How do i solve a 2 variable polynomial over 1 variable
So i have a polynomial over 2 variables:
R.<X, Y> = GF(8009)[]
Phi = -X^2*Y^2 + X^3 + 1488*X^2*Y + 1488*X*Y^2 + Y^3 \
- 162000*X^2 + 40773375*X*Y - 162000*Y^2 \
+ 8748000000*X + 8748000000*Y - 157464000000000
I want to know for what Y values the polynomial has a solution with X = 33. I've tried using the solve method:
Phi(33, Y).roots(Y)
But this yields the error
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'roots'
I also tried the following:
Phi(33).roots()
It yields the error
TypeError: number of arguments does not match number of variables in parent
So what is the correct way to do this?
3 answers in a row, yeah !