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2018-10-16 08:22:31 -0600 asked a question Reducing a polynomial over a function field modulo a valuation

In my situation, I have the following elliptic curve:

K.<t> = FunctionField(QQ)
E = EllipticCurve([t,t])

I want to be able to go modulo t to get the curve

z*y^2 - x^3 = 0

I cannot figure out how to do this. I would like to work with valuations if possible (like going mod K.valuation(0)), but any way to make this work would be great. In general, I'd like to be able to go modulo any irreducible polynomial.

2018-09-25 19:44:15 -0600 received badge  Scholar (source)
2018-09-25 19:33:42 -0600 commented answer Keyword can't be an expression error with subs()

Thank you, this fixed the issue!

2018-09-25 15:19:19 -0600 received badge  Student (source)
2018-09-25 13:54:19 -0600 asked a question Keyword can't be an expression error with subs()

I want to be able to iterate through a list of variables for function and make assignments to each of them. Here's an example that shows the issue I'm having:

R.<x,y> = PolynomialRing(QQ,2)
f = x^2+y^2
variables = [x,y]

This gives "SyntaxError: keyword can't be an expression." How can I get around this? The goal is to use a loop to make substitutions for some variables, look at what happens, then in the next iteration different substitutions will be made.