Dom::Tropical
--
tropical semiring
Dom::Tropical
creates a domain for the tropical semiring.
Dom::Tropical
(n)
represents the tropical constant n
if n is a positive integer, or ∞ if n is infinity.
Dom::Tropical
(n)
n | - | integer or infinity. |
Cat::SemiRing
the 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
.This 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
Ax::canonicalRep, Ax::normalRep
Dom::Tropical
is a new function
MuPAD Combinat, an open source algebraic combinatorics package