# Rational expression check

`rational-expression-check` · version 1.0.0 · Numbers & math · free, no key needed

Check a claimed exact rational value of an integer/fraction expression; reports the true value and the difference.

**Use when you need to: verify a claimed fraction result · check exact value of a fraction expression · is this rational arithmetic answer correct.**

## Decide before calling

Read the [versioned contract](/v1/tools/rational-expression-check/versions/1.0.0) and the supported scope below. Reuse `rational-expression-check@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `rational-expression-check@1.0.0` for verify a claimed fraction result. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- verify a claimed fraction result
- check exact value of a fraction expression
- is this rational arithmetic answer correct
- validate a claimed sum of fractions
- check my fraction calculation exactly
- confirm reduced fraction answer of an expression
- בדיקת תוצאה של חישוב שברים

## Not supported

- decimal literals, exponents or functions (use decimal-expression-evaluate)
- variables or symbolic algebra
- floating-point or approximate comparison
- rounding the result

## Behavior

- Reference: ISO/IEC 10967-2:2001 (LIA-2) exact-result terminology; exact arithmetic over the rationals with canonical reduced form; RFC 8259 sec. 6 integer grammar and sec. 7 strings.
- Grammar: expr := term (("+" | "-") term)*; term := unary (("*" | "/") unary)*; unary := "-" unary | primary; primary := INTEGER | "(" expr ")". Left associative (1/2/2 = 1/4); unary minus binds tighter than * and / (2*-3 = -6). No unary plus, no ^, no implicit multiplication.
- INTEGER is RFC 8259 int (0 or no leading zero); decimals, exponents and separators are invalid_input. U+2212, U+00D7 and U+00F7 are accepted as - * /; whitespace is space, tab, LF, CR. Positions are 0-based code point offsets.
- claimed_value is a string -?(0|[1-9][0-9]*)(/[1-9][0-9]*)?, never a JSON number; it is compared exactly by value. require_canonical (required): true also demands the canonical form (reduced, no "/1", no "-0").
- Check order: fields; expression bytes and surrogates; claimed_value; require_canonical; tokenise and parse (errors); evaluation in post-order, left before right (division_by_zero with position and divisor_text of the first zero divisor); value (value_mismatch with difference = value - claim); form (not_canonical).
- value is the canonical exact value, or null for division_by_zero. Reported differences are exact and not subject to the digit cap.
- Limits: 4096 UTF-8 bytes, 1024 tokens, nesting depth 64 (parentheses plus pending unary minus), 500 digits per literal, claim or reduced intermediate value; over a limit is limit_exceeded.

## Input

- `expression` (string, required): min length 1
- `claimed_value` (string, required): pattern `^-?(0|[1-9][0-9]*)(/[1-9][0-9]*)?$`
- `require_canonical` (boolean, required)

## Output

- `valid` (boolean, required)
- `reason` (one of null, "division_by_zero", "value_mismatch", "not_canonical", required)
- `value` (string or null, required): pattern `^-?(0|[1-9][0-9]*)(/[1-9][0-9]*)?$`
- `first_discrepancy` (object or null, required)
- `reference_version` (constant "ISO/IEC 10967-2:2001 (LIA-2) exact-result terminology; exact arithmetic over the rationals with canonical reduced form; RFC 8259 sec. 6 integer grammar and sec. 7 strings", required)

## Limits

- max expression bytes: 4096
- max tokens: 1024
- max depth: 64
- max value digits: 500

## Example

Request input:

```json
{
  "expression": "1 + 1/2 + 1/3 + 1/4",
  "claimed_value": "25/12",
  "require_canonical": true
}
```

Response:

```json
{
  "result": {
    "valid": true,
    "reason": null,
    "value": "25/12",
    "first_discrepancy": null,
    "reference_version": "ISO/IEC 10967-2:2001 (LIA-2) exact-result terminology; exact arithmetic over the rationals with canonical reduced form; RFC 8259 sec. 6 integer grammar and sec. 7 strings"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "rational-expression-check",
  "version": "1.0.0",
  "input": {
    "expression": "1 + 1/2 + 1/3 + 1/4",
    "claimed_value": "25/12",
    "require_canonical": true
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/rational-expression-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"expression":"1 + 1/2 + 1/3 + 1/4","claimed_value":"25/12","require_canonical":true}'
```

The machine-readable contract is at [/v1/tools/rational-expression-check/versions/1.0.0](/v1/tools/rational-expression-check/versions/1.0.0).

### CLI

```sh
node cli.mjs run rational-expression-check 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Lp primal feasibility check](/tools/lp-primal-feasibility-check): Check that a claimed LP point satisfies x >= 0 and Ax <= b exactly; report the first violated bound or row.
- [Rational equation check](/tools/rational-equation-check): Check a chained claim like 1/2 + 1/3 = 5/6 < 1 exactly; returns the first false relation or division by zero.
- [Rational trace check](/tools/rational-trace-check): Check a step-by-step rational calculation trace; reports the first step whose operand, operator or result disagrees.
- [Linear residual check](/tools/linear-residual-check): Check a claimed residual r = b - A x (per component and/or its max norm) exactly for an approximate solution x.
- [Chi square decomposition check](/tools/chi-square-decomposition-check): Check a claimed Pearson chi-square, its per-cell (O-E)^2/E terms and df exactly; returns the first wrong term.
- [Maximum flow certificate check](/tools/maximum-flow-certificate-check): Check a claimed max flow with a min-cut certificate or residual search; reports the first failure or augmenting path.