Re: ComplexExpand in Mathematica 5.2 and 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg77988] Re: [mg77955] ComplexExpand in Mathematica 5.2 and 6*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 21 Jun 2007 05:34:42 -0400 (EDT)*References*: <200706200939.FAA10222@smc.vnet.net>

On 20 Jun 2007, at 18:39, Jepessen wrote: > Hi to all. > > I'm working with the new version of Mathematica, and I've noticed that > ComplexExpand works in a different way. > > I've used this code, that allows me to find center and radius of a > circle mappend by a bilinear transformation from plane X to plane Y > > ----------------------- > > moebius = y == (a + b*x)/(c + d*x); > cirX = Abs[x - cen] == rad; > t1 = Solve[moebius, x][[1, 1]]; > cirY = cirX /. t1; > t2 = Abs[Together[cirY[[1, 1]]]] == rad; > t3 = Abs[a + b*cen - c*y - cen*d*y] == rad*Abs[-b + d*y]; > t4 = t3[[1]]^2 - t3[[2]]^2; > > (* Use of ComplexExpand *) > t5 = ComplexExpand[t4 /. Abs[q_]^2 -> Re[q]^2 + Im[q]^2,{a, b, c, d, > cen, y}] /. {Re[y] -> U, Im[y] -> V} > > ------------------------ > > What I obtain is an expression stored in t5, with unknowns U and V, > that are coordinates of the Y plane of the mapped circle. What I > obtain is t5, that's the equation of this mapped circle. > > In Mathematica 5.2, I obtain a result that's is a conic expression, in > U and V, and I can use Collect to extract coefficients of U, V, U^2 > and V^2. > > In Mathematica 6.0, instead, I obtain the same equation, but in a > different form, that contains Re, Im and Abs function with aurgments > with U and V variables; in this way, I can't use Collect to extract > coefficient of the expression. > > I'd like to have the old behavior of ComplexExpand, because this > allows me to extract coefficient. How can I obtain the same result > with the 6.0 version? > > Thanks for answers > > Daniele > > Try: Collect[ComplexExpand[t4 /. Abs[q_]^2 -> Re[q]^2 + Im[q]^2, {a, b, c, d, cen, y}, TargetFunctions -> {Re, Im}] /. {Re[y] -> U, Im[y] -> V}, {U, V}, Simplify] or, if you do not ming waiting longer Collect[ComplexExpand[t4 /. Abs[q_]^2 -> Re[q]^2 + Im[q]^2, {a, b, c, d, cen, y}, TargetFunctions -> {Re, Im}] /. {Re[y] -> U, Im[y] -> V}, {U, V}, FullSimplify] will give you a much shorter answer.

**References**:**ComplexExpand in Mathematica 5.2 and 6***From:*Jepessen <jepessen@gmail.com>