{"uid":"cap_D91mIo23Ip9Sc53kgxUjx","slug":"rational-polynomial-complete-squarefree-multiplicity-decomposition-d21fc8d1","name":"Rational Polynomial Complete Squarefree Multiplicity Decomposition Verifier","description":"Verify every monic squarefree multiplicity block and leading coefficient of a supplied rational polynomial.","url":"https://detect.halowerk.com/v1/F-REST-B15/rational-polynomial-complete-squarefree-multiplicity-decomposition?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["squarefree"],"properties":{"squarefree":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["polynomial"],"properties":{"polynomial":{"type":"array","items":{"anyOf":[{"type":"integer","maximum":100,"minimum":-100},{"type":"string","maxLength":2048}]},"maxItems":13,"minItems":1}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","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":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_m0LOqI0wm73fYrHQS-AMX","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Verifies every monic squarefree multiplicity block and leading coefficient of a supplied rational polynomial decomposition.","exampleAgentPrompt":"Can you verify the squarefree multiplicity decomposition and leading coefficients of this polynomial — the coefficients are [1, -3, 3, -1] — and confirm whether the claimed squarefree blocks and their multiplicities are all correct?","exampleUseCases":[{"title":"CAS output validation for symbolic solver","prompt":"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?"},{"title":"Automated algebra homework checker","prompt":"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."},{"title":"Polynomial preprocessing pipeline audit","prompt":"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?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:37:40.463Z","isFirstParty":false,"canonicalSlug":"rational-polynomial-complete-squarefree-multiplicity-decomposition-d21fc8d1"}