Dom::MinMaxSemiRing

Dom::MinMaxSemiRing creates a domain for the MinMax semiring.

Creating Elements

MinMaxSemiRing(x)

Parameters:

x:	real number, infinity or -infinity.

Superdomain

Dom::BaseDomain

Categories

Cat::SemiRing

Axioms

Ax::canonicalRep, Ax::normalRep

Details:

The domain element Dom::MinMaxSemiRing(x) represents the constant in the MinMax semiring 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 MinMax

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

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

This method overloads the function _plus.

_mult – product of MinMax

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

The product is defined to be the biggest of real numbers, .

This method overloads the function _mult.

_power – power of MinMax

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

The nth power of the MinMax scalar a.

This method overloads the function _power.

Conversion Methods

convert – conversion of an object into a MinMax scalar

Dom::MinMaxSemiRing::convert(any x)

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

convert_to – conversion of a MinMax scalar into another type

Dom::MinMaxSemiRing::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 MinMax scalar into a real number, infinity or -infinity.

Dom::MinMaxSemiRing::expr(dom a)

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

Example 1:

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

T:=Dom::MinMaxSemiRing:

T(infinity) + T(infinity);

T(3) + T(3)