Hello,
I found that if my (multivariate) polynomial ring has coefficients from a
number field, then with certain monomial orders (such as 'deglex')
I don't get the expected result when applying the reduce method of an ideal
onto a polynomial.
Example:
sage: var('X')
sage: K.<sqrt2>=NumberField(X^2-2)
sage: R.<x,y>=PolynomialRing(K,2)
sage: I=R.ideal(x^2+y^2-1)
sage: I.reduce(x^2+y^3)
y^3 + x^2
sage: I.reduce(y^3-y^2+1)
y^3 - y^2 + 1
I would expect the same answer for the last two commands since the polynomials
differ by an element (in fact, the generator) of I. Indeed, if the coefficient
field K is replaced by QQ, it produces the expected result.
Is this a bug?
Stefan
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