{"uid":"cap_2m-RFRHwQA_M9jqSu2eUH","slug":"numora-hessian-matrix-computation-a1874f15","name":"Numora Hessian 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://numorapoi.orbonomy.xyz/api/calculus/hessian","method":"POST","headers":{},"bodySchema":{"type":"object","required":["fn","point"],"properties":{"fn":{"type":"string"},"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":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.04/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.04","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.04","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_luyVCOlYDfn2jbe_yRwNl","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.04","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a given point","exampleAgentPrompt":"Compute the Hessian matrix of f(x, y) = x^3 + y^3 - 3*x*y at the point [1, 1] so I can determine the nature of the critical point there.","exampleUseCases":null,"resultDescription":"Returns a JSON object with success=true, the Hessian matrix as a 2D array in 'result', and a human-readable 'computation' string describing what was computed — e.g. the n×n matrix of all second-order partial derivatives evaluated at the given point.","failureModes":["Invalid or unparseable function expression returns an error","Point array dimension mismatch with number of variables in function","Non-differentiable function at the given point causes computation failure","Malformed input JSON or missing required fields returns 400-level error","Payment not completed via x402 micropayment returns 402 Payment Required"],"whenToPreferThis":"Use this endpoint when you need pure server-side symbolic or numerical computation of the Hessian matrix with no external dependencies — ideal for optimization tasks, convexity analysis, Newton's method steps, or saddle point detection where you need the full matrix of second partial derivatives at a specific point. Prefer this over general-purpose math libraries when you need a lightweight, stateless API call paid per-use via USDC micropayment.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:04:18.031Z","isFirstParty":false}