FORM is a symbolic manipulation system. It reads text files containing definitions of mathematical expressions as well as statements that tell it how to manipulate these expressions. Its original author is
Jos Vermaseren
Jos is a city in the North-Central region of Nigeria. The city has a population of about 900,000 residents based on the 2006 census. Popularly called "J-Town", it is the administrative capital and largest city of Plateau State. The city is situ ...
of
Nikhef, the Dutch institute for subatomic physics.
It is widely used in the theoretical particle physics community, but it is not restricted to applications in this specific field.
Features
*Definition of mathematical expressions containing various objects (symbols, functions, indices, ...) with elementary arithmetic operations
*Arbitrary long mathematical expressions (limited only by disk space)
*Multi-threaded execution, parallelized version for
computer cluster
A computer cluster is a set of computers that work together so that they can be viewed as a single system. Unlike grid computers, computer clusters have each node set to perform the same task, controlled and scheduled by software. The newes ...
s
*Powerful pattern matching and replacing
*Fast trace calculation especially of
gamma matrices
In mathematical physics, the gamma matrices, \ \left\\ , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra \ \mathr ...
*Built-in mathematical functions
*Output into various formats (plain text,
Fortran code,
Mathematica
Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...
code)
*External communication with other software programs
Example usage
A text file containing
Symbol x,y;
Local myexpr = (x+y)^3;
Id y = x;
Print;
.end
would tell FORM to create an expression named ''myexpr'', replace therein the symbol ''y'' by ''x'', and print the result on the screen. The result would be given like
myexpr =
8*x^3;
History
FORM was started in 1984 as a successor to
Schoonschip
Schoonschip was one of the first computer algebra systems, developed in 1963 by Martinus J. G. Veltman, for use in particle physics.
"Schoonschip" refers to the Dutch expression "schoon schip maken": to make a clean sweep, to clean/clear things u ...
, an algebra engine developed by
M. Veltman. It was initially coded in
FORTRAN 77, but rewritten in
C before the release of version 1.0 in 1989.
Version 2.0 was released in 1991. The version 3.0 of FORM has been publicized in 2000. It has been made open-source on August 27, 2010 under the
GPL license.
Applications in high-energy physics and other fields
*Mincer: A software package using FORM to compute
massless propagator diagrams with up to three loops.
*FORM has been the essential tool to calculate the higher-order
QCD
In theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in ...
beta function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral
: \Beta(z_1,z_2) = \int_0^1 t^ ...
.
*The mathematical structure of
multiple zeta values has been researched with dedicated FORM programs.
*The software package FormCalc which is widely used in the physics community to calculate Feynman diagrams is built on top of FORM.
References
External links
*
The FORM online manualDebian — Details of package form
*Linux packages
ArchLinuxDebianGentooUbuntu
*
{{Authority control
Computer algebra systems
Free computer algebra systems
Free software programmed in C
Mathematical software
Physics software
Science software