# Singular          #### D.4.2.8 is_bijective

Procedure from library `algebra.lib` (see algebra_lib).

Usage:
is_bijective(phi,pr); phi map to basering, pr preimage ring

Return:
an integer, 1 if phi is bijective, 0 if not

Note:
The algorithm checks first injectivity and then surjectivity. To interprete this for local/mixed orderings, or for quotient rings type help is_surjective; and help is_injective;

Display:
A comment if printlevel >= voice-1 (default)

Example:
 ```LIB "algebra.lib"; int p = printlevel; printlevel = 1; 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_bijective(phi,R); ==> // map not injective ==> 0 qring Q = std(z-x2+y3); is_bijective(ideal(x,y,x2-y3),Q); ==> 1 ring S = 0,(a,b,c,d),dp; map psi = R,ideal(a,a+b,c-a2+b3,0); // a map from R to S, is_bijective(psi,R); // x->a, y->a+b, z->c-a2+b3 ==> // map injective, but not surjective ==> 0 qring T = std(d,c-a2+b3); ==> // ** _ is no standard basis map chi = Q,a,b,a2-b3; // amap between two quotient rings is_bijective(chi,Q); ==> 1 printlevel = p; ```

### Misc 