# Python Data Types

One of the things that can make Python a little tricky is the different interpretations it can put on a value. Python uses a few simple data types, and any time a value is entered, python must decide how that value is to be interpreted. Python can support very sophisticated user-constructed data types, but we will only concern ourselves here with the basic predefined ways that input can be interpreted.

## Floating Point Numbers

The most important data type for mathematicians is the floating
point number. By default, python interprets any number that includes
a decimal point as a *double precision floating point* number.
We will not discuss the true binary representation of these numbers.
In order to make good use of python, we need only to observe that
floating point representatations are effectively writing numbers
in scientific notation:
$a\times {10}^{b}$.
The number $a$ is called the mantissa of the
number, while $b$ is the exponent. In a double precision
representation, the number $a$ may be thought of
as a sixteen-digit number between -1 and 1. This is not exactly right,
but it is a decent rule of thumb. The number $b$ is
an integer between -1022 and 1023, inclusive.

>>> a = 3 >>> a/4 0 >>> float(a)/4 0.75

## Integers

When you type `a=3` at the prompt, python interprets
the number 3 as an integer. This is probably what you want, but
it might lead to arithmetic results that surprise you. Consider the
following python commands.

>>> a = 3 >>> a/4 0 >>> float(a)/4 0.75

When python does arithmetic with integers, it always truncates
the result to an integer. Thus in python, `3/4=0`. If we
want to get decimal answers, at least one number in the
computation must be in a floating point representation.

We can convert integers to floating point numbers in python using
the `float` and `double` functions. These are almost the same -
two names are provided because in some programming languages there are
differences between float and double types. There are no such
differences in python, but note that `float` is built in to python,
while `double` comes from numpy, and hence is slightly different.
Interestingly, it turns out that the `double` function is somewhat
slower than `float`.

>>> from numpy import * >>> a=3 >>> 1/a 0 >>> 1/float(a) 0.3333333333333333 >>> 1/double(a) 0.33333333333333331

By the same token, we can truncate floating
point numbers to integers in python using the `int` command.

>>> pi 3.141592653589793 >>> int(pi) 3

## Strings

Strings (in *any* programming language) are just plain ol' text.
Computers like to deal in numbers, so when we want to type plain ol'
text, we must enclose it in quotation marks. We can use any ol' kind
of quotation marks we want, whether single or double, just so long as we
match them properly.

>>> hi="Hello, world!" >>> bye='Goodbye, cruel world!' >>> wut="What is this 'world' you speak of?" >>> hi 'Hello, world!' >>> bye 'Goodbye, cruel world!' >>> wut "What is this 'world' you speak of?"

Evidently we can enclose one quote inside another, so long
as we manage the types of quotation marks used. There is one other
type of quotation mark, created by typing three single-quotes together.
This lets us type multiple line strings. The `\n` you see
is a representation for a newline character - the invisible
character a computer uses to move to the next line.

>>> longstring='''This is a preposterously long string, ... which we use to illustrate that we can be quite verbose ... in python if we want to.''' >>> longstring 'This is a preposterously long string,\nwhich we use to illustrate that we can be quite verbose\nin python if we want to.'

Assignment 6 is posted.

The midterm exam will take place on Friday,
12 October. As always, you are permitted any paper
notes you find useful, but no electronic devices are
allowed. The test is cumulative, but emphasizes
the material covered in the last fours weeks.
A sample exam is
available.

You need to install
Matlab
on your computer by Wednesday.
You do not need Simulink or any particular toolboxes, though
you might find the Symbolic toolbox useful at some time
in the future (not in this class).