Archive Related Systems Candidates

Related systems: MATLAB, and other candidates

Carried over from the earlier enumeratio (the Postgres-era predecessor, archived). The base_reference registry and the docs-site Resources page this refers to are gone; the current repo's cross-reference layer is the reference crosswalk in packages/reference (see the symbol-crosswalk naming precedence: CE > Wolfram ≈ Sage > self-consistency). MATLAB and the other candidates below have not been re-checked against that crosswalk yet — treat this as a prior-art survey, not current status.

Companion to the docs site's Resources page and its References table (the base_reference registry). The systems with real cross-references live there; this page holds the thinner write-up (MATLAB) and the broader survey of what else is worth considering, so the main docs stay focused on what's actually verified.

MATLAB

Thin, as expected — MATLAB is a numerical-computing platform, not a combinatorics system, and doc-verified only (no MATLAB or Octave installed in the dev environment, so no oracle is possible; every row checked against mathworks.com/help/ directly). Five rows in base_reference today: nchoosek (k_subsets), perms (permutations, reverse-lex order — a real delta), factorial (factorial_numbers), primes (prime_numbers, value-bounded vs. our rank-indexed query — a real delta), and factor (integer_factorizations, flat multiplicity vector vs. our exponent notation). Checked and excluded: bernoulli/euler (Symbolic Math Toolbox has them, but no matching collection, or the same sign-convention mismatch already excluding Wolfram Language's EulerE), fullfact (too general — mixed per-factor radices, where words() takes one base for every position), combnk (deprecated alias of nchoosek). No Symbolic Math Toolbox equivalent exists for Stirling/Bell/ partition-counting functions at all — confirmed via MATLAB's own function reference, not assumed.

Candidate resources — data sources, references, and other systems worth associating to

Not yet cross-referenced; a rough survey for future passes, roughly grouped. Inclusion here isn't a commitment — just a shortlist worth checking before someone reinvents it.

Data sources

• LMFDB — the L-functions and Modular Forms Database; overlaps enumeratio's number-theory collections (partitions, modular forms context) more than its combinatorics core, but worth a look for the number-theoretic carriers.
• Wikidata — structured, queryable facts (via SPARQL) rather than OEIS/FindStat's narrative pages; could give machine-checkable cross-references rather than just links.

References (soft/conceptual associations — grounding, not structural claims)

• MathWorld — Wolfram's own encyclopedia; likely the single best next conceptual-relation source after Wikipedia, given how much combinatorics content it already carries.
• DLMF (Digital Library of Mathematical Functions) — most relevant to enumeratio's generating-function and special-number collections (Bell, Stirling, Eulerian numbers all have DLMF sections).
• The Encyclopedia of Combinatorial Structures (Flajolet–Sedgewick, via the combstruct/analytic-combinatorics tradition) — narrower and more structurally aligned with enumeratio's own "construction" model than Wikipedia/MathWorld are.

Full computer algebra systems (beyond Sage/Wolfram Language, already covered)

• Maple — has its own combinat package; also the home of gfun and the Superseeker OEIS-guessing tools, which are their own interesting cross-reference angle (sequence → conjectured generating function/recurrence, not just a named function).
• Magma — strong on algebraic combinatorics (permutation groups, algebras — would overlap partition_algebra, even_permutations, the group-theoretic collections).
• GAP — permutation groups and representation theory; likely the best fit for Young-tableau/representation-theoretic cross-references (its SPECHT package does symmetric-group representations directly).
• PARI/GP — number-theory-first; likely a better fit for enumeratio's number-theoretic collections (factorizations, prime-related sequences) than its combinatorics core.
• Macaulay2 — commutative algebra/algebraic geometry; a longer shot, relevant mainly if enumeratio ever grows collections tied to algebraic-combinatorics objects (Schubert polynomials, etc.).

Special-purpose combinatorics libraries

• nauty/plantri — canonical graph labeling and generation; relevant if/when enumeratio grows graph-enumeration collections.
• Combinatorica (the Mathematica package) — predates much of Wolfram Language's now-builtin combinatorics; likely superseded by the builtins already checked, but worth a citation-only look.
• Sage's own species machinery — a closer structural match to enumeratio's own species/construction model than the flat named-function rows currently in base_reference; a good candidate for the construction-syntax "derived mapping" idea (Backlog #30).
• R's partitions and combinat packages — worth a quick doc-verified pass, similar rigor to the MATLAB survey above.

General math libraries with combinatorics-adjacent coverage

• Julia's Combinatorics.jl — a live, scriptable candidate (Julia is easy to install/run headlessly) for a fourth real oracle alongside Sage/SymPy, if one is wanted.
• Coq/MathComp and Isabelle/HOL — proof assistants in the same spirit as mathlib4 (already covered); would extend the "proof-library pointer" category rather than add a new kind of association.