FORM Version 5.0

We present FORM 5, a major release of the symbolic-manipulation system FORM. Version 5 introduces an integrated diagram generator, based on the GRACE graph-generator, to produce Feynman diagrams directly from FORM scripts. This release also adds support for arbitrary precision floating point coefficients, together with statements for the numerical evaluation of common mathematical functions as well as multiple zeta values and Euler sums. In addition, FORM 5 provides an interface to the FLINT library, offering substantially faster polynomial arithmetic. Various further functions and commands have been added alongside these major features, as well as performance improvements for TFORM and improved compression of FORM’s temporary files. Compatibility with the previous release, FORM 4.3.1, is retained except where prior behaviour contradicted the manual or was experimental.

💡 Research Summary

The paper presents FORM 5.0, a major new release of the symbolic‑manipulation system FORM that builds on the long‑standing FORM 4.3.1 code base while adding several high‑impact capabilities. The authors first describe the integration of a built‑in Feynman‑diagram generator based on the Grace graph‑generator. Users can now define particle models directly in a FORM script using the new Model, Particle, and Vertex constructs, then call the diagrams_ function with sets of incoming/outgoing particles, external and internal momentum vectors, and a loop‑order or coupling‑power specification. A rich set of filtering keywords (OnePI_, NoTadpole_, Bipart_, etc.) mirrors the syntax of the widely used Qgraf tool, allowing fine‑grained control over which topologies are produced. An additional TopologiesOnly_ mode enables the generation of only distinct topologies, which can be processed before full graph expansion, dramatically reducing the combinatorial overhead for multi‑loop calculations.

The second major addition is arbitrary‑precision floating‑point support. By linking against the MPFR library, FORM 5 introduces a Float data type and a suite of evaluation commands (Evalf, EvalfMZV, etc.) that can numerically evaluate common mathematical functions, multiple zeta values, and Euler sums directly within a FORM session. This eliminates the need for external scripts or computer‑algebra systems when high‑precision numerical checks are required, a frequent demand in perturbative quantum‑field‑theory and number‑theory research.

Third, the authors integrate the FLINT library to accelerate polynomial arithmetic. FLINT provides state‑of‑the‑art algorithms for multiplication, division, GCD, and modular reduction of large‑degree polynomials. FORM 5 now delegates polynomial operations on its internal Poly objects to FLINT, yielding substantial speed‑ups in the algebraic reduction phases of large Feynman‑integral calculations.

Performance‑related improvements are also highlighted. The parallel version TFORM now scales better on multi‑core systems, and temporary file handling has been upgraded with Zstandard compression, reducing both I/O time and disk usage. A new command‑line switch -vv prints a detailed list of compile‑time feature flags and linked library versions, while the pre‑processor variable SubSubVersion_ allows scripts to detect fine‑grained version differences.

A comprehensive list of bug fixes and minor language changes is provided. Notable items include the introduction of IntoHide/NIntoHide for more flexible expression hiding, forced activation of the “multi‑run” mode (making the -M flag obsolete), corrected Fortran suffix handling for large integer literals, improved Mathematica output formatting, and new warnings for conflicting $‑variable ModuleOption specifications and for expression names exceeding the documented 16‑character limit.

The paper concludes with a deprecation roadmap: native Windows support, 32‑bit builds, and the ParFORM parallel engine are slated for removal because they are rarely used and impose maintenance burdens. The authors also acknowledge that the test suite, while expanded, still requires further coverage to ensure future robustness.

Overall, FORM 5.0 delivers a tightly integrated environment that combines symbolic manipulation, automatic diagram generation, high‑precision numerical evaluation, and fast polynomial arithmetic. By consolidating these capabilities into a single, open‑source platform, the release promises to streamline workflows for high‑energy‑physics phenomenology, perturbative quantum‑field‑theory calculations, and large‑scale algebraic research, while maintaining backward compatibility and encouraging community contributions for continued evolution.