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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 | )abbrev category XPOLYC XPolynomialsCat
++ Author: Michel Petitot petitot@lifl.fr
++ Date Created: 91
++ Date Last Updated: 7 Juillet 92
++ Fix History: compilation v 2.1 le 13 dec 98
++ Description:
++ The Category of polynomial rings with non-commutative variables.
++ The coefficient ring may be non-commutative too.
++ However coefficients commute with variables.
XPolynomialsCat(vl,R) : Category == SIG where
vl : OrderedSet
R : Ring
WORD ==> OrderedFreeMonoid(vl)
SIG ==> XFreeAlgebra(vl,R) with
maxdeg : % -> WORD
++ \spad{maxdeg(p)} returns the greatest leading word in the
++ support of \spad{p}.
degree : % -> NonNegativeInteger
++ \spad{degree(p)} returns the degree of \spad{p}.
++ Note that the degree of a word is its length.
trunc : (% , NonNegativeInteger) -> %
++ \spad{trunc(p,n)} returns the polynomial \spad{p} truncated
++ at order \spad{n}.
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