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Dom::Tropical -- tropical semiring

Introduction

Dom::Tropical creates a domain for the tropical semiring.

Details

Creating Elements


Dom::Tropical(n)

Parameters

n- integer or infinity.

Categories

Cat::SemiRing

Related Domains

Dom::Boolean

Entries

zero

the tropical constant infinity.

one

the tropical constant 0.

Method _plus: sum of tropicals

Method _mult: product of tropicals

Method _power: power of a tropical

Method expr: convert a tropical into an integer or infinity.

Example 1

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
        

Super-Domain

Dom::BaseDomain

Axioms

Ax::canonicalRep, Ax::normalRep

Changes

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