{"uid":"cap_Qcm0p3kMwvSZOhABRy5qK","slug":"numora-hessian-matrix-computation-840102a4","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://numormor.netlify.app/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":{"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_Rwc8kgjZY5aFT-ajRTuS_","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 Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a specified point","exampleAgentPrompt":"Can you compute the Hessian matrix of f(x,y) = x^2 + 3*x*y + y^3 at the point [1, 2]?","exampleUseCases":null,"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the Hessian matrix (an n×n matrix of second-order partial derivatives evaluated at the given point), and a 'computation' string with a human-readable description of what was calculated.","failureModes":["Invalid or unparseable function expression — returns error if 'fn' cannot be parsed","Point array dimension mismatch with the number of variables in the function","Non-numeric values in the point array","Payment not included or invalid x402 micropayment header — returns 402 Payment Required","Division by zero or undefined value at the specified evaluation point"],"whenToPreferThis":"Use this endpoint when you need the Hessian matrix for optimization tasks (e.g., Newton's method, checking second-order conditions for local minima/maxima), curvature analysis, or any calculus workflow requiring second-order partial derivatives — all without external library dependencies, paid per-call via x402 micropayments on Base.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T06:49:54.779Z","isFirstParty":false}