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Industrial Sounds. Sound Packs. All Sound Effects. Print Templates. You then need to write run before the program name if you execute the program in IPython, or if you prefer to run the program directly in a terminal window, you need to write python prior to the program name. Appendix H. Quick recovery of previous output. The output from the In [1] input above is 1.
We can now refer to this number by an underscore and, e. Output from Python statements or expressions in IPython are preceded by Out[X] where X is the command number corresponding to the previous In [X] prompt. When programs are executed, as with the run command, or when operating system commands are run as shown below , the output is from the operating system and then not preceded by any Out[X] label.
The command history from previous IPython sessions is available in a new session. This feature makes it easy to modify work from a previous session by just hitting the up-arrow to recall commands and edit them as necessary. Tab completion. Pressing the TAB key will complete an in- completely typed variable name.
This automatic expansion feature is called TAB completion and can save you from quite some typing. Recovering previous commands.
Any command you hit can be edited and re-executed. Also commands from previous interactive sessions are stored in the command history. Operating system commands can be run from IPython. IPython can do much more than what is shown here, but the advanced features and the documentation of them probably do not make sense before you are more experienced with Python - and with reading manuals.
A particularly interesting feature of IPython is the notebook, which allows you to record and replay exploratory interactive sessions with a mix of text, mathematics, Python code, and graphics. See Section H. Such numbers have many applications in science, and it is therefore important to be able to use such numbers in our programs.
On the following pages we extend the previous material on computing with real numbers to complex numbers. The text is optional, and readers without knowledge of complex numbers can safely drop this section and jump to Section 1. There are rules for addition, subtraction, multiplication, and division between two complex numbers.
There are also rules for raising a complex number to a real power, as well as rules for computing sin z, cos z, tan z, ez , ln z, sinh z, cosh z, tanh z, etc. We assume in the following that you are familiar with the mathematics of complex numbers, at least to the degree encountered in the program examples. The imaginary unit is written as j in Python, instead of i as in mathematics.
We remark that the number i is written as 1j, not just j. The reason is that the sin function from the math module only works with real float arguments, not complex. It would be nice to have functions that return a float object if the result is a real number and a complex object if the result is a complex number.
The Numerical Python package has such versions of the basic mathematical functions known from math and cmath. A session will illustrate what we obtain. ValueError: math domain error. More precisely, the name sqrt was previously bound to a function sqrt from the math module, but is now bound to another function sqrt from the cmath module. In this case, any square root results in a complex object:. That is, the two results are float objects.
We shall here only give a glimpse of SymPy in action with the purpose of drawing attention to this powerful part of Python. For interactive work with SymPy it is recommended to either use IPython or the special, interactive shell isympy, which is installed along with SymPy itself. For example, it will be important to know whether sin means the sine function from the math module or the special sine function from sympy aimed at symbolic computing.
Rational, define rational numbers Note here that t is a symbolic variable not a float as it is in numerical computing , and y is a symbolic expression not a float as it would be in numerical computing. A very convenient feature of SymPy is that symbolic expressions can be turned into ordinary Python functions via lambdify. Let us take the dydt expression above and turn it into a Python function v t, v0, g :.
We can easily check the answer by inserting the roots in y. Inserting an expression e2 for e1 in some expression e is done by e. In our case we check that. A Taylor polynomial of order n for an expression e in a variable t around the point t0 is computed by e.
Later chapters utilize SymPy where it can save some algebraic work, but this book is almost exclusively devoted to numerical computing. Statements can also be executed interactively in a Python shell. Any error in any statement may lead to termination of the execution or wrong results. The computer does exactly what the programmer tells the computer to do!
Here obj may also represent an expression, say a formula, whose value is a Python object. Names of variables can contain upper and lower case English letters, underscores, and the digits from 0 to 9, but the name cannot start with a digit. Nor can a variable name be a reserved word in Python. If there exists a precise mathematical description of the problem to be solved in a program, one should choose variable names that are in accordance with the mathematical description.
Well-chosen variable names are essential for making a program easy to read, easy to debug, and easy to extend. Well-chosen variable names also reduce the need for comments. Comment lines.
Everything after on a line is ignored by Python and used to insert free running text, known as comments. The purpose of comments is to explain, in a human language, the ideas of several forth- coming statements so that the program becomes easier to understand for humans. Some variables whose names are not completely self-explanatory also need a comment. Object types. In this chapter we have worked with the following types. Operators in arithmetic expressions follow the rules from mathematics: power is evaluated before multiplication and division, while the latter two are evaluated before addition and subtraction.
These rules are overridden by parentheses. We suggest using parentheses to group and clarify mathematical expressions, also when not strictly needed. Common mathematical functions. The math module contains common mathematical functions for real numbers. Modules must be imported before they can be used.
To print the result of calculations in a Python program to a terminal window, we apply the print command, i. Several objects can be printed in one statement if the objects are separated by commas. Be careful with integer division! A common error in mathematical computations is to divide two integers, because this results in integer division in Python 2.
To avoid integer division, ensure that every division involves at least one real number, e. Complex numbers. One example is If the real and imaginary parts are available as variables r and i, a complex number can be created by complex r, i. The cmath module must be used instead of math if the argument is a complex variable. This problem can be solved by basic high school physics as you are encouraged to do in Exercise 1.
Our programming goal is to make a program for evaluating 1. The program should write out the value of all the involved variables and what their units are. We remark that the formula 1.
For a hard kick, air resistance may be as important as gravity. We choose to write out all numerical values with one decimal. The backslash in the triple-quoted multi-line string makes the string continue on the next line without a newline.
This means that removing the backslash results in a blank line above the v0 line and a blank line between the x and y lines in the output on the screen. The rest of the program should be self-explanatory at this stage in the book. We can execute the program in IPython or an ordinary terminal window and watch the output: Terminal. Complete programs and parts of programs snippets are typeset with a light blue background.
A snippet looks like this:. As a reader of this book, you may wonder if a code shown is a complete program you can try out or if it is just a part of a program a snippet so that you need to add surrounding statements e. The appearance of a vertical line to the left or not will then quickly tell you what type of code you see. Recall from Section 1. We refer to Appendix H. Style guide for Python code. Some exceptions to the rules are made to make code snippets shorter: multiple imports on one line and less blank lines.
What does it mean to solve an exercise? The solution to most of the exercises in this book is a Python program. A complete solution to a pro- gramming exercises therefore consists of two parts: 1 the program text and 2 a demonstration that the program works correctly. In cases where the correctness of the output is not obvious, it is necessary to prove or bring evidence that the result is correct. The requirement is to provide evidence to the claim that the program is without programming errors.
The sample run of the program to check its correctness can be inserted at the end of the program as a triple-quoted string. Alternatively, the output lines can be inserted as comments, but using a multi-line string requires less typing. Technically, a string object is created, but not assigned to any name or used for anything in the program beyond providing useful information for the reader of the code. One can do Terminal. Filename: 1plus1. Make such a program in Python. Write a Python program for doing arithmetics to answer the question.
Filename: seconds2years. Use that one inch is 2. Filename: 1liter. Make a program for computing how much money euros have grown to after three years with 5 percent interest rate.
If your program does not work, check that you have copied the code correctly. When they do not work, identify and correct the erroneous statements. Filename: gaussian1. The function 1. Gauss introduced the function 1. We can use the formulas for Fd and Fg to study the importance of air resistance versus gravity when kicking a football. Make a program that computes the drag force and the gravity force on a football. Also print the ratio of the drag force and the gravity force. Filename: kick.
When the temperature exceeds a critical point, reactions begin and proceed faster as the temperature increases. In the egg white, the proteins start to coagulate for temperatures above 63 C, while in the yolk the proteins start to coagulate for temperatures above 70 C. For a soft boiled egg, the white needs to have been heated long enough to coagulate at a temperature above 63 C, but the yolk should not be heated above 70 C.
For a hard boiled egg, the center of the yolk should be allowed to reach 70 C. Furthermore, Tw is the temperature in C degrees of the boiling water, and To is the original temperature in C degrees of the egg before being put in the water.
Filename: egg. There is no programming in this exercise, just physics and mathematics. Let x t , y t be the position of the ball, i. There are well-known relations between acceleration, velocity, and position: the acceleration is the time derivative of the velocity, and the velocity is the time derivative of the position. Therefore we have that. Use the initial conditions on velocity and position,. Also show that if we eliminate t, we end up with the relation 1. You may read more about this type of motion in a physics book, e.
Filename: trajectory. Find the versions that will not work correctly and explain why in each case. Explain why some statements fail and correct the errors. It is wise to test the values of the expressions on the right-hand side, and the validity of the variable names, separately before you put the left- and right-hand sides together in statements.
The last two statements work, but explaining why goes beyond what is treated in this chapter. Correct the program so that it solves the given equation. Loops and lists 2. This chapter explains how repetitive tasks in a program can be auto- mated by loops. Loops and lists, together with functions and if tests from Chapter 3, lay the fundamental programming foundation for the rest of the book.
Such a table may look like this: We will return to this detail later. The main problem with the program above is that lots of statements are identical and repeated. First of all it is boring to write this sort of repeated statements, especially if we want many more C and F values in the table.
Second, the idea of the computer is to automate repetition. These constructs are called loops and come in two variants in Python: while loops and for loops.
Most programs in this book employ loops, so this concept is extremely important to learn. We shall introduce this kind of loop through an example. The task is to generate the rows of the table of C and F values. For each C value we compute the corresponding F value and write out the two temperatures. In addition, we also add a line of dashes above and below the table. A very important feature of Python is now encountered: the block of statements to be executed in each pass of the while loop must be indented.
In the example above the block consists of three lines, and all these lines must have exactly the same indentation. Our choice of indentation in this book is four spaces. Many novice Python programmers forget the colon at the end of the while line - this colon is essential and marks the beginning of the indented block of statements inside the loop.
Later, we will see that there are many other similar program constructions in Python where there is a heading ending with a colon, followed by an indented block of statements. Programmers need to fully understand what is going on in a program and be able to simulate the program by hand.
Let us do this with the program segment above. Since the loop condition is true, we enter the loop and execute all the indented statements. That is, we compute F corresponding to the current C value, print the temperatures, and increment C by dC.
Thereafter, we enter the second pass in the loop. We execute the statements in the indented loop block, C becomes , this is still less than or equal to 40, so we enter the loop block again. Before this assignment, C was already bound to an int object, and this object is automatically destroyed when C is bound to a new object and there are no other names variables referring to this previous object if you did not get this last point, just relax and continue reading!
Not only comparisons between numbers can be used as conditions in while loops: any expression that has a boolean True or False value can be used. Such expressions are known as logical or boolean expressions. The keyword not can be inserted in front of the boolean expression to change the value from True to False or from False to True. Mathematically it is easier to read C! If cond1 and cond2 are two boolean expressions with values True or False, the compound boolean expression cond1 and cond2 is True if both cond1 and cond2 are True.
On the other hand, cond1 or cond2 is True if at least one of the conditions, cond1 or cond2, is True. Remark In Python, cond1 and cond2 or cond1 or cond2 returns one of the operands and not just True or False values as in most other computer languages.
The operands cond1 or cond2 can be expres- sions or objects. To see such values in action, we recommend doing Exercises 2. Essentially, if a tests if a is a non-empty object or if it is non-zero value.
Such constructions are frequent in Python code. Erroneous thinking about boolean expressions is one of the most common sources of errors in computer programs, so you should be careful every time you encounter a boolean expression and check that it is correctly stated. For instance, the sine function can be calculated as a polynomial:.
Computing k! Say we want to compute the right-hand side of 2. Writing out and implementing each one of these terms is a tedious job that can easily be automated by a loop. Computation of the sum in 2. The purpose of each pass of the loop is to compute a new term and add it to s. The best way to understand such a program is to simulate it by hand. That is, we go through the statements, one by one, and write down on a piece of paper what the state of each variable is.
Up to now a variable has typically contained a single number. Sometimes numbers are naturally grouped together. With a variable that refers to the list, we can work with the whole group at once, but we can also access individual elements of the group. Figure 2. In general, a list may contain a sequence of arbitrary objects in a given order. Python has great functionality for examining and manipulating such sequences of objects, which will be demonstrated below. The variable C now refers to a list object holding 13 list elements.
All list elements are in this case int objects. Associated with the C list above we have 13 indices, starting with 0 and ending with To access the element with index 3, i. Elements in lists can be deleted, and new elements can be inserted anywhere. The functionality for doing this is built into the list object and accessed by a dot notation. Two examples are C. The number of elements in a list is given by len C. All this gives enormous power in the hands of programmers.
New elements can be inserted anywhere in the list and not only at the end as we did with C. With del C[i] we can remove an element with index i from the list C. Observe that this changes the list, so C[i] refers to another the next element after the removal:. The command C. Python allows negative indices, which leads to indexing from the right. As demonstrated below, C[-1] gives the last element of the list C. C[-2] is the element before C[-1], and so forth. Building long lists by writing down all the elements separated by commas is a tedious process that can easily be automated by a loop, using ideas from Section 2.
Say we want to build a list of degrees from to in steps of 2. We then start with an empty list and use a while loop to append one element at a time:. In the next sections, we shall see how we can express these six lines of code with just one single statement. There is a compact syntax for creating variables that refer to the various list elements. Simply list a sequence of variables on the left-hand side of an assignment to a list:.
The number of variables on the left-hand side must match the number of elements in the list, otherwise an error occurs. Although C. There are no strict rules in Python whether functionality regarding an object is reached through a method or a function.
When data are collected in a list, we often want to perform the same operations on each element in the list. We then need to walk through all list elements. Computer languages have a special construct for doing this conveniently, and this construct is in Python and many other languages called a for loop. The for C in degrees construct creates a loop over all elements in the list degrees. In each pass of the loop, the variable C refers to an element in the list, starting with degrees[0], proceeding with degrees[1], and so on, before ending with the last element degrees[n-1] if n denotes the number of elements in the list, len degrees.
Each statement in the block must be indented, as we explained for while loops. In the example above, the block belonging to the for loop contains only one statement. Then we enter the for loop. There are no more statements in the loop block, so we proceed with the next pass of the loop. After having printed the list element with value , we move on to the statement after the indented loop block, which prints out the number of list elements. The total output becomes list element: 0 list element: 10 list element: 20 list element: 40 list element: The degrees list has 5 elements.
Correct indentation of statements is crucial in Python, and we therefore strongly recommend you to work through Exercise 2. Making the table. The complete program may look like this:. The print C, F statement just prints the value of C and F with a default format, where each number is separated by one space character blank. This does not look like a nice table the output is identical to the one shown in Section 2. We may also add a headline to the table.
We have already solved the problem of printing out a nice-looking con- version table for Celsius and Fahrenheit degrees. The next paragraphs explore some other possible Python con- structs and programs to store numbers in lists and print out tables.
We should use a loop to automate the construction of the Cdegrees list. For example, range 2, 8, 3 returns 2 and 5 and not 8 , while range 1, 11, 2 returns 1, 3, 5, 7, 9. A for loop over integers are written as for i in range start, stop, step Note that the upper limit must be greater than 40 to ensure that 40 is included in the range of integers. The following Python code implements this task:. Since len somelist returns the length of somelist and the largest legal index is len somelist -1, because indices always start at 0, range len somelist will generate all the correct indices: 0, 1,.
This might be necessary or convenient, but if possible, Python programmers are encouraged to use for element in somelist, which is more elegant to read. Iterating over loop indices is useful when we need to process two lists simultaneously. Creating a list of length n consisting of zeros for instance is done by.
Suppose we want to change the Cdegrees list by adding 5 to all elements. This object is never inserted in the list. The variable c can only be used to read list elements and never to change them. Only an assignment of the form. There is a way of traversing a list where we get both the index and an element in each pass of the loop:. The general syntax reads.
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