# Numora Calculus Gradient API

> Numora Calculus Gradient API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

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

## Facts

- Endpoint: POST https://numormo.vercel.app/api/calculus/gradient
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-gradient-api-47433b20
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_w3YgI6MPnPzHda3YrE9JB

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-47433b20 -d '<json body>'
```

Example prompt: Compute the gradient of the function 'x^2 + y^2 + z^2' at the point [1, 2, 3] using Numora's calculus API.

## When to prefer this

Choose this endpoint when you need fast, dependency-free numerical gradient computation for any scalar multivariable function without setting up a local math library. Ideal for AI agents performing optimization steps, sensitivity analysis, or scientific computing tasks that require directional derivative information at a specific coordinate. Prefer over symbolic CAS tools when exact symbolic derivatives are not required and numerical approximation suffices.

## Known failure modes

- Malformed or unparseable function string — returns error indicating invalid expression
- Point array dimension mismatch or empty array — validation error
- Division by zero or mathematical singularity at evaluation point — numerical error returned
- Unsupported mathematical operators or functions in the expression string
- Network timeout on Vercel serverless cold start

## 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 derivatives, one per dimension matching the input point), and a 'computation' string describing what was calculated in human-readable form.

## 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-47433b20/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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