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 882 articles , 4 standard articles )

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  1. Alberich-Carramiñana, Maria; Dachs-Cadefau, Ferran; Àlvarez Montaner, Josep: Multiplier ideals in two-dimensional local rings with rational singularities (2016)
  2. Bivià-Ausina, Carles; Fukui, Toshizumi: Mixed \Lojasiewiczexponents and $\log$ canonical thresholds of ideals (2016)
  3. Bobowik, Justyna; Szafraniec, Zbigniew: Counting signed swallowtails of polynomial selfmaps of $\mathbb R^3$ (2016)
  4. Boels, Rutger H.; Kniehl, Bernd A.; Yang, Gang: Master integrals for the four-loop Sudakov form factor (2016)
  5. Böhm, Janko; Decker, Wolfram; Fieker, Claus; Laplagne, Santiago; Pfister, Gerhard: Bad primes in computational algebraic geometry (2016)
  6. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  7. Böhm, Janko; Marais, Magdaleen S.; van der Merwe, André F.: 3D printing dimensional calibration shape: Clebsch cubic (2016)
  8. Botbol, Nicolás; Dickenstein, Alicia: Implicitization of rational hypersurfaces via linear syzygies: a practical overview (2016)
  9. Brunat, Josep M.; Montes, Antonio: Computing the canonical representation of constructible sets (2016)
  10. Cano, Guillaume; Cohen, Cyril; Dénès, Maxime; Mörtberg, Anders; Siles, Vincent: Formalized linear algebra over elementary divisor rings in Coq (2016)
  11. Casnati, Gianfranco; Notari, Roberto: A structure theorem for $2$-stretched Gorenstein algebras (2016)
  12. Chung, Kiryong; Lee, Wanseok; Park, Euisung: On the space of projective curves of maximal regularity (2016)
  13. Cifuentes, Diego; Parrilo, Pablo A.: Exploiting chordal structure in polynomial ideals: a Gröbner bases approach (2016)
  14. Cimpoeaş, Mircea; Stamate, Dumitru I.: On intersections of complete intersection ideals (2016)
  15. Coutinho, S.C.; Saccomori, C.C.jun.: Families of minimal involutive surfaces in projective space (2016)
  16. Dimca, Alexandru; Sticlaru, Gabriel: Syzygies of Jacobian ideals and weighted homogeneous singularities (2016)
  17. Dumnicki, M.; Farnik, Ł.; Główka, A.; Lampa-Baczyńska, M.; Malara, G.; Szemberg, T.; Szpond, J.; Tutaj-Gasińska, H.: Line arrangements with the maximal number of triple points (2016)
  18. Dumnicki, M.; Szemberg, T.; Tutaj-Gasińska, H.: Symbolic powers of planar point configurations. II. (2016)
  19. Eick, Bettina; King, Simon: The isomorphism problem for graded algebras and its application to $\mathrmmod-p$ cohomology rings of small $p$-groups. (2016)
  20. Eisenbud, David; Harris, Joe: 3264 and all that. A second course in algebraic geometry (2016)

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