用Sympy计算有限集的笛卡尔积

如何解决用Sympy计算有限集的笛卡尔积

似乎下面的sympy代码的最后一行应返回“ True”

a = ProductSet(FiniteSet(1),FiniteSet(2))
b = FiniteSet((1,2))
simplify(Eq(a,b))

但它返回此可怕的错误：

Traceback (most recent call last):
  File "<string>",line 1,in <module>
  File "/base/data/home/apps/s~sympy-live-hrd/sympy/sympy/simplify/simplify.py",line 557,in simplify
    return _eval_simplify(**kwargs)
  File "/base/data/home/apps/s~sympy-live-hrd/sympy/sympy/core/relational.py",line 627,in _eval_simplify
    e = super(Equality,self)._eval_simplify(**kwargs)
  File "/base/data/home/apps/s~sympy-live-hrd/sympy/sympy/core/relational.py",line 290,in _eval_simplify
    r = r.func(*[i.simplify(**kwargs) for i in r.args])
AttributeError: 'ProductSet' object has no attribute 'simplify'

有什么方法可以使sympy实际计算有限集的笛卡尔积吗？

解决方法

我不确定您使用的是什么版本的sympy，但是当前的master提供了：

In [1]: a = ProductSet(FiniteSet(1),FiniteSet(2)) 
   ...: b = FiniteSet((1,2)) 
   ...: simplify(Eq(a,b))
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-1-3a3ef38457b0> in <module>
      1 a = ProductSet(FiniteSet(1),FiniteSet(2))
      2 b = FiniteSet((1,2))
----> 3 simplify(Eq(a,b))

~/current/sympy/sympy/sympy/simplify/simplify.py in simplify(expr,ratio,measure,rational,inverse,doit,**kwargs)
    559     _eval_simplify = getattr(expr,'_eval_simplify',None)
    560     if _eval_simplify is not None:
--> 561         return _eval_simplify(**kwargs)
    562 
    563     original_expr = expr = collect_abs(signsimp(expr))

~/current/sympy/sympy/sympy/core/relational.py in _eval_simplify(self,**kwargs)
    555         from sympy.solvers.solveset import linear_coeffs
    556         # standard simplify
--> 557         e = super()._eval_simplify(**kwargs)
    558         if not isinstance(e,Equality):
    559             return e

~/current/sympy/sympy/sympy/core/relational.py in _eval_simplify(self,**kwargs)
    308             if dif.is_comparable:
    309                 v = dif.n(2)
--> 310             elif dif.equals(0):  # XXX this is expensive
    311                 v = S.Zero
    312             if v is not None:

AttributeError: 'Complement' object has no attribute 'equals'

这是Relational._eval_simplify中的错误，因为它显然假设lhs和rhs均为Expr，这对LessThan等适用，但对{ {1}}。

为集实现Equality并不难，因为Eq应该等效于Eq(A,B)。不过，目前只有其中一个给出明确的答案：

A.is_subset(B) and B.is_subset(A)

可以添加处理程序以评估In [6]: a Out[6]: {1} × {2} In [7]: b Out[7]: {(1,2)} In [8]: print(a.is_subset(b)) None In [9]: print(b.is_subset(a)) True ，其中a.is_subset(b)是a，而ProductSet是b。