODO1.spad" 1035063 1035073 1035343 1035382) (-642 "LODEEF.spad" 1033835 1033853 1035053 1035058) (-641 "LNAGG.spad" 1029637 1029647 1033825 1033830) (-640 "LNAGG.spad" 1025403 1025415 1029593 1029598) (-639 "LMOPS.spad" 1022139 1022156 1025393 1025398) (-638 "LMODULE.spad" 1021781 1021791 1022129 1022134) (-637 "LMDICT.spad" 1021064 1021074 1021332 1021359) (-636 "LITERAL.spad" 1020970 1020981 1021054 1021059) (-635 "LIST.spad" 1018688 1018698 1020117 1020144) (-634 "LIST3.spad" 1017979 1017993 1018678 1018683) (-633 "LIST2.spad" 1016619 1016631 1017969 1017974) (-632 "LIST2MAP.spad" 1013496 1013508 1016609 1016614) (-631 "LINEXP.spad" 1012928 1012938 1013476 1013491) (-630 "LINDEP.spad" 1011705 1011717 1012840 1012845) (-629 "LIMITRF.spad" 1009619 1009629 1011695 1011700) (-628 "LIMITPS.spad" 1008502 1008515 1009609 1009614) (-627 "LIE.spad" 1006516 1006528 1007792 1007937) (-626 "LIECAT.spad" 1005992 1006002 1006442 1006511) (-625 "LIECAT.spad" 1005496 1005508 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130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2276533 2276538 2276543 2276548) (-2 NIL 2276513 2276518 2276523 2276528) (-1 NIL 2276493 2276498 2276503 2276508) (0 NIL 2276473 2276478 2276483 2276488) (-1274 "ZMOD.spad" 2276282 2276295 2276411 2276468) (-1273 "ZLINDEP.spad" 2275326 2275337 2276272 2276277) (-1272 "ZDSOLVE.spad" 2265175 2265197 2275316 2275321) (-1271 "YSTREAM.spad" 2264668 2264679 2265165 2265170) (-1270 "XRPOLY.spad" 2263888 2263908 2264524 2264593) (-1269 "XPR.spad" 2261679 2261692 2263606 2263705) (-1268 "XPOLY.spad" 2261234 2261245 2261535 2261604) (-1267 "XPOLYC.spad" 2260551 2260567 2261160 2261229) (-1266 "XPBWPOLY.spad" 2258988 2259008 2260331 2260400) (-1265 "XF.spad" 2257449 2257464 2258890 2258983) (-1264 "XF.spad" 2255890 2255907 2257333 2257338) (-1263 "XFALG.spad" 2252914 2252930 2255816 2255885) (-1262 "XEXPPKG.spad" 2252165 2252191 2252904 2252909) (-1261 "XDPOLY.spad" 2251779 2251795 2252021 2252090) (-1260 "XALG.spad" 2251439 2251450 2251735 2251774) (-1259 "WUTSET.spad" 2247278 2247295 2251085 2251112) (-1258 "WP.spad" 2246477 2246521 2247136 2247203) (-1257 "WHILEAST.spad" 2246275 2246284 2246467 2246472) (-1256 "WHEREAST.spad" 2245946 2245955 2246265 2246270) (-1255 "WFFINTBS.spad" 2243509 2243531 2245936 2245941) (-1254 "WEIER.spad" 2241723 2241734 2243499 2243504) (-1253 "VSPACE.spad" 2241396 2241407 2241691 2241718) (-1252 "VSPACE.spad" 2241089 2241102 2241386 2241391) (-1251 "VOID.spad" 2240766 2240775 2241079 2241084) (-1250 "VIEW.spad" 2238388 2238397 2240756 2240761) (-1249 "VIEWDEF.spad" 2233585 2233594 2238378 2238383) (-1248 "VIEW3D.spad" 2217420 2217429 2233575 2233580) (-1247 "VIEW2D.spad" 2205157 2205166 2217410 2217415) (-1246 "VECTOR.spad" 2203832 2203843 2204083 2204110) (-1245 "VECTOR2.spad" 2202459 2202472 2203822 2203827) (-1244 "VECTCAT.spad" 2200359 2200370 2202427 2202454) (-1243 "VECTCAT.spad" 2198067 2198080 2200137 2200142) (-1242 "VARIABLE.spad" 2197847 2197862 2198057 2198062) (-1241 "UTYPE.spad" 2197491 2197500 2197837 2197842) (-1240 "UTSODETL.spad" 2196784 2196808 2197447 2197452) (-1239 "UTSODE.spad" 2194972 2194992 2196774 2196779) (-1238 "UTS.spad" 2189761 2189789 2193439 2193536) (-1237 "UTSCAT.spad" 2187212 2187228 2189659 2189756) (-1236 "UTSCAT.spad" 2184307 2184325 2186756 2186761) (-1235 "UTS2.spad" 2183900 2183935 2184297 2184302) (-1234 "URAGG.spad" 2178532 2178543 2183890 2183895) (-1233 "URAGG.spad" 2173128 2173141 2178488 2178493) (-1232 "UPXSSING.spad" 2170771 2170797 2172209 2172342) (-1231 "UPXS.spad" 2167919 2167947 2168903 2169052) (-1230 "UPXSCONS.spad" 2165676 2165696 2166051 2166200) (-1229 "UPXSCCA.spad" 2164241 2164261 2165522 2165671) (-1228 "UPXSCCA.spad" 2162948 2162970 2164231 2164236) (-1227 "UPXSCAT.spad" 2161529 2161545 2162794 2162943) (-1226 "UPXS2.spad" 2161070 2161123 2161519 2161524) (-1225 "UPSQFREE.spad" 2159482 2159496 2161060 2161065) (-1224 "UPSCAT.spad" 2157075 2157099 2159380 2159477) (-1223 "UPSCAT.spad" 2154374 2154400 2156681 2156686) (-1222 "UPOLYC.spad" 2149352 2149363 2154216 2154369) (-1221 "UPOLYC.spad" 2144222 2144235 2149088 2149093) (-1220 "UPOLYC2.spad" 2143691 2143710 2144212 2144217) (-1219 "UP.spad" 2140848 2140863 2141241 2141394) (-1218 "UPMP.spad" 2139738 2139751 2140838 2140843) (-1217 "UPDIVP.spad" 2139301 2139315 2139728 2139733) (-1216 "UPDECOMP.spad" 2137538 2137552 2139291 2139296) (-1215 "UPCDEN.spad" 2136745 2136761 2137528 2137533) (-1214 "UP2.spad" 2136107 2136128 2136735 2136740) (-1213 "UNISEG.spad" 2135460 2135471 2136026 2136031) (-1212 "UNISEG2.spad" 2134953 2134966 2135416 2135421) (-1211 "UNIFACT.spad" 2134054 2134066 2134943 2134948) (-1210 "ULS.spad" 2124606 2124634 2125699 2126128) (-1209 "ULSCONS.spad" 2117000 2117020 2117372 2117521) (-1208 "ULSCCAT.spad" 2114729 2114749 2116846 2116995) (-1207 "ULSCCAT.spad" 2112566 2112588 2114685 2114690) (-1206 "ULSCAT.spad" 2110782 2110798 2112412 2112561) (-1205 "ULS2.spad" 2110294 2110347 2110772 2110777) (-1204 "UFD.spad" 2109359 2109368 2110220 2110289) (-1203 "UFD.spad" 2108486 2108497 2109349 2109354) (-1202 "UDVO.spad" 2107333 2107342 2108476 2108481) (-1201 "UDPO.spad" 2104760 2104771 2107289 2107294) (-1200 "TYPE.spad" 2104692 2104701 2104750 2104755) (-1199 "TYPEAST.spad" 2104611 2104620 2104682 2104687) (-1198 "TWOFACT.spad" 2103261 2103276 2104601 2104606) (-1197 "TUPLE.spad" 2102745 2102756 2103160 2103165) (-1196 "TUBETOOL.spad" 2099582 2099591 2102735 2102740) (-1195 "TUBE.spad" 2098223 2098240 2099572 2099577) (-1194 "TS.spad" 2096812 2096828 2097788 2097885) (-1193 "TSETCAT.spad" 2083939 2083956 2096780 2096807) (-1192 "TSETCAT.spad" 2071052 2071071 2083895 2083900) (-1191 "TRMANIP.spad" 2065418 2065435 2070758 2070763) (-1190 "TRIMAT.spad" 2064377 2064402 2065408 2065413) (-1189 "TRIGMNIP.spad" 2062894 2062911 2064367 2064372) (-1188 "TRIGCAT.spad" 2062406 2062415 2062884 2062889) (-1187 "TRIGCAT.spad" 2061916 2061927 2062396 2062401) (-1186 "TREE.spad" 2060487 2060498 2061523 2061550) (-1185 "TRANFUN.spad" 2060318 2060327 2060477 2060482) (-1184 "TRANFUN.spad" 2060147 2060158 2060308 2060313) (-1183 "TOPSP.spad" 2059821 2059830 2060137 2060142) (-1182 "TOOLSIGN.spad" 2059484 2059495 2059811 2059816) (-1181 "TEXTFILE.spad" 2058041 2058050 2059474 2059479) (-1180 "TEX.spad" 2055173 2055182 2058031 2058036) (-1179 "TEX1.spad" 2054729 2054740 2055163 2055168) (-1178 "TEMUTL.spad" 2054284 2054293 2054719 2054724) (-1177 "TBCMPPK.spad" 2052377 2052400 2054274 2054279) (-1176 "TBAGG.spad" 2051413 2051436 2052357 2052372) (-1175 "TBAGG.spad" 2050457 2050482 2051403 2051408) (-1174 "TANEXP.spad" 2049833 2049844 2050447 2050452) (-1173 "TABLE.spad" 2048244 2048267 2048514 2048541) (-1172 "TABLEAU.spad" 2047725 2047736 2048234 2048239) (-1171 "TABLBUMP.spad" 2044508 2044519 2047715 2047720) (-1170 "SYSTEM.spad" 2043782 2043791 2044498 2044503) (-1169 "SYSSOLP.spad" 2041255 2041266 2043772 2043777) (-1168 "SYNTAX.spad" 2037525 2037534 2041245 2041250) (-1167 "SYMTAB.spad" 2035581 2035590 2037515 2037520) (-1166 "SYMS.spad" 2031566 2031575 2035571 2035576) (-1165 "SYMPOLY.spad" 2030573 2030584 2030655 2030782) (-1164 "SYMFUNC.spad" 2030048 2030059 2030563 2030568) (-1163 "SYMBOL.spad" 2027475 2027484 2030038 2030043) (-1162 "SWITCH.spad" 2024232 2024241 2027465 2027470) (-1161 "SUTS.spad" 2021131 2021159 2022699 2022796) (-1160 "SUPXS.spad" 2018266 2018294 2019263 2019412) (-1159 "SUP.spad" 2015035 2015046 2015816 2015969) (-1158 "SUPFRACF.spad" 2014140 2014158 2015025 2015030) (-1157 "SUP2.spad" 2013530 2013543 2014130 2014135) (-1156 "SUMRF.spad" 2012496 2012507 2013520 2013525) (-1155 "SUMFS.spad" 2012129 2012146 2012486 2012491) (-1154 "SULS.spad" 2002668 2002696 2003774 2004203) (-1153 "SUCHTAST.spad" 2002437 2002446 2002658 2002663) (-1152 "SUCH.spad" 2002117 2002132 2002427 2002432) (-1151 "SUBSPACE.spad" 1994124 1994139 2002107 2002112) (-1150 "SUBRESP.spad" 1993284 1993298 1994080 1994085) (-1149 "STTF.spad" 1989383 1989399 1993274 1993279) (-1148 "STTFNC.spad" 1985851 1985867 1989373 1989378) (-1147 "STTAYLOR.spad" 1978249 1978260 1985732 1985737) (-1146 "STRTBL.spad" 1976754 1976771 1976903 1976930) (-1145 "STRING.spad" 1976163 1976172 1976177 1976204) (-1144 "STRICAT.spad" 1975951 1975960 1976131 1976158) (-1143 "STREAM.spad" 1972809 1972820 1975476 1975491) (-1142 "STREAM3.spad" 1972354 1972369 1972799 1972804) (-1141 "STREAM2.spad" 1971422 1971435 1972344 1972349) (-1140 "STREAM1.spad" 1971126 1971137 1971412 1971417) (-1139 "STINPROD.spad" 1970032 1970048 1971116 1971121) (-1138 "STEP.spad" 1969233 1969242 1970022 1970027) (-1137 "STBL.spad" 1967759 1967787 1967926 1967941) (-1136 "STAGG.spad" 1966834 1966845 1967749 1967754) (-1135 "STAGG.spad" 1965907 1965920 1966824 1966829) (-1134 "STACK.spad" 1965258 1965269 1965514 1965541) (-1133 "SREGSET.spad" 1962962 1962979 1964904 1964931) (-1132 "SRDCMPK.spad" 1961507 1961527 1962952 1962957) (-1131 "SRAGG.spad" 1956604 1956613 1961475 1961502) (-1130 "SRAGG.spad" 1951721 1951732 1956594 1956599) (-1129 "SQMATRIX.spad" 1949337 1949355 1950253 1950340) (-1128 "SPLTREE.spad" 1943889 1943902 1948773 1948800) (-1127 "SPLNODE.spad" 1940477 1940490 1943879 1943884) (-1126 "SPFCAT.spad" 1939254 1939263 1940467 1940472) (-1125 "SPECOUT.spad" 1937804 1937813 1939244 1939249) (-1124 "SPADXPT.spad" 1929943 1929952 1937794 1937799) (-1123 "spad-parser.spad" 1929408 1929417 1929933 1929938) (-1122 "SPADAST.spad" 1929109 1929118 1929398 1929403) (-1121 "SPACEC.spad" 1913122 1913133 1929099 1929104) (-1120 "SPACE3.spad" 1912898 1912909 1913112 1913117) (-1119 "SORTPAK.spad" 1912443 1912456 1912854 1912859) (-1118 "SOLVETRA.spad" 1910200 1910211 1912433 1912438) (-1117 "SOLVESER.spad" 1908720 1908731 1910190 1910195) (-1116 "SOLVERAD.spad" 1904730 1904741 1908710 1908715) (-1115 "SOLVEFOR.spad" 1903150 1903168 1904720 1904725) (-1114 "SNTSCAT.spad" 1902750 1902767 1903118 1903145) (-1113 "SMTS.spad" 1901010 1901036 1902315 1902412) (-1112 "SMP.spad" 1898449 1898469 1898839 1898966) (-1111 "SMITH.spad" 1897292 1897317 1898439 1898444) (-1110 "SMATCAT.spad" 1895402 1895432 1897236 1897287) (-1109 "SMATCAT.spad" 1893444 1893476 1895280 1895285) (-1108 "SKAGG.spad" 1892405 1892416 1893412 1893439) (-1107 "SINT.spad" 1891231 1891240 1892271 1892400) (-1106 "SIMPAN.spad" 1890959 1890968 1891221 1891226) (-1105 "SIG.spad" 1890287 1890296 1890949 1890954) (-1104 "SIGNRF.spad" 1889395 1889406 1890277 1890282) (-1103 "SIGNEF.spad" 1888664 1888681 1889385 1889390) (-1102 "SIGAST.spad" 1888045 1888054 1888654 1888659) (-1101 "SHP.spad" 1885963 1885978 1888001 1888006) (-1100 "SHDP.spad" 1875674 1875701 1876183 1876314) (-1099 "SGROUP.spad" 1875282 1875291 1875664 1875669) (-1098 "SGROUP.spad" 1874888 1874899 1875272 1875277) (-1097 "SGCF.spad" 1867769 1867778 1874878 1874883) (-1096 "SFRTCAT.spad" 1866697 1866714 1867737 1867764) (-1095 "SFRGCD.spad" 1865760 1865780 1866687 1866692) (-1094 "SFQCMPK.spad" 1860397 1860417 1865750 1865755) (-1093 "SFORT.spad" 1859832 1859846 1860387 1860392) (-1092 "SEXOF.spad" 1859675 1859715 1859822 1859827) (-1091 "SEX.spad" 1859567 1859576 1859665 1859670) (-1090 "SEXCAT.spad" 1857118 1857158 1859557 1859562) (-1089 "SET.spad" 1855418 1855429 1856539 1856578) (-1088 "SETMN.spad" 1853852 1853869 1855408 1855413) (-1087 "SETCAT.spad" 1853337 1853346 1853842 1853847) (-1086 "SETCAT.spad" 1852820 1852831 1853327 1853332) (-1085 "SETAGG.spad" 1849341 1849352 1852800 1852815) (-1084 "SETAGG.spad" 1845870 1845883 1849331 1849336) (-1083 "SEQAST.spad" 1845573 1845582 1845860 1845865) (-1082 "SEGXCAT.spad" 1844695 1844708 1845563 1845568) (-1081 "SEG.spad" 1844508 1844519 1844614 1844619) (-1080 "SEGCAT.spad" 1843415 1843426 1844498 1844503) (-1079 "SEGBIND.spad" 1842487 1842498 1843370 1843375) (-1078 "SEGBIND2.spad" 1842183 1842196 1842477 1842482) (-1077 "SEGAST.spad" 1841897 1841906 1842173 1842178) (-1076 "SEG2.spad" 1841322 1841335 1841853 1841858) (-1075 "SDVAR.spad" 1840598 1840609 1841312 1841317) (-1074 "SDPOL.spad" 1837988 1837999 1838279 1838406) (-1073 "SCPKG.spad" 1836067 1836078 1837978 1837983) (-1072 "SCOPE.spad" 1835212 1835221 1836057 1836062) (-1071 "SCACHE.spad" 1833894 1833905 1835202 1835207) (-1070 "SASTCAT.spad" 1833803 1833812 1833884 1833889) (-1069 "SAOS.spad" 1833675 1833684 1833793 1833798) (-1068 "SAERFFC.spad" 1833388 1833408 1833665 1833670) (-1067 "SAE.spad" 1831563 1831579 1832174 1832309) (-1066 "SAEFACT.spad" 1831264 1831284 1831553 1831558) (-1065 "RURPK.spad" 1828905 1828921 1831254 1831259) (-1064 "RULESET.spad" 1828346 1828370 1828895 1828900) (-1063 "RULE.spad" 1826550 1826574 1828336 1828341) (-1062 "RULECOLD.spad" 1826402 1826415 1826540 1826545) (-1061 "RSTRCAST.spad" 1826119 1826128 1826392 1826397) (-1060 "RSETGCD.spad" 1822497 1822517 1826109 1826114) (-1059 "RSETCAT.spad" 1812281 1812298 1822465 1822492) (-1058 "RSETCAT.spad" 1802085 1802104 1812271 1812276) (-1057 "RSDCMPK.spad" 1800537 1800557 1802075 1802080) (-1056 "RRCC.spad" 1798921 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179434) (-155 "COLONAST.spad" 177942 177950 178266 178271) (-154 "CMPLXRT.spad" 177651 177668 177932 177937) (-153 "CLLCTAST.spad" 177313 177321 177641 177646) (-152 "CLIP.spad" 173405 173413 177303 177308) (-151 "CLIF.spad" 172044 172060 173361 173400) (-150 "CLAGG.spad" 168529 168539 172034 172039) (-149 "CLAGG.spad" 164885 164897 168392 168397) (-148 "CINTSLPE.spad" 164210 164223 164875 164880) (-147 "CHVAR.spad" 162288 162310 164200 164205) (-146 "CHARZ.spad" 162203 162211 162268 162283) (-145 "CHARPOL.spad" 161711 161721 162193 162198) (-144 "CHARNZ.spad" 161464 161472 161691 161706) (-143 "CHAR.spad" 159332 159340 161454 161459) (-142 "CFCAT.spad" 158648 158656 159322 159327) (-141 "CDEN.spad" 157806 157820 158638 158643) (-140 "CCLASS.spad" 155955 155963 157217 157256) (-139 "CATEGORY.spad" 155045 155053 155945 155950) (-138 "CATCTOR.spad" 154936 154944 155035 155040) (-137 "CATAST.spad" 154563 154571 154926 154931) (-136 "CASEAST.spad" 154277 154285 154553 154558) (-135 "CARTEN.spad" 149380 149404 154267 154272) (-134 "CARTEN2.spad" 148766 148793 149370 149375) (-133 "CARD.spad" 146055 146063 148740 148761) (-132 "CAPSLAST.spad" 145829 145837 146045 146050) (-131 "CACHSET.spad" 145451 145459 145819 145824) (-130 "CABMON.spad" 145004 145012 145441 145446) (-129 "BYTE.spad" 144325 144333 144994 144999) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
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