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Bracketed Polynomial Root Finder
x402
Bracketed Polynomial Root Finder is a paid API for AI agents from www.mahastrategies.com, paid per call via x402, $0.009/call, status unknown (last checked 2026-09-14).
Bisects a sign-changing rational bracket for a polynomial of degree 1–8 to certify a root bracket or exact rational root within up to 64 iterations.
Price / call$0.009
Success—
StatusUnknown
How this service works
Get a checked rational bracket for a degree 1-8 polynomial root. Bisect a sign-changing rational bracket for at most 64 iterations; return a certified bracket or exact rational root. No arbitrary code, all-roots or uniqueness claim.
Output
Returns a JSON object containing the certified bracket or exact rational root, the offer ID, version string, input and receipt digests, amount in base units, and an array of boundary points accumulated during bisection — providing an auditable, certified numerical result.
Example use cases
Certify cubic polynomial zero
“I have the cubic polynomial with ascending coefficients [-2, 0, 1, 1] and I know there's a sign change between x = 0 and x = 2. Can you bisect it with a tolerance of 1e-10 and up to 50 iterations to give me a certified root bracket?”
Isolate quadratic root interval
“For the quadratic polynomial with coefficients [6, -5, 1] (ascending), find a certified bracket or exact rational root between lower bound 2 and upper bound 4, tolerance 1e-8, max 32 iterations.”
Numerical root for engineering model
“I need to verify the zero-crossing of a degree-5 polynomial with ascending coefficients [-1, 3, -2, 0, 1, -1] that I know falls between 0.5 and 1.5. Please run up to 64 bisection iterations with a tolerance of 0.000001 and return a certified bracket.”
Technical details
Endpoint
POSThttps://www.mahastrategies.com/api/v1/micro/bracketed-polynomial-rootWhen to prefer
Choose this endpoint when you need a numerically certified, audit-traceable root bracket for a univariate polynomial of degree 1–8, and you have a known sign-changing interval. It is ideal for deterministic, reproducible numerical results with rational arithmetic guarantees — not for finding all roots, roots of higher-degree polynomials, or complex roots. Prefer it over general-purpose computer algebra systems when certified bracketing and receipt-level auditability matter.
Side effects
- No sign change detected between lower and upper bounds — bisection cannot proceed
- Polynomial degree exceeds 8 (more than 9 coefficients) — rejected
- Max iterations exceeds 64 — rejected by schema validation
- Tolerance or bound values malformed or too long (>21 chars) — schema rejection
- Lower bound equals upper bound — degenerate bracket
- Payment failure via x402 protocol — call not executed
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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