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Daniele Lupo
06/18/07 4:07pm

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 equation, 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.

You can see the attached file, that contains both calculations, made with the two version of Mathematica (I've copied result of one in the other notebook).

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


Attachment: moebius-mathematica-5.2-vs-6.nb, URL: ,

Subject (listing for 'ComplexExpand in Mathematica 5.2 and 6')
Author Date Posted
ComplexExpand in Mathematica 5.2 and 6 Daniele Lupo 06/18/07 4:07pm
Re: ComplexExpand in Mathematica 5.2 and 6 Daniele Lupo 06/20/07 08:21am
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