SymPy

Infobox_Software
name=SymPy
logo=
genre=Computer algebra system
license=New BSD license
website=http://code.google.com/p/sympy/
latest release version=0.6.2
latest release date=August 17, 2008
programming language=Python
operating system=Cross-platform
developer=Independent group of people:"Not to be confused with SimPy, a Python discrete-event simulation language."

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python and does not require any external libraries, except optionally for plotting support.

SymPy is free software. It is currently under active development, the lead developer is Ondřej Čertík.

Features

Currently, SymPy core has around 6300 lines of code (including extensive comments and docstrings) and its capabilities include:

* basic arithmetics *,/,+,-,**
* basic simplification (like a*b*b + 2*b*a*b -> 3*a*b^2)
* expansion (like (a+b)^2 -> a^2 + 2*a*b + b^2)
* functions (exp, ln, ...)
* complex numbers (like exp(I*x).expand(complex=True) -> cos(x)+I*sin(x))
* differentiation
* taylor (laurent) series
* substitution (like x -> ln(x), or sin -> cos)
* arbitrary precision integers, rationals and floats
* noncommutative symbols
* pattern matching

Then there are SymPy modules (18200 lines including documentation) for these tasks:

* more functions (sin, cos, tan, atan, asin, acos, factorial, zeta, legendre)
* limits (like limit(x*log(x), x, 0) -> 0)
* integration using extended Risch-Norman heuristic
* polynomials (division, gcd, square free decomposition, groebner bases, factorization)
* solvers (algebraic, difference and differential equations, and systems of equations)
* symbolic matrices (determinants, LU decomposition...)
* Pauli and Dirac algebra
* geometry module
* plotting (2D and 3D)

There are extensive tests (6148 lines in 58 files) for every single feature in SymPy.

Related projects

* SAGE: an open source alternative to Mathematica, Maple, Matlab and Magma (SymPy is included in SAGE)
* [http://code.google.com/p/mpmath/ mpmath] : a Python library for arbitrary-precision floating-point arithmetic (included in SymPy)
* [http://code.google.com/p/sympycore/ sympycore] : a fork of SymPy
* symbide: GUI for SymPy in PyGTK
* symfe: Lightweight symbolic finite element calculations in Python

Usage examples

Differentiation:>>> from sympy import *>>> x,y = symbols('x', 'y')>>> f = x**2 / y + 2 * x - ln(y)>>> diff(f,x)2 + 2*x/y>>> diff(f,y)-1/y - x**2*y**(-2)>>> diff(diff(f,x),y)-2*x*y**(-2)

Plotting:>>> from sympy import *>>> Plot(cos(x*3)*cos(y*5)-y) [0] : -y + cos(3*x)*cos(5*y), 'mode=cartesian'

See also

* Comparison of computer algebra systems

External links

* [http://code.google.com/p/sympy/ SymPy Project Home]
* [http://planet.sympy.org/ Planet SymPy]