Re: [sage-support] Re: Sage Speed Issues

[Jim Clark]

Since you are writing your own algorithms in python, I suggest you investigate cython:

http://docs.cython.org

to compile your python into machine code, instead of python's quasi-compiled byte code.

Cython is included with sage -- just add the code %cython as the first line of a Sage worksheet cell.

Alternatively, put you Sage code into a file with the extension .spyx, then load the file from the Sage command line.

There are a couple of Sage-isms that won't work in cython, for example, you must replace e^{whatever} with e**{whatever}.

Also, as others have pointed out, you might analyze your code a bit to calculate the number of operations you want to perform.

You can easily reach a point that would require the fastest computer on earth hundreds, thousand, millions,... of years to compute.

Jim Clark

Thanks for your reply. Actually I have exponential function f(u) in 8-dimensions and I am using the general formula for Taylor series at available at http://en.wikipedia.org/wiki/Taylor_series (Taylor series in several variables). I want to expand summations in this equations for up to 6 or even more as I am using this expansion to calculate the bit error rate for the E8 lattice. The exponential function f(u) is of the following form. 

$$ f(u) = e^{(-(3.15987540437407e-36)*(99446621081482098*u1 + 99446621081482098*u2 + 99446621081482098*u3 + 49723310540741049*u4 + 99446621081482098*u5 + 165744368469136820*u6 + 198893242162964181*u7 +298339863244446264)^2 - (3.15987540437407e-38)*(1790039179466677674*u1 - 2983398632444462490*u2 - 2983398632444462490*u3 - 1491699316222231245*u4 - 2983398632444462490*u5 - 2320421158567915270*u6 - 1988932421629641660*u7 - 994466210814820830)^2 - (3.15987540437407e-38)*(1790039179466677674*u1 + 2983398632444462715*u2 + 2320421158567915470*u3 - 1491699316222231245*u4 - 2983398632444462490*u5 - 2320421158567915270*u6 + 1988932421629641810*u7 - 994466210814820830)^2 - (3.15987540437407e-38)*(1790039179466677674*u1 + 2983398632444462715*u2 + 2320421158567915470*u3 - 1491699316222231245*u4 + 4972331054074104450*u5 - 2320421158567915270*u6 + 1988932421629641810*u7 - 994466210814820830)^2 - (3.15987540437407e-38)*(1790039179466677674*u1 + 2983398632444462715*u2 + 2320421158567915470*u3 + 4475097948666693960*u4 + 4972331054074104450*u5 + 5635308527950651670*u6 + 1988932421629641810*u7 - 994466210814820830)^2 - (3.15987540437407e-38)*(1790039179466677674*u1 + 2983398632444462715*u2 + 4972331054074104450*u3 + 4475097948666693960*u4 + 4972331054074104450*u5 + 5635308527950651670*u6 + 1988932421629641810*u7 - 994466210814820830)^2 - (3.15987540437407e-36)*(99446621081482098*u1 + 99446621081482098*u2 + 99446621081482098*u3 + 49723310540741049*u4 + 99446621081482098*u5 + 165744368469136820*u6 - 198893242162964166*u7 - 397786484325928347*u8 + 298339863244446264)^2 - (3.15987540437407e-36)*(99446621081482098*u1 + 99446621081482098*u2 + 99446621081482098*u3 + 49723310540741049*u4 + 99446621081482098*u5 + 165744368469136820*u6 + 198893242162964181*u7 + 397786484325928347*u8 + 298339863244446264)^2)}$$

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