Re: Help needed: How to add constraints into FullSimplify

• To: mathgroup at smc.vnet.net
• Subject: [mg22369] Re: [mg22330] Help needed: How to add constraints into FullSimplify
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sat, 26 Feb 2000 22:04:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```on 2/26/00 3:13 AM, Ilya Zavorin at iaz at cs.umd.edu wrote:

> Hi!
>
> I am trying to simplify a complicated expression F[x1,x2,...] using
> FullSimplify.  What I know is that the variables involved satisfy
> certain conditions. For instance, I know that
>
> x1^2 + x5^2 + x7^2 = 1.
>
> How can I supply this information into FullSimplify so that it
> processes input further?
>
> Thanks,
>
> Ilya
>
>

If you are using Mathematica 4.0 you can try putting the assumption  x1^2 +
x5^2 + x7^2 = 1 into FullSimplify or Simplify. For example:

In[17]:=
v = ExpandAll[(x1^2 + x5^2 + x7^2 + 1)^3 +
Exp[x1^2 + x5^2 + x7^2] + (x1 + x5 + x7)^3*
Sin[Pi/16*Sqrt[(x1^2 + x5^2 + x7^2 + 3)^3]]];
In[18]:=
FullSimplify[v, x1^2 + x5^2 + x7^2 == 1]
Out[18]=
3     3
8 + E + 3 x5 + 3 x7 - 2 (x5  + x7 ) +

2               2
x1 (1 + 2 (x5  + 3 x5 x7 + x7 ))

Of course you can't guarantee that Mathematica will always make good use of
the extra information. Sometimes you can get better results by splitting
your expression into parts and simplifying them separately. It all depends
on your expression: there is really no panacea in this area.

```

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