trop specification
canonical reference for tropical semiring arithmetic: the (min, +) semiring, its matrix algebra, and dual certificate verification.
spec pages
| page |
defines |
| semiring |
tropical semiring axioms, (min, +) definition, identity elements, idempotency |
| matrix |
tropical matrix multiplication, power, eigenvalue, determinant, rank |
| kleene |
Kleene star (tropical closure), A* = I ⊕ A ⊕ ... ⊕ A^(n-1) |
| eigenvalue |
tropical eigenvalue, critical cycle, Karp's characterization |
| determinant |
tropical determinant, optimal assignment value, tropical rank |
| dual |
(max, +) dual semiring, negation duality |
| verification |
LP duality certificates for optimality proofs over F_p |
| encoding |
F_p ↔ tropical element conversion, +∞ sentinel, matrix serialization |
| vectors |
known-answer test values, edge cases |
design boundary
trop defines arithmetic. algorithms that use trop arithmetic (Dijkstra, Hungarian, Viterbi, Sinkhorn) are programs that execute on nox with optional jet acceleration. this separation mirrors nebu: nebu defines field ops, not FFT — NTT is a nox program that calls nebu arithmetic.
see also
- nebu — Goldilocks field (verification backbone)
- nox — VM (tropical algorithms execute as nox programs)
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