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Rational Polynomial Complete Squarefree Multiplicity Decomposition Verifier
x402
Rational Polynomial Complete Squarefree Multiplicity Decomposition Verifier is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Verifies every monic squarefree multiplicity block and leading coefficient of a supplied rational polynomial decomposition.
Price / call$0.003
Success—
StatusUnknown
How this service works
Verify every monic squarefree multiplicity block and leading coefficient of a supplied rational polynomial.
Output
The endpoint returns a verification result indicating whether the claimed squarefree multiplicity blocks, their multiplicities, and the leading coefficient of the supplied rational polynomial are all correct and consistent with the mathematical definition of a complete squarefree decomposition.
Example use cases
CAS output validation for symbolic solver
“My computer algebra system says the polynomial [1, 0, -5, 0, 4] has a certain squarefree decomposition — can you verify that the monic squarefree multiplicity blocks and leading coefficients it claims are actually correct?”
Automated algebra homework checker
“I need to check whether a student's claimed squarefree factorization of the polynomial [1, -6, 11, -6] is valid — verify the multiplicity structure and leading coefficients for me.”
Polynomial preprocessing pipeline audit
“Before I feed this polynomial [2, -4, 2] into my numerical solver, can you confirm that its squarefree decomposition claim — the blocks, multiplicities, and leading coefficient — all check out?”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-REST-B15/rational-polynomial-complete-squarefree-multiplicity-decomposition?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need automated, authoritative verification of a rational polynomial's squarefree multiplicity decomposition, particularly when checking CAS outputs, validating student work, or auditing intermediate results in a symbolic computation pipeline. It is specifically suited for cases where you have a polynomial and a claimed squarefree decomposition and need to confirm correctness of each multiplicity block and leading coefficient.
Side effects
- Polynomial coefficients outside allowed range (-100 to 100 integers) return a validation error
- Polynomial array exceeds maximum item count (13) returns rejection
- Malformed or missing squarefree claim object causes request failure
- Empty polynomial array (fewer than 1 item) is rejected
- Inconsistent claim data that cannot be parsed may return an error response
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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