orbital.math
Interface Integer

All Superinterfaces:

Arithmetic, java.lang.Comparable, Complex, Euclidean, Normed, Rational, Real, Scalar

public interface Integer
extends Rational, Euclidean

Representation of an integer number k in Z.

Integer numbers are a subgroup of Q for '+', it is embedded in Q for the field operation '*'. Integers are the group of differences of N.

On the importance of Quotient<Integer>: all cyclic groups are Z/nZ with n in Z. All finitely generated Abelian groups are direct sums of cyclic groups, hence Vector<Quotient<Integer>>

Author:

André Platzer

See Also:

ValueFactory.valueOf(int), ValueFactory.valueOf(long), ValueFactory.valueOf(short), ValueFactory.valueOf(byte), ValueFactory.valueOf(java.math.BigInteger)

Structure:

specializes Rational (needs covariant parameters and covariant results) Since integers are a special case of integers, and thus only adding integers to integers will make sense - on the first sight - but not adding rationals. In order to achieve that integers behave like rationals they additionally have a subtype relation., subtypeOf Rational (needs contravariant parameters and covariant result) In order to realize Z=<Q we embed Z↪Q, implemented with multiple argument dynamic dispatch.

Stereotype:

data-type

Field Summary

static Predicate	hasType Checks whether the given number is in the set of integers and not a subset.
static Predicate	isa Checks whether the given number is in the set of integers.

Method Summary

Integer	add(Integer b)
byte	byteValue() Returns the value of the specified integer as a byte.
int	intValue() Returns the value of the specified integer as a int.
long	longValue() Returns the value of the specified integer as a long.
Integer	multiply(Integer b)
Rational	power(Integer b) Return ab.
short	shortValue() Returns the value of the specified integer as a short.
Integer	subtract(Integer b)

Methods inherited from interface orbital.math.Rational

add, denominator, divide, multiply, numerator, power, representative, subtract

Methods inherited from interface orbital.math.Real

add, compareTo, divide, doubleValue, floatValue, multiply, power, subtract

Methods inherited from interface orbital.math.Complex

add, arg, conjugate, divide, equals, hashCode, im, isInfinite, isNaN, multiply, norm, power, re, subtract

Methods inherited from interface orbital.math.Arithmetic

add, divide, equals, inverse, isOne, isZero, minus, multiply, one, power, scale, subtract, toString, zero

Methods inherited from interface orbital.math.Euclidean

degree, modulo, quotient

Field Detail

isa

static final Predicate isa

Checks whether the given number is in the set of integers. return whether v is an integer.

hasType

static final Predicate hasType

Checks whether the given number is in the set of integers and not a subset. return whether v in Z is an integer.

Method Detail

byteValue

byte byteValue()

Returns the value of the specified integer as a byte. This may involve rounding or truncation. Similar to the standard narrowing primitive conversion as defined in The Java Language Specification: if this integer is too big to fit in an int, only the low-order bits are returned.

Returns:

the numeric value represented by this object after conversion to type byte.

shortValue

short shortValue()

Returns the value of the specified integer as a short. This may involve rounding or truncation. Similar to the standard narrowing primitive conversion as defined in The Java Language Specification: if this integer is too big to fit in an int, only the low-order bits are returned.

Returns:

the numeric value represented by this object after conversion to type short.

intValue

int intValue()

Returns the value of the specified integer as a int. This may involve rounding or truncation. Similar to the standard narrowing primitive conversion as defined in The Java Language Specification: if this integer is too big to fit in an int, only the low-order bits are returned.

Returns:

the numeric value represented by this object after conversion to type int.

longValue

long longValue()

Returns the value of the specified integer as a long. This may involve rounding or truncation. Similar to the standard narrowing primitive conversion as defined in The Java Language Specification: if this integer is too big to fit in an int, only the low-order bits are returned.

Returns:

the numeric value represented by this object after conversion to type long.

add

Integer add(Integer b)

subtract

Integer subtract(Integer b)

multiply

Integer multiply(Integer b)

power

Rational power(Integer b)

Return a^b.

Specified by:

power in interface Rational

Postconditions:

(b > 0 -> RES instanceof Integer) and (b < 0 -> RES instanceof Rational)