Sympyとは？

 Pythonの記号計算ライブラリ
 公式ドキュメント : http://www.sympy.org/en/index.html
 日本語資料 : http://www.turbare.net/transl/scipy-lecture-notes/packages/sympy.html

使い方
 In [3]: from sympy import *
 In [4]: init_session() 
 IPython console for SymPy 0.7.6 (Python 3.4.6-64-bit) (ground types: python)
 
 These commands were executed:
 >>> from __future__ import division
 >>> from sympy import *
 >>> x, y, z, t = symbols('x y z t')
 >>> k, m, n = symbols('k m n', integer=True)
 >>> f, g, h = symbols('f g h', cls=Function)
 >>> init_printing()
  
 


Symbols - 変数定義

 In [1]: from sympy import *
 In [2]: x + 1
 ---------------------------------------------------------------------------
 NameError                                 Traceback (most recent call last)
 <ipython-input-2-4cf92658b648> in <module>()
 ----> 1 x + 1
 
 NameError: name 'x' is not defined
 
 In [3]: x = symbols('x')
 In [4]: x + 1
 Out[4]: x + 1
 
 π : 円周率
 In [13]: pi
 Out[13]: π
 
 In [14]: pi.evalf(50)
 Out[14]: 3.1415926535897932384626433832795028841971693993751

expand - 展開

 In [5]: expand((x + 1)**2)
 Out[5]: x**2 + 2*x + 1
 factor - 因数分解
 
 In [6]: factor(x**4 - 3*x**2 + 1)
 Out[6]: (1 + x - x**2)*(1 - x - x**2)

simplify - 簡約

 In [7]: simplify((x**3 + x**2 - x - 1)/(x**2 + 2*x + 1))
 Out[7]: x - 1

limit - 極限
 
 In [8]: limit(x, x, oo)
 Out[8]: oo

diff - 微分

 In [9]: diff(cos(x), x)
 Out[9]: -sin(x)
 In [10]: diff(x**3 + x**2 - x - 1, x)
 Out[10]: 3*x**2 + 2*x - 1

integrate - 積分

 In [11]: integrate(cos(x), x)
 Out[11]: sin(x)
 In [12]: integrate(x**3 + x**2 - x - 1, x)
 Out[12]: x**4/4 + x**3/3 - x**2/2 - x

Matrix - 行列

 In [13]: Matrix([[1, 2, 3], [-2, 0, 4]])
 Out[13]:
 Matrix([
 [ 1, 2, 3],
 [-2, 0, 4]])

solve - 式を解く

 In [14]: solve(x**2 - 1, x)
 Out[14]: [-1, 1]