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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 | )abbrev package FRIDEAL2 FractionalIdealFunctions2
++ Author: Manuel Bronstein
++ Date Created: 1 Feb 1989
++ Date Last Updated: 27 Feb 1990
++ Description:
++ Lifting of morphisms to fractional ideals.
FractionalIdealFunctions2(R1, F1, U1, A1, R2, F2, U2, A2) : SIG == CODE where
R1 : EuclideanDomain
R2 : EuclideanDomain
F1 : QuotientFieldCategory R1
U1 : UnivariatePolynomialCategory F1
A1 : Join(FramedAlgebra(F1, U1), RetractableTo F1)
F2 : QuotientFieldCategory R2
U2 : UnivariatePolynomialCategory F2
A2 : Join(FramedAlgebra(F2, U2), RetractableTo F2)
SIG ==> with
map : (R1 -> R2, FractionalIdeal(R1, F1, U1, A1)) ->
FractionalIdeal(R2, F2, U2, A2)
++ map(f,i) \undocumented{}
CODE ==> add
fmap: (F1 -> F2, A1) -> A2
fmap(f, a) ==
v := coordinates a
represents
[f qelt(v, i) for i in minIndex v .. maxIndex v]$Vector(F2)
map(f, i) ==
b := basis i
ideal [fmap(s +-> f(numer s) / f(denom s), qelt(b, j))
for j in minIndex b .. maxIndex b]$Vector(A2)
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