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Re: [Axiom-developer] choose the better expand


From: Martin Rubey
Subject: Re: [Axiom-developer] choose the better expand
Date: 03 Apr 2006 10:03:03 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Francois Maltey <address@hidden> writes:

> Dear Martin,
> 
> > You probably should provide the three syntaxs.
> 
> OK.
> 
> > Could you define (exactly!) what expand is supposed to do. 
> > I guess that it's similar to ... maxima...
> 
> I don't forget mupad, results are (almost) the same.
> I'm looking for a syntax which is easy for easy computation 
> but which allows various interessing abilities.
> 
> But might you help me for extracting real part and imag part for 
> Expression ... Complex ... ? in manip.spad.
> Perhaps do you want I send you my working manip.spad.

Yes, please. But I'm a little out of time currently. In the worst case, I can
only help after the workshop, but I'll do my best.

> I'm going to test an expand which 
>      1/ separates real part and imag part, if it's a Complex domain
> then 2/ always applies sum formula,
>  and 3/ applies Integer * formula_without_denominator
> for sin, cos, tan, cot, sinh, cosh, tanh, coth, exp...
> 
> A list of String describes the parameters and precises the expand use : 
> 
> noComplex bypass the first step, noSum the second, noTimes the third.
> allDenom  expands also sin (2*x/3) in 2 sin (x/3) cos (x/3)
> evenConst expands sin (sqrt 2 + sqrt 3) in sin... cos... + cos... sin...
> recursif  does the silly expand (sin (sin (a+b)))
> ?????     expands sin (x/3+y/2) * cos (x/2-y/7) in sin... cos... x/6 and y/14 
> !
>           (but I'm not sure I can do it !)

Since I'm very bad at trigonometrics, I find the description above a little
terse. Precise definitions would be very helpful.

Martin





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