{"uid":"cap_w3YgI6MPnPzHda3YrE9JB","slug":"numora-calculus-gradient-api-47433b20","name":"Numora Calculus Gradient 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://numormo.vercel.app/api/calculus/gradient","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_74FxTlMgDyDknKmodUBX_","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 numerical gradient (vector of partial derivatives) of a multivariable function at a specified point","exampleAgentPrompt":"Compute the gradient of the function 'x^2 + y^2 + z^2' at the point [1, 2, 3] using Numora's calculus API.","exampleUseCases":[{"title":"Gradient descent step direction","prompt":"I'm implementing gradient descent by hand — can you compute the gradient of 'x^2 + 3*y^2 - x*y' at the point [2, 1] so I know which direction to step?"},{"title":"Steepest ascent on terrain model","prompt":"I have a surface defined by 'sin(x)*cos(y)' and I need to know the gradient at the point [0.5, 1.0] to find the steepest uphill direction."},{"title":"Sensitivity analysis for engineering","prompt":"What are the partial derivatives of the function '2*x^3 + y*z - z^2' evaluated at [1, 4, 2]? I need them for a sensitivity analysis."}],"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the gradient vector (array of partial derivatives, one per dimension matching the input point), and a 'computation' string describing what was calculated in human-readable form.","failureModes":["Malformed or unparseable function string — returns error indicating invalid expression","Point array dimension mismatch or empty array — validation error","Division by zero or mathematical singularity at evaluation point — numerical error returned","Unsupported mathematical operators or functions in the expression string","Network timeout on Vercel serverless cold start"],"whenToPreferThis":"Choose this endpoint when you need fast, dependency-free numerical gradient computation for any scalar multivariable function without setting up a local math library. Ideal for AI agents performing optimization steps, sensitivity analysis, or scientific computing tasks that require directional derivative information at a specific coordinate. Prefer over symbolic CAS tools when exact symbolic derivatives are not required and numerical approximation suffices.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:57:10.651Z","isFirstParty":false}