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A nice one...
Consider
sage: R.<x>=InfinitePolynomialRing(QQ)
sage: f=R(x[1]^3)
Note that :
sage: [u.parent() for u in f.variables()]
[Multivariate Polynomial Ring in x_2, x_1, x_0 over Rational Field]
(yes, I played with R a bit...) contrasting with:
sage: x[1].parent()
Infinite polynomial ring in x over Rational Field
Hence the error you noticed. However :
sage: x[1] in f.variables()
True
It is there ; you just have to find it :
sage: f.variables().index(x[1])
0
Hence the (awkward) :
sage: f.derivative(f.variables()[f.variables().index(x[1])])
3*x_1^2
A better way would be to cast x[1] to the proper class. Finding which isn't intuitive...
