# Numora Calculus — Jacobian Matrix Computation

> Numora Calculus — Jacobian Matrix Computation is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-16).

Computes the Jacobian matrix of a vector-valued function at a specified point in n-dimensional space

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/jacobian
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-jacobian-matrix-computation-016460c8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_2XiS7jPoy_M3PCxvE3ce4

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-computation-016460c8 -d '<json body>'
```

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

## When to prefer this

Choose this endpoint when you need exact or numerical Jacobian matrices for vector-valued functions in scientific, engineering, or optimization contexts. Ideal for robotics, nonlinear systems analysis, optimization algorithms (Newton's method, Levenberg-Marquardt), and any scenario requiring a matrix of first-order partial derivatives. Prefer this over symbolic math libraries when you need a lightweight, dependency-free API call without setting up a local CAS environment.

## Known failure modes

- Invalid or non-parseable function expressions in fns array — returns error
- Point array dimension mismatch with number of variables in functions
- Division by zero or singularity at the evaluation point
- Non-numeric values in the point array
- Unsupported function syntax or operators
- Payment failure via x402 micropayment — returns 402 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 a 'result' containing the Jacobian matrix (2D array of partial derivatives), a 'success' boolean flag, and a 'computation' string describing what was computed in human-readable form.

## 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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