# Revision history [back]

Since 1 does not belong to the ideal, it is not possible to express 1 as a linear combination (with polynomial coefficients) of the generators of the ideal (which is what lift tries to do).

So lift correctly gives an error; it even provides the reason.

Since 1 does not belong to the ideal, it is not possible to express 1 as a linear combination (with polynomial coefficients) of the generators of the ideal (which is what lift tries to do).

So lift correctly gives an error; it even provides the reason.

Edit (after the generators were changed): you should work over a field with exact arithmetic, such as the smallest field that contains the coefficients of your polynomials; in this case you can work over QQ:

sage: A.<x, y> = PolynomialRing(QQ, 2, order='degrevlex')
sage: I = A.ideal([x + y, x + y + 1])
sage: A(1).lift(I)
[-1, 1]


This result implies the result over $\mathbb{C}$.