/usr/share/axiom-20170501/src/algebra/PSCAT.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | )abbrev category PSCAT PowerSeriesCategory
++ Author: Clifton J. Williamson
++ Date Created: 21 December 1989
++ Date Last Updated: 25 February 1990
++ Description:
++ \spadtype{PowerSeriesCategory} is the most general power series
++ category with exponents in an ordered abelian monoid.
PowerSeriesCategory(Coef,Expon,Var) : Category == SIG where
Coef : Ring
Expon : OrderedAbelianMonoid
Var : OrderedSet
I ==> Integer
RN ==> Fraction Integer
SIG ==> AbelianMonoidRing(Coef,Expon) with
monomial : (%,Var,Expon) -> %
++ \spad{monomial(a,x,n)} computes \spad{a*x**n}.
monomial : (%,List Var,List Expon) -> %
++ \spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes
++ \spad{a * x1**n1 * .. * xk**nk}.
leadingMonomial : % -> %
++ leadingMonomial(f) returns the monomial of \spad{f} of lowest order.
leadingCoefficient : % -> Coef
++ leadingCoefficient(f) returns the coefficient of the lowest order
++ term of \spad{f}
degree : % -> Expon
++ degree(f) returns the exponent of the lowest order term of \spad{f}.
variables : % -> List Var
++ \spad{variables(f)} returns a list of the variables occuring in the
++ power series f.
pole? : % -> Boolean
++ \spad{pole?(f)} determines if the power series f has a pole.
complete : % -> %
++ \spad{complete(f)} causes all terms of f to be computed.
++ Note that this results in an infinite loop
++ if f has infinitely many terms.
add
n:I * ps:% == (zero? n => 0; map((r1:Coef):Coef +-> n * r1,ps))
r:Coef * ps:% == (zero? r => 0; map((r1:Coef):Coef +-> r * r1,ps))
ps:% * r:Coef == (zero? r => 0; map((r1:Coef):Coef +-> r1 * r,ps))
- ps == map((r1:Coef):Coef +-> -r1,ps)
if Coef has Algebra Fraction Integer then
r:RN * ps:% == (zero? r => 0; map((r1:Coef):Coef +-> r * r1,ps))
ps:% * r:RN == (zero? r => 0; map((r1:Coef):Coef +-> r1 * r,ps))
if Coef has Field then
ps:% / r:Coef == map((r1:Coef):Coef +-> r1 / r,ps)
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