当我试图用非线性方程组求解非线性方程组时出错

Question

我试着用SymPy来解一个非线性方程组，这是我以前从来没有做过的，但是我不能让它工作

以下是我尝试过的：

from sympy import *

a, b, c, d, e, f, x, y, z, g0, g1, g2 = symbols('a:f x:z g:3')
system = [(a * (x - y*z))/(b * (1 - z**2)) - g1,
(a * (y - x*z))/(c * (1 - z**2)) - g2,
f - d * (a * (x - y*z))/(b * (1 - z**2)) - e * (a * (y - x*z))/(c * (1 - z**2)) - g0]
nonlinsolve(system, [x, y, z])

我想要的是x，y和z的值，用其他符号来解这个系统。但我得到以下错误信息：

Traceback (most recent call last):
  File "/Users/phl43/Desktop/test.py", line 7, in <module>
    nonlinsolve(system, [x, y, z])
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/sympy/solvers/solveset.py", line 3053, in nonlinsolve
    res = _handle_positive_dimensional(polys, symbols, denominators)
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/sympy/solvers/solveset.py", line 2801, in _handle_positive_dimensional
    denominators)
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/sympy/solvers/solveset.py", line 2719, in substitution
    old_result, solveset_real)
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/sympy/solvers/solveset.py", line 2708, in _solve_using_known_values
    result.remove(res)
ValueError: list.remove(x): x not in list

你知道怎么做吗

Answer 1

查看通过手动解决系统而无需检查可以学到什么：

>>> r = solve(system, dict=True, manual=True, check=False)
>>> r
[{x: -y, z: -1}, {x: y, z: 1}, {x: (b*g1 + c*g2*z)/a, y: (b*g1*z + c*g2)/a}]

前两个解不起作用，因为这将导致被0除。最后一个解将前两个方程设置为0，而最后一个解满足前两个方程，但这使得最后一个表达式与z无关：

>>> [simplify(i.subs(r[-1])) for i in r]
[0, 0, -d*g1 - e*g2 + f - g0]

所以z可以是任何提供g0 = f -d*g1 - e*g2的东西。它是求解x，y和z的不适定方程组