Computational techniques for proving identities in symmetric

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Computational techniques for proving identities in symmetric

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b((a z2)·23, (a z2)· (B z4)) + 9(21)q(23)+qla z2) 9(23) + 9(21) 9(ß z4) + q(a ze) 9(824) – (b(21, a z2) + .... h[1 y + 4x + ax.y + B y ·x]); rightside = (1 – 3 8) (3 b[x .... 3 u b(x, y)2 – 3 p q(x) 2 – 3 bly, y•y) 9(x) 2 + 9 u q(x)q(y) 1 +. 3 u (b(y 1, x + a x•y + B ...

Computational techniques for proving identities in symmetric compositions Pablo Alberca Bjerregaard a and Cándido Martín González b a University of Málaga, Department of Applied Mathematics. Málaga. Spain. E-mail: [email protected] b University of Málaga, Department of Algebra, Geometry and Topology. Málaga. Spain. E-mail: [email protected] January - 2007

Abstract. We present in this work a complete session in a Mathematica notebook. The aim of this notebook is to check identities in symmetric compositions. This notebook is a complement of our work [1] and it has all the explicit computations. We refer the reader to that paper which can be seen in http://www.uibk.ac.at/mathematik/loos/jordan/index.html. First of all we will present a few number of comands in order to simplify identities by extracting scalars, SOut. The rest of the strategy holds on the powerfull of using patterns and rules.

à Rules and functions for linearization expandq = 8q@x_ + y_D → b@x, yD + q@xD + q@yD, q@x_ ⋅ y_D → q@xD q@yD