D.5.5.19 squarefree

Procedure from library hnoether.lib (see hnoether_lib).

Usage:

squarefree(f); f poly

Assume:

f is a bivariate polynomial (in the first 2 ring variables).

Return:

poly, a squarefree divisor of f.

Note:

Usually, the return value is the greatest squarefree divisor, but there is one exception: factors with a p-th root, p the characteristic of the basering, are lost.

Example:

LIB "hnoether.lib";
ring exring=3,(x,y),dp;
squarefree((x3+y)^2);
→ x3+y
squarefree((x+y)^3*(x-y)^2); // Warning: (x+y)^3 is lost
→ x-y
squarefree((x+y)^4*(x-y)^2); // result is (x+y)*(x-y)
→ x2-y2

See also: allsquarefree.