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

NIKHEF is an acronym for Nationaal Instituut voor Kernfysica en Hoge-Energiefysica . Nowadays this acronym is not used anymore and the name is changed to Nationaal instituut voor subatomaire fysica...

, 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 clusters
• Powerful pattern matching and replacing
• Fast trace calculation especially of gamma matrices
• Built-in mathematical functions
• Output into various formats (plain text, Fortran
  Fortran
  Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...
  
  code, Mathematica
  Mathematica
  Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
  
  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

Schoonschip was one of the first computer algebra systems, developed in 1963 by Martinus J. G. Veltman, for use in particle physics."Schoonschip" literally means "clean ship" in Dutch.FORM can be regarded, in a sense, as the successor to Schoonschip....

, an algebra engine developed by
M. Veltman. It was initially coded in FORTRAN 77, but rewritten in C

C (programming language)

C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....

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
  Feynman diagram
  Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
  
   with up to three loops.
• FORM has been the essential tool to calculate the higher-order QCD
  Quantum chromodynamics
  In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
  
   Beta function.
• 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.

External links

• The FORM online manual