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 > > Dipl.-Math. Adalbert Hanszen >

**References**:**Simplify for ca^2+sa^2==1***From:*Adalbert Hanssen <hanssen@Zeiss.de>