Re: Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
- To: mathgroup at smc.vnet.net
- Subject: [mg50653] Re: [mg50617] Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
- From: Andrzej Kozlowski <andrzej at akikoz.net>
- Date: Wed, 15 Sep 2004 07:54:22 -0400 (EDT)
- References: <200409130619.CAA14342@smc.vnet.net> <8C2E6168-0558-11D9-A0AA-000A95B4967A@akikoz.net> <00bc01c49991$4d2d5260$4f604ed5@lap5100> <656B2636-0588-11D9-A0AA-000A95B4967A@akikoz.net> <4145BB27.9070409@wolfram.com> <50B003A8-05EE-11D9-A0AA-000A95B4967A@akikoz.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 14 Sep 2004, at 10:35, Andrzej Kozlowski wrote: > But there is still something that puzzles me, why > > > Simplify[Sqrt[1 - eta^2]] > > Sqrt[1 - eta^2] > > rather than Im[Sqrt[-1 + eta^2]]? I think I can answer my own question: f[Sqrt[x_]] := Im[Sqrt[-x]] Simplify[Sqrt[1 - eta^2], TransformationFunctions -> {f, Automatic}] Im[Sqrt[eta^2 - 1]] There are certain operations that are included among the transformation rules that Simplify automatically uses but their "inverses" are not included. That is one reason why Simplify will sometimes fail to find the "simplest" expression even based on the current ComplexityFunction. I think this also accounts why it is often useful to apply ComplexExpand first in cases like this one. Simplify[ComplexExpand[Im[Sqrt[eta^2 - 1]]], -1 < eta < 1] Sqrt[1 - eta^2] Simplify[Im[Sqrt[eta^2 - 1]], -1 < eta < 1] Im[Sqrt[eta^2 - 1]] Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/
- References:
- Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
- From: psa@laplacian.co.uk (peteraptaker)
- Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]