math.polynomial.roots

Three distinct suites: educational examples on the calculator page, this legacy regression count (21/21 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.2.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-28.metric-scope-v3. Calculation version 1.2.2. CVP 1.0.0-proposed. 67/67 golden · 3/3 CVP boundary · 34/34 invalid · 3/3 property · 2/2 metamorphic · 95/95 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest eca488fa2ce7. 67 listed independent full-pack vectors only

• Golden (oracle-backed) 67 / 67
• CVP boundary 3 / 3
• Invalid input 34 / 34
• Property 3 / 3
• Metamorphic 2 / 2
• Cross-interface 95 / 95
• Cross-calculator 1 / 1
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 28/28 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope all published methods
• Assurance Core

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:3abd0fcd292b44b441ce3ee81bf5a4c08088ba45a935f040daba543514e46afd

Input schema sha256:59ff6f0d9c8221359f8e7b8b047f2641a66de48e301090643cbbbc0ec64b21d3 · Output schema sha256:adde668f2cd7988cb2e3c5cc4469cdf4b0fec92d089c6cccae78fe663b741568 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

polynomial-roots

Engine

polynomial-roots

Engine build

2026-10-27

Evidence core

2026-10-27T09:16:21.351Z

Rendered

2026-10-29T17:04:55.776Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of p (markers are published real roots on y=0; complex roots stay off the real plane). Same Horner nesting as REST/MCP. Curve samples are not a REST field.
• Real coefficients
• Leading coefficient nonzero
• Degree ≤ 8
• Not a second quadratic page
• Not Ferrari quartic
• Not CAS factoring

Limitations

• Finite real constant-first coefficients,degree1–8,leadingnonzero. Arrayorcomma/semicolon/space-separated text;numeric tokens≤512chars,totaltext≤4608. Strict decimal/scientific;nonzero text→zero rejectsNUMERIC_UNDERFLOW;unknown/conflicting aliases andinapplicablex reject. Cubic a,b,c,d forms mustagreewithcoefficients;b/c/d omitteddefaultzero.
• all_roots acceptsall/roots/durand_kerner/durand/weierstrass/dk aliases;cardano accepts cubic/cubic_equation/cubic_formula;evaluate accepts eval/horner/polynomial_evaluate/polynomial_evaluation. Method/mode aliases agree;case/space/hyphennormalized. Presetpages locktheir method.
• Exact acceptedbinary64 rational arithmetic bounded16384bits;Horner projects once. Exact GCD square-free decomposition preservesmultiplicity. Stablequadratic/Cardano orscaledDK withtwo2048iterationattempts;exactSturm classifiesrealroots (512levels/4096steps).
• Every square-free rootset mustpass exactrational Weierstrass/Gershgorin diskdisjointness and2e-10relativeL1 inclusion-error budget,plusnormalizedL1residual≤2e-12. Unresolved/overlappingdisks,reals oriteration failNON_CONVERGENCE;normalizationrange losescoefficient→NUMERICAL_RANGE_ERROR;unrepresentable root/value rejects RESULT_OVERFLOW/UNDERFLOW. Not a universalfinite-input success guarantee.
• residual_max isunscaled Euclidean |p(z)|max,nullablewhenoutside finitebinary64;normalized_residual ismax (|Re p|+|Im p|)/sum |ci|(|re|+|im|)^i roundedbinary64. A zero displayedresidual isnot proof ofexactroots. Cubic delta usesexactdepresseddiscriminant sign,cubic_case true evenwhendelta isnull on range.
• Independent Fraction-factor/Decimal250/750 fixedvectors checkcomplete multisets inclmultiplicity with4e-10relativeL2+2subnormalquanta;zero roots exact,Horner≤1ULP. IndependentPython recomputesdiagnosticsfromreturnedroots. No whole-domain orcross-runtime bitwiseguarantee;nearclustersandcoeffperturbations areillconditioned.
• Display never snapsnonzero roots/coefficients. Real curve usesexactHorner;complexroots arelistedoffrealplane. Graphomittedwhenfinitecoordinates/labels cannotbedistinguished. NativeCSV/JSON preservefullpack/rawinputs. Typinglocal;sharedURLs andREST/MCP sendinputs andmayenterlogs.