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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 $w_1$ and $w_2$. But if my variables are $x$ and $y$ or say $\chi$ and $\zeta$. 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 $\chi$ as the first variable $d\chi$must substitute to $dw_1$.

Recently i have beenhelped been helped 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 $w_1$ and $w_2$. But if my variables are $x$ and $y$ or say $\chi$ and $\zeta$. It will not work. I have not ound found 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 $\chi$ as the first variable $d\chi$must substitute to $dw_1$.

Recently i have been helped 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 $w_1$ and $w_2$. But if my variables are $x$ and $y$ or say $\chi$ and $\zeta$. It will not work. I have not found 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. d... to it its correlative argument that is if I use $\chi$ as the first variable $d\chi$must $d\chi$ must substitute to $dw_1$.