Elamur Groupantsmath-linsys-elimination
The groupant beside math/src/linsys.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 |
pivot_selection | pivot_selection | partial source derived model | pivot_selection |
rank_classification | rank_classification | partial source derived model | rank_classification |
shape_precedence | shape_precedence | partial source derived model | shape_precedence |
arithmetic_cost | arithmetic_cost | partial source derived model | arithmetic_cost |
Model text
descriptant
math-linsys-elimination
gauss classifies rank with first nonzero pivots and free-zero particular solutions on rectangular matched data. check_solution rejects count then width mismatches before exact substitution; empty equations accept arbitrary x. Ax=b and rank constrain inverse fibers. Shape scan O(m), elimination rational cubic-scale work.
Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.
approximant
Scoped forward and cost
gauss classifies rank with first nonzero pivots and free-zero particular solutions on rectangular matched data. check_solution rejects count then width mismatches before exact substitution; empty equations accept arbitrary x. Ax=b and rank constrain inverse fibers. Shape scan O(m), elimination rational cubic-scale work.
No executable percent surrogate claimed.
invariant
Scoped invariant
gauss classifies rank with first nonzero pivots and free-zero particular solutions on rectangular matched data. check_solution rejects count then width mismatches before exact substitution; empty equations accept arbitrary x. Ax=b and rank constrain inverse fibers. Shape scan O(m), elimination rational cubic-scale work.
Source range[2922,5197) bound by manifest digest. Parent domain applies, not arbitrary public states.
models
Source-scoped typed relations
behavior_complement
check_solution rejects A.len!=b.len, then any row.len!=x.len, before arithmetic; a malformed shape cannot pass by truncated zip. Matching shapes with any dot product !=b_i also reject.
reverse_reconstruction
Accepted x constrains b=A*x for every shape-valid A, so many systems share it. Unique additionally requires full column rank. Infinite particular/free does not encode a nullspace basis or recover A.
pivot_selection
gauss chooses first nonzero row at/after current row for each column, normalizes entire augmented row and eliminates pivot from all other rows. Exact arithmetic needs no epsilon tie policy.
rank_classification
Any remaining reduced row0=c!=0 gives Inconsistent; otherwise pivot coordinates take RHS and all free coordinates remain0. Pivots count n means Unique, fewer gives Infinite with ascending free indices.
shape_precedence
Checker count mismatch is O(1) and precedes O(m) width scan. Empty A,b accepts arbitrary x. gauss retains its own unchecked rectangular/matched precondition and is not made total by checker repair.
arithmetic_cost
After shape validation substitution evaluates m length-n rational dot products O(mn) plus mismatch text. Gauss is O(mnmin(m,n)) rational operations/O(mn) storage; bit growth is additional.
tests
Evidence
See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.
gauss classifies rank with first nonzero pivots and free-zero particular solutions on rectangular matched data. check_solution rejects count then width mismatches before exact substitution; empty equations accept arbitrary x. Ax=b and rank constrain inverse fibers. Shape scan O(m), elimination rational cubic-scale work.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/linsys.rs.groupant/elimination.groupant/