{"uid":"cap_GKsLx189isLlRPQzpbUHA","slug":"numora-hessian-matrix-calculator-d515ea65","name":"Numora Hessian Matrix Calculator","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://numormo.vercel.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":"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_0w7PqZe_1QLtEsclgFyli","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 Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a specified point","exampleAgentPrompt":"Compute the Hessian matrix of f(x,y) = x^3 + y^3 - 3*x*y at the point [1, 1].","exampleUseCases":[{"title":"Optimization critical point classification","prompt":"I have a function f(x,y) = x^2 + 4*y^2 - x*y and I found a critical point at [0, 0] — can you compute the Hessian matrix there so I can determine if it's a local minimum, maximum, or saddle point?"},{"title":"Convexity check for ML loss surface","prompt":"Compute the Hessian of f(x,y,z) = x^2 + y^2 + z^2 + x*y at the point [1, 2, 3] so I can check whether the loss surface is convex at that location."},{"title":"Curvature analysis for physics simulation","prompt":"I need the Hessian matrix for f(x,y) = sin(x)*cos(y) evaluated at [0, 0] to understand the local curvature of the potential energy surface."}],"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the Hessian matrix (as a 2D array of second-order partial derivatives), and a 'computation' string with a human-readable description of what was computed. The matrix entry H[i][j] corresponds to the mixed partial derivative ∂²f/∂xᵢ∂xⱼ evaluated at the given point.","failureModes":["Invalid or unparseable function expression in 'fn' field — returns error with parsing failure message","Point array dimension mismatch with function variables — matrix computation cannot proceed","Singular or undefined derivatives at the given point (e.g., discontinuities) — may return NaN or error","Malformed JSON input or missing required fields — returns 400-style error","Symbolic differentiation unsupported for certain exotic function forms — fallback to numerical approximation or error"],"whenToPreferThis":"Choose this endpoint when you need the exact Hessian matrix of a mathematical function at a specific point for optimization analysis, convexity checking, or curvature evaluation. Prefer this over general-purpose symbolic math systems when you want a lightweight, zero-dependency, paid-per-call API on Base via x402 micropayments. Ideal for AI agents embedded in optimization pipelines, ML training diagnostics, or physics simulations that need reliable second-derivative computation without spinning up a full computer algebra system.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:52:26.387Z","isFirstParty":false}