       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[]^2 - t3[]^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?