Yes, those are certainly interesting issues. So far, I have taken the route of making a general algorithm and letting Sage handle the specific constructions. I assume that the underlying construction will throw the appropriate error when a calculation fails or is not implemented.
Your specific example ZZ[sqrt(-5)] is interesting and will be kept strongly in mind and used in examples as a "difficult" ring. I'll post the current version of the patch to sage-trac later today. Ben On Saturday, June 16, 2012 6:16:01 AM UTC-4, David Kohel wrote: > > Hi, > > Let me just comment on two related issues: > > 1. Rational maps are indeed interesting in geometry and the question > of whether > a given rational map is (i.e. extends to) a morphism is a hard > question. In some > situations one might want to consider two categories. For instance, > do you assert > that Aut(PP^2) is PGL_3? Do you at the same time allow the > construction of the > birational autormorphism given by [1/X,1/Y,1/Z]? > > 2. Projective spaces PP^n over rings S are hard, since they require > one to solve > the problem whether Spec(S) -> PP^n is a morphism. If S is a PID and > you can > test whether an ideal is the unit ideal (e.g. by an effective > Euclidean algorithm), > then you can solve this problem (e.g. for ZZ, ZZ_p, and ZZ/NZZ). > > One example is the point on PP^1 over ZZ[t = \sqrt(-5)] of class > number 2. The > point P = [(2:1+t),(1-t,3)] requires both representatives to cover it > everywhere. > The single point (2:1+t) (or (1-t:3)) defines a rational map Spec(S) - > > PP^1, > which uniquely extends to a morphism. However, from only one > representative, > the specialization to FF_2 or FF_3 fails (which will lead to code > crashing if a > special mechanism); the invalid point (0:0) will arise. Imagine here > you are > studying elliptic curves over ZZ[t] and you look at the FF_2 or FF_3 > points. > rational maps. > > Design questions are: do you restrict to a finite list of acceptable > rings over > which you handle normalizations and reduction maps? Have general > algorithms assuming Sage can handle specific ideal constructions and > testing? > Or some combination of the two? > > Note that the integers (which should probably be treated as a special > case) > does have sufficient general ideal theory code available: > > sage: I = ZZ.ideal(2) > sage: I = ZZ.ideal(2) > sage: ZZ.ideal(1) == I + J > True > > but the p-adics apparently do not: > > sage: ZZp = pAdicRing(2) > sage: I = ZZp.ideal(2) > sage: J = ZZp.ideal(3) > sage: ZZp.ideal(1) == I + J > > --David > > On Jun 10, 6:08 pm, Ben Hutz <bn4...@gmail.com> wrote: > > There are a critical mass of people interested (~10?) and who worked on > at > > least some aspect during the ICERM semester. However, there is very > little > > Sage developing experience (Sage usage: yes). I would expect to have no > > trouble finding people willing to review changes. For this first type of > > patch where I am changing some basic scheme architecture in morphism.py, > > point.py, homeset.py, and not just implementing some dynamics > > functionality, it would probably be better if someone with a little more > > experience did the review. > > > > > > > > > > > > > > > > On Sunday, June 10, 2012 10:57:24 AM UTC-4, Volker Braun wrote: > > > > > On Sunday, June 10, 2012 3:30:41 PM UTC+1, William wrote: > > > > >> The key question: do you have enough people to both write *and > > >> referee* the code? > > > > > AKA: You need at least two people to put something into Sage :-) > > > > On Sunday, June 10, 2012 10:57:24 AM UTC-4, Volker Braun wrote: > > > > > On Sunday, June 10, 2012 3:30:41 PM UTC+1, William wrote: > > > > >> The key question: do you have enough people to both write *and > > >> referee* the code? > > > > > AKA: You need at least two people to put something into Sage :-) -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
