Hello, I have encountered a problem if we work with the fraction field of a polynomial ring with a local ordering. The following code is done in 6.4:
sage: R2.<x,y>=PolynomialRing(QQ,order='lex') sage: g=1+x sage: 1/g 1/(x + 1) sage: (1/g).parent() Fraction Field of Multivariate Polynomial Ring in x, y over Rational Field sage: S2.<x,y>=PolynomialRing(QQ,order='negdeglex') sage: f=1+x sage: 1/f 1 sage: f.parent() Multivariate Polynomial Ring in x, y over Rational Field sage: (1/f).parent() Fraction Field of Multivariate Polynomial Ring in x, y over Rational Field sage: f.is_unit() True Note that the result is correct with a global ordering but not with a local one. Miguel Marco looked into the definitions and it seems that since the problem may come from the definition of division. If the denominator is a unit then the result is a polynomial with all the monomial divided by the denominator; assuming that the base ring is a field the units are the non-zero scalars. It seems that Singular rings are not actual polynomial rings but localizations of those (a polynomial is a unit if and only if its leading monomial is 1) and hence a fraction p/q becomes the quotient between p and the leading monomial of q when q is a scalar. Besides that, I tried to reproduce the example with only one variable but in that case both rings are equal. Unfortunately I do not know the best way to correct it. The quotient algorithm should be modified and I wonder if S2 as set should be the polynomial ring or the ordering ring (in this case the localisation on the maximal ideal). Best, Enrique. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
