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
