Re: ComplexExpand in Mathematica 5.2 and 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg78001] Re: [mg77955] ComplexExpand in Mathematica 5.2 and 6*From*: Carl Woll <carlw at wolfram.com>*Date*: Thu, 21 Jun 2007 05:41:22 -0400 (EDT)*References*: <200706200939.FAA10222@smc.vnet.net>

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 > > > What about using ComplexExpand[t4, {a, b, c, d, cen, y}, TargetFunctions -> {Re, Im}] /. {Re[y] -> U, Im[y] -> V} instead of your version of ComplexExpand? Carl Woll Wolfram Research

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