SymPy 是否失去了除以多个多项式的功能？

Question

SymPy 的新手，正在尝试除法多项式。目前，我是运行 Python 3.6.4 和 SymPy 1.1.1（已安装 pip）。浏览他们的文档后，我在他们的 0.6.7 documentation page 上找到了以下有用的示例：

Another option is division by multiple polynomials at the same time. In general, the output is not unique and depends on the order of the divisors and the given monomial order (if specified).
>>> f = x*y + y*z + z*x
>>> g1 = x + 1
>>> g2 = 2*y + 1
>>> q, r = div(f, [g1, g2], x, y, z)
>>> q
               z
[y + z, -1/2 + -]
               2
>>> r
      3*z
1/2 - ---
       2

不过，这个功能，至少在1.1.1 documentation page是不存在的。而且，更重要的是，如果我尝试在 1.1.1 上尝试类似的操作，我会收到以下错误：

>>> f = x*y + y*z + z*x
>>> g1 = x + 1
>>> g2 = 2*y + 1
>>> q, r = div(f, [g1, g2], x, y, z)
Traceback (most recent call last):
  File "C:\[...]\Python\Python36\lib\site-packages\sympy\polys\polytools.py", line 4659, in div
    (F, G), opt = parallel_poly_from_expr((f, g), *gens, **args)
  File "C:\[...]\Python\Python36\lib\site-packages\sympy\polys\polytools.py", line 4266, in parallel_poly_from_expr
    return _parallel_poly_from_expr(exprs, opt)
  File "C:\[...]\Python\Python36\lib\site-packages\sympy\polys\polytools.py", line 4312, in _parallel_poly_from_expr
    raise PolificationFailed(opt, origs, exprs, True)
sympy.polys.polyerrors.PolificationFailed: can't construct polynomials from x*y + x*z + y*z, [x + 1, 2*y + 1]

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\[...]\Python\Python36\lib\site-packages\sympy\polys\polytools.py", line 4661, in div
    raise ComputationFailed('div', 2, exc)
sympy.polys.polyerrors.ComputationFailed: div(x*y + x*z + y*z, [x + 1, 2*y + 1]) failed without generators

我非常怀疑这个特征已经被删除了，因为这是一个非常重要的特征，特别是对于仿射变量和 Groebner 基分析，（我正在研究的主题）

有人可以指出我使用 SymPy 的工作示例吗？

Answer 1

此功能现在可从函数 reduced 获得。使用示例中的 f、g1、g2，

>>> reduced(f, [g1, g2], x, y, z)
([y + z, z/2 - 1/2], -3*z/2 + 1/2)

SymPy 是否失去了除以多个多项式的功能？

Has SymPy lost the functionality to divide by multiple polynomials?

python

sympy

polynomial-math