How to call a constant polynomial with lift()?
I am trying to call a constant polynomial with lift(),
but I get an error. The following is a minimal example
of my input that produces an error:
sage: A.<x, y> = PolynomialRing(CC, 2, order='degrevlex')
sage: I = A.ideal([x + y, x + y + 1])
sage: A(1).lift(I)
When I input a non-constant polynomial (say, f = (x+y)^2),
Sage executes lift(I) as expected. I only get an error
for constant polynomials like A(1).
Note that
CCisComplex Field with 53 bits of precision, so this "field" consisting of floating point approximations is generally unsuitable for exact algebraic applications like Gröbner bases and the division algorithm (which are used here). Often you can reduce your problem to a computation over a number field and/or over $\mathbb{Q}$.