D.5.5.20 allsquarefree

Procedure from library hnoether.lib (see hnoether_lib).

Usage :

allsquarefree(f,g); f,g poly

Assume:

g is the output of squarefree(f).

Return:

the greatest squarefree divisor of f.

Note :

This proc uses factorize to get the missing factors of f not in g and, therefore, may be slow.

Example:

LIB "hnoether.lib";
ring exring=7,(x,y),dp;
poly f=(x+y)^7*(x-y)^8;
poly g=squarefree(f);
g;                      // factor x+y lost, since characteristic=7
→ x-y
allsquarefree(f,g);     // all factors (x+y)*(x-y) found
→ x2-y2

See also: squarefree.