[Paper Review] FORM version 4.2

Ben Ruijl, Takahiro Ueda+1 more|arXiv (Cornell University)|Jul 20, 2017

Teaching and Learning Programming56 citations

TL;DR

FORM 4.2 is a new minor release of the symbolic manipulation toolkit introducing features like all-pattern matching, output optimization improvements, automatic rational-function expansion, and output-text dictionaries, plus various programming enhancements. It documents improvements over FORM 4.1 and illustrates use cases in physics workflows and Forcer integration.

ABSTRACT

We introduce FORM 4.2, a new minor release of the symbolic manipulation toolkit. We demonstrate several new features, such as a new pattern matching option, new output optimization, and automatic expansion of rational functions.

Motivation & Objective

• Motivate and document the new features and bug fixes in FORM 4.2 compared to FORM 4.1.
• Demonstrate practical applications and use cases in physics computations and Forcer workflows.
• Provide guidance on installation, usage, and integration via the GitHub repository and reference manual.

Proposed method

• Introduce a new id all option to generate all pattern matches and demonstrate with automorphism finding in graphs.
• Enhance output optimization with improved common subexpression detection and a new Format O4 algorithm based on local search methods for faster, better Horner schemes.
• Add automatic expansion of multivariate rational functions in one variable via Polyratfun expand mode.
• Provide dictionaries to translate output into other textual formats (e.g., LaTeX, Fortran, C) for downstream tooling.
• Introduce the Spectator system to filter and buffer terms through processing pipelines.

Experimental results

Research questions

• RQ1 What new features in FORM 4.2 improve pattern matching and enable exhaustive matching scenarios?
• RQ2 How do the new output optimization strategies (O4) compare to previous methods in terms of efficiency and core usage?
• RQ3 What benefits does automatic one-variable expansion of rational functions provide for large expressions and term limits?
• RQ4 How do dictionaries and spectators affect usability and performance for large-scale symbolic computations?
• RQ5 What practical impacts do these features have on workflows like Forcer and big-scale physics reductions?

Key findings

• The id all feature enables generation of all matches, enabling exhaustive symmetry searches (e.g., graph automorphisms).
• Output optimization improvements (Format O4) generally yield better results and speed than previous Monte Carlo Tree Search-based methods.
• Polyratfun expansion allows rapid one-variable expansions that truncate series and can avoid MaxTermSize limitations.
• Dictionaries provide flexible textual manipulation of output for targeted languages and formats.
• Spectator functionality significantly reduces processing overhead by filtering unmodified terms.
• The partitioning and expression handling features expand FORM’s capabilities for modular and combinatorial manipulations.