Sympy 解方程

1. 解普通方程

   from sympy import *
   x = Symbol('x')
   y = Symbol('y')
   print solve([2 * x - y - 3, 3 * x + y - 7],[x, y])
   

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2. 解微积分
   

   from sympy import *
   n = Symbol('n')
   s = ((n+3)/(n+2))**n
   
   #无穷为两个小写o
   
   print limit(s, x, oo)
   

3. 求定积分
   

   from sympy import *
   t = Symbol('t')
   x = Symbol('x')
   m = integrate(sin(t)/(pi-t),(t,0,x))
   n = integrate(m,(x,0,pi))
   print n
   

   

4. 解微分方程

   #y' = 2xy  的通解
   
   from sympy import *
   f = Function('f')
   x = Symbol('x')
   print dsolve(diff(f(x),x) - 2*f(x)*x,f(x))
   
   
   #说明：
   
   f = Function('f')
   x = Symbol('x')
   
   #表示f(x)的导：
   
   diff(f(x), x, index)    
   >>> diff(sin(x), x, 1)
   cos(x)
   
   dsolve(eq, f(x))
       #第一个参数为微分方程（要先将等式移项为右端为0的形式)
       #第二个参数为要解的函数(在微分方程中)
   

5. 矩阵化简

   from sympy import *
   x1,x2,x3 = symbols('x1 x2 x3')
   a11,a12,a13,a22,a23,a33 = symbols('a11 a12 a13 a22 a23 a33')
   m = Matrix([[x1,x2,x3]])
   n = Matrix([[a11,a12,a13],[a12,a22,a23],[a13,a23,a33]])
   v = Matrix([[x1],[x2],[x3]])
   f = m * n * v
   f[0] 化简， subs代入计算
   print f[0].subs({x1:1, x2:1, x3:1})