orbital.math
Interface Rational

All Superinterfaces:

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

All Known Subinterfaces:

Integer

public interface Rational
extends Real

Representation of a rational number a⁄s ∈ Q.

Q := Quot(Z) := (Z∖{0})^-1Z = {a⁄s ¦ a,s∈Z ∧ s≠0} is the field of fractions of the ring Z.

A rational number a⁄s ∈ Q with numerator a and denominator s is usually written as

  a
  s
 

Rational numbers are a subfield of R, and the smallest subfield of all fields of characteristic 0.

Author:

André Platzer

See Also:

ValueFactory.rational(Integer, Integer), ValueFactory.rational(int, int), ValueFactory.rational(Integer), ValueFactory.rational(int), Fraction, "N. Bourbaki, Algebra I.9.4: The field of rational numbers.", "N. Bourbaki, Algebra I.2.4: Monoid of fractions of a commutative monoid."

Structure:

synonym for Fraction

Stereotype:

data-type

Field Summary

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

Fields inherited from interface orbital.math.Arithmetic

numerical

Method Summary

Rational	add(Rational b) adds two rationals returning a third as a result
Integer	denominator() Returns the denominator component.
Rational	divide(Rational b) divides two rationals returning a third as a result
Rational	multiply(Rational b) multiplies two rationals returning a third as a result
Integer	numerator() Returns the numerator component.
Rational	power(Integer b) Return ab.
Real	power(Rational b) Return ab.
Rational	representative() Get the "canonical" representative (cancelled out and normalized) of the equivalence class of rationals equal to this.
Rational	subtract(Rational b) subtracts two rationals returning a third as a result

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, valueFactory, zero

Field Detail

isa

static final Predicate isa

Checks whether the given number is in the set of rationals. return whether v is rational or an integer.

hasType

static final Predicate hasType

Checks whether the given number is in the set of rationals and not a subset. return whether v∈Q is a rational and not an integer.

Method Detail

numerator

Integer numerator()

Returns the numerator component.

Returns:

a of this rational number a⁄s.

denominator

Integer denominator()

Returns the denominator component.

Returns:

s of this rational number a⁄s.

representative

Rational representative()

Get the "canonical" representative (cancelled out and normalized) of the equivalence class of rationals equal to this.

Returns:

a cancelled and normalized rational.

Postconditions:

RES.equals(this) && MathUtilities.gcd(RES.numerator(), RES.denominator()) == 1 && RES.denominator() > 0.

Note:

S' = Z∖{0} is the set of allowed denominators.

add

Rational add(Rational b)

adds two rationals returning a third as a result

subtract

Rational subtract(Rational b)

subtracts two rationals returning a third as a result

multiply

Rational multiply(Rational b)

multiplies two rationals returning a third as a result

divide

Rational divide(Rational b)

divides two rationals returning a third as a result

power

Rational power(Integer b)

Return a^b.

Postconditions:

(b != 0 → RES instanceof Rational)

power

Real power(Rational b)

Return a^b.