Dom::MaxMinSemiRing

Dom::MaxMinSemiRing creates a domain for the MaxMin semi-ring.

Creating Elements

MaxMinSemiRing(x)

Parameters:

x:	real number, infinity or -infinity.

Superdomain

Dom::BaseDomain

Categories

Cat::SemiRing

Axioms

Ax::canonicalRep, Ax::normalRep

Details:

The domain element Dom::MaxMinSemiRing(x) represents the constant in the MaxMin semi-ring if is a real number or real constant, or infinity or -infinity if is infinity or -infinity.

Entries

"zero"	the constant infinity.
"one"	the constant -infinity.

Mathematical Methods

_plus – sum of MaxMin

Dom::MaxMinSemiRing::_plus(dom , ...)

The sum is defined to be the biggest of real numbers .

This method overloads the function _plus.

_mult – product of MaxMin

Dom::MaxMinSemiRing::_mult(dom , ...)

The product is defined to be the smallest of real numbers, infinity or -infinity .

This method overloads the function _mult.

_power – power of MaxMin

Dom::MaxMinSemiRing::_power(dom a, Dom::Integer n)

The nth power of the MaxMin scalar a.

This method overloads the function _power.

Conversion Methods

convert – conversion of an object into a MaxMin scalar

Dom::MaxMinSemiRing::convert(any x)

This method tries to convert x into a MaxMin scalar. This is only possible if x is a real number, infinity or -infinity.

convert_to – conversion of a MaxMin scalar into another type

Dom::MaxMinSemiRing::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 MaxMin scalar into a real number, infinity or -infinity.

Dom::MaxMinSemiRing::expr(dom a)

This method returns a real number, infinity or -infinity such that generating a MaxMin scalar from that real number, infinity or -infinity would result in a.

Example 1:

This example shows the idempotency of the MaxMin semi-ring:

T:=Dom::MaxMinSemiRing:

T(infinity) + T(infinity);

T(3) + T(3)