{"uid":"cap_2XiS7jPoy_M3PCxvE3ce4","slug":"numora-calculus-jacobian-matrix-computation-016460c8","name":"Numora Calculus — Jacobian Matrix Computation","description":"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.","url":"https://numomo.vercel.app/api/calculus/jacobian","method":"POST","headers":{},"bodySchema":{"type":"object","required":["fns","point"],"properties":{"fns":{"type":"array"},"point":{"type":"array"}}},"responseSchema":{"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"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_D7jGXG5v0y0zufjTXraVU","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the Jacobian matrix of a vector-valued function at a specified point in n-dimensional space","exampleAgentPrompt":"Compute the Jacobian matrix of the vector function [x^2*y, sin(x)+y^2] at the point [1, 2].","exampleUseCases":[{"title":"Robotics inverse kinematics Jacobian","prompt":"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."},{"title":"Nonlinear system sensitivity analysis","prompt":"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."},{"title":"Neural network gradient checking","prompt":"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?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T00:52:53.416Z","isFirstParty":false}