
Orbital library  
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public interface Fraction
Representation of a fraction a⁄s ∈ S^{1}M = M_{S}.
S^{1}M := M_{S} := M×S/~ = {a⁄s ¦ a∈M ∧ s∈S} with congruence relation ~ defined by
Especially, for an integrity domain R, Quot(R) := R_{(0)} = (R∖{0})^{1}R is the
field of fractions of R, and for Rmodules M, M_{R∖{0}} is a Quot(R)vector space.
If the underlying integrity domain R has an order, its field of fractions supports
a unique order that restricts to the order on R (an extends Comparable
).
A fraction a⁄s ∈ S^{1}M with numerator a and denominator s is usually written as
a
s
There is the canonical embedding homomorphism ι_{S}:a↦a⁄1 which is injective if and only if S does not contain zero divisors. The ring of fractions R_{S}is the presenting object of the presentable functor
Rng1  →  Ens 
R'  ↦  {φ∈Hom_{Rng1}(R,R') ¦ φ(S)⊆(R')^{×}} 
For Rmodules M and S≤(R,⋅) it is
ValueFactory.fraction(Arithmetic,Arithmetic)
,
"N. Bourbaki, Algebra I.2.4: Monoid of fractions of a commutative monoid.",
"N. Bourbaki, Algebra VI.2.2: Ordered fields."Field Summary 

Fields inherited from interface orbital.math.Arithmetic 

numerical 
Method Summary  

Fraction 
add(Fraction bt)
Adds two fractions returning a third as a result. 
Arithmetic 
denominator()
Returns the denominator component. 
Fraction 
divide(Fraction bt)
Divides two fractions returning a third as a result. 
Fraction 
multiply(Fraction bt)
Multiplies two fractions returning a third as a result. 
Arithmetic 
numerator()
Returns the numerator component. 
Arithmetic 
scale(Arithmetic alpha)
Multiplies a scalar with this arithmetic object returning the result. 
Fraction 
subtract(Fraction bt)
Subtracts two fractions returning a third as a result. 
Methods inherited from interface orbital.math.Arithmetic 

add, divide, equals, inverse, isOne, isZero, minus, multiply, one, power, subtract, toString, valueFactory, zero 
Methods inherited from interface orbital.math.Normed 

norm 
Method Detail 

Arithmetic numerator()
Arithmetic denominator()
Fraction add(Fraction bt)
Fraction subtract(Fraction bt)
Fraction multiply(Fraction bt)
Fraction divide(Fraction bt)
java.lang.ArithmeticException
 if b∉S and b is not invertible.Arithmetic scale(Arithmetic alpha)
scale
in interface Arithmetic
alpha
 the factor α to scale this arithmetic object with (per law of action of scalar multiplication).
Arithmetic.multiply(Arithmetic)

Orbital library 1.3.0: 11 Apr 2009 

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