Subsections

• Generic Ideal Functions
• Ideal Arithmetic

ideal< R | a_1, ..., a_r > : RngIntRes, RngIntResElt, ..., RngIntResElt -> RngIntResIdl

quo< R | a_r, ..., a_r > : RngIntRes, RngIntResElt, ..., RngIntResElt -> GenRng

R / I : RngIntRes, RngIntResIdl -> GenRng

I + J : RngIntResIdl, RngIntResIdl -> RngIntResIdl

I * J : RngIntResIdl, RngIntResIdl -> RngIntResIdl

I meet J : RngIntResIdl, RngIntResIdl -> RngIntResIdl

I / J : RngIntResIdl, RngIntResIdl -> RngIntResIdl

a in I : RngIntResElt, RngIntResIdl -> BoolElt

a notin I : RngIntResElt, RngIntResIdl -> BoolElt

I eq J : RngIntResIdl, RngIntResIdl -> BoolElt

I ne J : RngIntResIdl, RngIntResIdl -> BoolElt

I subset J : RngIntResIdl, RngIntResIdl -> BoolElt

I notsubset J : RngIntResIdl, RngIntResIdl -> BoolElt

Gcd(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

GCD(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

Greatest common divisor of the elements a and b of R, that is, a generator for the R-ideal (a) + (b).

GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt

Gcd(Q) : [RngIntResElt] -> RngIntResElt

GCD(Q) : [RngIntResElt] -> RngIntResElt

Greatest common divisor of the sequence of elements Q, that is, a generator for the R-ideal generated by the elements in Q.

Lcm(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

LCM(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

Least common multiple of the elements a and b of R, that is, a generator for the R-ideal (a) intersect (b).

LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt

Lcm(Q) : Seq(RngIntResElt) -> RngIntResElt

LCM(Q) : Seq(RngIntResElt) -> RngIntResElt

Least common multiple of the sequence of elements Q, that is, a generator for the R-ideal formed by the intersection of the principal ideals generated by elements of Q.