Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Lexicographic order on exponent tuples and the multidegree of a nonzero polynomial
Definition
For , write when, at the first coordinate where they differ, the coordinate of is larger. This is the lexicographic order.
If , its leading multidegree is the lexicographically greatest exponent tuple for which ; the corresponding monomial and coefficient are its leading monomial and leading coefficient. The maximum exists because a polynomial has finite support.
Depends on
Used by
- A fixed unbalanced one-variable substitution need not preserve lexicographic leading terms Counterexample
- The lexicographic reduction algorithm in three variables Example
- The leading multidegree of a symmetric polynomial is weakly decreasing Lemma
- The leading multidegree of e₁^b₁⋯ eₙ^bₙ is (b₁+⋯+bₙ,b₂+⋯+bₙ,…,bₙ) with coefficient one Lemma
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 8 results over 5 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- K. Conrad, Symmetric Polynomials, Sections 1-5 (standard reference, not scraped)