The functions in this section are restricted to multivariate polynomials over a field, over the integers, or any polynomial ring over these.

Subsections

• Common Divisors and Common Multiples
• Content and Primitive Part

Gcd(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt

GCD(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt

The greatest common divisor of f and g in a multivariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers, or a polynomial ring over any of these.

Lcm(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt

LCM(f, g) : RngDPolElt, RngDPolElt -> RngDPolElt

The least common multiple of f and g in a multivariate polynomial ring P. The coefficient ring of P must be either a field, the ring of integers, or a polynomial ring over any of these.

The content of p, that is, the greatest common divisor of the coefficients of p as an element of the coefficient ring.

The primitive part of p, being p divided by the content of p.

Contpp(p) : RngDPolElt -> RngIntElt, RngDPolElt

The content (the greatest common divisor of the coefficients) of p, as an element of the coefficient ring, as well as the primitive part (p divided by the content) of p.