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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 | )abbrev package MMAP MultipleMap
++ Author: Manuel Bronstein
++ Date Created: May 1988
++ Date Last Updated: 11 Jul 1990
++ Description:
++ Lifting of a map through 2 levels of polynomials;
MultipleMap(R1,UP1,UPUP1,R2,UP2,UPUP2) : SIG == CODE where
R1 : IntegralDomain
UP1 : UnivariatePolynomialCategory R1
UPUP1: UnivariatePolynomialCategory Fraction UP1
R2 : IntegralDomain
UP2 : UnivariatePolynomialCategory R2
UPUP2: UnivariatePolynomialCategory Fraction UP2
Q1 ==> Fraction UP1
Q2 ==> Fraction UP2
SIG ==> with
map : (R1 -> R2, UPUP1) -> UPUP2
++ map(f, p) lifts f to the domain of p then applies it to p.
CODE ==> add
import UnivariatePolynomialCategoryFunctions2(R1, UP1, R2, UP2)
rfmap: (R1 -> R2, Q1) -> Q2
rfmap(f, q) == map(f, numer q) / map(f, denom q)
map(f, p) ==
map(x +-> rfmap(f,x),
p)$UnivariatePolynomialCategoryFunctions2(Q1, UPUP1, Q2, UPUP2)
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