chore: 添加虚拟环境到仓库

- 添加 backend_service/venv 虚拟环境
- 包含所有Python依赖包
- 注意：虚拟环境约393MB，包含12655个文件

backend_service/venv/lib/python3.13/site-packages/sympy/sets/powerset.py

@@ -0,0 +1,119 @@
+from sympy.core.decorators import _sympifyit
+from sympy.core.parameters import global_parameters
+from sympy.core.logic import fuzzy_bool
+from sympy.core.singleton import S
+from sympy.core.sympify import _sympify
+
+from .sets import Set, FiniteSet, SetKind
+
+
+class PowerSet(Set):
+    r"""A symbolic object representing a power set.
+
+    Parameters
+    ==========
+
+    arg : Set
+        The set to take power of.
+
+    evaluate : bool
+        The flag to control evaluation.
+
+        If the evaluation is disabled for finite sets, it can take
+        advantage of using subset test as a membership test.
+
+    Notes
+    =====
+
+    Power set `\mathcal{P}(S)` is defined as a set containing all the
+    subsets of `S`.
+
+    If the set `S` is a finite set, its power set would have
+    `2^{\left| S \right|}` elements, where `\left| S \right|` denotes
+    the cardinality of `S`.
+
+    Examples
+    ========
+
+    >>> from sympy import PowerSet, S, FiniteSet
+
+    A power set of a finite set:
+
+    >>> PowerSet(FiniteSet(1, 2, 3))
+    PowerSet({1, 2, 3})
+
+    A power set of an empty set:
+
+    >>> PowerSet(S.EmptySet)
+    PowerSet(EmptySet)
+    >>> PowerSet(PowerSet(S.EmptySet))
+    PowerSet(PowerSet(EmptySet))
+
+    A power set of an infinite set:
+
+    >>> PowerSet(S.Reals)
+    PowerSet(Reals)
+
+    Evaluating the power set of a finite set to its explicit form:
+
+    >>> PowerSet(FiniteSet(1, 2, 3)).rewrite(FiniteSet)
+    FiniteSet(EmptySet, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3})
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Power_set
+
+    .. [2] https://en.wikipedia.org/wiki/Axiom_of_power_set
+    """
+    def __new__(cls, arg, evaluate=None):
+        if evaluate is None:
+            evaluate=global_parameters.evaluate
+
+        arg = _sympify(arg)
+
+        if not isinstance(arg, Set):
+            raise ValueError('{} must be a set.'.format(arg))
+
+        return super().__new__(cls, arg)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    def _eval_rewrite_as_FiniteSet(self, *args, **kwargs):
+        arg = self.arg
+        if arg.is_FiniteSet:
+            return arg.powerset()
+        return None
+
+    @_sympifyit('other', NotImplemented)
+    def _contains(self, other):
+        if not isinstance(other, Set):
+            return None
+
+        return fuzzy_bool(self.arg.is_superset(other))
+
+    def _eval_is_subset(self, other):
+        if isinstance(other, PowerSet):
+            return self.arg.is_subset(other.arg)
+
+    def __len__(self):
+        return 2 ** len(self.arg)
+
+    def __iter__(self):
+        found = [S.EmptySet]
+        yield S.EmptySet
+
+        for x in self.arg:
+            temp = []
+            x = FiniteSet(x)
+            for y in found:
+                new = x + y
+                yield new
+                temp.append(new)
+            found.extend(temp)
+
+    @property
+    def kind(self):
+        return SetKind(self.arg.kind)