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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