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

*To*: mathgroup at smc.vnet.net*Subject*: [mg26352] Re: [mg26339] Simplify for ca^2+sa^2==1*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>*Date*: Wed, 13 Dec 2000 02:41:14 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I am frequently discouraged from even attempting to answer questions like this one because they consist of generalities without any concrete example. As it is I have to make a guess, whcih may not be right. Anyway, do you mean something like this: In[1]:= Simplify[c^4*s^2 + 2c^2*s^4 + s^6 + c*s, {c^2 + s^2 == 1}] Out[1]= s (c + s) ? There are other ways to get equivalent answers, which may sometime be more suitable than th eone given by SImplify. In the above case you could, for example, do: In[12]:= PolynomialReduce[ c^4*s^2 + 2c^2*s^4 + s^6 + c*s, {c^2 + s^2 - 1}, {c, s}][[2]] Out[12]= 2 c s + s Which is the same as before, or In[13]:= PolynomialReduce[ c^4*s^2 + 2c^2*s^4 + s^6 + c*s, {c^2 + s^2 - 1}, {s, c}][[2]] Out[13]= 2 1 - c + c s and there are other ways (all of them based on GroebnerBasis). I don't think there is a single best approach, which one to choose will depend largely on your example and what sort of output you are trying to get. -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ http://sigma.tuins.ac.jp/ on 12/12/00 4:54 PM, Adalbert Hanssen at hanssen at Zeiss.de wrote: > 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 >