Ideal Operations

ideal< R | a₁, ..., aᵣ >: RngIntRes, RngIntResElt, ..., RngIntResElt -> RngIntRes

The ideal of the residue ring \(R\) generated by the greatest common divisor of the elements \(a_i\) and the modulus of \(R\).

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

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 \(Q\).

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

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 \((a)\cap (b)\).

LeastCommonMultiple(Q): [RngIntResElt] -> RngIntResElt

Lcm(Q): [RngIntResElt] -> RngIntResElt

LCM(Q): [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 \(Q\).

I + J: RngIntRes, RngIntRes -> RngIntRes

I * J: RngIntRes, RngIntRes -> RngIntRes

I meet J: RngIntRes, RngIntRes -> RngIntRes

a in I: RngIntResElt, RngIntRes -> BoolElt

a notin I: RngIntResElt, RngIntRes -> BoolElt

I eq J: RngIntRes, RngIntRes -> BoolElt

I ne J: RngIntRes, RngIntRes -> BoolElt

I subset J: RngIntRes, RngIntRes -> BoolElt

I notsubset J: RngIntRes, RngIntRes -> BoolElt