The Projective Noether Maple Package: Computing the Dimension of a Projective Variety

Classical methods to study and solve systems of polynomial equations are based on numerous avatars of Gröbner (standard) basis algorithms or Riquier-Janet type methods (Ritt-Wu’s algorithm). All these methods use implicitly but deeply the dense or sparse representation of multivariate polynomials, which is the computer science counterpart of the expansion of these mathematical objects on the monomial basis of the polynomial algebra. Also, all these methods can be interpreted as rewriting techniques. Considerable efforts have been made in order to improve both theoretical and practical aspects of these techniques and to produce efficient algorithms and implementations. Restricting to this last aspect, all most commonly available computer algebra systems offer Gröbner basis implementations.