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Rational Lie Bracket Universal Enveloping Algebra PBW Normal Form Verifier
x402
Rational Lie Bracket Universal Enveloping Algebra PBW Normal Form 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 the ordered-monomial (PBW basis) coefficients of a universal enveloping algebra expression against an explicitly supplied Lie bracket tensor.
Price / call$0.003
Success—
StatusUnknown
How this service works
Verify every ordered-monomial coefficient of a supplied enveloping-algebra expression under an explicit Lie bracket tensor.
Output
Returns a verification result indicating whether each ordered-monomial (PBW basis) coefficient in the supplied universal enveloping algebra expression is correct under the given Lie bracket tensor, flagging any coefficient mismatches or ordering violations.
Example use cases
PBW coefficient correctness check
“I have a universal enveloping algebra expression with monomials: word [0,1] coefficient 2, word [1,2] coefficient -1, word [2] coefficient 4. My Lie bracket tensor is [[[1,-1],[0,1]]]. Can you verify that all these PBW ordered-monomial coefficients are correct?”
Automated Lie algebra homework checker
“I'm building a tool to check student answers in a Lie theory course. Here are the student's claimed PBW terms — word [0,1,2] with coefficient 3 and word [1] with coefficient -2 — along with the bracket tensor [[[0,1,0],[1,0,0]]]. Please check if the claim is valid.”
Symbolic algebra system validation
“My symbolic algebra pipeline produced a PBW normal form for a rank-2 Lie algebra with brackets [[[1,0],[0,-1]]] and terms: word [0,0,1] coefficient 7, word [1,2] coefficient -4. Verify whether these ordered-monomial coefficients are consistent with the given bracket structure.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-REST-B20/rational-lie-bracket-universal-enveloping-pbw-normal-form?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need to programmatically verify the mathematical correctness of a PBW (Poincaré–Birkhoff–Witt) normal form expansion in a universal enveloping algebra given an explicit Lie bracket tensor — particularly useful for automated algebra checkers, symbolic computation pipelines, or educational tools that need ground-truth validation of Lie-theoretic calculations.
Side effects
- Invalid bracket tensor dimensions (exceeds 3×8×8 shape)
- Word indices out of range (must be 0–255)
- Coefficients out of supported range (-100 to 100)
- Too many terms supplied (max 40)
- Malformed or missing 'pbw' artifact object
- Claim field inconsistent with data, causing validation rejection
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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