D.5.8.3 is_active

Procedure from library sing.lib (see sing_lib).

Usage:

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

Return:

1 if f is an active element modulo id (i.e. dim(id)=dim(id+f*R^n)+1, if id is a submodule of R^n) resp. 0 if f is not active. The basering may be a quotient ring

Note:

regular parameters are active but not vice versa (id may have embedded components). proc is_reg tests whether f is a regular parameter

Example:

LIB "sing.lib";
ring r   =32003,(x,y,z),ds;
ideal i  = yx3+y,yz3+y3z;
poly f   = x;
is_active(f,i);
→ 1
qring q  = std(x4y5);
poly f   = x;
module m = [yx3+x,yx3+y3x];
is_active(f,m);
→ 0