# Numora Calculus Gradient API

> Numora Calculus Gradient API is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

Computes the numerical gradient (vector of partial derivatives) of a multivariable function at a specified point

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/gradient
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-gradient-api-7b9f10e1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Vf03SyVSTWHoAgxYFHX_G

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-gradient-api-7b9f10e1 -d '<json body>'
```

Example prompt: Can you compute the gradient of the function x^2 + y^2 + z^2 at the point [1, 2, 3]?

## When to prefer this

Choose this endpoint when you need a reliable, zero-dependency numerical gradient computation for any multivariable scalar function without setting up a local math library. Ideal for AI agents performing optimization, sensitivity analysis, or calculus steps on the fly. Prefer over symbolic differentiation services when speed and simplicity matter more than exact closed-form results, and when the function is complex or numerically defined.

## Known failure modes

- Invalid or unparseable function expression string returns an error
- Point array dimension mismatch with the function's variables causes failure
- Division by zero or undefined values at the evaluation point
- Malformed JSON body or missing required fields 'fn' or 'point'
- Payment failure via x402 micropayment if insufficient USDC balance

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a 'success' boolean, a 'result' object containing the gradient vector (array of partial derivative values, one per input dimension), and a 'computation' string describing in human-readable terms what was calculated.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "point"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "point": {
   "type": "array"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-gradient-api-7b9f10e1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)