Re: Simplify for ca^2+sa^2==1

• To: mathgroup at smc.vnet.net
• Subject: [mg26358] Re: [mg26339] Simplify for ca^2+sa^2==1
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Wed, 13 Dec 2000 02:41:18 -0500 (EST)
• References: <200012120754.CAA14347@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Adalbert,

I don't know if this will help, but in version 4 one idea is to include ca^2
+sa^2==1 as an assumption.

For example,

expr = (-1 - ca^2 - sa^2)*
Sqrt[Expand[2 +
(ca^2 + sa^2)^4]]

2     2
(-1 - ca  - sa )

8       6   2
Sqrt[2 + ca  + 4 ca  sa  +

4   4       2   6
6 ca  sa  + 4 ca  sa  +

8
sa ]

Simplify[expr, ca^2 + sa^2 ==
1]

-2 Sqrt[3]

Carl Woll
Physics Dept
U of Washington

----- Original Message -----
From: "Adalbert Hanssen" <hanssen at Zeiss.de>
To: mathgroup at smc.vnet.net
Subject: [mg26358] [mg26339] Simplify for ca^2+sa^2==1

> Hi, MathGroup,
>
> in a lengthy expression, I know, a lot
> of simplification can be done, if Simplify
> and the like would take into account that
> for varaibles ca and sa
>
> ca^2+sa^2==1
>
> I know, that I can set ca=Sqrt[1-sa^2] and
> deal with the branch cut by hand.
>
> The bad thing is, that these ca^2 and sa^2
> are expanded out in lenghty subexpressions
> involving lots of other symbols. So far, I
> have found no way (but would be glad, if
> someone could advise me one), to factor out
> (ca^2+sa^2).
>
> Unfortunately, there are also terms, where
> (1+ca^2+sa^2) or (2*ca^2+2*sa^2) can be
> factored out, also others with (-ca^2-sa^2)
> and so on.
>
> Any general tip, how to best cope with such
> algebraic manipulations?
>
>
> kind regards
>