---
title: "math-poly-rational — 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/rational.groupant/"
---
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# math-poly-rational

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:** rf converts expressions to reduced fractions, evaluating constant subtrees through calc Env; only exact Q constants and target-independent integer powers admitted. Divisor roots are saved before cancellation. Original syntax is not reconstructible from normalized fraction/domain. Parent Poly operations supply cost and normalization assumptions. (bytes 6191–9459)
- **part of:** [math-poly](https://md.groupants.elamur.ai/free/en/mova/math/src/poly.rs.groupant/)
- **repository folder:** [`math/src/poly.rs.groupant/rational.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/poly.rs.groupant/rational.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) |
| `constant_evaluation` | constant_evaluation | partial source derived model | [constant_evaluation](#constant-evaluation) |
| `fraction_join` | fraction_join | partial source derived model | [fraction_join](#fraction-join) |
| `power_domain` | power_domain | partial source derived model | [power_domain](#power-domain) |
| `failure_order` | failure_order | partial source derived model | [failure_order](#failure-order) |

## Model text


### descriptant

#### math-poly-rational

rf converts expressions to reduced fractions, evaluating constant subtrees through calc Env; only exact Q constants and target-independent integer powers admitted. Divisor roots are saved before cancellation. Original syntax is not reconstructible from normalized fraction/domain. Parent Poly operations supply cost and normalization assumptions.

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

### approximant

#### Scoped forward and cost

rf converts expressions to reduced fractions, evaluating constant subtrees through calc Env; only exact Q constants and target-independent integer powers admitted. Divisor roots are saved before cancellation. Original syntax is not reconstructible from normalized fraction/domain. Parent Poly operations supply cost and normalization assumptions.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

rf converts expressions to reduced fractions, evaluating constant subtrees through calc Env; only exact Q constants and target-independent integer powers admitted. Divisor roots are saved before cancellation. Original syntax is not reconstructible from normalized fraction/domain. Parent Poly operations supply cost and normalization assumptions.

Source range[6191,9459) bound by manifest digest. Parent domain applies, not arbitrary public states.

### models

## Source-scoped typed relations

### behavior_complement

rf division by identically zero divisor numerator excludes success. After (x²-1)/(x-1) reduction, a result omitting the recorded denominator root1 contradicts the domain trace.

### reverse_reconstruction

Reduced(x+1)/1 admits both x+1 and (x²-1)/(x-1), but dens distinguishes their admitted domains. Even num,den,dens together admit multiple syntax/evaluation histories.

### constant_evaluation

If target variable absent, evaluate through calc Env before syntax dispatch; only V::Q is accepted as constant. Approximate/string/list constants error, potentially after effects in Env.

### fraction_join

Add/sub combine n1*d2 ± n2*d1 over d1*d2; multiply n1*n2/d1*d2; division n1*d2/d1*n2 after recording nonconstant n2. reduce divides gcd and makes denominator monic.

### power_domain

Exponent must be target-independent and exact integer with |k|<=200. Negative powers swap numerator/denominator and record nonconstant numerator; no explicit identically-zero check on this negative-power branch.

### failure_order

For ordinary binary forms rf processes left child then right. Division tests right numerator zero after both; power evaluates/checks exponent before base conversion. Failed conversion can retain earlier Env effects.

### tests

#### Evidence

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

rf converts expressions to reduced fractions, evaluating constant subtrees through calc Env; only exact Q constants and target-independent integer powers admitted. Divisor roots are saved before cancellation. Original syntax is not reconstructible from normalized fraction/domain. Parent Poly operations supply cost and normalization assumptions.