Implementation Of A Modified Procesi Algorithm To Compute Covariants Of Binary Forms Of Up To Degree Five And Their Relations

ABSTRACT

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.

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