On Apr 18, 2011, at 11:51 AM, mario wrote:
> Hi,
>
> I released rmpoly-0.0.6;
> elementary functions now work on arbitrary rings and on free algebras
>
> example on rationals: series(1/cos(x),x,0,100)
>>>> from time import time
>>>> from rmpoly import *
>>>> from gmpy import mpq
>>>> rp,x = rgens('x',10,mpq)
>>>> h=100
>>>> t0=time();p = x.cos('x',h).pow_trunc(-1,'x',h); '%.2f'%(time()-t0)
> '0.03'
>
> which is 3 orders of magnitude faster than sympy-0.6.7
Has the speed of SymPy increased with any of the recent improvements to the
series, or in polys12?
Anyway, I think that we can make our series faster by doing a similar thing,
i.e., using the polys internally.
Aaron Meurer
>
> example on free algebras: compute the Baker-Campbell_Hausdorff series
> up to order h=12
>
>>>> from rmpoly.free_algebra import *
>>>> fa,A,B = fgens('A,B',mpq)
>>>> rp,x = ncrgens('x',10,fa)
>>>> def bch(x,A,B,h):
> ... return
> ((x*A).exp('x',h)).mul_trunc((x*B).exp('x',h),'x',h).log('x',h)
> ...
>>>> t0=time();p = bch(x,A,B,12); '%.2f'%(time()-t0)
> '0.26'
>
> One can add rules to the free algebra, like commutation and
> annihilation
> rules, see examples in http://code.google.com/p/rmpoly/wiki/Tutorial
>
> Mario
>
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