{"uid":"cap_oAZFlXVspHeSSl4ft6OT4","slug":"numora-calculus-jacobian-matrix-api-ea0fe69a","name":"Numora Calculus Jacobian Matrix API","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://numormor.netlify.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":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":{"p10Cents":"10.0000","medianCents":"10.0000","p90Cents":"10.0000","minCents":"10.0000","maxCents":"10.0000","p95Cents":"10.0000","sampleCount":1,"varies":false,"failureChargeRate":1},"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_xhRCqHYUu-3Gov8B-OKnn","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the Jacobian matrix of a vector-valued function evaluated at a given point","exampleAgentPrompt":"Compute the Jacobian matrix for the vector function [x*y, x^2 + y, sin(x)*z] evaluated at the point [1, 2, 3].","exampleUseCases":null,"resultDescription":"Returns a JSON object with 'success' (true), 'result' containing the Jacobian matrix (a 2D array of partial derivatives evaluated at the given point), and 'computation' providing a human-readable description of what was computed.","failureModes":["Invalid or non-parseable function expressions in 'fns' array — returns error","Mismatched dimensions between functions and point coordinates","Point array contains non-numeric values — parsing error","Singular or undefined partial derivatives at the given point (e.g. division by zero)","Payment not provided or insufficient — x402 payment required","Malformed JSON body — 400 bad request"],"whenToPreferThis":"Choose this endpoint when you need a pure server-side computation of a Jacobian matrix with no external library dependencies, especially when the computation needs to be performed programmatically by an AI agent using micropayments. Ideal for robotics, optimization, numerical methods, or coordinate transformations where you need the full matrix of first-order partial derivatives. Prefer over symbolic math tools when you need a numeric result at a specific point quickly.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T00:51:13.345Z","isFirstParty":false}