How do I differentiate an implicit function in sagemath?

lolora
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I'm trying to differentiate an implicit expression

$x e^{y} = x -y$

This is my sagemath code

x = var('x')
f(x,y)= x*e**y - x + y
show(diff(f))

Sagemath Answer is $\left( x, y \right) \ {\mapsto} \ \left(e^{y} - 1,\,x e^{y} + 1\right)$

But the actual answer is $\frac{1 - e^{y}}{x e^{y} + 1}$

How do I get the actual answer using sagemath?

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Initially asked as

slelievre ( 2021-05-16 15:12:10 +0100 )edit

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The code

x = var('x')
y = function("y")(x)
eq = x*e**y == x - y
dy = diff(y,x)
sol = solve(diff(eq), dy)
show(dy.subs(sol))

yields $$-\frac{e^{y\left(x\right)} - 1}{x e^{y\left(x\right)} + 1}$$ as expected

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Asked: 2020-06-27 14:50:08 +0100

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Last updated: Jun 28 '20