# Numora Calculus Jacobian Matrix API

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

Computes the Jacobian matrix of a vector-valued function evaluated at a given point

## Facts

- Endpoint: POST https://numormor.netlify.app/api/calculus/jacobian
- 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-jacobian-matrix-api-ea0fe69a
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_oAZFlXVspHeSSl4ft6OT4

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-jacobian-matrix-api-ea0fe69a -d '<json body>'
```

Example prompt: Compute the Jacobian matrix for the vector function [x*y, x^2 + y, sin(x)*z] evaluated at the point [1, 2, 3].

## When to prefer this

Choose this endpoint when you need a pure server-side computation of a Jacobian matrix with no external library dependencies, especially when the computation needs to be performed programmatically by an AI agent using micropayments. Ideal for robotics, optimization, numerical methods, or coordinate transformations where you need the full matrix of first-order partial derivatives. Prefer over symbolic math tools when you need a numeric result at a specific point quickly.

## Known failure modes

- Invalid or non-parseable function expressions in 'fns' array — returns error
- Mismatched dimensions between functions and point coordinates
- Point array contains non-numeric values — parsing error
- Singular or undefined partial derivatives at the given point (e.g. division by zero)
- Payment not provided or insufficient — x402 payment required
- Malformed JSON body — 400 bad request

## 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 'success' (true), 'result' containing the Jacobian matrix (a 2D array of partial derivatives evaluated at the given point), and 'computation' providing a human-readable description of what was computed.

## Request schema (JSON Schema)

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

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