GiNaC is a

free Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procur ...

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 License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the Four Freedoms (Free software), four freedoms to run, study, share, and modify the software. The license was th ...

. 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 Hof ...

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 (383 packages as of January 2022), 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 operat ...

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

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s directly in

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

, which is GiNaC's implementation

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

. 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 is ...

. 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 li ...

. 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 in ...

, and compute with

matrices Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

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

theoretical A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...

high energy physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and b ...

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. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyper ...

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

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

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 Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Fe ...

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 the source code, design documents, or content of the product. The open-source model is a decentralized sof ...

projects: there is a symbolic extension for

GNU Octave GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a langu ...

, a simulator for

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

, and since May 2009
Pynac
a

fork In cutlery or kitchenware, a fork (from la, furca '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 ei ...

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, numerical analysis, numbe ...

References

External links

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

See also

References

External links