GiNaC
Encyclopedia
GiNaC is a free
computer algebra system
released under the GNU General Public License
. The name is a recursive acronym
for "GiNaC is Not a CAS" (Computer Algebra System
). This is similar to the GNU
acronym "GNU is not Unix".
What distinguishes GiNaC from most other computer algebra systems is that it does not provide a high-level interface for user interaction. Rather, it encourages its users to write symbolic algorithms directly in C++
, which is GiNaC's implementation programming language
. Algebraic syntax is achieved in C++ through the use of operator overloading
. The name GiNaC is also explained by its developers' perception that most "computer algebra systems" put too much emphasis on a high-level interface and too little on interoperability.
GiNaC uses the CLN
library for implementing arbitrary precision arithmetic. Symbolically, it can do multivariate polynomial arithmetic, factor polynomials
, compute GCD
s, expand series
, and compute with matrices
. It is equipped to handle certain non-commutative algebras which are extensively used in theoretical high energy physics: Clifford algebras
, SU
(3) Lie algebra
s, and Lorentz tensors
. Due to this, it is extensively used in dimensional regularization
computations—but it is not restricted to physics.
GiNaC is the symbolic foundation in several open-source projects: there is a symbolic extension for GNU Octave
, a simulator for magnetic resonance imaging, and since May 2009 it provides the backend for symbolic expressions in Sage via the Python library Pynac.
Free software
Free software, software libre or libre software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions that only ensure that further recipients can also do...
computer algebra system
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
released under the GNU General Public License
GNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
. The name is a recursive acronym
Recursive acronym
A recursive acronym is an acronym or initialism that refers to itself in the expression for which it stands...
for "GiNaC is Not a CAS" (Computer Algebra System
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
). This is similar to the GNU
GNU
GNU is a Unix-like computer operating system developed by the GNU project, ultimately aiming to be a "complete Unix-compatible software system"...
acronym "GNU is not Unix".
What distinguishes GiNaC from most other computer algebra systems is that it does not provide a high-level interface for user interaction. Rather, it encourages its users to write symbolic algorithms directly in C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
, which is GiNaC's implementation programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
. Algebraic syntax is achieved in C++ through the use of operator overloading
Operator overloading
In object oriented computer programming, operator overloading—less commonly known as operator ad-hoc polymorphism—is a specific case of polymorphism, where different operators have different implementations depending on their arguments...
. The name GiNaC is also explained by its developers' perception that most "computer algebra systems" put too much emphasis on a high-level interface and too little on interoperability.
GiNaC uses the CLN
Class Library for Numbers
CLN is a free library for arbitrary precision arithmetic. It operates on signed integers, rational numbers, floating point numbers, complex numbers, modular numbers, and univariate polynomials...
library for implementing arbitrary precision arithmetic. Symbolically, it can do multivariate polynomial arithmetic, factor polynomials
Polynomial factorization
In mathematics and computer algebra, polynomial factorization refers to factoring a polynomial into irreducible polynomials over a given field.-Formulation of the question:...
, compute GCD
Greatest common divisor
In mathematics, the greatest common divisor , also known as the greatest common factor , or highest common factor , of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.For example, the GCD of 8 and 12 is 4.This notion can be extended to...
s, expand series
Laurent series
In mathematics, the Laurent series of a complex function f is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where...
, and compute with matrices
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
. It is equipped to handle certain non-commutative algebras which are extensively used in theoretical high energy physics: Clifford algebras
Clifford algebra
In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal...
, SU
Special unitary group
The special unitary group of degree n, denoted SU, is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication...
(3) Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s, and Lorentz tensors
Electromagnetic tensor
The electromagnetic tensor or electromagnetic field tensor is a mathematical object that describes the electromagnetic field of a physical system in Maxwell's theory of electromagnetism...
. Due to this, it is extensively used in dimensional regularization
Dimensional regularization
In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of an auxiliary complex parameter d, called the...
computations—but it is not restricted to physics.
GiNaC is the symbolic foundation in several open-source projects: there is a symbolic extension for GNU Octave
GNU Octave
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB...
, a simulator for magnetic resonance imaging, and since May 2009 it provides the backend for symbolic expressions in Sage via the Python library Pynac.