Hi there, I have a release candidate of my libSINGULAR code available. The HG patch is at
http://sage.math.washington.edu/home/malb/pkgs/libsingular.hg and the required (!) updated SPKG is at: http://sage.math.washington.edu/home/malb/pkgs/singular-3-0-2-20070517.spkg . This spkg also re-enables building of libfac and libcf which are required by the optional M2. This patch does: * switch the default implementation for MPolynomials over QQ and GF(p) to libSINGULAR * MPolynomial_libsingular should provide everything provided by MPolynomial_polydict so far * print all MPolynomials with respect to their monomial ordering * add a couple of methods to aid Gröbner basis algorithms, stuff like monomial_lcm etc. This patch misses: * much of the cool stuff in SINGULAR * e.g. block orderings * support for MPolynomials over GF(p^n) etc. * intense testing. As a proof of concept I made a stand alone version of my F4 implementation (over GF(p)) available at: http://sage.math.washington.edu/home/malb/f4.py # old implementation sage: P1.<a,b,c,d,e,f,g,h,i,j> = MPolynomialRing_polydict_domain(GF(127),10,order=TermOrder('degrevlex')) sage: F1 = sage.rings.ideal.Katsura(P1,6) sage: time gb = f4(F1) CPU times: user 4.45 s, sys: 0.07 s, total: 4.51 s Wall time: 4.55 # new implementation sage: P2.<a,b,c,d,e,f,g,h,i,j> = MPolynomialRing(GF(127),10,order=TermOrder('degrevlex')) sage: F2 = sage.rings.ideal.Katsura(P2,6) sage: time gb = f4(F2) CPU times: user 0.37 s, sys: 0.01 s, total: 0.38 s Wall time: 0.38 Please note that this is still way slower than SINGULAR (0.10 seconds) mainly because so much time is wasted converting between the polynomial representation and the matrix representation. Another fun example, Buchberger's original algorithm: ------------------------------------------ # should these be defined globally? LM = lambda f: f.lm() LT = lambda f: f.lt() Spol = lambda f,g: LCM(LM(f),LM(g)) // LT(f) * f - LCM(LM(f),LM(g)) // LT(g) * g def buchberger(F): G = set(F) while True: Gprime = G.copy() for p in Gprime: for q in Gprime: if p != q: S = Spol(p,q).reduce(Gprime) if S != 0: G.add(S) if G == Gprime: break return list(G) ------------------------------------------ This is of course very very slow but it shows that we have machinery in place for this kind of commutative algebra and that this machinery looks pretty natural. Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
