Python Programming: An Introduction to Computer ScienceObjectivesObjectives (cont.)Numeric Data TypesSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Using the Math LibrarySlide 13Slide 14Slide 15Slide 16Slide 17Math LibraryAccumulating Results: FactorialSlide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30The Limits of IntSlide 32Slide 33Slide 34Handling Large NumbersHandling Large Numbers: Long IntSlide 37Slide 38Type ConversionsSlide 40Type ConversionSlide 42Python Programming, 2/e 1Python Programming:An Introduction toComputer ScienceChapter 3Computing with NumbersPython Programming, 2/e 2ObjectivesTo understand the concept of data types.To be familiar with the basic numeric data types in Python.To understand the fundamental principles of how numbers are represented on a computer.Python Programming, 2/e 3Objectives (cont.)To be able to use the Python math library.To understand the accumulator program pattern.To be able to read and write programs that process numerical data.Python Programming, 2/e 4Numeric Data TypesThe information that is stored and manipulated bu computers programs is referred to as data.There are two different kinds of numbers!(5, 4, 3, 6) are whole numbers – they don’t have a fractional part(.25, .10, .05, .01) are decimal fractionsPython Programming, 2/e 5Numeric Data TypesInside the computer, whole numbers and decimal fractions are represented quite differently!We say that decimal fractions and whole numbers are two different data types.The data type of an object determines what values it can have and what operations can be performed on it.Python Programming, 2/e 6Numeric Data TypesWhole numbers are represented using the integer (int for short) data type.These values can be positive or negative whole numbers.Python Programming, 2/e 7Numeric Data TypesNumbers that can have fractional parts are represented as floating point (or float) values.How can we tell which is which?A numeric literal without a decimal point produces an int valueA literal that has a decimal point is represented by a float (even if the fractional part is 0)Python Programming, 2/e 8Numeric Data TypesPython has a special function to tell us the data type of any value.>>> type(3)<class 'int'>>>> type(3.1)<class 'float'>>>> type(3.0)<class 'float'>>>> myInt = 32>>> type(myInt)<class 'int'>>>>Python Programming, 2/e 9Numeric Data TypesWhy do we need two number types?Values that represent counts can’t be fractional (you can’t have 3 ½ quarters)Most mathematical algorithms are very efficient with integersThe float type stores only an approximation to the real number being represented!Since floats aren’t exact, use an int whenever possible!Python Programming, 2/e 10Numeric Data TypesOperations on ints produce ints, operations on floats produce floats (except for /).>>> 3.0+4.07.0>>> 3+47>>> 3.0*4.012.0>>> 3*412>>> 10.0/3.03.3333333333333335>>> 10/33.3333333333333335>>> 10 // 33>>> 10.0 // 3.03.0Python Programming, 2/e 11Numeric Data TypesInteger division produces a whole number.That’s why 10//3 = 3!Think of it as ‘gozinta’ , where 10//3 = 3 since 3 gozinta (goes into) 10 3 times (with a remainder of 1)10%3 = 1 is the remainder of the integer division of 10 by 3.a = (a/b)(b) + (a%b)Python Programming, 2/e 12Using the Math LibraryBesides (+, -, *, /, //, **, %, abs), we have lots of other math functions available in a math library.A library is a module with some useful definitions/functions.Python Programming, 2/e 13Using the Math LibraryLet’s write a program to compute the roots of a quadratic equation!The only part of this we don’t know how to do is find a square root… but it’s in the math library!242b b acxa- � -=Python Programming, 2/e 14Using the Math LibraryTo use a library, we need to make sure this line is in our program:import mathImporting a library makes whatever functions are defined within it available to the program.Python Programming, 2/e 15Using the Math LibraryTo access the sqrt library routine, we need to access it as math.sqrt(x).Using this dot notation tells Python to use the sqrt function found in the math library module.To calculate the root, you can dodiscRoot = math.sqrt(b*b – 4*a*c)Python Programming, 2/e 16Using the Math Library# quadratic.py# A program that computes the real roots of a quadratic equation.# Illustrates use of the math library.# Note: This program crashes if the equation has no real roots.import math # Makes the math library available.def main(): print("This program finds the real solutions to a quadratic") print() a, b, c = eval(input("Please enter the coefficients (a, b, c): ")) discRoot = math.sqrt(b * b - 4 * a * c) root1 = (-b + discRoot) / (2 * a) root2 = (-b - discRoot) / (2 * a) print() print("The solutions are:", root1, root2 )main()Python Programming, 2/e 17Using the Math LibraryThis program finds the real solutions to a quadraticPlease enter the coefficients (a, b, c): 3, 4, -1The solutions are: 0.215250437022 -1.54858377035What do you suppose this means?This program finds the real solutions to a quadraticPlease enter the coefficients (a, b, c): 1, 2, 3Traceback (most recent call last): File "<pyshell#26>", line 1, in -toplevel- main() File "C:\Documents and Settings\Terry\My Documents\Teaching\W04\CS 120\Textbook\code\chapter3\quadratic.py", line 14, in main discRoot = math.sqrt(b * b - 4 * a * c)ValueError: math domain error>>>Python Programming, 2/e 18Math LibraryIf a = 1, b = 2, c = 3, then we are trying to take the square root of a negative number!Using the sqrt function is more efficient than using **. How could you use ** to calculate a square root?Python Programming, 2/e 19Accumulating Results: FactorialSay you are waiting in a line with five other people. How many ways are there to arrange the six people?720 -- 720 is the factorial of 6 (abbreviated 6!)Factorial is defined as:n! = n(n-1)(n-2)…(1)So, 6! = 6*5*4*3*2*1 = 720Python Programming, 2/e 20Accumulating Results: FactorialHow we could we write a program to do this?Input number to take factorial of, nCompute factorial of n, factOutput factPython Programming, 2/e 21Accumulating Results: FactorialHow did we calculate 6!?6*5 = 30Take that 30, and 30 * 4 = 120Take that 120, and 120 * 3 = 360Take that 360, and 360 *