---
title: "math-poly-inequalities — Mova code model"
description: "Mova code model of math/src/poly.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/math/src/poly.rs.groupant/inequalities.groupant/"
---
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# math-poly-inequalities

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

- **kind:** groupant_fragment
- **status:** partial source bound model
- **source:** [`math/src/poly.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/poly.rs)
- **source SHA-256:** `28c7c69c8282270b…`
- **covers:** solve_ineq collects approximate critical points, samples intervals and merges through accepted endpoints. dens preserves canceled holes. Many functions share interval output. Nonfinite sort, close roots and Ne exact-check mismatch limit guarantees; count root work plus per-interval evaluations. (bytes 22090–25985)
- **part of:** [math-poly](https://md.groupants.elamur.ai/free/en/mova/math/src/poly.rs.groupant/)
- **repository folder:** [`math/src/poly.rs.groupant/inequalities.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/poly.rs.groupant/inequalities.groupant)
- **repository commit:** `48f2e6f74146`

> **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](#approximant) |
| **ast** | partial | `../syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#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](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `critical_merge` | critical_merge | partial source derived model | [critical_merge](#critical-merge) |
| `interior_choice` | interior_choice | partial source derived model | [interior_choice](#interior-choice) |
| `operator_mismatch` | operator_mismatch | partial source derived model | [operator_mismatch](#operator-mismatch) |
| `endpoint_join` | endpoint_join | partial source derived model | [endpoint_join](#endpoint-join) |

## Model text


### descriptant

#### math-poly-inequalities

solve_ineq collects approximate critical points, samples intervals and merges through accepted endpoints. dens preserves canceled holes. Many functions share interval output. Nonfinite sort, close roots and Ne exact-check mismatch limit guarantees; count root work plus per-interval evaluations.

Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.

### approximant

#### Scoped forward and cost

solve_ineq collects approximate critical points, samples intervals and merges through accepted endpoints. dens preserves canceled holes. Many functions share interval output. Nonfinite sort, close roots and Ne exact-check mismatch limit guarantees; count root work plus per-interval evaluations.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

solve_ineq collects approximate critical points, samples intervals and merges through accepted endpoints. dens preserves canceled holes. Many functions share interval output. Nonfinite sort, close roots and Ne exact-check mismatch limit guarantees; count root work plus per-interval evaluations.

Source range[22090,25985) bound by manifest digest. Parent domain applies, not arbitrary public states.

### models

## Source-scoped typed relations

### behavior_complement

A sample where reduced denominator or any retained dens evaluates zero excludes inclusion. An interval sample failing requested sign excludes the corresponding open interval from output; this is float-sample policy, not an exact theorem.

### reverse_reconstruction

Output(-2,2) for Lt is compatible with x²-4 and positive multiples, among other rational functions. Interval text cannot recover coefficients, multiplicities or original canceled factors.

### critical_merge

Gather real roots from numerator and product of all denominator factors; dedup within tolerance1e-12*max(|v|,1) only when numerator flag matches. Same coordinate from both sides can remain duplicated.

### interior_choice

Unbounded intervals use boundary±1 or0; bounded intervals use midpoint. Convert sample f64 to simplest Q and check exact num/den sign, while actual inside also tests dens in f64.

### operator_mismatch

holds supports Ne as v!=0. Exact interior check handles Lt/Le/Gt/Ge, otherwise v==0, so Ne diagnostics can disagree even when floating interval membership follows Ne.

### endpoint_join

Merge neighboring inside intervals only if holds at shared endpoint is true; otherwise emit open/closed boundary or isolated point. Float rounding, collapsed roots and NaN sorting can invalidate exact endpoint claims.

### tests

#### Evidence

See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.

solve_ineq collects approximate critical points, samples intervals and merges through accepted endpoints. dens preserves canceled holes. Many functions share interval output. Nonfinite sort, close roots and Ne exact-check mismatch limit guarantees; count root work plus per-interval evaluations.