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Numora Hessian Matrix Computation
x402
Numora Hessian 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 Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a specified point
Price / call$0.1
Success—
StatusUnknown
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, a result object containing the Hessian matrix (2D array of second-order partial derivatives evaluated at the given point), and a human-readable computation string describing what was computed.
Example use cases
Optimization critical point classification
“I have the function f(x,y) = x^3 - 3*x*y + y^3 and I found a critical point at [1, 1]. Can you compute the Hessian matrix there so I can determine if it's a local min, max, or saddle point?”
Convexity check for machine learning loss
“My loss function is f(w1,w2) = w1^2 + 4*w1*w2 + 2*w2^2. Can you compute the Hessian at [0, 0] so I can verify whether it's convex?”
Newton's method second-order step
“For Newton's method, I need the Hessian of f(x,y,z) = x^2 + y^2 + z^2 + x*y evaluated at the point [2, -1, 3].”
Technical details
Endpoint
POSThttps://numomo.vercel.app/api/calculus/hessianWhen to prefer
Choose this endpoint when you need the exact Hessian matrix of a multivariable scalar function at a specific point, especially for optimization (classifying critical points, Newton's method steps, convexity analysis). It runs with zero external dependencies and micropayment billing, making it ideal for agents that need on-demand calculus computation without provisioning a CAS (computer algebra system). Prefer it over general-purpose symbolic math APIs when you want a lightweight, pay-per-call solution focused purely on numerical/symbolic differentiation.
Side effects
- Invalid or unparseable function expression — returns error if fn string uses unsupported syntax
- Point array dimension mismatch with function variables — may return error or NaN entries
- Division by zero or undefined values at the evaluation point — may return Infinity or error
- Missing required fields fn or point — returns 400-level error
- Non-numeric values in point array — validation error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| fnrequired | string | |
| pointrequired | array |
Output
Schema · Response
| Field | Type | Description |
|---|---|---|
| resultrequired | object | Computation result varies by endpoint |
| successrequired | boolean | Always true on success |
| computationrequired | string | Human-readable description of what was computed |
Tags
x402
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