Writing a Fraction Class
•  Sofarwehaveworkedwithfloa0ng-pointnumbersbutcomputers
storebinaryvalues,sonotallrealnumberscanberepresented
precisely
•  Inapplica0onswheretheprecisionofrealnumbersisimportant,we
canusera#onalnumberstostoreexactvalues
•  Thishelpstoreduceoreliminateround-offerrorsthatcanoccur
whenperformingarithme0copera0ons
•  Ara0onalnumberisanumberthatcanbeexpressedasara0oof
twointegers:7/8
•  ThetopvalueiscalledthenumeratorandtheboFomvalue,which
cannotbezero,iscalledthedenominator
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Designing the Fraction Class
•  Wewanttouseourra0onalnumbersaswewoulduseintegersand
floa0ngpointvalues
•  Thus,ourFractionclassmustperformthefollowingopera0ons:
1.  Createara0onalnumber
2.  Accessthenumeratoranddenominatorvalues,individually
3.  Determineifthera0onalnumberisnega0veorzero
4.  Performnormalmathema0calopera0onsontwora0onal
numbers(addi0on,subtrac0on,mul0plica0on,division,
exponen0a0on)
5.  Logicallycomparetwora0onalnumbers
6.  Produceastringrepresenta0onofthera0onalnumber
•  TheobjectsoftheFrac0onclasswillbeimmutablebecausenoneof
theopera0onsmodifytheobjects’instancevariables
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Required Data Attributes
•  Becauseara0onalnumberconsistsoftwointegers,weneedtwo
instancevariablestostorethosevalues:
self._numerator=0
self._denominator=1
•  Atno0meshouldthera0onalnumberbeconvertedtoafloa0ng-point
valueorwewilllosetheprecisiongainedfromworkingwithra0onal
numbers
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Representing Values Equivalently
•  Signedvalues
•  Nega0veandposi0vera0onalnumberseachhavetwoformsthat
canbeusedtospecifythecorrespondingvalue
•  Posi0vevaluescanbeindicatedas1/2 or –1/–2,andnega0vevalues
as–2/5 or 2/–5
•  Whenperforminganarithme0copera0onorlogicallycomparing
twora0onalnumbers,itwillbemucheasierifwehaveasingleway
torepresentanega0vevalue
•  Forsimplicity,wechoosetosetonlythenumeratortoanega0ve
valuewhenthera0onalnumberisnega0ve,andboththenumerator
anddenominatorwillbeposi0veintegerswhenthera0onalnumber
isposi0ve
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Representing Values Equivalently
•  Equivalentfrac0ons
•  Forexample,1/4canbewriFenas1/4,2/8,16/64,or123/492
•  Itwillbemucheasiertoperformtheopera0onifthenumberis
storedinreducedform
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The Constructor (1)
•  BecauseFractionobjectsareimmutable,theirvaluesmustbeset
whentheyarecreated.Thisrequiresparametervariablesforboththe
numeratoranddenominator
def__init__(self,numerator,denominator):
•  Themethodmustcheckforspecialcases:
•  Zerodenominators
•  Thenumberrepresentszerooranega0venumber
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The Constructor
def__init__(self,numerator=0,denominator=1):
ifdenominator==0:
raiseZeroDivisionError("Denominatorcannotbezero.")
ifnumerator==0:
self._numerator=0
self._denominator=1
else:
if(numerator<0anddenominator>=0or
numerator>=0anddenominator<0):
sign=-1
else:
sign=1
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The Constructor
a=abs(numerator)
b=abs(denominator)
whilea%b!=0:
tempA=a
tempB=b
a=tempB
b=tempA%tempB
self._numerator=abs(numerator)#b*sign
self._denominator=abs(denominator)#b
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Testing the Constructor
frac1=Fraction(1,8)#Storedas1/8
frac2=Fraction(-2,-4)#Storedas1/2
frac3=Fraction(-2,4)#Storedas-1/2
frac4=Fraction(3,-7)#Storedas-3/7
frac5=Fraction(0,15)#Storedas0/1
frac6=Fraction(8,0)#Error!exceptionisraised.
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Comparing Fractions (1)
•  InPython,wecandefineandimplementmethodsthatwillbecalled
automa0callywhenastandardPythonoperator(+,*,==,<)isapplied
toaninstanceoftheclass
•  Forexample,totestwhethertwofrac0onsareequal,wecould
implementamethod:
•  isequal()anduseitasfollows:
iffrac1.isequal(frac2):
print("Thefractionsareequal.")
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Comparing Fractions (2)
•  Ofcourse,wewouldprefertousetheoperator==
•  Thisisachievedbydefiningthespecialmethod:
__eq__():
def__eq__(self,rhsValue):
return(self._numerator==rhsValue.numeratorand
self._denominator==rhsValue.denominator)
•  Automa0callycallsthismethodwhenwecomparetwoFraction
objectsusingthe==operator:
iffrac1==frac2:#Callsfrac1.__eq__(frac2)
print("Thefractionsareequal.")
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Special Methods
•  Somespecialmethodsarecalledwhenaninstanceoftheclassis
passedtoabuilt-infunc0on.Forexample,supposeyouaFemptto
convertaFractionobjecttoafloa0ngpointnumberusingthe
float()func0on:
x=float(frac1)
•  Thenthe__float__()specialmethodiscalled.
•  Hereisadefini0onofthatmethod:
def__float__(self):
returnself._numerator/self._denominator
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Common Special Methods
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Common Special Methods
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Addition of Fractions
•  Allofthearithme0copera0onsthatcanbeperformedonaFraction
objectshouldreturntheresultinanewFractionobject
•  Forexample,whenthestatementbelowisexecuted,frac1shouldbe
addedtofrac2andtheresultreturnedasanewFractionobjectthat
isassignedtothenewFracvariable
newFrac=frac1+frac2
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Fractional Addition
•  Fromelementaryarithme0c,youknowthattwofrac0onsmusthavea
commondenominatorinordertoaddthem.Iftheydonothavea
commondenominator,wecans0lladdthemusingtheformula:
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Defining the Method For Addition
def__add__(self,rhsValue):
num=(self._numerator*rhsValue._denominator+
self._denominator*rhsValue._numerator)
den=self._denominator*rhsValue._denominator
returnFraction(num,den)
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Logic: Less Than
•  Notethata / b < c / dwhend · a < b · c.(Mul0plybothsideswithb ·
d.)
•  Basedonthisobserva0on,thelessthanopera0onisimplementedby
the__lt__()methodasfollows:
def__lt__(self,rhsValue):
return(self._numerator*rhsValue._denominator
self._denominator*rhsValue._numerator)
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Fraction.py
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Fraction.py
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Fraction.py
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Fraction.py
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Checking Type
•  Toensurethatvariablesarethecorrecttype,Pythonprovidesthe
built-inisinstance()func0onthatcanbeusedtocheckthetypeof
objectreferencedbyavariable.
•  Forexample,theconstructorfortheFractionclassrequirestwo
integers
classFraction:
def__init__(self,numerator,denominator):
if(notisinstance(numerator,int)or
notisinstance(denominator,int)):
raiseTypeError
("Thenumeratoranddenominatormustbeintegers.")
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Summary: Classes and Objects
•  Aclassdescribesasetofobjectswiththesamebehavior
•  Everyclasshasapublicinterface:acollec0onofmethodsthrough
whichtheobjectsoftheclasscanbemanipulated
•  Encapsula0onistheactofprovidingapublicinterfaceandhiding
theimplementa0ondetails
•  Encapsula0onenableschangesintheimplementa0onwithout
affec0ngusersofaclass
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Summary: Variables and Methods
•  Anobject’sinstancevariablesstorethedatarequiredforexecu0ngits
methods
•  Eachobjectofaclasshasitsownsetofinstancevariables
•  Aninstancemethodcanaccesstheinstancevariablesoftheobjecton
whichitacts
•  Aprivateinstancevariableshouldonlybeaccessedbythemethodsof
itsownclass
•  Classvariableshaveasinglecopyofthevariablesharedamongallof
theinstancesoftheclass
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Summary: Method Headers, Data
•  MethodHeaders
•  Youcanusemethodheadersandmethodcommentstospecifythe
publicinterfaceofaclass
•  Amutatormethodchangestheobjectonwhichitoperates
•  Anaccessormethoddoesnotchangetheobjectonwhichit
operates
•  DataRepresenta0on
•  Foreachaccessormethod,anobjectmusteitherstoreorcompute
theresult
•  Commonly,thereismorethanonewayofrepresen0ngthedataof
anobject,andyoumustmakeachoice
•  Besurethatyourdatarepresenta0onsupportsmethodcallsinany
order
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Summary: Constructors
•  Aconstructorini0alizestheobject’sinstancevariables
•  Aconstructorisinvokedwhenanobjectiscreated
•  Theconstructorisdefinedusingthespecialmethodname:__init_
_()
•  Defaultargumentscanbeusedwithaconstructortoprovidedifferent
waysofcrea0nganobject
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Summary: Method Implementation
•  Theobjectonwhichamethodisappliedisautoma0callypassedtothe
selfparametervariableofthemethod
•  Inamethod,youaccessinstancevariablesthroughtheself
parametervariable
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Summary: Testing Classes
•  Aunittestverifiesthataclassworkscorrectlyinisola0on,outsidea
completeprogram
•  Totestaclass,useanenvironmentforinterac0vetes0ng,orwritea
testerclasstoexecutetestinstruc0ons
•  Determiningtheexpectedresultinadvanceisanimportantpartof
tes0ng
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Summary: Object Tracing
•  Objecttracingisusedtovisualizeobjectbehavior
•  Writethemethodsonthefrontofacard,andtheinstancevariables
ontheback
•  Updatethevaluesoftheinstancevariableswhenamutatormethodis
called
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Summary: Patterns for Classes
•  Aninstancevariableforthetotalisupdatedinmethodsthatincrease
ordecreasethetotalamount
•  Acounterthatcountseventsisincrementedinmethodsthat
correspondtotheevents
•  Anobjectcancollectotherobjectsinalist
•  AnobjectpropertycanbeaccessedwithageFermethodandchanged
withaseFermethod
•  Ifyourobjectcanhaveoneofseveralstatesthataffectthebehavior,
supplyaninstancevariableforthecurrentstate
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Summary: Patterns for Classes
•  Tomodelamovingobject,youneedtostoreandupdateitsposi0on
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Summary: Object References
•  Anobjectreferencespecifiestheloca0onofanobject
•  Mul0pleobjectvariablescancontainreferencestothesameobject
•  Usetheisandisnotoperatorstotestwhethertwovariablesare
aliases
•  TheNonereferencereferstonoobject
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Summary: Defining Special Methods
•  Touseastandardoperatorwithobjects,definethecorresponding
specialmethod
•  Definethespecial__repr__()methodtocreateastring
representa0onofanobject
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