Arithmetic with Python  
24jun13, additions 3mar16


\begin{document}
\maketitle

\section{Introduction}
Python is a popular computer language which has a useful feature, enabling you 
to do arithmetic. Every calculator can do that! True, but Python is \textit{extensible}. That means that you can build your own algorithms. It is as if you 
could add a new button to your calculator to do something new, easily.

MORE on the introduction.

\textbf{If you know Python and use it on your computer, skip to the section on solving Diophantine Equations}

\section{SymPy Live}
Many computer operating systems come with Python built in. If yours does not
already have it installed, you can download (free) a Python installation. But
for a start, we can use a webservice called 
 SymPy Live .

This is a webservice, much like our texWins, where a full Python program is 
on a remote server, and you have access to it via your webpage. Using SymPy
is not as nice, or as versatile as using the "real thing" on your computer. 
But it works well enough for our purposes. 


\section{SymPy Lessons}
 First Lesson on Long Division 

MORE on how to use SymPy Live
\section{On Solving Diophantine Equations}

The lesson that ends this discuss is on 
 Solving Diophantine Equations 
using the Python functions in Jim Carlson's essay, and also how 
to solve these equations by hand. You will need to understand Euclid's
algorithm for it. 

To use Carlson's functions you will need to import or import * the 
module  carlson.py  into your interactive
Python session. If you already know Python, you can read the module and
see that 
\begin{itemize}
\item \texttt{ldv(a,b)} prints the quotient and remainder of long division of the dividend $a$ by the divisor $b$.
\item \texttt{euc(a,b)} prints the greatest commond divisor $gcd(a,b)$.
\item \texttt{isolve(a,b,c)} prints one solution to $ax+by=c$.
\end{itemize}

If you use Sympy for these functions, copy and paste their code into the
interactive session.
\end{document}