Hey Salvatore, So first I would point you towards TropicalSemiring, but I don't think that has the functionality you want, which seems to be tropical polynomials, correct?
> Unfortunately, if one does that, there are few issues arising from how gcd > are computed; here is a small zoo of examples: > > sage: P = LaurentPolynomialRing(ZZ, 'y', 3) > sage: P > Multivariate Laurent Polynomial Ring in y0, y1, y2 over Integer Ring > sage: L = LaurentPolynomialRing(P,'x',3) > sage: L > Multivariate Laurent Polynomial Ring in x0, x1, x2 over Multivariate > Laurent Polynomial Ring in y0, y1, y2 over Integer Ring > sage: L.inject_variables() > Defining x0, x1, x2 > sage: x0/x0 > 1 > sage: x0.gcd(x0) > ... > AttributeError: > 'sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_mpair' object > has no attribute 'gcd' > sage: gcd(x0,x0) > ... > TypeError: unable to find gcd > sage: R = L.fraction_field() > sage: R.inject_variables() > Defining x0, x1, x2 > sage: x0.gcd(x0) > 1 > sage: x0/x0 > x0/x0 > sage: _.denominator() > x0 > > The reason the latter works is because of the following: sage: R = LaurentPolynomialRing(ZZ, 'y', 3) sage: R.fraction_field() Fraction Field of Multivariate Polynomial Ring in y0, y1, y2 over Integer Ring I'm not completely sure mathematically if the gcd of a multivariate Laurent polynomial ring is well defined. I imagine it is, and it would be a matter of doing the gcd on the corresponding polynomial and then doing the gcd of the monomial (which is how the univariate works). > Ok, I figured this was not the way to go. The next best thing would be to > have > > sage: L = LaurentPolynomialRing(ZZ, 'x0,x1,x2,y0,y1,y2') > sage: P = LaurentPolynomialRing(ZZ, 'y0,y1,y2') > > but then: > > sage: P.inject_variables() > Defining y0, y1, y2 > sage: y0 in P > True > sage: y0 in L > False > sage: y0.parent().fraction_field()(y0) in L > True > > Note that this is an issue of the multivariate implementation since > > sage: R = LaurentPolynomialRing(ZZ,'x,y') > sage: T = LaurentPolynomialRing(ZZ,'y') > sage: T.inject_variables() > Defining y > sage: y in T > True > sage: y in R > True > > as expected. > I am not sure about a solution for that. However, it definitely is a bug, > > It looks to me that the implementation of LaurentPolynomialRing is full of > such corner case bugs and, if I understand correctly, it is still based on > the old architecture not the new Category/Parent/Element framework. Is > there > any plan to replace it in the near future with a more modern > implementation? > Should I decide to invest time in improving it, would anyone here be > interested to help? Do you have any suggestion/reference on how this > should > be done properly? I am relatively a newbie to all this so I might need as > many pointers as possible. > > Yes, it is one of the last parents that is of the old style and is something that we should switch over. However I don't think it should get a complete rewrite from the ground up as there already are plenty of good, working features there. Moreover, it shouldn't be too hard to change it over; at least, one would hope. I would be willing to help where I can. I think we should work our way up and fix the bugs we know about first, and then after that try to replace ParentWithGens with Parent (ideally would be in the ABC of ``Ring``) and hope that only a little breaks. Best, Travis -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
