在15*8-2**x=x中求解x的公式求解器无法完成计算

Question

所以我不知道问题的根源是什么(我不知道其他公式是否会发生这种情况)，但是每当我输入15*8-2^x=x，并使用r = solve(leftside - rightside, user_choice)用我的公式求解器求解x时，程序就永远不会结束运行。我在函数中有一行pprint(r)代码，但是程序从来没有到过这一步。(-2**x=x对x的求解效果很好)

在我终止程序后，我收到大约20条错误消息，例如：

File "/Users/myusername/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/solvers/solvers.py", line 1095, in solve
    solution = _solve(f[0], *symbols, **flags)

我在Symbolab中尝试了15*8-2**x=x，它很好地解决了这个问题：https://www.symbolab.com/solver/step-by-step/solve%20for%20x%2C%2015%5Ccdot8-2%5E%7Bx%7D%3Dx

*我不是数学家，这些计算远远超出了我的理解，我只是觉得奇怪的是，当Symbolab设法解决它时，它从未完成或显示错误。那么，是什么导致了这种行为呢？

编辑:堆栈跟踪：

Traceback (most recent call last):
  File "/Users/torrinleonard/PycharmProjects/formula calculator/Complete_solver.py", line 38, in <module>
    Rearrange_input()
  File "/Users/torrinleonard/PycharmProjects/formula calculator/Complete_solver.py", line 29, in Rearrange_input
    r = solve(l - r, user_choice)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/solvers/solvers.py", line 1095, in solve
    solution = _solve(f[0], *symbols, **flags)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/solvers/solvers.py", line 1717, in _solve
    result = list(map(simplify, result))
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 606, in simplify
    expr = expr.replace(
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1497, in replace
    rv = walk(self, rec_replace)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1471, in walk
    newargs = tuple([walk(a, F) for a in args])
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1471, in <listcomp>
    newargs = tuple([walk(a, F) for a in args])
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1471, in walk
    newargs = tuple([walk(a, F) for a in args])
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1471, in <listcomp>
    newargs = tuple([walk(a, F) for a in args])
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1481, in walk
    rv = F(rv)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1490, in rec_replace
    v = _value(expr, result)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/basic.py", line 1455, in <lambda>
    _value = lambda expr, result: value(expr)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 614, in <lambda>
    lambda x: x.func(*[simplify(i, **kwargs) for i in x.args]),
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 614, in <listcomp>
    lambda x: x.func(*[simplify(i, **kwargs) for i in x.args]),
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 699, in simplify
    expr = shorter(expand_log(expr, deep=True), logcombine(expr))
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 1119, in logcombine
    return bottom_up(expr, f)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 1198, in bottom_up
    rv = F(rv)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 1097, in f
    log1[Mul(*k)] = log(logcombine(Mul(*[
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/simplify/simplify.py", line 1098, in <listcomp>
    l.args[0]**Mul(*c) for c, l in log1.pop(k)]),
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/expr.py", line 239, in __pow__
    return self._pow(other)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/decorators.py", line 266, in _func
    return func(self, other)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/decorators.py", line 136, in binary_op_wrapper
    return func(self, other)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/expr.py", line 235, in _pow
    return Pow(self, other)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/cache.py", line 72, in wrapper
    retval = cfunc(*args, **kwargs)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/power.py", line 336, in __new__
    obj = b._eval_power(e)
  File "/Users/torrinleonard/.conda/envs/formula calculator/lib/python3.8/site-packages/sympy/core/numbers.py", line 2347, in _eval_power
    result = Integer(x**abs(expt.p))
KeyboardInterrupt

Answer 1

看起来常数的大小造成了麻烦，因为较小的值很容易求解：

>>> from sympy.abc import x
>>> from sympy import *
>>> solve(1-2**x-x)
[0]
>>> solve(2-2**x-x)
[(-LambertW(log(16)) + log(4))/log(2)]
>>> solve(5-2**x-x)
[(-LambertW(log(4294967296)) + log(32))/log(2)]

但是，在本例中，精确值并不能帮助我们找到解决方案，因此我们可以用Symbol('120')替换120

>>> solve(Symbol('120')-2**x-x,x)
120 - LambertW(exp(120*log(2))*log(2))/log(2)

正如@oscar-本杰明指出的那样，设置simpliy=False将在相同的时间内给出答案，但您也会在结果中得到一个大整数：

[-LambertW(1329227995784915872903807060280344576*log(2))/log(2) + 120]

如果你只想要一个数值，你可以直接用nsolve和一个合理的猜测来解决这个问题：

>>> nsolve(120-2**x-x, 7)
6.82244407754025