FORM

FORM: Symbolic Manipulation of Very Large Expressions for Quantum Field Theory

Added to the survey on 2026-10-06 by the Research Toolkit's research pass. The scores below are that pass's assessment from the evidence cited under References, on the survey's four axes and scale; they are not the original survey's (2026-09-26), and no rule of the Principia Machina reads them. See the additions on the front page.

Overview & Architectural Fit

FORM is a symbolic manipulation system built for expressions too large for memory, which it streams from disk; TFORM runs it in parallel. FORM 5 adds a Feynman-diagram generator based on GRACE, arbitrary-precision floating-point coefficients and polynomial arithmetic from FLINT. It is built for the very large expressions of multi-loop calculations in particle physics.

Mathematical Evaluation for TPM

Lagrangian / Action (3/10): No variational machinery: FORM works after the Feynman rules are fixed.
Field / PDE (2/10): Not a field or PDE tool.
Relativity (3/10): Lorentz and Dirac algebra in d dimensions, not curved spacetime.
Quantum / Data (7/10): Industrial-scale perturbative quantum-field-theory algebra, including multi-loop work.

Integration Pipeline

Derive the Feynman rules from the Lagrangian, for example with FeynCalc.
Generate the diagrams with FORM 5's generator, or import them.
Reduce the amplitudes: Dirac traces, colour algebra, tensor reduction, in batch scripts.
Check numerically with arbitrary-precision coefficients at chosen kinematic points.

Status, Licence and Limits

Status: Active. Latest tagged release 5.0.1, 24 June 2024; the FORM 5 paper was posted on 27 January 2026, so check which of its features the build in use carries.
Licence: GPL-3.0.
Home: https://github.com/form-dev/form and https://www.nikhef.nl/~form
Limits: The language is idiosyncratic and favours batch scripts. Interactive exploration is better done in FeynCalc.

On the Principia Machina

A tool runs only where the sponsor installed and bound it, and what it returns is untrusted input, vetted before use; its numbers are never values of the site's calculator, TPC. An equation it derives is transcribed into the kernel's form grammar before anything checks it, and lands as a RESULT of regime L with EQUATION and ROLE. See Agent/Tools and the operator's guide.

References

FORM5-2026 – Davies J., Kaneko T., Marinissen C., Ueda T., Vermaseren J.A.M. (2026). FORM Version 5.0. arXiv:2601.19982.
FORMREPO – FORM developers. form-dev/form (releases, COPYING). github.com/form-dev/form.