Elamur Groupantsmath-comb-products
The groupant beside math/src/comb.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
guard_order | guard_order | partial source derived model | guard_order |
product_tree | product_tree | partial source derived model | product_tree |
legendre_relation | legendre_relation | partial source derived model | legendre_relation |
machine_boundary | machine_boundary | partial source derived model | machine_boundary |
Model text
descriptant
math-comb-products
Balanced products build factorial/permutation/binomial; signed generalization and conversion-before-symmetry determine failure ordering. Legendre reconstructs prime powers using sieve. Exact outputs exclude differing products on bounded domain; unavailable checks do not. O(k) big multiplies plus sieve.
Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.
approximant
Scoped forward and cost
Balanced products build factorial/permutation/binomial; signed generalization and conversion-before-symmetry determine failure ordering. Legendre reconstructs prime powers using sieve. Exact outputs exclude differing products on bounded domain; unavailable checks do not. O(k) big multiplies plus sieve.
No executable percent surrogate claimed.
invariant
Scoped invariant
Balanced products build factorial/permutation/binomial; signed generalization and conversion-before-symmetry determine failure ordering. Legendre reconstructs prime powers using sieve. Exact outputs exclude differing products on bounded domain; unavailable checks do not. O(k) big multiplies plus sieve.
Source range[475,4466) bound by manifest digest. Parent domain applies, not arbitrary public states.
models
Source-scoped typed relations
behavior_complement
factorial(n>MAX_N) excludes Ok; binomial(k<0) excludes Err and returns0. With nonnegative n and admitted k<=n, output must equal exact product ratio, not rounded f64.
reverse_reconstruction
Result1 admits factorial0/1 and binomial(n,0)/binomial(n,n) for many n. For fixed nonnegative n, symmetry k and n-k can share a count; negative-n generalization adds signed fibers.
guard_order
binomial checks negative k, then k->u64, then negative n recursion, then k>n, then symmetry and MAX_N. Oversized k can fail before a small symmetric complement is found.
product_tree
prod_range(lo>hi)=1; spans<16 multiply serially, larger spans split m=lo+(hi-lo)/2 and multiply subproducts. prod_offset uses the same balanced traversal shifted by arbitrary Z base.
legendre_relation
Independent factorial/binomial checks use sums floor(n/p^i) from sieve primes. binomial_legendre returns None for k>n or n>1e7, while check_binomial outside admitted n labels unavailable and accepts true.
machine_boundary
catalan computes2*n and n+1 as u64 before arbitrary precision, so direct huge calls can overflow despite binomial work caps. Tests do not establish safety at every u64.
tests
Evidence
See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.
Balanced products build factorial/permutation/binomial; signed generalization and conversion-before-symmetry determine failure ordering. Legendre reconstructs prime powers using sieve. Exact outputs exclude differing products on bounded domain; unavailable checks do not. O(k) big multiplies plus sieve.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/comb.rs.groupant/products.groupant/