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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 ?
>

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
-----
17
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
2
Type: PartialFraction Integer

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

Tim