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

From: Tim Daly
Subject: [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify.
Date: Tue, 7 Oct 2003 10:19:14 -0400

> // 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.

Axiom produces answers whose appearance depends on the type. For example:

-> (x+1)/17

  1      1
 -- x + --
 17     17
               Type: Polynomial Fraction Integer

so the first input gets output as a polynomial of the form A*x+B
where A=1/17 and B=1/17.

-> %::Fraction(Polynomial(Integer))

 x + 1
               Type: Fraction Polynomial Integer

(% is the last result. "::" does type conversion)

We then asked for a fraction whose numerator and denominator are 
polynomials over the integers. So we wanted a fraction of the form:
(A*x+B)/(C*x+D) and got one with A=1, B=1, C=0, D=17

The output you get depends on the type you request.

> // 2 //
> I call partfrac the transform as 2x^3 / (1-x^2) = 1/(1-x) - 1/(1+x) - 2x
> What is its name in axiom ?

The partialFraction function will create a partial fraction thus:

-> partialFraction(7,12)

       3   1
  1 - -- + -
       2   3
                  Type: PartialFraction Integer

If you need more help let me know and I'll try to resolve the problem.


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