Package org.tensorics.core.math.structures.ringlike

Interface OrderedField<T>

Type Parameters:

T - the type of the scalars in the field

All Superinterfaces:

Field<T>, Ring<T>, RinglikeStructure<T>, Semiring<T>, Structure<T>

All Known Implementing Classes:

AbstractOrderedField, DoubleField

public interface OrderedField<T>
extends Field<T>

Represents the mathemetical structure of a field which, in addition to the properties of a field provides a 'total order'. In the given context the total order is defined by a is-less-or-equal predicate (≤). This predicate follows the following properties:

• If a ≤ b and b ≤ a then a = b (antisymmetry);
• If a ≤ b and b ≤ c then a ≤ c (transitivity);
• a ≤ b or b ≤ a (totality).

For a,b and c being elements of the field.

See Also:

http://en.wikipedia.org/wiki/Ordered_field, http://en.wikipedia.org/wiki/Total_order

Method Summary

Modifier and Type	Method	Description
BinaryPredicate<T>	lessOrEqualPredicate()	Has to retrieve the predicate which represents the less-or-equal condition.

Methods inherited from interface org.tensorics.core.math.structures.ringlike.Field

multiplicationStructure

Methods inherited from interface org.tensorics.core.math.structures.ringlike.Ring

additionStructure

Method Detail

lessOrEqualPredicate

BinaryPredicate<T> lessOrEqualPredicate()

Has to retrieve the predicate which represents the less-or-equal condition.

Returns:

a predicate which will returen true if the left argument is less than the right argument and false otherwise.