88 lines
2.2 KiB
Python
88 lines
2.2 KiB
Python
"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/14684
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"""
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import sympy
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# 定义符号
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print()
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print('定义符号：')
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x, y, z = sympy.symbols('x y z') # 使用sympy.symbols
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print(x)
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print(y+1)
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print(z**2)
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print()
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# 替换（Substitution）
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print('变量替换：')
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expression_1 = x**2+1
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value_1 = expression_1.subs(x, 3) # 使用.subs()方法
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print(value_1)
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print()
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# 字符串转成符号表达式
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print('字符串转成符号表达式：')
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expression_string = 'x**3+1'
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print(expression_string)
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expression_2 = sympy.sympify(expression_string) # 使用sympy.sympify()
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print(expression_2)
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value_2 = expression_2.subs(x, 2)
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print(value_2)
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print()
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# 简化表达式
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print('简化表达式：')
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expression_3 = sympy.simplify(sympy.sin(x)**2 + sympy.cos(x)**2) # 使用sympy.simplify()
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print(expression_3)
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print()
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# 符号矩阵
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print('符号矩阵：')
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a, b = sympy.symbols('a b')
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matrix = sympy.Matrix([[1, a], [0, b]]) # 使用sympy.Matrix()
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print(matrix)
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print()
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sympy.init_printing(use_unicode=True)
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# 符号矩阵的特征值和特征向量
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print('符号矩阵的特征值和特征向量：')
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eigenvalue = matrix.eigenvals() # 使用.eigenvals()方法
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print('特征值\n', eigenvalue, '\n')
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sympy.pprint(eigenvalue) # 使用sympy.pprint()输出
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print('\n', sympy.pretty(eigenvalue)) # 使用sympy.pretty()美化后输出
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print()
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eigenvector = matrix.eigenvects() # 使用.eigenvects()方法
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print('特征向量\n', eigenvector, '\n')
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sympy.pprint(eigenvector)
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print('\n', sympy.pretty(eigenvector))
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print()
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P, D = matrix.diagonalize() # 使用.diagonalize()方法
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print('特征值\n', D, '\n')
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print(sympy.pretty(D), '\n')
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print('特征向量\n', P, '\n')
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print(sympy.pretty(P), '\n')
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print()
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print('特征值\n', D.subs(a, -4).subs(b, 2), '\n')
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print(sympy.pretty(D.subs(a, -4).subs(b, 2)), '\n')
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print('特征向量\n', P.subs(a, -4).subs(b, 2), '\n')
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print(sympy.pretty(P.subs(a, -4).subs(b, 2)), '\n')
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print()
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# 和numpy对比
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print('和numpy对比：')
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import numpy as np
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matrix = np.array([[1, -4], [0, 2]])
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eigenvalue, eigenvector = np.linalg.eig(matrix)
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print('特征值\n', eigenvalue)
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print('特征向量\n', eigenvector)
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print() |