Sage has the method solve (or function, I'm not sure what's the correct terminology) that finds solutions to 'symbolic expressions'. In particular, if one wants to find solutions for a given set of equations using solve, one has to define all variables beforehand using "var('x,y,z,...')".
My problem is that I'd like to solve equations in specific polynomial rings. In particular, I want to solve an equation over fields of characteristic 2, so I'm using $GF(2)$ as a prototype. However, I can neither apply solve nor even "collect" to the object $f$ that I generated in these few lines (and I believe it is because I didn't use var):
B.<x,y,x_0,y_0,a_1,a_2,a_3,a_4,a_6> = GF(2)[]
##the Weierstrass eq of an elliptic curve
eqn = y^2 + a_1*x*y + a_3*y - (x^3 + a_2*x^2 + a_4*x + a_6)
D_x_0 = eqn.derivative(x).substitute(x=x_0,y=y_0)
D_y_0 = eqn.derivative(y).substitute(x=x_0,y=y_0)
la = -D_x_0/D_y_0
nu = (D_y_0*y_0 + D_x_0*x_0)/D_y_0
f=eqn.substitute(y=la*x+nu))
