Tropical Algebra (MinPlus/MaxPlus)

Questions
1

Hi, my first question is on how to make tropical calculations on Mathematica, like tropical matrix addition, multiplication, powers and so on.
for instance, if A,B are tropical matrices, compute
A⊕B, A⊗B, A^⊗B
Secondly, If A,B and U are given matrices, how can i solve the system of equations below for x and y;
ax=xa,
by=yb,
u=xy.
Thank you.

2

Hi there,

this might be some definitions that could help:

x_\[CirclePlus]y_ := Max[x, y]
x_\[CircleTimes]y_ := x + y
mplus[x_, y_] := MapThread[Max, {x, y}]
mtimes[x_, y_] := Inner[Plus, x, y, Max] 
scalarplus[x_, y_] := Outer[Max, {x}, y]

see also max plus on Community

Cheers,
Marco

3

Crossposted here.

4

Thank so much Mr. Marco for your help.

5

Thank you so much, Mr. Rohit.