Hi David, I believe that the answer is yes. There is an optional package called database_kohel, which is a database of various types of modular polynomials, gathered by David Kohel. You can add it to your Sage install as usual by doing
sage -i database_kohel-20060803 After that, you get access to these polynomials as follows: Classical modular polynomials: sage: C = ClassicalModularPolynomialDatabase() sage: f = C[29] sage: f.degree() 58 sage: f.coefficient([28, 28]) 400152899204646997840260839128 Atkin modular polynomials: sage: A = AtkinModularPolynomialDatabase() sage: f = A[29] sage: f.degree() 30 sage: f x^30 - x^29*j + 714*x^29 + 29*x^28*j + 175653*x^28 - 319*x^27*j + 16216684*x^27 + 1421*x^26*j + 340795182*x^26 + 580*x^25*j + 3339922344*x^25 - 26680*x^24*j + 18681529256*x^24 + 53679*x^23*j + 65190964932*x^23 + 189399*x^22*j + 145746939921*x^22 - 622398*x^21*j + 193096339978*x^21 - 853818*x^20*j + 79225176183*x^20 + 3427365*x^19*j - 213842083608*x^19 + 3592085*x^18*j - 434696047201*x^18 - 10954634*x^17*j - 278856446718*x^17 - 14041394*x^16*j + 154093039581*x^16 + 18871083*x^15*j + 391233115204*x^15 + 37142939*x^14*j + 212930064261*x^14 - 9216142*x^13*j - 78041237118*x^13 - 54103270*x^12*j - 159006324329*x^12 - 19207947*x^11*j - 71430269112*x^11 + 38397537*x^10*j + 10575486927*x^10 + 31795426*x^9*j + 31231369098*x^9 - 9708910*x^8*j + 17209092681*x^8 - 19103721*x^7*j + 1339615908*x^7 - 2357613*x^6*j - 3310173216*x^6 + 5229135*x^5*j - 2067026040*x^5 + 1754181*x^4*j - 591595650*x^4 - 570024*x^3*j + 73993500*x^3 - 281880*x^2*j + 118918125*x^2 + 12150*x*j + j^2 + 41006250*x + 6750*j + 11390625 There is also a DedekindEtaModularPolynomialDatabase, with the same syntax as the others. If I read the Magma documentation correctly, this is what they call canonical modular polynomials (maybe David Kohel can correct me here, if I'm wrong). In fact, Magma's commands also use databases, and I think they are the same as the ones in Sage's optional package. Best, Alex On Sun, Feb 15, 2009 at 9:37 AM, David Joyner <[email protected]> wrote: > > Hi: > > I'm wondering if the analog of the following Magma commands > exist in Sage yet: > > ClassicalModularPolynomial, CanonicalModularPolynomial, > AtkinModularPolynomial. > > The modular polynomil $H_N$ has the property that > $H_N(x,y)= 0$ describes (an affine patch of) $X_0(N)$. > (I'm trying to remove all mention of Magma from a paper > I wrote long ago http://arxiv.org/abs/math.NT/0403548 > and this question arose from that.) > > Thanks, > David JOyner > > > > -- Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne -- Australia -- http://www.ms.unimelb.edu.au/~aghitza/ --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
