# Numora Hessian Matrix Computation

> Numora Hessian Matrix Computation 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 Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a specified point

## Facts

- Endpoint: POST https://numormor.netlify.app/api/calculus/hessian
- 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-hessian-matrix-computation-840102a4
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Qcm0p3kMwvSZOhABRy5qK

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-hessian-matrix-computation-840102a4 -d '<json body>'
```

Example prompt: Can you compute the Hessian matrix of f(x,y) = x^2 + 3*x*y + y^3 at the point [1, 2]?

## When to prefer this

Use this endpoint when you need the Hessian matrix for optimization tasks (e.g., Newton's method, checking second-order conditions for local minima/maxima), curvature analysis, or any calculus workflow requiring second-order partial derivatives — all without external library dependencies, paid per-call via x402 micropayments on Base.

## Known failure modes

- Invalid or unparseable function expression — returns error if 'fn' cannot be parsed
- Point array dimension mismatch with the number of variables in the function
- Non-numeric values in the point array
- Payment not included or invalid x402 micropayment header — returns 402 Payment Required
- Division by zero or undefined value at the specified evaluation point

## 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 Hessian matrix (an n×n matrix of second-order partial derivatives evaluated at the given point), and a 'computation' string with a human-readable description of 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-hessian-matrix-computation-840102a4/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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