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])
    

    Sympy 解方程_第1张图片


  2. 解微积分
    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
    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

    Sympy 解方程_第2张图片

  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

    Sympy 解方程_第3张图片

    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})

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