Singular

D.4.2.7 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 if and only if all the variables of the basering are contained in the polynomial subalgebra generated by the polynomials defining phi. Hence, it tests surjectivity in the case of a global odering. 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 needs to be interpreted with care.

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 ```