D.4.1.7 is_surjective

Procedure from library algebra.lib (see algebra_lib).

Usage:

is_surjective(phi); phi map to basering, or ideal defining it

Return:

an integer, 1 if phi is surjective, 0 if not

Note:

The algorithm returns 1 iff all the variables of the basering are contained in the polynomial subalgebra generated by the polynomials defining phi. Hence, if the basering has local or mixed ordering or if the preimage ring is a quotient ring (in which case the map may not be well defined) then the return value 1 means
"surjectivity" in this sense.

Example:

LIB "algebra.lib";
ring R = 0,(x,y,z),dp;
ideal i = x, y, x2-y3;
map phi = R,i;                    // a map from R to itself, z->x2-y3
is_surjective(phi);
→ 0
qring Q = std(ideal(z-x37));
map psi = R, x,y,x2-y3;           // the same map to the quotient ring
is_surjective(psi);
→ 1
ring S = 0,(a,b,c),dp;
map psi = R,ideal(a,a+b,c-a2+b3); // a map from R to S,
is_surjective(psi);               // x->a, y->a+b, z->c-a2+b3
→ 1