Projective Noether

The Projective Noether Maple Package: Computing the dimension of a projective variety Recent theoretical advances in elimination theory use straight-line programs as a data structure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation of the dimension of a projective variety. Comparative results on benchmarks for time and space of several families of multivariate polynomial equation systems are given and we point out both weaknesses and advantages of different approaches

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Hashemi, Amir; Parnian, Hossein; Seiler, Werner M.: Nœther bases and their applications (2019)
  2. Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno: On the complexity of the (F_5) Gröbner basis algorithm (2015)
  3. Jeronimo, Gabriela; Perrucci, Daniel; Sabia, Juan: A parametric representation of totally mixed Nash equilibria (2009)
  4. Durvye, Clémence; Lecerf, Grégoire: A concise proof of the Kronecker polynomial system solver from scratch (2008)
  5. Hashemi, Amir: Efficient algorithms for computing Noether normalization (2008)
  6. Zhou, Wenqin; Carette, J.; Jeffrey, D. J.; Monagan, M. B.: Hierarchical representations with signatures for large expression management (2006)
  7. Sommese, Andrew J.; Wampler, Charles W. II: The numerical solution of systems of polynomials. Arising in engineering and science. (2005)
  8. Lecerf, Grégoire: Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers (2003)
  9. Bruno, N.; Heintz, J.; Matera, G.; Wachenchauzer, R.: Functional programming concepts and straight-line programs in computer algebra (2002)
  10. Lecerf, G.: Quadratic Newton iteration for systems with multiplicity (2002)
  11. Giusti, Marc; Lecerf, Grégoire; Salvy, Bruno: A Gröbner free alternative for polynomial system solving (2001)
  12. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical decomposition of the solution sets of polynomial systems into irreducible components (2001)
  13. Giusti, Marc; Hägele, Klemens; Lecerf, Grégoire; Marchand, Joël; Salvy, Bruno: The Projective Noether Maple Package: Computing the dimension of a projective variety (2000)
  14. Heintz, Joos; Krick, Teresa; Puddu, Susana; Sabia, Juan; Waissbein, Ariel: Deformation techniques for efficient polynomial equation solving. (2000)
  15. Sommese, Andrew J.; Verschelde, Jan: Numerical homotopies to compute generic points on positive dimensional algebraic sets (2000)