Hello, suppose I want to solve a system of equations
w,x,y,z = SR.var('w, x, y, z')
eqn1=2*w*y^2 + y^2*z + z^3==0
eqn2=4*x^3 - 2*x*y^2 - y^3==0
eqn3=2*w^2*y - 2*x^2*y - 3*x*y^2 + 2*w*y*z==0
eqn4=w*y^2 + 3*w*z^2==0
sol = solve([eqn1, eqn2, eqn3, eqn4], w,x,y,z, solution_dict=True)
sol
This gives me solutions over complex numbers I believe? How can I ask for solutions over say a finite field. Let's make it more simple and say the field is a prime and not a prime power. Hence, just reducing modulo p. As you all know, it is possible more solutions arise when moving to finite fields.
