# Numora Jacobian Matrix Computation

> Numora Jacobian Matrix Computation is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-15).

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

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/jacobian
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-jacobian-matrix-computation-0ab5dff0
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_J71RljeafD9PxvCItGEyN

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-jacobian-matrix-computation-0ab5dff0 -d '<json body>'
```

Example prompt: Compute the Jacobian matrix for these two functions — f1 = x^2 + y, f2 = sin(x) + y^2 — evaluated at the point (1, 2).

## When to prefer this

Use this endpoint when you need a pure server-side numerical or symbolic Jacobian matrix computation without setting up a local math library. Ideal for AI agents performing optimization, sensitivity analysis, or Newton-method iterations where no local compute environment is available.

## Known failure modes

- Invalid function expressions in fns array result in parse or evaluation error
- Point array dimension mismatch with number of functions causes computation failure
- Non-numeric values in point array return validation error
- Empty fns or point arrays return required field error
- Payment failure via x402 returns 402 status before computation

## 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 status, the Jacobian matrix (2D array of partial derivatives evaluated at the given point), and 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

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-jacobian-matrix-computation-0ab5dff0/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)