The original Sage code from the googlegroups/trac message you link to doesn't seem to work in current sage any more. I couldn't find a multivariable power series ring in the reference manual either, but may not have been looking hard enough.
Doing these computations in Sage generically, seems to take forever. Actually the raising to the power takes no time, but the inverse doesn't seem to know what it's doing. However Pari does them instantly, and we have Pari in Sage..... (But I only checked the first benchmark in the list and that Pari gave the right answer for it.) I don't know if Pari does series reversion or not. I couldn't see it in the help menu, though I also didn't look hard. How do the timings for your code compare to Magma. I was confused about the benchmarks you gave, and couldn't tell which ones were from your code and which were from elsewhere. I see three columns of timings. Which ones are yours? I think the first column is from an old version of Sage as reported on Trac, right? But I didn't understand the other columns. I'm curious how you are getting good timings in Pure python? Is it a new/clever algorithm? How does it fare for longer power series? Are there even good algorithms that are asymptotically fast for these sorts of problems? And can some of these be reduced to ordinary multivariate polynomial computations? Bill. On 29 July, 15:26, mario <mario.pern...@gmail.com> wrote: > 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 > inhttp://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
