Re: Substitute all known relations in result

• To: mathgroup at smc.vnet.net
• Subject: [mg86627] Re: [mg86614] Substitute all known relations in result
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 15 Mar 2008 17:42:26 -0500 (EST)
• References: <200803150809.DAA15208@smc.vnet.net>

```As long as your relations are all algebraic you can use GroebnerBasis.
For example suppose your relatins are r==x^2+y^2 and s==x^3+y^3 and
you would like to substitute them into x^5 + y^2*x^3 + y^3*x^2 + y^5.
First form an ideal made up of your formula and the relations you wish
to hold:

id = {x^5 + y^2*x^3 + y^3*x^2 + y^5, r - x^2 - y^2, s - x^3 - y^3};

And now use GroebnerBasis:

First[GroebnerBasis[id, {r, s}, {x, y}]]

r s

Andrzej Kozlowski

On 15 Mar 2008, at 09:09, Dr. Johannes Zellner wrote:

> Hi,
>
> How do I make mathematica to display results with all known
> relations / variables?
> E.g. if a result is
>   x^2+y^2
> and before I'd defined
>   r = x^2+y^2
> I'd like mathematica to display the result rather as "r".
>
> And: I'd like mathematica to do this for each relation defined before
> w/o specifying every possible replacement.
>
> Any help much appreciated.
>

```

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