Dom::Tropical --
tropical semiring
IntroductionDom::Tropical creates a domain for the tropical semiring.
DetailsDom::Tropical(n) represents the tropical constant n
if n is a positive integer, or ∞ if n is infinity.
Creating Elements
Dom::Tropical(n)
Parametersn | - | integer or infinity. |
Cat::SemiRing
Related Domainsthe tropical constant infinity.
the tropical constant 0.
_plus(dom a1...)a1+a2+...+ak of tropicals is defined to be the smallest
of positive integers or infinity a1,a2,...,ak._plus.
_mult(dom a1...)a1*a2*...*ak of tropicals is defined to be
a1+a2+...+ak._mult.
_power(dom a,Dom::Integer n)a^n of the tropical a._power.
expr(dom a)a.
Example 1This example shows the idempotency of the tropical semiring:
>> T:=Dom::Tropical:
>> T(infinity) + T(infinity);
T(3) + T(3)
infinity
3
>> T(6) + T(infinity);
T(6) + T(3);
T(6)*T(infinity);
T(6)*T(3)
6
3
infinity
9
Super-DomainAx::canonicalRep, Ax::normalRep
Dom::Tropical is a new function
MuPAD Combinat, an open source algebraic combinatorics package