Function Composition

[Dan Buchoff]

What's the right way to compose a multivariate polynomial with a unary polynomial in an argument other than the first?

A simple example is:

f = (x, y) ↦ x + y

g = y ↦ 2⋅y

f composed with g = (x, y) ↦ x + 2⋅y

I've tried substitution which doesn't seem to even give a valid polynomial (is a polynomial with expressions as generators even mathematically meaningful?):

>>> Poly("x+y").subs(S("y"),"y*2")
Poly(x + 2*y, x, 2*y, domain='ZZ')

I've also tried composition, but this seems to only compose in the first argument (and for some reason only works for polynomials):

>>> Poly("x+y").compose(Poly("y*2",S("y")))
Poly(3*y, x, y, domain='ZZ')

And evaluating on polynomial arguments:

>>> Poly("x+y")(Poly("x"),Poly("2*y"))
Poly(x, x, domain='ZZ') + Poly(2*y, y, domain='ZZ')

[Aaron Meurer]

Perhaps use as_poly to convert the multivariate polynomial into a
univariate polynomial.

Aaron Meurer

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