So I was just browsing some code, and I came across a cool module I’d never seen before: SymPy
Basically, SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS).
What is symbolic mathematics?
Symbolic computation deals with the computation of mathematical objects symbolically. This means that the mathematical objects are represented exactly, not approximately, and mathematical expressions with unevaluated variables are left in symbolic form. Symbolic computation is handling non-numerical values, this means symbols like in algebra. Variables are defined as
In simple word, “Variables are defined as Symbols in Symbolic Computation instead of defining variables as numerical values ”
This will be more clear from an example from SymPy official documentation.
Let us define a symbolic expression, representing the mathematical expression x+2xy+2y.
>>> from sympy import symbols >>> x, y = symbols('x y') >>> expr = x + 2*y >>> expr x + 2*y
Instead of evaluating to something by convention, the expression remains as just, x+2*y
>>> x*expr x*(x + 2*y)
Here, we might have expected x(x+2y) to transform into x^2+2xy, but instead, we see that the expression was left alone. This is a common theme in SymPy.
The Power of Symbolic Computation
The real power of a symbolic computation system such as SymPy is the ability to do all sorts of computations symbolically.
SymPy can simplify expressions, compute derivatives, integrals, and limits, solve equations, work with matrices, and much, much more, and do it all symbolically. It includes modules for plotting, printing (like 2D pretty printed output of math formulas,), code generation, physics, statistics, combinatorics, number theory, geometry, logic, and more.
Examples from official SymPy tutorial
Solve x^2 – 2 = 0
>>> solve(x**2 - 2, x) [-√2, √2
>>> integrate(sin(x**2), (x, -oo, oo)) √2⋅√π ───── 2
To install SymPy run:
sudo pip install SymPy
If you already have Anaconda and want to update SymPy to the latest version, use:
conda update sympy
After installation, it is best to verify that your freshly-installed SymPy works. To do this, start up Python and import the SymPy libraries:
$ python >>> from sympy import *
From here, execute some simple SymPy statements like the ones below:
>>> x = Symbol('x') >>> limit(sin(x)/x, x, 0) 1 >>> integrate(1/x, x) log(x)
Currently, I am going through the tutorial and documentation to get familiar with using the software.
Github: Introduction to contribution