CoCoA
Summary
CoCoA is a system for Computations in Commutative Algebra.
It is able to perform simple and sophisticated operations on multivaraiate
polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Grobner bases, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language. For convenience, the system offers a textual interface, an Emacs mode, and a graphical user interface common to most platforms.
Authors
CoCoA Team
Vendor
Freely distributed from the website http://cocoa.dima.unige.it
Status
officially approved by the authors
Aims and scope
Mathematical Classification
- 02.04.01 Ideals, modules, homomorphisms
- 02.04.02 Polynomial and power series rings
- 02.04.04 Graded rings and Hilbert functions
- 02.04.06 Dimension theory
- 02.04.07 Factorization and primary decomposition
- 02.04.08 Syzygies and resolutions
- 02.04.10 Groebner bases
- 02.05.01 Linear equations
- 02.05.04 Matrix factorization
- 03.01.09 Special varieties
Keywords
- algebraic field extensions
- algebraic fields
- algebraic geometric codes
- annihilators
- associated primes
- betti numbers
- Bigatti-La Scala-Robbiano algorithm
- block matrices
- Buchberger algorithm
- Cohen-Macaulay module
- Cohen-Macaulay ring
- commutative algebra
- commutative algebras
- complete intersections
- computer algebra
- conductors
- Conti-Traverso algorithm
- differential operators
- dimensions
- dimension theory
- elimination
- emacs interface
- equation solvers
- equations solving
- euclidean geometry
- exact sequences
- expression manipulation
- ext groups
- finite fields
- finite point sets
- floating point arithmetic
- free modules
- free resolution of modules
- gcd
- geometry
- gmp
- greatest common divisors
- Groebner bases
- Hilbert function
- Hilbert functions
- Hilbert series
- hom
- homological algebra
- homomorphism
- homomorphisms
- Hosten-Sturmfels algorithm
- ideal memberships
- ideal operations
- ideal quotients
- ideals
- ideal theoretic operations
- implicitization
- initial ideals
- integer arithmetics
- integer programming
- interpolation
- invariant rings
- invariant theory
- irreducible components
- Jacobian matrices
- Jordan normal forms
- kernels
- lcm
- least common multiples
- linear algebra
- linear equations
- long coefficients
- long integer arithmetic
- matrices
- matrix
- matrix factorization
- matrix orderings
- maximal ideals
- minimal polynomials
- modular linear algebra
- module homomorphisms
- module operations
- module orderings
- module ranks
- modules
- monomial orderings
- multi-precision arithmetic
- multivariate polynomial factorization
- multivariate polynomials
- normal forms
- parametrization
- polynomial interpolations
- polynomial rings
- polynomials
- power series
- primary decompositions
- primary ideals
- quotient rings
- radicals
- random combinations
- random number generators
- rational arithmetic
- rational functions
- reduced standard bases
- Rees algebra
- resultants
- rings
- saturation
- Smith normal forms
- sparse polynomials
- special varieties
- squarefree
- standard bases
- symbolic algebra
- symbolic computations
- symbolic manipulations
- symbolic-numerical solving
- syzygies
- syzygy bases
- tangent cones
- term orderings
- theorem proving
- toric ideals
- triangular systems
- type vectors
- typevectors
- univariate polynomial factorization
- vector calculus
- vectors
- zero-dimensional scheme