GiNaC is a free

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

released under the

GNU General Public License The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

. The name is a

recursive acronym A recursive acronym is an acronym that refers to itself, and appears most frequently in computer programming. The term was first used in print in 1979 in Douglas Hofstadter's book '' Gödel, Escher, Bach: An Eternal Golden Braid'', in which Hofs ...

for "GiNaC is Not a CAS" (

Computer Algebra System A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

). This is similar to the

GNU GNU ( ) is an extensive collection of free software (394 packages ), which can be used as an operating system or can be used in parts with other operating systems. The use of the completed GNU tools led to the family of operating systems popu ...

acronym "GNU's 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

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s directly in C++, which is GiNaC's implementation

programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

. The algebraic syntax is achieved in C++ through the use of

operator overloading In computer programming, operator overloading, sometimes termed ''operator ad hoc polymorphism'', is a specific case of polymorphism, where different operators have different implementations depending on their arguments. 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 In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are po ...

. Symbolically, it can do multivariate polynomial arithmetic, factor polynomials, compute GCDs, expand

series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...

, and compute with

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

. It is equipped to handle certain noncommutative algebras which are extensively used in

theoretical A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

high energy physics Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the stu ...

Clifford algebras In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real numbers ...

SU(3) In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 i ...

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...

s, and Lorentz tensors. Due to this, it is extensively used in

dimensional regularization __NOTOC__ In theoretical physics, dimensional regularization is a method introduced by Juan José Giambiagi and as well as – independently and more comprehensively – by Gerard 't Hooft and Martinus J. G. Veltman for regularizing integral ...

computations – but it is not restricted to physics. GiNaC is the symbolic foundation in several

open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use and view the source code, design documents, or content of the product. The open source model is a decentrali ...

projects: there is a symbolic extension for

GNU Octave GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...

, a simulator for

magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and ...

, and since May 2009
Pynac
a

fork In cutlery or kitchenware, a fork (from 'pitchfork') is a utensil, now usually made of metal, whose long handle terminates in a head that branches into several narrow and often slightly curved tines with which one can spear foods either to h ...

of GiNaC, provides the backend for symbolic expressions in

SageMath SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentia ...

References

External links

* {{DEFAULTSORT:Ginac C++ libraries Free computer algebra systems Free software programmed in C++

See also

References

External links