Thanks Alex! On Sat, Feb 14, 2009 at 6:04 PM, Alex Ghitza <[email protected]> wrote: > 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/ > > > >
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