Data for "Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability", Desmond (2026)

Abstract

Data for the paper "Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability" (H. Desmond). Version 2 accompanies the revised paper submitted to Mathematics in Computer Science and adds a verified test of computer algebra systems (CAS). Contents - Archive.tar.gz (unchanged from version 1). It contains two things: - results/: paper result files, rho(k) and decomposition summaries, lookup-equivalence pickle files, raw derivative and fingerprint outputs, esi_hash_index.json, and the CAS-comparison outputs of the submitted version; - function_catalogues_unique_equations.tar.gz: the five-basis ESR function catalogues (unique_equations_k.txt files only).- cas_audit.tar.gz (new): inputs, outputs, intermediate files, logs, a code snapshot and cas_audit_summary.json for the verified CAS audit behind Sections 2.4 and 3.3 and Tables 3 and 4 of the revised paper. Every claimed antiderivative is verified by differentiation in the system that produced it. See cas_audit/README.md inside the archive.- README.md, MANIFEST.tsv (file list with byte sizes) and CHECKSUMS.sha256 (SHA256 checksums). Changes from version 1 In version 1 the CAS-comparison scripts:- counted some FriCAS error messages as solutions;- skipped RUBI for two of the three integrals reported as CAS-resistant;- never ran Giac. The verified audit finds nine integrals with elementary antiderivatives that resist SymPy 1.14, Mathematica 13.3, RUBI 4.17.3, FriCAS 1.3.12, Maxima 5.47 and Giac 2.0.0 under every strategy tested. It supersedes the CAS-resistance results of version 1 (results/final_cas_summary.json and the files it names). The integrability-fraction results and the lookup databases are unchanged. Scope The package provides the data files needed to:1. run esi_integrate.py and esi_integrate_demo.ipynb using the lookup pickle files and hash index;2. regenerate the paper tables and figures from the stored summaries; 3. reproduce and audit the CAS results from the inputs and outputs in cas_audit.tar.gz;4. rerun the ESI pipeline from the included unique-equation catalogues. The code is maintained in the GitHub repository https://github.com/harrydesmond/ExhaustiveSymbolicIntegration: the ESI pipeline, the lookup tool, the CAS-audit harness (cas_audit/) and the analysis and figure scripts. The record does not include:- raw ESR generation intermediates (trees_k.txt, orig_trees_k.txt, matches_k.txt, inv_subs_k.txt), which are many GB and reproducible from ESR and the grammar definitions;- CAS executables or installations;- cluster job outputs other than the logs needed for the sample check.