I'm completely new to Singular, and wish to obtain "non-trivial" solutions to a system of equations. More precisely, I create a ring
Code:
ring r = 0,(u(1..5),v(1..5),x(1..5),y(1..5)),lp;
and an ideal
Code:
ideal i = ...;
and its Gröbner basis. I want to find u(...),v(...),x(...),y(...) that satisfy the equations in i. Two problems:
(1) i has positive dimension (actually projective of dimension 11, degree 25), so
Code:
LIB "solve.lib"; solve(i);
does not work
(2) there are some trivial solutions, for example u=x,v=y which I want to avoid
I tried to specialize some variables at random (by defining ideal j = i,u(1)-1,...), but didn't manage to find a non-trivial 0-dimensional ideal in this manner, so something more systematic is welcome!