While the lines
sage: A.<x, y> = PolynomialRing(QQ, 2, order='deglex')
sage: I = A.ideal([x^10 + x^9*y^2, y^8 - x^2*y^7 ])
sage: f = x*y^13 + y^12
sage: M = f.lift(I)
sage: M
sage: y^7, x^7*y^2 + x^8 + x^5*y^3 + x^6*y + x^3*y^4 + x^4*y^2 + x*y^5 +
x^2*y^3 + y^4] sage: sum( map( mul , zip( M, I.gens() ) ) ) == f
True
from the doc give a correct result, we get a wrong result if we use the
term order 'neglex' (or certain other orders) instead of 'deglex'.
sage: A.<x, y> = PolynomialRing(QQ, 2, order='neglex')
sage: I = A.ideal([x^10 + x^9*y^2, y^8 - x^2*y^7 ])
sage: f = x*y^13 + y^12
sage: M = f.lift(I)
sage: M
[-y^7, -y^4 - x^2*y^3 - x^3*y^4 - x^4*y^2 - x^5*y^3 - x^6*y - x^7*y^2 - x^8]
sage: sum( map( mul , zip( M, I.gens() ) ) ) == f
False
This happens with v9.2 in the SageMathCell, and with v9.3.beta5 too.
-- Peter Mueller
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