Issue 192: Have Number Provide Complex Conjugate Message (#235)

* Added a complexConjugate message to the Short Float.

* Moved the method to the parent class.

* Added a failing test to get passing for next session

* Integer now responds to the complexConjugate message.

* Moved the methods up to Number

* Tested that the complex conjugate of a real fraction is itself.

* We cannot instanciate a fraction whose numerator and denominator are complex numbers. It may be that we need to normalise the
denominator first.

* We can now write fractions of complex numbers that have already been normalized.

* Added a test to demonstrate that we can write a complex number whose
real and imaginary parts are Fractions.

* Remove unnecessary comment.

* Corrected the name of the test method.

* May not make sense to convert a complex number to an integer, so inlined method and corrected a programmer test.

* Clarified the category of the tests.

* Clarified the category of the messages.

src/Math-Complex/Number.extension.st

@@ -13,6 +13,11 @@ Number >> asComplex [
 	^ PMComplex real: self imaginary: 0
 ]
 
+{ #category : #'*Math-Complex' }
+Number >> complexConjugate [
+	^ self.
+]
+
 { #category : #'*Math-Complex' }
 Number >> i [
 	^ PMComplex real: 0 imaginary: self

src/Math-Tests-Complex/PMComplexTest.class.st

@@ -750,6 +750,38 @@ PMComplexTest >> testTimesPolynomial [
 	self assert: (poly * c at: 0) equals: c
 ]
 
+{ #category : #'expressing complex numbers' }
+PMComplexTest >> testWeCanWriteComplexNumbersWhoseRealAndImaginaryPartsAreFractions [
+	| z |
+	z := PMComplex real: 3 / 5 imaginary: 4 / 5.
+
+	self assert: (z real) equals: (Fraction numerator: 3 denominator: 5).
+	self assert: (z imaginary) equals: (Fraction numerator: 4 denominator: 5).
+]
+
+{ #category : #'expressing complex numbers' }
+PMComplexTest >> testWeCannotWriteFractionsOfComplexNumbersWithDenominatorNormalized [
+
+	| z w numerator denominator |
+	z := 1 + 2 i.
+	w := 3 + 4 i.
+	numerator := z * w complexConjugate.
+	denominator := w squaredNorm.
+
+	self should: [ Fraction numerator: numerator denominator: w squaredNorm ] raise: Exception.
+]
+
+{ #category : #'expressing complex numbers' }
+PMComplexTest >> testWeCannotWriteFractionsWhoseNumeratorAndDenominatorAreComplexNumbers [
+	| numerator denominator |
+	"It is interesting that we cannot instanciate a fraction of the form z/w"
+	"Perhaps, we could do something like z * (w*)/ |w|**2"
+	numerator := PMComplex real: 1 imaginary: 1.
+	denominator := PMComplex real: 3 imaginary: 4 .
+
+	self should: [ Fraction numerator: numerator denominator: denominator ] raise: Exception .
+]
+
 { #category : #tests }
 PMComplexTest >> testZero [
 	| z |

src/Math-Tests-Complex/PMNumberTest.class.st

@@ -0,0 +1,30 @@
+Class {
+	#name : #PMNumberTest,
+	#superclass : #TestCase,
+	#category : #'Math-Tests-Complex'
+}
+
+{ #category : #'complex conjugation' }
+PMNumberTest >> testComplexConjugateOfAnIntegerIsAnInteger [
+	|complexConjugateOfInteger|
+
+	complexConjugateOfInteger := -5 complexConjugate. 
+
+	self assert: complexConjugateOfInteger equals: -5.
+]
+
+{ #category : #'complex conjugation' }
+PMNumberTest >> testComplexConjugateOfRealFractionIsARealFraction [
+	| complexConjugateOfFraction |
+	complexConjugateOfFraction := (Fraction numerator: 1 denominator: 6) complexConjugate.
+
+	self assert: complexConjugateOfFraction equals: (Fraction numerator: 1 denominator: 6) .
+]
+
+{ #category : #'complex conjugation' }
+PMNumberTest >> testComplexConjugateOfRealNumberIsItself [			
+	|realNumber|
+	realNumber := 4.5 complexConjugate. 
+
+	self assert: realNumber equals: 4.5
+]