Invariants of binary forms

In this work we want to give an introduction to the theory of invariants for binary forms, in order to later try to give a solution to some complex computational problems about invariants. The theory of invariants will be explained as viewed from its classical point of view, as it was studied by Hilbert (the main reference of this thesis), and we will explain all the concepts and results we consider necessaries for a basic understanding of the theory and for the approach to the problems we will implement. After the theory is exposed, we explain the computational problems we have faced in the thesis, and for which we have implemented a solution in Sage. We explain the details of the problems, as well as some details about our approach to the problems

The invariants of the binary decimic

We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants

The invariants of the binary nonic

We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets of degrees