Class FieldIntervalND<T extends Comparable<T>>

java.lang.Object

org.episteme.core.mathematics.algebra.intervals.OrderedSetIntervalND<T>

org.episteme.core.mathematics.algebra.intervals.RingIntervalND<T>

org.episteme.core.mathematics.algebra.intervals.FieldIntervalND<T>

All Implemented Interfaces:

Interval<T>

public class FieldIntervalND<T extends Comparable<T>>
extends RingIntervalND<T>

N-dimensional interval over a Field (elements support full arithmetic).

Extends RingIntervalND by requiring elements to form a Field structure, enabling operations that depend on division (like computing the center/midpoint of each dimension).

A Field requires all Ring operations plus:

• Division: (a / b) for b ≠0
• Multiplicative inverse

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
FieldIntervalND(T[] min, T[] max, boolean[] closedLeft, boolean[] closedRight, BinaryOperator<T> adder, BinaryOperator<T> subtractor, BinaryOperator<T> divider, Function<Integer,T> fromInt)	Creates an N-dimensional Field interval with specified bounds.
FieldIntervalND(T[] min, T[] max, BinaryOperator<T> adder, BinaryOperator<T> subtractor, BinaryOperator<T> divider, Function<Integer,T> fromInt)	Creates a closed N-dimensional Field interval [min, max].
FieldIntervalND(T min, T max, boolean closedLeft, boolean closedRight, BinaryOperator<T> adder, BinaryOperator<T> subtractor, BinaryOperator<T> divider, Function<Integer,T> fromInt)	Creates a 1-dimensional Field interval.
FieldIntervalND(T min, T max, BinaryOperator<T> adder, BinaryOperator<T> subtractor, BinaryOperator<T> divider, Function<Integer,T> fromInt)	Creates a closed 1-dimensional Field interval [min, max].

Method Summary

Modifier and Type	Method	Description
Interval<T>	boundingInterval(Interval<T> other)	Returns the smallest interval containing both this and another interval.
BinaryOperator<T>	getAdder()	Returns the adder operator.
BinaryOperator<T>	getDivider()	Returns the divider operator.
Function<Integer,T>	getFromInt()	Returns the fromInt converter.
T	getMidpoint(int dimension)	Returns the midpoint (center) in the specified dimension.
T[]	getMidpoints()	Returns the midpoints (center) in all dimensions.
Interval<T>	intersection(Interval<T> other)	Returns the intersection of this interval with another.

Methods inherited from class RingIntervalND

getSubtractor, getWidth, getWidths

Methods inherited from class OrderedSetIntervalND

contains, contains, equals, getDimension, getMax, getMin, hashCode, isClosedLeft, isClosedRight, isEmpty, notation, overlaps, toString

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface Interval

isClosed, isOpen

Constructor Details

FieldIntervalND

public FieldIntervalND(T[] min,
 T[] max,
 boolean[] closedLeft,
 boolean[] closedRight,
 BinaryOperator<T> adder,
 BinaryOperator<T> subtractor,
 BinaryOperator<T> divider,
 Function<Integer,T> fromInt)

Creates an N-dimensional Field interval with specified bounds.

Parameters:

min - array of minimum values for each dimension

max - array of maximum values for each dimension

closedLeft - array indicating if left endpoints are closed

closedRight - array indicating if right endpoints are closed

adder - function to compute (a + b)

subtractor - function to compute (a - b)

divider - function to compute (a / b)

fromInt - function to create element from integer (for computing 2 in midpoint)

FieldIntervalND

public FieldIntervalND(T[] min,
 T[] max,
 BinaryOperator<T> adder,
 BinaryOperator<T> subtractor,
 BinaryOperator<T> divider,
 Function<Integer,T> fromInt)

Creates a closed N-dimensional Field interval [min, max].

FieldIntervalND

public FieldIntervalND(T min,
 T max,
 boolean closedLeft,
 boolean closedRight,
 BinaryOperator<T> adder,
 BinaryOperator<T> subtractor,
 BinaryOperator<T> divider,
 Function<Integer,T> fromInt)

Creates a 1-dimensional Field interval.

FieldIntervalND

public FieldIntervalND(T min,
 T max,
 BinaryOperator<T> adder,
 BinaryOperator<T> subtractor,
 BinaryOperator<T> divider,
 Function<Integer,T> fromInt)

Creates a closed 1-dimensional Field interval [min, max].

Method Details

getMidpoint

public T getMidpoint(int dimension)

Returns the midpoint (center) in the specified dimension.

Computed as (min + max) / 2 using the Field's arithmetic operations.

Parameters:

dimension - the dimension index (0-based)

Returns:

the midpoint value in that dimension

getMidpoints

public T[] getMidpoints()

Returns the midpoints (center) in all dimensions.

Returns:

array of midpoint values for each dimension

getAdder

public BinaryOperator<T> getAdder()

Returns the adder operator.

getDivider

public BinaryOperator<T> getDivider()

Returns the divider operator.

getFromInt

public Function<Integer,T> getFromInt()

Returns the fromInt converter.

intersection

public Interval<T> intersection(Interval<T> other)

Description copied from interface: Interval

Returns the intersection of this interval with another.

Specified by:

intersection in interface Interval<T extends Comparable<T>>

Overrides:

intersection in class RingIntervalND<T extends Comparable<T>>

Parameters:

other - the interval to intersect with

Returns:

the intersection interval, or null if empty

boundingInterval

public Interval<T> boundingInterval(Interval<T> other)

Description copied from interface: Interval

Returns the smallest interval containing both this and another interval.

Specified by:

boundingInterval in interface Interval<T extends Comparable<T>>

Overrides:

boundingInterval in class RingIntervalND<T extends Comparable<T>>

Parameters:

other - the interval to union with

Returns:

the bounding interval