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Numora Calculus — Jacobian Matrix Computation
x402
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
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 '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.
Example use cases
Robotics inverse kinematics Jacobian
“Calculate the Jacobian of these joint-space to task-space mapping functions [l1*cos(q1)+l2*cos(q1+q2), l1*sin(q1)+l2*sin(q1+q2)] at the joint angles [0.5, 1.0] so I can use it for velocity control.”
Nonlinear system sensitivity analysis
“I need the Jacobian matrix of this system of equations [x^2 - y, x*y - z, z^2 - x] evaluated at the point [1, 1, 1] to analyze local behavior near that equilibrium.”
Neural network gradient checking
“Can you compute the Jacobian of these two output functions [w1*x1 + w2*x2, w1*x2 - w2*x1] at point [2, 3] so I can verify my manually computed partial derivatives?”
Technical details
Endpoint
POSThttps://numomo.vercel.app/api/calculus/jacobianWhen to prefer
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.
Side effects
- 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
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| fnsrequired | array | |
| 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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