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I'm dealing with elliptic curves in SAGE. Say the elliptic curve I have is $y^2=x^3+x$ working over GF(43) and I have a polynomial expression in x and y: $$y^2 + xy + 1.$$ I want to be able to substitute $y^2=x^3+x$ to get $(x^3+x)+xy+1$. How do I do this?

I'm dealing with elliptic curves in SAGE. Say the elliptic curve I have is $y^2=x^3+x$ working over GF(43) and I have a polynomial expression in x and y: $$y^2 + xy + 1.$$ I want to be able to substitute $y^2=x^3+x$ to get $(x^3+x)+xy+1$. How do I do this?

I'm dealing with elliptic curves in SAGE. Say the elliptic curve I have is $y^2=x^3+x$ working over GF(43) and I have a polynomial expression in x and y: $$y^2 + xy + 1.$$ I want to be able to substitute $y^2=x^3+x$ to get $(x^3+x)+xy+1$. How do I do this?