SINGULAR

SINGULAR is a Computer Algebra system (CAS) for polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR’s main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features fast and general implementations for computing Groebner and standard bases, including e.g. Buchberger’s algorithm and Mora’s Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities. Based on an easy-to-use interactive shell and a C-like programming language, SINGULAR’s internal functionality is augmented and user-extendible by libraries written in the SINGULAR programming language. A general and efficient implementation of communication links allows SINGULAR to make its functionality available to other programs.

This software is also referenced in ORMS.


References in zbMATH (referenced in 1268 articles , 4 standard articles )

Showing results 1141 to 1160 of 1268.
Sorted by year (citations)

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  1. Levandovskyy, Viktor: PBW bases, non-degeneracy conditions and applications. (2005)
  2. Levandovskyy, Viktor: On preimages of ideals in certain non-commutative algebras (2005)
  3. Luengo-Velasco, I.; Melle-Hernández, A.; Némethi, A.: Links and analytic invariants of superisolated singularities (2005)
  4. Martin, Bernd; Hirsch, Tobias: Modular strata of deformation functors (2005)
  5. Plesken, W.; Robertz, D.: Janet’s approach to presentations and resolutions for polynomials and linear PDEs (2005)
  6. Schulze, Mathias: A normal form algorithm for the Brieskorn lattice (2005)
  7. Schulze, Mathias: Good bases for tame polynomials (2005)
  8. Sommese, Andrew J.; Wampler, Charles W. II: The numerical solution of systems of polynomials. Arising in engineering and science. (2005)
  9. Stillman, Michael: Tools for computing primary decompositions and applications to ideals associated to Bayesian networks (2005)
  10. Valiant, Leslie G.: Holographic circuits (2005)
  11. Villamayor U., Orlando: On constructive desingularization (2005)
  12. Wang, Mingsheng; Kwong, C. P.: On multivariate polynomial matrix factorization problems (2005)
  13. Zerz, Eva: Characteristic frequencies, polynomial-exponential trajectories, and linear exact modeling with multidimensional behaviors (2005)
  14. Zerz, Eva; Levandovskyy, Viktor: Computer algebraic methods for the structural analysis of linear control systems (2005)
  15. Artal Bartolo, Enrique; Carmona Ruber, Jorge; Cogolludo Augustín, José Ignacio: Essential coordinate components of characteristic varieties (2004)
  16. Bauer, Frank: An alternative approach to the oblique derivative problem in potential theory (2004)
  17. Bayer, Thomas: Optimal descriptions of orbit spaces and strata of finite groups (2004)
  18. Bivià-Ausina, Carles: Nondegenerate ideals in formal power series rings (2004)
  19. Brandenberg, René; Theobald, Thorsten: Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices (2004)
  20. Deconinck, Bernard; Heil, Matthias; Bobenko, Alexander; van Hoeij, Mark; Schmies, Marcus: Computing Riemann theta functions (2004)

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Further publications can be found at: http://www.singular.uni-kl.de/index.php/publications/singular-related-publications.html