Hello, I started rmpoly (http://code.google.com/p/rmpoly/), a pure Python library for multivariate polynomials and power series on QQ.
I tried the benchmarks on series truncated with the total degree in http://www.mail-archive.com/sage-t...@googlegroups.com/msg42090.html MPowerSeriesRing (MSR) with Intel(R) Xeon(R) CPU X7460 @ 2.66GHz rmpoly with Intel Core2 Quad Q8200 2.33GHz Python2.7, gmpy.mpq (left), Sage 4.0.1, Rational (right) seconds MSR rmpoly expression 3.18 0.58 1.24 (1 + 2*a + 3*b + 4*d + L(0).O(16))^-5 0.02 0.01 0.01 (1 + a^3 + b^3 + c^4 + d^4 + L(0).O(15))^-20 0.16 0.07 0.12 (-1/6*b^6*d^14 - 1/9*a^4*b^10*c^4*d^12 +...+ L(0).O(50))^20 12.7 0.57 1.21 (1 + 1/2*a + 3*b + 4*a*b + ... + Z(0).O(30))^-20 0.05 0.001 0.002 (1+a^14*b^9+8/3*a^22*b^11-...+Z(0).O(51))^-20 1.9 0.4 1.03 (1 + a + b + a*b + a^2 + b^2 + Z(0).O(30))^-20 2.78 0.42 1.09 (1 + a + 2*b - a*b + 3*a^2 - b^2 + Z(0).O(30))^-20 3.14 0.42 1.10 (1+a+12*b-10*a*b+13*a^2-7*b^2+Z(0).O(30))^-20 I do not know how to get and run the code multi_power_series from trac, so I put the times for MPowerSeriesRing from the link above. The Sage version of rmpoly is obtained essentially replacing int with Integer in the Python version. Here is the code for the first benchmark load "rmpoly.sage" rp = RPoly(['d','c','b','a'], 10,Rational,'grlex') d,c,b,a = rp.gens() # (1 + 2*a + 3*b + 4*d + L(0).O(16))^-5 p = 1 + 2*a + 3*b + 4*d n = 16 # n grlex order the variable _t carries the total degree p = p.series_inversion('_t',n) p = p.pow_trunc(5,'_t',n) print p Notice that the Python version of rmpoly is faster than its Sage version. I guess that cythonizing rmpoly.sage it would become roughly as fast as the Python version. rmpoly deals also with series with O(a^na*b*nb*c^nc*d^nd) e.g. with p.pow_trunc(k,['a','b','c','d'],[na,nb,nc,nd]) It has multivariate series reversion: here is an example rp = RPoly(['w','z','y','x'],10,Rational) w,z,y,x = rp.gens() p = x*(2 + y^2 + z) + x^2*(1+y+z^6) + x^6*(5+y^6+z) n = nx=ny=nz=7 p1 = p.series_reversion2('x',nx,['y','z'],[ny,nz],'w') # check that p in x=p1 is equal to w + O(w^nx*y^ny*z^nz) sb = Subs(rp,rp,{'x':p1}) p2 = sb.subs_trunc(p,['w','y','z'],[nx,ny,nz]) assert p2 == w The reversion takes 0.7s I would like to know if there is an interest in including rmpoly.sage in Sage as a possible way of computing with power series Mario -- 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
