Sage
Summary
SAGE is a framework for number theory, algebra, and geometry computation. It is open source and freely available under the terms of the GNU General Public License (GPL). SAGE is a Python library with a
customized interpreter. It is written in Python, C++, and C (via Pyrex).
Python (http://www.python.org) is an open source object-oriented
interpreted language, with a large number of libraries, e.g.,
for numerical analysis, which are
available to users of SAGE. Python can also be accessed in library mode
from C/C++ programs. SAGE provides an interface to several
important open source libraries, including Cremona’s MWRANK library for
computing with elliptic curves, the PARI library (pari.math.u-bordeaux.fr)
for number theory, Shoup’s number theory library NTL (http://www.shoup.net/ntl/), SINGULAR (http://www.singular.uni-kl.de) for
commutative algebra, GAP (http://www.gap-system.org) for group theory and
combinatorics, and maxima (http://maxima.sourceforge.net) for symbolic
computation and calculus.
Authors
William Stein (project leader) David Joyner David Kohel John Cremona Iftikhar Burhanuddin
Vendor
William Stein (at Univ of Washington, Seattle)
Status
officially approved by the authors
Aims and scope
Mathematical Classification
Keywords
- advanced number theory
- algebra
- algebraic geometry
- algebraic schemes
- algebras
- ambient Hecke modules
- ambient spaces
- arbitrary precision numbers
- calculus
- categories
- category theory
- ciphers
- classical ciphers
- classical cryptosystems
- coding theory
- combinatorial functions
- combinatorial geometry
- combinatorics
- commutative algebra
- complex numbers
- cryptography
- cryptosystems
- curvse
- Cuspidal subspaces
- dense matrices
- differentiation
- Dirichlet characters
- Dokchitser's L-function calculator
- Eisenstein series
- elementary number theory
- elliptic curves
- Euler's method for differential equation systems
- factorizations
- finite fields
- finite groups
- formal sums
- fraction fields of integral domains
- free Abelian monoids
- free algebra quotients
- free algebras
- free modules
- free monoids
- functors
- general linear groups
- generic convolution
- graph theory
- Groebner fans
- groups
- group theory
- Hecke algebras
- Hecke modules
- Hecke operators
- Hecke polynomials
- Heilbronn matrix computation
- homsets
- hyperelliptic curves
- ideals
- infinity rings
- integers
- integration
- Jacobian of a general hyperelliptic curve
- Laplace transforms
- lattice polytopes
- Laurent series
- Laurent series rings
- L-functions
- linear algebra
- linear codes
- linear groups
- Manin symbols
- matrices
- matrix
- matrix group homomorphisms
- matrix group Homsets
- matrix groups
- matrix spaces
- modular abelian varieties
- modular forms
- modular symbols
- modules
- monoids
- morphisms
- multivariate polynomial rings
- multivariate polynomials
- number field elements
- number fields
- numerical computation
- numerical fields
- orthogonal linear groups
- orthogonal polynomials
- p-adic rings
- permutation group functions
- permutation group homomorphisms
- permutation groups
- plane curves
- plotting
- polynomial rings
- polynomials
- polytopes
- power series
- power series rings
- prime numberss
- probability
- probability spaces
- quaternion algebras
- quaternion ideals
- quaternion oders
- quotient rings
- quotients of univariate polynomial rings
- random variables
- rational numbers
- real numbers
- reflexive polytopes
- Riemann's zeta function
- rings
- Rubik's cube group functions
- Rubistein's L-function calculator
- schemes
- sparse matrices
- special linear groups
- stream cryptosystems
- sudoku solver
- symbolic calculus
- symplectic linear groups
- term orderings
- unitary groups
- univariate polynomial rings
- univariate power series rings
- vectors
- Victor Miller bases
- visualization
- Watkins symmetric power L-function calculator