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Numora Hessian Matrix Calculator
x402
Numora Hessian Matrix Calculator is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).
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 a 'success' boolean, a 'result' object containing the Hessian matrix (as a 2D array of second-order partial derivatives), and a 'computation' string with a human-readable description of what was computed. The matrix entry H[i][j] corresponds to the mixed partial derivative ∂²f/∂xᵢ∂xⱼ evaluated at the given point.
Example use cases
Optimization critical point classification
“I have a function f(x,y) = x^2 + 4*y^2 - x*y and I found a critical point at [0, 0] — can you compute the Hessian matrix there so I can determine if it's a local minimum, maximum, or saddle point?”
Convexity check for ML loss surface
“Compute the Hessian of f(x,y,z) = x^2 + y^2 + z^2 + x*y at the point [1, 2, 3] so I can check whether the loss surface is convex at that location.”
Curvature analysis for physics simulation
“I need the Hessian matrix for f(x,y) = sin(x)*cos(y) evaluated at [0, 0] to understand the local curvature of the potential energy surface.”
Technical details
Endpoint
POSThttps://numormo.vercel.app/api/calculus/hessianWhen to prefer
Choose this endpoint when you need the exact Hessian matrix of a mathematical function at a specific point for optimization analysis, convexity checking, or curvature evaluation. Prefer this over general-purpose symbolic math systems when you want a lightweight, zero-dependency, paid-per-call API on Base via x402 micropayments. Ideal for AI agents embedded in optimization pipelines, ML training diagnostics, or physics simulations that need reliable second-derivative computation without spinning up a full computer algebra system.
Side effects
- Invalid or unparseable function expression in 'fn' field — returns error with parsing failure message
- Point array dimension mismatch with function variables — matrix computation cannot proceed
- Singular or undefined derivatives at the given point (e.g., discontinuities) — may return NaN or error
- Malformed JSON input or missing required fields — returns 400-style error
- Symbolic differentiation unsupported for certain exotic function forms — fallback to numerical approximation or 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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