SymPy

SymPy

Developer(s)	Independent group of people
Stable release	0.6.6 / 2009-12-20; 21 hours ago
Written in	Python
Operating system	Cross-platform
Type	Computer algebra system
License	New BSD license
Website	sympy.org

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)
• mpmath: a Python library for arbitrary-precision floating-point arithmetic (included in SymPy)
• sympycore: another Python CAS
• symbide: GUI for SymPy in PyGTK
• symfe: Lightweight symbolic finite element calculations in Python

Usage examples

Differentiation:

>>> from sympy import *
>>> x,y = symbols('xy')
>>> 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)

Output of the plotting example

Plotting:

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

See also

Free software portal

• Comparison of computer algebra systems

External links

• SymPy Project Home
• Planet SymPy