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 of
Nikhef
Nikhef is the Dutch National Institute for Subatomic Physics that performs research in particle physics and astroparticle physics. Amongst others, it is a research partner of the CERN institute in Switzerland and a member of the European Gravit ...
, 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 comp ...
s
*Powerful pattern matching and replacing
*Fast trace calculation especially of
gamma matrices
*Built-in mathematical functions
*Output into various formats (plain text,
Fortran code,
Mathematica 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, 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, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...
beta function.
*The mathematical structure of
multiple zeta values
In mathematics, the multiple zeta functions are generalizations of the Riemann zeta function, defined by
:\zeta(s_1,\ldots,s_k) = \sum_\ \frac = \sum_\ \prod_^k \frac,\!
and converge when Re(''s''1) + ... + Re(''s'i'')&nb ...
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