在 SymPy 求和中替换值

发布于 2025-01-11 01:51:34 字数 612 浏览 0 评论 0原文

当将值替换为 SymPy sum 时，它似乎无法识别变量是否已索引，而只是简单地分解出所有索引变量，如下所示：

# Define variables.
z_tilde_i = sympy.IndexedBase('\\tilde{z}')
rho_i = sympy.IndexedBase('\\rho')
M = sympy.symbols('M')
n = sympy.symbols('n', integer = True)
i = sympy.Idx('i', n)

# Define equation M = sum(rho * deltaZ).
eq_total_mass = sympy.Eq(M, sympy.Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, n - 1)))

# Try to substitute values.
print(eq_total_mass.rhs.subs(n, 3).doit())
>>> 3*(\tilde{z}[i + 1] - \tilde{z}[i])*\rho[i]

如何使 SymPy sum 识别索引变量？

原文

When substituting values into a SymPy sum, it doesn't seem to recognise that the variables are indexed, and simply factors out all the indexed variables, like so:

# Define variables.
z_tilde_i = sympy.IndexedBase('\\tilde{z}')
rho_i = sympy.IndexedBase('\\rho')
M = sympy.symbols('M')
n = sympy.symbols('n', integer = True)
i = sympy.Idx('i', n)

# Define equation M = sum(rho * deltaZ).
eq_total_mass = sympy.Eq(M, sympy.Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, n - 1)))

# Try to substitute values.
print(eq_total_mass.rhs.subs(n, 3).doit())
>>> 3*(\tilde{z}[i + 1] - \tilde{z}[i])*\rho[i]

How to make the SymPy sum recognise the indexed variables?

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撩心不撩汉 2025-01-18 01:51:34

解决方法：

无需将 i 定义为 Idx：

>>> i = var('i')
>>> Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, 1)).doit()
(-\tilde{z}[0] + \tilde{z}[1])*\rho[0] + (-\tilde{z}[1] + \tilde{z}[2])*\rho[1]

或者如果需要，请在定义 n 时不要使用 integer=True：

>>> n = var('n')
>>> i = sympy.Idx('i', n)
>>> Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, 1)).doit()
(-\tilde{z}[0] + \tilde{z}[1])*\rho[0] + (-\tilde{z}[1] + \tilde{z}[2])*\rho[1]

For a workaround:

There is no need to define i as Idx:

>>> i = var('i')
>>> Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, 1)).doit()
(-\tilde{z}[0] + \tilde{z}[1])*\rho[0] + (-\tilde{z}[1] + \tilde{z}[2])*\rho[1]

Or if you do, don't use the integer=True when defining n:

>>> n = var('n')
>>> i = sympy.Idx('i', n)
>>> Sum(rho_i[i] * (z_tilde_i[i + 1] - z_tilde_i[i]), (i, 0, 1)).doit()
(-\tilde{z}[0] + \tilde{z}[1])*\rho[0] + (-\tilde{z}[1] + \tilde{z}[2])*\rho[1]

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