Re: How to get an optimal simplification?

• To: mathgroup at smc.vnet.net
• Subject: [mg89441] Re: How to get an optimal simplification?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 9 Jun 2008 06:20:27 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g2iir2\$rj5\$1@smc.vnet.net>

```yaqi wrote:

> I expected to get:
>   {t1,t2,t3}
>
> with the expression:
>   Simplify[{a - b, b - c, c - a}, {t1 == a - b, t2 == b - c, t3 == c -
> a}]
>
> But I only get {-t2-t3,t2,t3}, which is a little bit annoying.
>
> I know I can do the simplifications separately like,
>   Simplify[Simplify[Simplify[{a - b, b - c, c - a}, t1 == a - b], t2
> == b - c], t3 == c - a]
>
> But I still like to get the optimal result with one simplify
> operation.
>
> Is there an answer? (the answer is useful for one of my big
> derivations.)

I am not sure if the following will apply straightforwardly to your
bigger expressions, but you could use a list of rules with the
*ReplaceRepeated[]* operator (short cut //. double-forward slash and
period, though in your example *ReplaceAll[]* is enough) or compute a
*GroebnerBasis[]* for the variables t1, t2, t3, and eliminating a, b,
and c. For instance,

In[1]:= {a - b, b - c, c - a} //. {a - b -> t1, b - c -> t2,
c - a -> t3}

Out[1]= {t1, t2, t3}

In[2]:= GroebnerBasis[{a - b, b - c, c - a, t1 - a + b, t2 - b + c,
t3 - c + a}, {t1, t2, t3}, {a, b, c}]

Out[2]= {t3, t2, t1}

Regards,
-- Jean-Marc

```

• Prev by Date: Re: Show and 6.0
• Next by Date: Re: where is "Mathematica in education and research"?
• Previous by thread: Re: How to get an optimal simplification?
• Next by thread: Re: How to get an optimal simplification?