This tutorial assumes that the reader already knows the basics of the Python programming
language. If you do not, the `official Python
tutorial <http://docs.python.org/3/tutorial/index.html>`_ is excellent.
This tutorial assumes a decent mathematical background. Most examples require
knowledge lower than a calculus level, and some require knowledge at a
calculus level. Some of the advanced features require more than this. If you
come across a section that uses some mathematical function you are not
familiar with, you can probably skip over it, or replace it with a similar one
that you are more familiar with. Or look up the function on Wikipedia and
learn something new. Some important mathematical concepts that are not common
knowledge will be introduced as necessary.
.. sidebar:: Quick Tip
You do not need to install SymPy to try it. You can use the online shell
at http://live.sympy.org, or the shell at the bottom right of this
You will need to install SymPy first. See the :ref:`installation guide
Alternately, you can just use the SymPy Live Sphinx extension to run the code
blocks in the browser. For example, click on the green "Run code block in
SymPy Live" button below
>>> from sympy import *
>>> x = symbols('x')
>>> a = Integral(cos(x)*exp(x), x)
>>> Eq(a, a.doit())
Eq(Integral(exp(x)*cos(x), x), exp(x)*sin(x)/2 + exp(x)*cos(x)/2)
The SymPy Live shell in the bottom corner will pop up and evaluate the code
block. You can also click any individual line to evaluate it one at a time.
The SymPy Live shell is a fully interactive Python shell. You can type any
expression in the input box to evaluate it. Feel free to use it throughout
the tutorial to experiment.
To show or hide the SymPy Live shell at any time, just click the green button
on the bottom right of the screen.
By default, the SymPy Live shell uses LaTeX for output. If you want the
output to look more like the output in the documentation, change the
output format to ``Str`` or ``Unicode`` in the settings.
If you wish to modify an example before evaluating it, change the evaluation
mode to "copy" in the SymPy Live settings. This will cause clicking on an
example to copy the example to the SymPy Live shell, but not evaluate it,
allowing you to change it before execution. You can also use the up/down
arrow keys on your keyboard in the input box to move through the shell
The SymPy Live shell is also available at http://live.sympy.org, with extra
features, like a mobile phone enhanced version and saved history.
This tutorial was the basis for a tutorial given at the 2013 SciPy conference
in Austin, TX. The website for that tutorial is `here
<http://certik.github.io/scipy-2013-tutorial/html/index.html>`_. It has links
to videos, materials, and IPython notebook exercises. The IPython notebook
exercises in particular are recommended to anyone going through this tutorial.
About This Tutorial
This tutorial aims to give an introduction to SymPy for someone who has not
used the library before. Many features of SymPy will be introduced in this
tutorial, but they will not be exhaustive. In fact, virtually every
functionality shown in this tutorial will have more options or capabilities
than what will be shown. The rest of the SymPy documentation serves as API
documentation, which extensively lists every feature and option of each
These are the goals of this tutorial:
.. NB: This is mainly here for you, the person who is editing and adding to
this tutorial. Try to keep these principles in mind.
- To give a guide, suitable for someone who has never used SymPy (but who has
used Python and knows the necessary mathematics).
- To be written in a narrative format, which is both easy and fun to follow.
It should read like a book.
- To give insightful examples and exercises, to help the reader learn and to
make it entertaining to work through.
- To introduce concepts in a logical order.
.. In other words, don't try to get ahead of yourself.
- To use good practices and idioms, and avoid antipatterns. Functions or
methodologies that tend to lead to antipatterns are avoided. Features that
are only useful to advanced users are not shown.
- To be consistent. If there are multiple ways to do it, only the best way is
.. For example, there are at least five different ways to create Symbols.
``symbols`` is the only one that is general and doesn't lead to
antipatterns, so it is the only one used.
- To avoid unnecessary duplication, it is assumed that previous sections of
the tutorial have already been read.
Feedback on this tutorial, or on SymPy in general is always welcome. Just
write to our `mailing list