SINGULAR
Summary
SINGULAR is a Computer Algebra system 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.
Authors
Gert-Martin Greuel, Gerhard Pfister, Hans Schönemann
Vendor
Centre for Computer Algebra, University of Kaiserslautern
Status
officially approved by the authors
Aims and scope
Mathematical Classification
- 02.04 Commutative rings and algebras
- 02.04.01 Ideals, modules, homomorphisms
- 02.04.02 Polynomial and power series rings
- 02.04.03 Special rings
- 02.04.04 Graded rings and Hilbert functions
- 02.04.05 Integral dependence and normalization
- 02.04.06 Dimension theory
- 02.04.07 Factorization and primary decomposition
- 02.04.08 Syzygies and resolutions
- 02.04.09 Differential algebra
- 02.04.10 Groebner bases
- 02.05 Linear and multilinear algebra; matrix theory
- 02.05.01 Linear equations
- 02.05.02 Eigenvalues, singular values, and eigenvectors
- 02.05.03 Canonical forms
- 02.05.05 Integral matrices
- 02.05.06 Multilinear algebra
- 02.07 Category theory; homological algebra
- 02.08 Group theory and generalizations
- 03.01 Algebraic geometry
- 03.01.01 Local theory, singularities
- 03.01.02 Cycles and subschemes
- 03.01.03 Families, fibrations
- 03.01.04 Birational theory
- 03.01.05 Co(homology) theory
- 03.01.06 Arithmetic problems
- 03.01.08 Algebraic groups and geometric invariant theory
- 03.01.09 Special varieties
- 03.01.10 Real algebraic geometry
- 03.03 Several complex variables and analytic spaces
- 03.10 Visualization