SINGULAR is a computer algebra system specialising in polynomial computations. It is designed for research in commutative and non-commutative algebra, algebraic geometry, singularity theory and related mathematical disciplines.
The software operates on mathematical objects such as polynomial rings, ideals and modules. It supports computations over a broad range of coefficient fields and rings, including rational numbers, finite fields and algebraic extensions.
SINGULAR provides highly developed algorithms for computing Gröbner and standard bases, together with facilities for factorisation, syzygies, resolutions and polynomial system solving. These capabilities make it especially valuable for investigating algebraic varieties and complicated polynomial relationships.
The system combines efficient algorithms implemented in C and C++ with an interpreted programming language. Its functionality can be extended through specialised libraries, making it a flexible environment for mathematical research and experimentation.
This is free and open source software.
Key Features
- Polynomial computations over numerous coefficient fields and rings.
- Support for ideals, modules, quotient rings and polynomial rings.
- Efficient algorithms for computing Gröbner and standard bases.
- Buchberger’s algorithm and other specialised basis computation methods.
- Polynomial factorisation, greatest common divisors and resultant calculations.
- Computations involving syzygies and free resolutions.
- Primary decomposition and normalisation of algebraic structures.
- Facilities for studying singularities and deformation theory.
- Support for commutative and selected non-commutative algebraic calculations.
- Extensive library collection covering specialised mathematical algorithms.
- Built-in programming language with procedures, data structures and control statements.
- Support for extending computations through external libraries and compiled functionality.
- Integration with mathematical software and an Emacs-based interface.
- Cross-platform support – runs on Linux and macOS.
Website: github.com/Singular
Support:
Developer: Centre for Computer Algebra, University of Kaiserslautern, and contributors
License: GNU General Public License v2.0 / v3.0
SINGULAR is written in C++. Learn C++ with our recommended free books and free tutorials.
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