D.5.8.6 is_reg

Procedure from library sing.lib (see sing_lib).

Usage:

is_reg(f,id); f poly, id ideal or module

Return:

1 if multiplication with f is injective modulo id, 0 otherwise

Note:

let R be the basering and id a submodule of R^n. The procedure checks injectivity of multiplication with f on R^n/id. The basering may be a quotient ring

Example:

LIB "sing.lib";
ring r  = 32003,(x,y),ds;
ideal i = x8,y8;
ideal j = (x+y)^4;
i       = intersect(i,j);
poly f  = xy;
is_reg(f,i);
→ 0