PHD-Department of Mathematics

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Implementation of a modified procesi algorithm to compute covariants of binary forms of up to degree five and their relations
(Kenyatta University, 2016-11) Kariuki, Njau Lawrence
In his book (Procesi,C., 2007), Claudio Procesi suggested a new algorithm for computing covariants of binary forms under the action of SL(2;C), based on an iterative computations of covariants of the simpler group U+. In Procesi book the computation was carried out only for binary forms of degree 3 and 4, but the rst signi cant test for the algorithm would be the computation for degree 5. In 2010 summer school in Algebra organized by ICTP in Kenya, Procesi suggested the implementation of his algorithm as a project. In this thesis we implement a modi cation of the original Procesi algorithm on the computer algebra system CoCoA, study its general properties and test it with the complete description of generators and relations of the algebra of covariants of binary forms of degree 5. The modi ed form of Procesi algorithm computes covariants iteratively with respect to the degree of a covariant. The implementation was tested in the computation of covariants of binary forms of degree 5, which produces 23 covariants of degree up to 18. The algorithm produces the explicit list of covariants and rheir relations. As far as we know this is the most explicit description of the complete list of relations which is made available so far.