Re: how to simplify a complicated equation?

• To: mathgroup at smc.vnet.net
• Subject: [mg43580] Re: [mg43529] how to simplify a complicated equation?
• From: Bob Walker <walkerbg at ieee.org>
• Date: Sun, 21 Sep 2003 05:42:19 -0400 (EDT)
• References: <200309190741.DAA22243@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Bryan
Let
In[1 ]=  aa = Transpose[rx].Transpose[ry].rz.ry.rx;

In[2]=  Simplify[aa == correct, b^2 == 1 - a^2 - c^2]
Out[2]= True

Applying the Simplify to aa and correct individually, in this case,
returns identical expressions

The following also works
In[3]= Simplify[aa == correct] //. b^2 -> 1 - a^2 - c^2
Out[3]= True

Applying this Simplify to aa and correct individually gives two
different expressions (both different from the first Simplify), but
Mathematica still determines that they are equal.

Note that in general, you will still have to help.

Take care
Bob Walker

bryan wrote:

>Dear All,
>  I'm dealing with the problem about the coordinate rotation matrix
>around an arbitrary axis; and I have a correct answer. How can I use
>some constraints to reduce or simplify an equation to desired form ?
>For example, here
>
>In[1]:  correct={{a^2 (1-Cos[t])+Cos[t],a b (1-Cos[t])+c Sin[t],a c
>(1-Cos[t])-b Sin[t]},{a b (1-Cos[t])-c Sin[t],b^2 (1-Cos[t])+Cos[t],b
>c (1-Cos[t])+a Sin[t]},{a c (1-Cos[t])+b Sin[t],b c (1-Cos[t])-a
>Sin[t],c^2 (1-Cos[t])+Cos[t]}};
>
>In[2]:  rx={{1,0,0},{0,c/Sqrt[b^2+c^2],-b/Sqrt[b^2+c^2]},{0,b/Sqrt[b^2+c^2],c/Sqrt[b^2+c^2]}};
>        ry={{Sqrt[b^2+c^2],0,-a},{0,1,0},{a,0,Sqrt[b^2+c^2]}};
>        rz={{Cos[t],Sin[t],0},{-Sin[t],Cos[t],0},{0,0,1}};
>
>I wanna to compare if correct equal
>Transpose[rx].Transpose[ry].rz.ry.rx
>I use Replace and Simplify alternately and the methos is very stupid
>and troublesome. Because I have to observe the resulte equation in
>advance to decide what "form" or what symbol I should replace it ~
>Below is what I do:
>
>In[3]:  aaa = ReplaceRepeated[Simplify[ReplaceAll[Simplify[Transpose[
>        rx].Transpose[ry].rz.ry.rx] // MatrixForm, {b^2 -> 1 - a^2 -
>                  c^2, b^4 -> (1 - a^2 - c^2)^2}]], {a^2 + c^2 ->
>                1 - b^2, -a^2 - c^2 -> -1 + b^2}] // MatrixForm
>
>And finally, I found that aaa is the same as the correct matrix, but
>it took me a lot of work. Could anyone have good idea or some method
>to simplify an equation with some constraints ? Thanks for your help.
>
>           Best   Regards                          Bryan
>
>
>
>

```

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