I don't usually work over such fields but it looks like a bug to me. (y^3-y^2+1).quo_rem(x^2 + y^2 - 1) and (x^2+y^3).quo_rem(x^2 + y^2 - 1) both give the same answer for the remainder (-x^2*y + x^2 + y) which I think is what the reduce method should be returning.
-Marshall Hampton On Feb 9, 4:31 pm, Stefan Boettner <[email protected]> wrote: > 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 -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
