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Re: How to get an optimal simplification?

• To: mathgroup at smc.vnet.net
• Subject: [mg89465] Re: How to get an optimal simplification?
• From: yaqi <yaqiwang at gmail.com>
• Date: Tue, 10 Jun 2008 03:41:18 -0400 (EDT)
• References: <g2iir2$rj5$1@smc.vnet.net> <g2j078$528$1@smc.vnet.net>

On Jun 9, 5:21 am, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> 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, t=
3 == 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- Hide quoted text -
>
> - Show quoted text -

'Replace' is not the way I want, because it can only replace the terms
that exactly match the expression. For example,

{ b - a, b - c, c - a} /. {a - b -> t1, b - c -> t2,
c - a -> t3}

does not work.

I am guessing that 'Simplify' is trying to simplify the equation with
conditions one-by-one but not simutaneously.

Acturally what I am doing is to integrate a function on an arbitrary
triangle with coordinates of three vertices, I am expecting to get a
formula with something like triangle area, surface-volume ratio, etc.
The function could be very complicated.

Regards,

• Follow-Ups:
  • Re: Re: How to get an optimal simplification?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>