/usr/share/axiom-20170501/src/algebra/MODFIELD.spad is in axiom-source 20170501-3.
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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 | )abbrev domain MODFIELD ModularField
++ Author: Mark Botch
++ Description:
++ 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}
ModularField(R,Mod,reduction,merge,exactQuo) : SIG == CODE where
R : CommutativeRing
Mod : AbelianMonoid
reduction : (R,Mod) -> R
merge : (Mod,Mod) -> Union(Mod,"failed")
exactQuo : (R,R,Mod) -> Union(R,"failed")
SIG ==> Field with
modulus : % -> Mod
++ modulus(x) is not documented
coerce : % -> R
++ coerce(x) is not documented
reduce : (R,Mod) -> %
++ reduce(r,m) is not documented
exQuo : (%,%) -> Union(%,"failed")
++ exQuo(x,y) is not documented
CODE ==> ModularRing(R,Mod,reduction,merge,exactQuo)
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