Recently i have beenhelped to write an implicit function differentiator (nice neologism isn't it). Here is the code
def implicit_derivative(V):
var("dw1, dw2")
V_w1 = diff(V, w1)
V_w2 = diff(V, w2)
# Differential
dV = V_w1 * dw1 + V_w2 * dw2
# Dérivée du premier ordre
sol=solve(dV==0, dw2)
impder=(sol[0]/dw1)
return impder
This work without difficulty for V function of w1 and w2. But if my variables are x and y or say χ and ζ. It will not work. I have not ound the mechanism to define a general function not dependant of the name of its arguments. And here there is a second problem to find thway to associate the increase d. to it correlative argument that is if I use χ as the first variable dχmust substitute to dw1.