[Axiom-math] Re: [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify.

[Dylan Thurston]

On Tue, Oct 07, 2003 at 10:19:14AM -0400, Tim Daly wrote:
> 
> > // 1 //
> > I use mupad and I find very pretty the only 4 commands :
> >   expand, combine, rewrite and simplify (with or without an option)
> > 
> > expand (binomial (n, 3))                          -> n(n-1)(n-2)/6
> > expand (sin (2*x))                                -> 2 sin(x) cos(x)
> > 
> > combine (sin(x)^2, sincos)                        ->(1-cos(2x))/2
> > 
> > rewrite (..., opt) with opt=exp, sincos, sinhcosh, etc.
> >   for rewriting
> > 
> > simplify tries to simplify, but it's not so sure.
> > 
> > In axiom I find a lot of functions as factorials, htrigs, expandTrigProducts
> > but no pretty front-end function. Is there ?
> > What tells axiom about such general functions ?
> > 
> 
> Unfortunately your question doesn't seem to have a simple answer.
> I've never used mupad but it appears that the functions you mention
> are using a tree-like representation of the expression and allow you
> to manipulate the tree.

So how do you actually get the answer n(n-1)(n-2)/6 for binomial(n,3)?
Is there a way to do this?

binomial(n,3) is not evaluated; applying factorials gives n!/6*(n-3)!;
but I don't see how to get n(n-1)(n-2)/6.

Peace,
        Dylan

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