in the MinPlus semiring if 
is a real number or real constant, or 
if 
is infinity.Dom::MinPlusSemiRing – MinPlus semi-ring
Dom::MinPlusSemiRing creates a domain for the MinPlus semiring.
Creating Elements
MinPlusSemiRing(x)
Parameters:
|
x: |
real number or infinity. |
Superdomain
Categories
Axioms
Ax::canonicalRep, Ax::normalRep
Related Domains:
Dom::MaxMinSemiRing, Dom::MaxPlusSemiRing, Dom::MinMaxSemiRing
Details:
The domain element Dom::MinPlusSemiRing(x) represents the constant in the MinPlus semiring if is a real number or real constant, or if is infinity.
Entries
|
"zero" |
the constant infinity. |
|
"one" |
the constant |
Mathematical Methods
_plus – sum of MinPlus
Dom::MinPlusSemiRing::_plus(dom 
, ...)
The sum 
is defined to be the smallest of real numbers 
.
This method overloads the function _plus.
_mult – product of MinPlus
Dom::MinPlusSemiRing::_mult(dom 
, ...)
The sum 
is defined to be 
.
This method overloads the function _mult.
_power – power of MinPlus
Dom::MinPlusSemiRing::_power(dom a, Dom::Integer n)
The nth power 
of the MinPlus scalar a.
This method overloads the function _power.
Conversion Methods
convert – conversion of an object into a MinPlus scalar
Dom::MinPlusSemiRing::convert(any x)
This method tries to convert x into a MinPlus scalar. This is only possible if x is a real number or infinity.
convert_to – conversion of a MinPlus scalar into another type
Dom::MinPlusSemiRing::convert_to(dom a, any T)
Tries to convert a into type T. Currently, only a conversion into a type of scalars.
expr – convert a MinPlus scalar into a real number or infinity.
Dom::MinPlusSemiRing::expr(dom a)
This method returns a real number or infinity such that generating a MinPlus scalar from that real number or infinity would result in a.
This example shows the idempotency of the MinPlus semi-ring:
T:=Dom::MinPlusSemiRing:
T(infinity) + T(infinity);
T(3) + T(3)
T(6) + T(infinity);
T(6) + T(3);
T(6)*T(infinity);
T(6)*T(3)
We can use real number and constants:
T(sin(2))*T(-2.15) + T(-PI)
We can change the domain of scalars:
T::convert_to(T(1), Dom::Integer) + T::convert_to(T(2), Dom::Integer)
