ComplexExpand in Mathematica 5.2 and 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg77955] ComplexExpand in Mathematica 5.2 and 6*From*: Jepessen <jepessen at gmail.com>*Date*: Wed, 20 Jun 2007 05:39:13 -0400 (EDT)

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

**Follow-Ups**:**Re: ComplexExpand in Mathematica 5.2 and 6***From:*Carl Woll <carlw@wolfram.com>

**Re: ComplexExpand in Mathematica 5.2 and 6***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>