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

[Bill Page]

Dylan,

Perhaps Tim meant to leave this as an "exercise for the reader"
but you could try this

  -> expandBinomial := rule binomial(n,(m | integer? m and m>1)) ==
       (n-m+1)/m*binomial(n,m-1)

  -> % :: UP(x,FRAC INT)

Do you think such a transformation should be available as a
coercion?

Cheers,
Bill Page.


> -----Original Message-----
> From: address@hidden
> [mailto:address@hidden
>  On Behalf Of Dylan Thurston
> Sent: Saturday, October 11, 2003 10:42 PM
> To: address@hidden
> Subject: [Axiom-math] Re: [Axiom-developer] Re: partfrac,
> expand, combine,rewrite and simplify.
> 
> 
> 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
>