```python
import sympy as sm
s1 = sm.FiniteSet(1,2)
s11 = sm.FiniteSet(1,2,3)
s2 = sm.FiniteSet(1,2,3,4,5)
s3 = sm.FiniteSet(*range(5,9))
# element
1 in s
# subset
s1.is_subset(s2)
s2.is_superset(s1)
s1.is_proper_subset(s11)
# pwoerset
s1.powerset()
#union
s3.union(s1)
# intersect
s3.intersect(s2)
for i in s1**2:
    print(i)
```

    (1, 1)
    (2, 1)
    (1, 2)
    (2, 2)



```python
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.add_subplot()
x = np.linspace(-2,2,1000)
y = np.exp(-x**2)
ax.plot(x,y)
ax.plot(x,np.exp(-x))
```


```python
x = sm.symbols('x')
a = sm.symbols('a',real=True)
C = sm.symbols('C')
p = C* sm.exp(-x**2/2/a**2)
sm.Integral(p,(x,-sm.oo,sm.oo)).doit()
```




$\displaystyle \begin{cases} \sqrt{2} \sqrt{\pi} C a & \text{for}\: 2 \left|{\arg{\left(a \right)}}\right| \leq \frac{\pi}{2} \\\int\limits_{-\infty}^{\infty} C e^{- \frac{x^{2}}{2 a^{2}}}\, dx & \text{otherwise} \end{cases}$




```python
import sympy.functions
sm.functions.combinatorial.numbers.nP(5,2)
sm.factorial(5)/sm.factorial(3)
sm.functions.combinatorial.numbers.nC(5,2)
sm.factorial(5)/sm.factorial(3)/sm.factorial(2)
```




$\displaystyle 20$




```python

```




$\displaystyle \operatorname{atan}{\left(\sqrt{2} \right)}$




```python

```




$\displaystyle \frac{\sqrt{2}}{2}$




```python

```

91ac6decf20b40cc17e1b3863720741219b524d9
ipynb
Jupyter Notebook
python/Vectors/Set.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/Set.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
python/Vectors/Set.ipynb
karng87/nasm_game
a97fdb09459efffc561d2122058c348c93f1dc87
MIT
Qwen/Qwen-72B
1. YES
2. YES