Hello,
The reason why the symbolic stuff in Sage is slow is that it uses a
psuedo-tty interface to talk to Maxima. There is a lot of overhead
with this due to waiting, synchronization, parsing the string output,
etc. One way to get the symbolic stuff to be faster is to make using
Sympy since it won't have that overhead (even though it is slower than
native maxima at the moment).
--Mike
On Dec 27, 2007 2:53 PM, pgdoyle <[EMAIL PROTECTED]> wrote:
>
> I'm having problems doing symbolic computations in Sage. Calls to
> rational_simplify() seem to take about .2 seconds each. Working
> directly in Maxima is about 100 times faster. Mathematica is
> something like 500 times faster.
>
> In Sage, where does the time go? Is there something I can do right
> now to speed things up? Is this something that will eventually go
> faster?
>
> Cheers,
>
> Peter Doyle
> -------------------------
> sage: var(x)
> x
> sage: time sum(((x+sin(i))/x+(x-sin(i))/x).rational_simplify() for i
> in xrange(100))
> 200
> CPU time: 5.29 s, Wall time: 39.10 s
> sage: time maxima('sum(ratsimp((x+sin(i))/x+(x-sin(i))/x),i,1,100)')
> 200
> CPU time: 0.02 s, Wall time: 0.55 s
> sage: time mathematica('Sum[Simplify[(x+Sin[i])/x+(x-Sin[i])/x],{i,
> 1,100}]')
> 200
> CPU time: 0.00 s, Wall time: 0.09 s
> sage: time maxima('sum(ratsimp((x+sin(i))/x+(x-sin(i))/x),i,1,10000)')
> 20000
> CPU time: 0.01 s, Wall time: 30.21 s
> sage: time mathematica('Sum[Simplify[(x+Sin[i])/x+(x-Sin[i])/x],{i,
> 1,10000}]')
> 20000
> CPU time: 0.01 s, Wall time: 2.20 s
> sage: time mathematica('Sum[Simplify[(x+Sin[i])/x+(x-Sin[i])/x],{i,
> 1,100000}]')
> 200000
> CPU time: 0.00 s, Wall time: 70.05 s
> sage: time mathematica('Sum[Evaluate[Simplify[(x+Sin[i])/x+(x-Sin[i])/
> x]],{i,1,100000}]')
> 200000
> CPU time: 0.00 s, Wall time: 0.03 s
> >
>
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