From 88170919318a9d6de5d6bb6d329719a590e0eaf2 Mon Sep 17 00:00:00 2001
From: yosshi4486 <yoshiharuseijin@gmail.com>
Date: Sat, 26 Dec 2020 10:00:27 +0900
Subject: [PATCH 1/5] test: Add tests for arithmetic.

---
 .../Rational/RationalArithmeticTests.swift    | 26 +++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/Tests/SternBroctTreeSwiftTests/Rational/RationalArithmeticTests.swift b/Tests/SternBroctTreeSwiftTests/Rational/RationalArithmeticTests.swift
index 20e890f..ce10ead 100644
--- a/Tests/SternBroctTreeSwiftTests/Rational/RationalArithmeticTests.swift
+++ b/Tests/SternBroctTreeSwiftTests/Rational/RationalArithmeticTests.swift
@@ -130,4 +130,30 @@ class RationalArithmeticTests: XCTestCase {
         XCTAssertTrue(result.overflow)
     }
 
+    // This is benefit of adopting SignedNumeric. The protocol use `public init(integerLiteral value: IntegerLiteralType)` to adding integer.
+    func testAddingToIntegerNumber() {
+        let r = Rational8("2/3")
+        let result = r + 1
+        XCTAssertEqual(result.description, "5/3")
+    }
+
+    func testIntegerNumberAddingToRational() {
+        let r = Rational8("2/3")
+        let result = 1 + r
+        XCTAssertEqual(result.description, "5/3")
+    }
+
+    func testMultiplyByIntegerNumber() {
+        let r = Rational8("2/3")
+        let result = r * 3
+        XCTAssertEqual(result.description, "6/3")
+    }
+
+    func testIntegerNumberMultiplyByRational() {
+        let r = Rational8("2/3")
+        let result = 3 * r
+        XCTAssertEqual(result.description, "6/3")
+    }
+
+
 }

From a70adfcec03078883b2d689c9ce23bdff73d9709 Mon Sep 17 00:00:00 2001
From: yosshi4486 <yoshiharuseijin@gmail.com>
Date: Sat, 26 Dec 2020 10:27:55 +0900
Subject: [PATCH 2/5] refactor: Move elements to proper position.

---
 .../SternBroctTreeSwift/Core/Fraction.swift   |  14 ++
 .../SternBroctTreeSwift/Core/NSRational.swift |   2 +-
 .../SternBroctTreeSwift/Core/Rational.swift   |   2 +-
 .../SternBroctTreeSwift/Core/Rational16.swift |   2 +-
 .../SternBroctTreeSwift/Core/Rational32.swift |   2 +-
 .../SternBroctTreeSwift/Core/Rational64.swift |   2 +-
 .../SternBroctTreeSwift/Core/Rational8.swift  |   2 +-
 .../Core/SignedRational.swift                 | 226 ++++++++----------
 .../Fraction/FractionTests.swift              |   8 +-
 9 files changed, 121 insertions(+), 139 deletions(-)

diff --git a/Sources/SternBroctTreeSwift/Core/Fraction.swift b/Sources/SternBroctTreeSwift/Core/Fraction.swift
index b8c8948..cac94e0 100644
--- a/Sources/SternBroctTreeSwift/Core/Fraction.swift
+++ b/Sources/SternBroctTreeSwift/Core/Fraction.swift
@@ -64,3 +64,17 @@ public protocol Fraction : SBTreeNode, SignedNumeric, Comparable, Hashable {
     func simplified() -> Self
 
 }
+
+extension Fraction where Number : BinaryInteger {
+
+    /// Returns the interger value of mixed rational.
+    public var integerPartOfMixedFraction: Number {
+        return numerator / denominator
+    }
+
+    /// Returns the numerator of mixed rational.
+    public var numeratorOfMixedFraction: Number {
+        return numerator % denominator
+    }
+
+}
diff --git a/Sources/SternBroctTreeSwift/Core/NSRational.swift b/Sources/SternBroctTreeSwift/Core/NSRational.swift
index b03502c..f74da18 100644
--- a/Sources/SternBroctTreeSwift/Core/NSRational.swift
+++ b/Sources/SternBroctTreeSwift/Core/NSRational.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for reference semantics. The type stores and uses value rational internally.
-public final class NSRational : NSObject, NSSecureCoding, SignedRational {
+public final class NSRational : NSObject, NSSecureCoding, SignedRational, SBTreeNode {
 
     public typealias Number = Int
 
diff --git a/Sources/SternBroctTreeSwift/Core/Rational.swift b/Sources/SternBroctTreeSwift/Core/Rational.swift
index 5be5066..d75bfb4 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational.swift
@@ -11,7 +11,7 @@ import Foundation
 ///
 /// Rational is specialized fraction which has interger denominator and numerator.
 /// On 32-bit platforms, Number is the same size as Int32, and on 64-bit platforms, Number is the same size as Int64.
-public struct Rational : MutableSignedRational {
+public struct Rational : MutableSignedRational, SBTreeNode {
 
     public typealias Number = Int
 
diff --git a/Sources/SternBroctTreeSwift/Core/Rational16.swift b/Sources/SternBroctTreeSwift/Core/Rational16.swift
index 0513226..a45d91f 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational16.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational16.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational16 : MutableSignedRational {
+public struct Rational16 : MutableSignedRational, SBTreeNode {
 
     public typealias Number = Int16
 
diff --git a/Sources/SternBroctTreeSwift/Core/Rational32.swift b/Sources/SternBroctTreeSwift/Core/Rational32.swift
index ea409ac..252d0c0 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational32.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational32.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational32 : MutableSignedRational {
+public struct Rational32 : MutableSignedRational, SBTreeNode {
 
     public typealias Number = Int32
 
diff --git a/Sources/SternBroctTreeSwift/Core/Rational64.swift b/Sources/SternBroctTreeSwift/Core/Rational64.swift
index fce4d92..b6fe1ed 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational64.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational64.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational64 : MutableSignedRational {
+public struct Rational64 : MutableSignedRational, SBTreeNode {
 
     public typealias Number = Int64
 
diff --git a/Sources/SternBroctTreeSwift/Core/Rational8.swift b/Sources/SternBroctTreeSwift/Core/Rational8.swift
index c4b2621..5220202 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational8.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational8.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational8 : MutableSignedRational {
+public struct Rational8 : MutableSignedRational, SBTreeNode {
 
     public typealias Number = Int8
 
diff --git a/Sources/SternBroctTreeSwift/Core/SignedRational.swift b/Sources/SternBroctTreeSwift/Core/SignedRational.swift
index 839b1c6..021472c 100644
--- a/Sources/SternBroctTreeSwift/Core/SignedRational.swift
+++ b/Sources/SternBroctTreeSwift/Core/SignedRational.swift
@@ -13,25 +13,6 @@ import Foundation
 /// like `addingReportingOverflow(:)` if you consider about overflow.
 public protocol SignedRational : Fraction, CustomFloatConvertible, CustomDoubleConvertible, CustomDecimalConvertible where Number : SignedInteger & FixedWidthInteger {
 
-    /// Returns a mediant from two fractions.
-    static func mediant(left: Self, right: Self) -> Self
-
-    /// Retuns the result of mediant of the given left and right, along with a Boolean value indicating whether overflow occurred in the operation.
-    ///
-    /// - Parameters:
-    ///   - left: The left value to mediant.
-    ///   - right: The right value to mediant.
-    static func mediantReportingOverflow(left: Self, right: Self) -> (partialValue: Self, overflow: Bool)
-
-    /// Returns a boolean value whether this and the other are adjacent.
-    ///
-    /// - Parameter other: The other concrete rational to determine adjacent.
-    /// - Returns: The two values are adjacent or not.
-    func isAdjacent(to other: Self) -> Bool
-
-    /// Returns an array of R or L sequence which are backwardeded from this rational.
-    func backwardingMatrixSequence() -> [Matrix2x2]
-
     /// Returns the sum of this value and the given value, along with a Boolean value indicating whether overflow occurred in the operation.
     ///
     /// - Parameter other: The value to add to this value.
@@ -86,58 +67,6 @@ extension SignedRational {
         return commonFactor != 1 && commonFactor != -1
     }
 
-    /// Returns a mediant from two fractions.
-    public static func mediant(left: Self, right: Self) -> Self {
-        let numerator = left.numerator + right.numerator
-        let denominator = left.denominator + right.denominator
-        return Self(numerator: numerator, denominator: denominator)
-    }
-
-    /// Returns a mediant from two fractions.
-    public static func mediantReportingOverflow(left: Self, right: Self) -> (partialValue: Self, overflow: Bool) {
-        let (numeratorAddingResult, numeratorAddingOverflow) = left.numerator.addingReportingOverflow(right.numerator)
-        let (denominatorAddingResult, denominatorAddingOverflow) = left.denominator.addingReportingOverflow(right.denominator)
-
-        if numeratorAddingOverflow || denominatorAddingOverflow {
-            return (Self(numerator: numeratorAddingResult, denominator: denominatorAddingResult), true)
-        }
-
-        return (Self(numerator: numeratorAddingResult,denominator: denominatorAddingResult), false)
-    }
-
-    public func backwardingMatrixSequence() -> [Matrix2x2] {
-
-        // Start from R.
-        var mixPartSequence: [Number] = []
-        var continueFraction = self
-
-        while continueFraction.numerator > 1 || continueFraction.denominator > 1 {
-            let isEndIndeciesOfContinueFraction = continueFraction.numerator == 2 && continueFraction.denominator == 1
-            if isEndIndeciesOfContinueFraction {
-                mixPartSequence.append(1)
-                break
-            } else {
-                mixPartSequence.append(continueFraction.mixedPart)
-            }
-            continueFraction = Self(numerator: continueFraction.denominator, denominator: continueFraction.mixedRemainder)
-        }
-
-        let boxOfRLMatrixes: [[Matrix2x2]] = mixPartSequence.enumerated().compactMap({ index, value in
-            guard value > 0 else {
-                return nil
-            }
-
-            let isEven = index % 2 == 0
-            if isEven || index == 0 {
-                return Array(repeating: Matrix2x2.R, count: Int(value))
-            } else {
-                return Array(repeating: Matrix2x2.L, count: Int(value))
-            }
-        })
-
-        return boxOfRLMatrixes.flatMap({ $0 })
-    }
-
     public func comparedReportingOverflow(with other: Self) -> (partialValue: RationalComparisonResult, overflow: Bool) {
         let a = Number(numerator)
         let b = Number(denominator)
@@ -170,60 +99,6 @@ extension SignedRational {
 
 }
 
-/// Default implementation for SBTreeNode.
-extension SignedRational {
-
-    /// Returns a boolean value whether this and the other are adjacent.
-    ///
-    /// - Parameter other: The other concrete rational to determine adjacent.
-    /// - Returns: The two values are adjacent or not.
-    public func isAdjacent(to other: Self) -> Bool {
-        let (ad, adOverflow) = Number(numerator).multipliedReportingOverflow(by: Number(other.denominator))
-        let (bc, bcOverflow) = Number(denominator).multipliedReportingOverflow(by: Number(other.numerator))
-
-        if !adOverflow && !bcOverflow {
-            return abs(ad - bc) == 1
-        } else {
-            return false
-        }
-    }
-
-    /// Returns simplicity of a rational.
-    ///
-    /// if **r=a/b** is in reduced form, **the simplicity of r** is defined to be **L(r)≡1/ab**.
-    public func simplicity() -> (partialValue: Self, overflow: Bool) {
-        let (ab, overflow) = Number(numerator).multipliedReportingOverflow(by: Number(denominator))
-        return (Self("1/\(ab)"), overflow)
-    }
-
-    /// Returns total of a rational.
-    ///
-    /// if **r=a/b** is in reduced form, define the total of r to be **t(r) ≡ a+b**.
-    public var total: Number {
-        return numerator + denominator
-    }
-
-    /// Returns the interger value of mixed rational.
-    public var mixedPart: Number {
-        return numerator / denominator
-    }
-
-    /// Returns the numerator of mixed rational.
-    public var mixedRemainder: Number {
-        return numerator % denominator
-    }
-
-}
-
-/// Default implementation for Equtable.
-extension SignedRational {
-
-    public static func == (lhs: Self, rhs: Self) -> Bool {
-        return lhs.numerator == rhs.numerator && lhs.denominator == rhs.denominator
-    }
-
-}
-
 /// Default implementation for Comparable.
 extension SignedRational {
 
@@ -251,10 +126,10 @@ extension SignedRational {
 
     public func hash(into hasher: inout Hasher) {
 
-        // In reduced form, SBTree node's fruction must be identified in the tree.
-        let x = simplified()
-        hasher.combine(x.numerator)
-        hasher.combine(x.denominator)
+        // Rational should be hashed in reduced form.
+        let reducedForm = simplified()
+        hasher.combine(reducedForm.numerator)
+        hasher.combine(reducedForm.denominator)
     }
 
 }
@@ -330,6 +205,98 @@ extension SignedRational where Magnitude == Double, IntegerLiteralType == Number
 
 }
 
+/// Default implementation for SBTreeNode.
+extension SignedRational where Self : SBTreeNode {
+
+    /// Returns a mediant from two fractions.
+    public static func mediant(left: Self, right: Self) -> Self {
+        let numerator = left.numerator + right.numerator
+        let denominator = left.denominator + right.denominator
+        return Self(numerator: numerator, denominator: denominator)
+    }
+
+    /// Retuns the result of mediant of the given left and right, along with a Boolean value indicating whether overflow occurred in the operation.
+    ///
+    /// - Parameters:
+    ///   - left: The left value to mediant.
+    ///   - right: The right value to mediant.
+    public static func mediantReportingOverflow(left: Self, right: Self) -> (partialValue: Self, overflow: Bool) {
+        let (numeratorAddingResult, numeratorAddingOverflow) = left.numerator.addingReportingOverflow(right.numerator)
+        let (denominatorAddingResult, denominatorAddingOverflow) = left.denominator.addingReportingOverflow(right.denominator)
+
+        if numeratorAddingOverflow || denominatorAddingOverflow {
+            return (Self(numerator: numeratorAddingResult, denominator: denominatorAddingResult), true)
+        }
+
+        return (Self(numerator: numeratorAddingResult,denominator: denominatorAddingResult), false)
+    }
+
+    /// Returns an array of R or L sequence which are backwardeded from this rational.
+    public func backwardingMatrixSequence() -> [Matrix2x2] {
+
+        // Start from R.
+        var mixPartSequence: [Number] = []
+        var continueFraction = self
+
+        while continueFraction.numerator > 1 || continueFraction.denominator > 1 {
+            let isEndIndeciesOfContinueFraction = continueFraction.numerator == 2 && continueFraction.denominator == 1
+            if isEndIndeciesOfContinueFraction {
+                mixPartSequence.append(1)
+                break
+            } else {
+                mixPartSequence.append(continueFraction.integerPartOfMixedFraction)
+            }
+            continueFraction = Self(numerator: continueFraction.denominator, denominator: continueFraction.numeratorOfMixedFraction)
+        }
+
+        let boxOfRLMatrixes: [[Matrix2x2]] = mixPartSequence.enumerated().compactMap({ index, value in
+            guard value > 0 else {
+                return nil
+            }
+
+            let isEven = index % 2 == 0
+            if isEven || index == 0 {
+                return Array(repeating: Matrix2x2.R, count: Int(value))
+            } else {
+                return Array(repeating: Matrix2x2.L, count: Int(value))
+            }
+        })
+
+        return boxOfRLMatrixes.flatMap({ $0 })
+    }
+
+    /// Returns a boolean value whether this and the other are adjacent.
+    ///
+    /// - Parameter other: The other concrete rational to determine adjacent.
+    /// - Returns: The two values are adjacent or not.
+    public func isAdjacent(to other: Self) -> Bool {
+        let (ad, adOverflow) = Number(numerator).multipliedReportingOverflow(by: Number(other.denominator))
+        let (bc, bcOverflow) = Number(denominator).multipliedReportingOverflow(by: Number(other.numerator))
+
+        if !adOverflow && !bcOverflow {
+            return abs(ad - bc) == 1
+        } else {
+            return false
+        }
+    }
+
+    /// Returns simplicity of a rational.
+    ///
+    /// if **r=a/b** is in reduced form, **the simplicity of r** is defined to be **L(r)≡1/ab**.
+    public func simplicity() -> (partialValue: Self, overflow: Bool) {
+        let (ab, overflow) = Number(numerator).multipliedReportingOverflow(by: Number(denominator))
+        return (Self("1/\(ab)"), overflow)
+    }
+
+    /// Returns total of a rational.
+    ///
+    /// if **r=a/b** is in reduced form, define the total of r to be **t(r) ≡ a+b**.
+    public var total: Number {
+        return numerator + denominator
+    }
+
+}
+
 extension SignedRational {
 
 
@@ -347,3 +314,4 @@ extension SignedRational {
 
 
 }
+
diff --git a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
index a75c94b..6b199e7 100644
--- a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
+++ b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
@@ -167,22 +167,22 @@ class FractionTests: XCTestCase {
 
     func testMixedPart() {
         let f = Rational("11/3")
-        XCTAssertEqual(f.mixedPart, 3)
+        XCTAssertEqual(f.integerPart, 3)
     }
 
     func testMixedPartZero() {
         let f = Rational("3/11")
-        XCTAssertEqual(f.mixedPart, 0)
+        XCTAssertEqual(f.integerPart, 0)
     }
 
     func testMixedRemainder() {
         let f = Rational("11/3")
-        XCTAssertEqual(f.mixedRemainder, 2)
+        XCTAssertEqual(f.numeratorOfMixedFraction, 2)
     }
 
     func testMixedRemainderZer0() {
         let f = Rational("3/3")
-        XCTAssertEqual(f.mixedRemainder, 0)
+        XCTAssertEqual(f.numeratorOfMixedFraction, 0)
     }
 
     func testBackwardsMatrixSequnce1() {

From e15a5728bb422c6c7cd71d96f5cfceb5442e6817 Mon Sep 17 00:00:00 2001
From: yosshi4486 <yoshiharuseijin@gmail.com>
Date: Sat, 26 Dec 2020 11:00:17 +0900
Subject: [PATCH 3/5] feat: Add fraction methods.

---
 .../SternBroctTreeSwift/Core/Fraction.swift   | 23 +++++++
 .../Fraction/FractionTests.swift              | 63 ++++++++++++++++++-
 2 files changed, 84 insertions(+), 2 deletions(-)

diff --git a/Sources/SternBroctTreeSwift/Core/Fraction.swift b/Sources/SternBroctTreeSwift/Core/Fraction.swift
index cac94e0..c5b03a1 100644
--- a/Sources/SternBroctTreeSwift/Core/Fraction.swift
+++ b/Sources/SternBroctTreeSwift/Core/Fraction.swift
@@ -77,4 +77,27 @@ extension Fraction where Number : BinaryInteger {
         return numerator % denominator
     }
 
+    /// Returns a Boolean value whether this fraction is unit fraction or not.
+    public var isUnit: Bool {
+        return numerator == 1
+    }
+
+    /// Returns a Boolean value whther this fraction is proper fraction or not.
+    public var isProper: Bool {
+        return numerator < denominator
+    }
+
+    /// Returns a Boolean value whether this fraction is improper or not.
+    public var isImproper: Bool {
+        return denominator > numerator
+    }
+
+    /// Returns a mixed fraction from this value.
+    ///
+    /// - Returns: The result touple cantains two values intergetPart and fraction.
+    /// The intergetPart is equal to `intergerPartOfMixedFraction` and  the fraction numerator is equal to `numeratorOfMixedFraction` property.
+    public func mixed() -> (integerPart: Number, fraction: Self) {
+        return (integerPartOfMixedFraction, Self(numerator: numeratorOfMixedFraction, denominator: denominator))
+    }
+
 }
diff --git a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
index 6b199e7..183c3ad 100644
--- a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
+++ b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
@@ -167,12 +167,12 @@ class FractionTests: XCTestCase {
 
     func testMixedPart() {
         let f = Rational("11/3")
-        XCTAssertEqual(f.integerPart, 3)
+        XCTAssertEqual(f.integerPartOfMixedFraction, 3)
     }
 
     func testMixedPartZero() {
         let f = Rational("3/11")
-        XCTAssertEqual(f.integerPart, 0)
+        XCTAssertEqual(f.integerPartOfMixedFraction, 0)
     }
 
     func testMixedRemainder() {
@@ -199,4 +199,63 @@ class FractionTests: XCTestCase {
         XCTAssertEqual(matrixSequence, [.R, .R, .L, .L, .R, .L])
     }
 
+    func testUnitFraction() {
+        let rational = Rational("1/9")
+        XCTAssertTrue(rational.isUnit)
+    }
+
+    func testNotUnitFraction() {
+        let rational = Rational("2/9")
+        XCTAssertFalse(rational.isUnit)
+    }
+
+    func testNotUnitFractionWhenZero() {
+        let rational = Rational("0/9")
+        XCTAssertFalse(rational.isUnit)
+    }
+
+    func testProperFraction() {
+        let rational = Rational("1/3")
+        XCTAssertTrue(rational.isProper)
+    }
+
+    func testNotProperFraction() {
+        let rational = Rational("4/3")
+        XCTAssertFalse(rational.isProper)
+    }
+
+    func testNotProperFractionWhenEqual() {
+        let rational = Rational("3/3")
+        XCTAssertFalse(rational.isProper)
+    }
+
+    func testImproperFraction() {
+        let rational = Rational("3/4")
+        XCTAssertTrue(rational.isImproper)
+    }
+
+    func testNotImproperFraction() {
+        let rational = Rational("3/2")
+        XCTAssertFalse(rational.isImproper)
+    }
+
+    func testNotImproperFractionWhenEqual() {
+        let rational = Rational("3/3")
+        XCTAssertFalse(rational.isImproper)
+    }
+
+    func testMixedForm() {
+        let rational = Rational("7/3")
+        let result = rational.mixed()
+        XCTAssertEqual(result.integerPart, 2)
+        XCTAssertEqual(result.fraction.description, "1/3")
+    }
+
+    func testMixedFormIntegerZero() {
+        let rational = Rational("2/3")
+        let result = rational.mixed()
+        XCTAssertEqual(result.integerPart, 0)
+        XCTAssertEqual(result.fraction.description, "2/3")
+    }
+
 }

From 1e4590fb0f529311e38152c7f8a0bf5e20435567 Mon Sep 17 00:00:00 2001
From: yosshi4486 <yoshiharuseijin@gmail.com>
Date: Sat, 26 Dec 2020 11:08:45 +0900
Subject: [PATCH 4/5] refactor: Migrate to mixed() method.

---
 .../SternBroctTreeSwift/Core/Fraction.swift   | 12 +----------
 .../Core/SignedRational.swift                 |  6 ++++--
 .../Fraction/FractionTests.swift              | 20 -------------------
 3 files changed, 5 insertions(+), 33 deletions(-)

diff --git a/Sources/SternBroctTreeSwift/Core/Fraction.swift b/Sources/SternBroctTreeSwift/Core/Fraction.swift
index c5b03a1..52680f9 100644
--- a/Sources/SternBroctTreeSwift/Core/Fraction.swift
+++ b/Sources/SternBroctTreeSwift/Core/Fraction.swift
@@ -67,16 +67,6 @@ public protocol Fraction : SBTreeNode, SignedNumeric, Comparable, Hashable {
 
 extension Fraction where Number : BinaryInteger {
 
-    /// Returns the interger value of mixed rational.
-    public var integerPartOfMixedFraction: Number {
-        return numerator / denominator
-    }
-
-    /// Returns the numerator of mixed rational.
-    public var numeratorOfMixedFraction: Number {
-        return numerator % denominator
-    }
-
     /// Returns a Boolean value whether this fraction is unit fraction or not.
     public var isUnit: Bool {
         return numerator == 1
@@ -97,7 +87,7 @@ extension Fraction where Number : BinaryInteger {
     /// - Returns: The result touple cantains two values intergetPart and fraction.
     /// The intergetPart is equal to `intergerPartOfMixedFraction` and  the fraction numerator is equal to `numeratorOfMixedFraction` property.
     public func mixed() -> (integerPart: Number, fraction: Self) {
-        return (integerPartOfMixedFraction, Self(numerator: numeratorOfMixedFraction, denominator: denominator))
+        return (numerator / denominator, Self(numerator: numerator % denominator, denominator: denominator))
     }
 
 }
diff --git a/Sources/SternBroctTreeSwift/Core/SignedRational.swift b/Sources/SternBroctTreeSwift/Core/SignedRational.swift
index 021472c..0208ae0 100644
--- a/Sources/SternBroctTreeSwift/Core/SignedRational.swift
+++ b/Sources/SternBroctTreeSwift/Core/SignedRational.swift
@@ -239,14 +239,16 @@ extension SignedRational where Self : SBTreeNode {
         var continueFraction = self
 
         while continueFraction.numerator > 1 || continueFraction.denominator > 1 {
+            let mixed = continueFraction.mixed()
             let isEndIndeciesOfContinueFraction = continueFraction.numerator == 2 && continueFraction.denominator == 1
             if isEndIndeciesOfContinueFraction {
                 mixPartSequence.append(1)
                 break
             } else {
-                mixPartSequence.append(continueFraction.integerPartOfMixedFraction)
+                mixPartSequence.append(mixed.integerPart)
             }
-            continueFraction = Self(numerator: continueFraction.denominator, denominator: continueFraction.numeratorOfMixedFraction)
+            continueFraction = Self(numerator: mixed.fraction.denominator,
+                                    denominator: mixed.fraction.numerator)
         }
 
         let boxOfRLMatrixes: [[Matrix2x2]] = mixPartSequence.enumerated().compactMap({ index, value in
diff --git a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
index 183c3ad..4acdb4b 100644
--- a/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
+++ b/Tests/SternBroctTreeSwiftTests/Fraction/FractionTests.swift
@@ -165,26 +165,6 @@ class FractionTests: XCTestCase {
         XCTAssertEqual(f.denominator, 3)
     }
 
-    func testMixedPart() {
-        let f = Rational("11/3")
-        XCTAssertEqual(f.integerPartOfMixedFraction, 3)
-    }
-
-    func testMixedPartZero() {
-        let f = Rational("3/11")
-        XCTAssertEqual(f.integerPartOfMixedFraction, 0)
-    }
-
-    func testMixedRemainder() {
-        let f = Rational("11/3")
-        XCTAssertEqual(f.numeratorOfMixedFraction, 2)
-    }
-
-    func testMixedRemainderZer0() {
-        let f = Rational("3/3")
-        XCTAssertEqual(f.numeratorOfMixedFraction, 0)
-    }
-
     func testBackwardsMatrixSequnce1() {
         let rational = Rational("3/11")
         let matrixSequence = rational.backwardingMatrixSequence()

From c47a64108c3867552a44498822fb65ab81b1e16a Mon Sep 17 00:00:00 2001
From: yosshi4486 <yoshiharuseijin@gmail.com>
Date: Sat, 26 Dec 2020 11:11:53 +0900
Subject: [PATCH 5/5] refactor: Isolate SBTree inheritance from declear.

---
 Sources/SternBroctTreeSwift/Core/Rational.swift   | 4 +++-
 Sources/SternBroctTreeSwift/Core/Rational16.swift | 3 ++-
 Sources/SternBroctTreeSwift/Core/Rational32.swift | 3 ++-
 Sources/SternBroctTreeSwift/Core/Rational64.swift | 3 ++-
 Sources/SternBroctTreeSwift/Core/Rational8.swift  | 3 ++-
 5 files changed, 11 insertions(+), 5 deletions(-)

diff --git a/Sources/SternBroctTreeSwift/Core/Rational.swift b/Sources/SternBroctTreeSwift/Core/Rational.swift
index d75bfb4..ec8cb68 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational.swift
@@ -11,7 +11,7 @@ import Foundation
 ///
 /// Rational is specialized fraction which has interger denominator and numerator.
 /// On 32-bit platforms, Number is the same size as Int32, and on 64-bit platforms, Number is the same size as Int64.
-public struct Rational : MutableSignedRational, SBTreeNode {
+public struct Rational : MutableSignedRational {
 
     public typealias Number = Int
 
@@ -44,3 +44,5 @@ public struct Rational : MutableSignedRational, SBTreeNode {
     }
 
 }
+
+extension Rational : SBTreeNode { }
diff --git a/Sources/SternBroctTreeSwift/Core/Rational16.swift b/Sources/SternBroctTreeSwift/Core/Rational16.swift
index a45d91f..1dfdd24 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational16.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational16.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational16 : MutableSignedRational, SBTreeNode {
+public struct Rational16 : MutableSignedRational {
 
     public typealias Number = Int16
 
@@ -42,3 +42,4 @@ public struct Rational16 : MutableSignedRational, SBTreeNode {
 
 }
 
+extension Rational16 : SBTreeNode { }
diff --git a/Sources/SternBroctTreeSwift/Core/Rational32.swift b/Sources/SternBroctTreeSwift/Core/Rational32.swift
index 252d0c0..d79d024 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational32.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational32.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational32 : MutableSignedRational, SBTreeNode {
+public struct Rational32 : MutableSignedRational {
 
     public typealias Number = Int32
 
@@ -42,3 +42,4 @@ public struct Rational32 : MutableSignedRational, SBTreeNode {
         
 }
 
+extension Rational32 : SBTreeNode { }
diff --git a/Sources/SternBroctTreeSwift/Core/Rational64.swift b/Sources/SternBroctTreeSwift/Core/Rational64.swift
index b6fe1ed..0f0a0b2 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational64.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational64.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational64 : MutableSignedRational, SBTreeNode {
+public struct Rational64 : MutableSignedRational {
 
     public typealias Number = Int64
 
@@ -42,3 +42,4 @@ public struct Rational64 : MutableSignedRational, SBTreeNode {
 
 }
 
+extension Rational64 : SBTreeNode { }
diff --git a/Sources/SternBroctTreeSwift/Core/Rational8.swift b/Sources/SternBroctTreeSwift/Core/Rational8.swift
index 5220202..c9bf8d0 100644
--- a/Sources/SternBroctTreeSwift/Core/Rational8.swift
+++ b/Sources/SternBroctTreeSwift/Core/Rational8.swift
@@ -8,7 +8,7 @@
 import Foundation
 
 /// A rational type for value semantics.
-public struct Rational8 : MutableSignedRational, SBTreeNode {
+public struct Rational8 : MutableSignedRational {
 
     public typealias Number = Int8
 
@@ -42,3 +42,4 @@ public struct Rational8 : MutableSignedRational, SBTreeNode {
 
 }
 
+extension Rational8 : SBTreeNode { }