{"uid":"cap_bfiDh10TzRq0AITHu5B8k","slug":"numora-hessian-matrix-computation-77ed84f8","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://numomo.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_dgEd0uTTcKT_vCrt0Cvgn","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":"Can you compute the Hessian matrix of f(x,y) = x^2 + 3*x*y + y^3 at the point [1, 2]?","exampleUseCases":[{"title":"Optimization critical point classification","prompt":"I have the function f(x,y) = x^3 - 3*x*y + y^3 and I found a critical point at [1, 1]. Can you compute the Hessian matrix there so I can determine if it's a local min, max, or saddle point?"},{"title":"Convexity check for machine learning loss","prompt":"My loss function is f(w1,w2) = w1^2 + 4*w1*w2 + 2*w2^2. Can you compute the Hessian at [0, 0] so I can verify whether it's convex?"},{"title":"Newton's method second-order step","prompt":"For Newton's method, I need the Hessian of f(x,y,z) = x^2 + y^2 + z^2 + x*y evaluated at the point [2, -1, 3]."}],"resultDescription":"Returns a JSON object with success=true, a result object containing the Hessian matrix (2D array of second-order partial derivatives evaluated at the given point), and a human-readable computation string describing what was computed.","failureModes":["Invalid or unparseable function expression — returns error if fn string uses unsupported syntax","Point array dimension mismatch with function variables — may return error or NaN entries","Division by zero or undefined values at the evaluation point — may return Infinity or error","Missing required fields fn or point — returns 400-level error","Non-numeric values in point array — validation error"],"whenToPreferThis":"Choose this endpoint when you need the exact Hessian matrix of a multivariable scalar function at a specific point, especially for optimization (classifying critical points, Newton's method steps, convexity analysis). It runs with zero external dependencies and micropayment billing, making it ideal for agents that need on-demand calculus computation without provisioning a CAS (computer algebra system). Prefer it over general-purpose symbolic math APIs when you want a lightweight, pay-per-call solution focused purely on numerical/symbolic differentiation.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T00:53:10.492Z","isFirstParty":false}