Elamur Groupantsmath-poly-roots
The groupant beside math/src/poly.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 |
squarefree_relation | squarefree_relation | partial source derived model | squarefree_relation |
candidate_filter | candidate_filter | partial source derived model | candidate_filter |
surd_transport | surd_transport | partial source derived model | surd_transport |
numeric_residual | numeric_residual | partial source derived model | numeric_residual |
Model text
descriptant
math-poly-roots
Root variants distinguish rational/surd/f64. Yun multiplicities, rational validation and product checks compose; remaining factors use500-sweep Aberth with residual tests. Root-only inverse needs leading scalar and original domain. No convergence theorem or total error bound.
Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.
approximant
Scoped forward and cost
Root variants distinguish rational/surd/f64. Yun multiplicities, rational validation and product checks compose; remaining factors use500-sweep Aberth with residual tests. Root-only inverse needs leading scalar and original domain. No convergence theorem or total error bound.
No executable percent surrogate claimed.
invariant
Scoped invariant
Root variants distinguish rational/surd/f64. Yun multiplicities, rational validation and product checks compose; remaining factors use500-sweep Aberth with residual tests. Root-only inverse needs leading scalar and original domain. No convergence theorem or total error bound.
Source range[9459,22090) bound by manifest digest. Parent domain applies, not arbitrary public states.
models
Source-scoped typed relations
behavior_complement
solve_poly zero polynomial excludes a root list and returns any-value error; nonzero constant returns no roots. An exact Q candidate failing substitution cannot be accepted by rational_roots.
reverse_reconstruction
Root list with multiplicities fixes only a monic polynomial under exact complete roots; any nonzero leading scalar shares it. Approximate roots admit many nearby polynomials and cannot recover exact coefficients.
squarefree_relation
Yun uses gcd(f,f'), then repeatedly gcd(b,c-b') and associates factor with multiplicity i. Loop stops after400; factor product/completeness checks must detect omissions rather than assume unbounded decomposition.
candidate_filter
Small primitive endpoint coefficients enumerate signed divisors pn/qd, checking exact Horner zero. Large-coefficient fallback rounds numeric real root*qd and still validates exact candidate; missing candidates remain possible.
surd_transport
Quadratic discriminant N/M becomes sqrt(N*M)/M; factorization extracts square part s and squarefree d, yielding a0±b0 sqrt(d). Exact substitution in Q(sqrt(d)) checks both coefficients zero; factor completion can include probable primes.
numeric_residual
Aberth iterates at most500 sweeps and skips nonfinite steps. solve_poly checks |p(z)|<=1e-8 max(scale,1), plus multiplicity sum and factor rebuild; residual/completeness is not convergence, conditioning or rational-domain certification.
tests
Evidence
See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.
Root variants distinguish rational/surd/f64. Yun multiplicities, rational validation and product checks compose; remaining factors use500-sweep Aberth with residual tests. Root-only inverse needs leading scalar and original domain. No convergence theorem or total error bound.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/poly.rs.groupant/roots.groupant/