{"uid":"cap_XTyG-aHrBLrU3mPHWRrGe","slug":"numora-calculus-gradient-api-8be1f6a8","name":"Numora Calculus Gradient Endpoint","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/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":"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_vFrKa6TqgQrLRIZYPjMYm","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 numerical gradient (vector of partial derivatives) of a multivariable function at a given point","exampleAgentPrompt":"Can you compute the gradient of f(x, y) = x^2 + 3*x*y + y^3 at the point [1.0, 2.0]?","exampleUseCases":[{"title":"Optimize pricing strategy with gradient analysis","prompt":"I need to find the direction of steepest increase for our revenue function R(price, volume) = price * volume * (1 - 0.01*price) at our current operating point of price=50 and volume=1000. What's the gradient telling us?"},{"title":"Machine learning model parameter tuning","prompt":"Help me compute the gradient of our loss function L(w1, w2) = (w1*x - w2*y)^2 at the current weights w1=0.5 and w2=0.3. I need to know which direction to adjust the weights for the steepest descent."},{"title":"Physics simulation obstacle avoidance","prompt":"Can you calculate the gradient vector of our potential field function U(x, y) = exp(-(x^2 + y^2)) at the agent's current position [2.5, 1.8]? I need to know the direction of steepest ascent to navigate away from obstacles."}],"resultDescription":"Returns a JSON object with a 'result' containing the gradient vector (array of partial derivative values), a 'success' boolean, and a 'computation' string describing what was computed in human-readable form.","failureModes":["Malformed function string causes parse error — returns error response","Point array dimension mismatch with number of variables in fn — may return NaN or error","Division by zero or singularity in function at evaluation point — undefined result","Non-numeric values in point array — validation error","Unsupported mathematical syntax in fn string — parse or evaluation error"],"whenToPreferThis":"Choose this endpoint when you need a pure serverless numerical gradient computation with no external library dependencies, billed per-call via x402 micropayments. Ideal for AI agents needing on-demand calculus without spinning up a compute environment. Best for single-point gradient queries rather than batch or symbolic differentiation.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:07:10.764Z","isFirstParty":false}