> > 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
>
> Those times above are really weird. On my laptop (OSX 10.5.1):
>
> sage: var(x)
> x
> sage: time sum(((x+sin(i))/x+(x-sin(i))/x).rational_simplify() for i
> in xrange(100))
> 200
> Time: CPU 0.97 s, Wall: 3.20 s
> sage: time maxima('sum(ratsimp((x+sin(i))/x+(x-sin(i))/x),i,1,100)')
> 200
> CPU time: 0.01 s, Wall time: 0.34 s
>
> Thus it takes 3.2 seconds wall time instead of 39.10 seconds for me.
>
This was on an old, slow machine, and maybe there is thrashing because
there isn't much RAM.
>
> But sympy is still way faster and is symbolic:
>
> sage: from sympy import Symbol, sin
> sage: x = Symbol('x')
> sage: time sum(((x+sin(i))/x+(x-sin(i))/x).expand() for i in xrange(100))
> 200
> Time: CPU 0.09 s, Wall: 0.09 s
>
> which is why it's a good thing that sympy is the future of symbolic
> computation in Sage :-).
>
This sounds promising.
> And since Sympy comes with Sage, maybe you can use it for
> your intended application right now?!
>
My intended application involves working with matrices, and I it looks
like this isn't going to work with sympy:
sage: from sympy import Symbol
sage: x = Symbol('x')
sage: m=matrix([[x]])
Traceback (most recent call last):
...
AssertionError: <class 'sympy.core.symbol.Symbol'>
Cheers,
Peter Doyle
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