Computation of Affine Covariants of Quadratic Bivariate Differential Systems

This paper deals with affine covariants of autonomous differential systems. The main result is the construction of a minimal system of generators of the algebra of affine covariants of quadratic bivariate differential systems which is helpful in qualitative and numerical study. To this end, we establish a theorem (true for general systems of dimension n and degree m) which provides a procedure of construction of systems of generators for affine covariants from those of center-affine invariants. After applying this theorem to the case n=m=2 we give the expansions of the obtained affine covariants in terms of center-affine covariants. All algorithms constitute the package SIB.