MATH 253 Python Commands

Information on Python

**Last updated 1/17/21 (Subfolders may have been updated more recently.)

Python is a programming language. We will largely be using Google's CoLaboratory, a collaborative Python environment, and I will share assignment files with you as needed.

Fortunately for us, we don't have to begin the programming from scratch; there are a number of useful commands built in, and there are also a lot of command libraries that others have written (and we can use!).

Two major packages of commands are numpy and sympy. These can be loaded via "import numpy" and "import sympy" respectively (without the quotes). Most of the commands we will need are in these two packages, although the "math" package will also be useful. There are other ways to go about this, as well, and there are some subtleties that may crop up from time to time, but this is a good start. Some find it useful to "import numpy as np" so that they when they need to refer to the numpy package (which comes up often), there is less to type.

Rather than attempt a Python tutorial here, I will offer some of the basic things that we will find useful so that you can search for how to implement them.

• To execute a command, use SHIFT+ENTER. ENTER alone will give you another line in the same command window (also useful).
• Loops look like "for i in range(100):" (for example). In Python, range(100) refers to the integers 0, 1, 2, ..., 99 (not 1 to 100). Generally, Python numbering starts at 0, not 1.
• Python requires that you declare variables. Use "symbols" for this; e.g., x,y=sp.symbols("x,y") (note the . notation - this is how we tell Python which library to look in for a particular command).
• You can use "factor" to factor a polynomial if you have the sympy package loaded: "sp.factor(x**2+3*x+2)".
• Exponentiation is performed with ** instead of ^ -- watch out for that!
• You can solve equations with the solve command: solve((x+y-2,x-y-4),(x,y)) (for example). Python's solve command assumes that the equation is of the form your_expression=0 -- note that neither "equation" in the command has an = in it. Also, be sure to declare your variables first.
• You can also simplify expressions with the simplify command: "sp.simplify(expression)" (replacing "expression" with the thing you want to simplify). This requires sympy (and a declaration of variables).
• Sometimes Python just does what you want but doesn't report out. If you want to be sure to see the output, you have to print it: print(whatever).

Classroom Demos

• Stochastic matrices
• Exam template

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