up previous next
ContentFreeFactor

factorization of multivariate polynomial into content-free factors

Syntax
ContentFreeFactor(F: RINGELEM): RECORD

Description
This function returns a factorization of the multivariate polynomial F into (polynomial) content-free factors; it works by calling ContentWRT repeatedly. The multiplicities will always be 1.

A polynomial which is (polynomial) content-free means that all its irreducible factors involve all indeterminate appearing the polynomial itself.

Example
/**/ use P ::= QQ[x,y,z];
/**/ f := 2*(x+1)*(y+2)*(x+y)^2*(x-y);
/**/ indent(ContentFreeFactor(f));
record[
  RemainingFactor := 2,
  factors := [y +2, x +1, x^3 +x^2*y -x*y^2 -y^3],
  multiplicities := [1, 1, 1]
]

See Also