On Monday, April 2, 2012 12:15:28 AM UTC+2, Dr. David Kirkby wrote:
>
> On 03/31/12 10:01 PM, William Stein wrote:
>
> > That
> > seems surprisingly slow, given:
>
>
> Perhaps the server was under a lot of load at the time. I just tried the
> same
> and got an almost instant answer.
>
You're right, every now and then the server gets stuck with some "nasty"
calculations. I probably shouldn't say this out loud, but the security
model of Mathics isn't very evolved yet, so a troublesome query might lead
to endless CPU and even memory usage. There are some checks, but there's
still work to do.
> Timing[Integrate[Sin[x]*Cos[x+1],x]]
>
> gave the time as 0.52 seconds.
>
> That said, 0.52 seconds is almost 100x slower than Mathematica running on
> my Sun.
>
> In[2]:= Timing[Integrate[Sin[x]*Cos[x+1],x]]
>
> -Cos[1 + 2 x] x Sin[1]
> Out[2]= {0.004724, ------------- - --------}
> 4 2
>
> The output from MathICS is also in a more complicated form (more terms)
> than the
> output from Mathematica.
>
Integration is one of the functions where Sage can already be used as a
back-end instead of SymPy: SageIntegrate[Sin[x]*Cos[x+1],x] runs faster and
gives a more compact result.
I'm still thinking about a better way to choose Sage for integration (etc).
One would be to introduce a Sage "package" that overrides all corresponding
SymPy-enabled functions; this would require the implementation of
Mathematica-like packages first, of course. Another way would be to have an
option
Engine->Sage
for Integrate, for instance, which is probably still more Mathematica-like
than a totally different function (symbol) SageIntegrate.
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