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/sandbox/tests/test_indexed_integrals.py

@@ -0,0 +1,25 @@
+from sympy.sandbox.indexed_integrals import IndexedIntegral
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.tensor.indexed import (Idx, IndexedBase)
+
+
+def test_indexed_integrals():
+    A = IndexedBase('A')
+    i, j = symbols('i j', integer=True)
+    a1, a2 = symbols('a1:3', cls=Idx)
+    assert isinstance(a1, Idx)
+
+    assert IndexedIntegral(1, A[i]).doit() == A[i]
+    assert IndexedIntegral(A[i], A[i]).doit() == A[i] ** 2 / 2
+    assert IndexedIntegral(A[j], A[i]).doit() == A[i] * A[j]
+    assert IndexedIntegral(A[i] * A[j], A[i]).doit() == A[i] ** 2 * A[j] / 2
+    assert IndexedIntegral(sin(A[i]), A[i]).doit() == -cos(A[i])
+    assert IndexedIntegral(sin(A[j]), A[i]).doit() == sin(A[j]) * A[i]
+
+    assert IndexedIntegral(1, A[a1]).doit() == A[a1]
+    assert IndexedIntegral(A[a1], A[a1]).doit() == A[a1] ** 2 / 2
+    assert IndexedIntegral(A[a2], A[a1]).doit() == A[a1] * A[a2]
+    assert IndexedIntegral(A[a1] * A[a2], A[a1]).doit() == A[a1] ** 2 * A[a2] / 2
+    assert IndexedIntegral(sin(A[a1]), A[a1]).doit() == -cos(A[a1])
+    assert IndexedIntegral(sin(A[a2]), A[a1]).doit() == sin(A[a2]) * A[a1]