```python
%matplotlib widget
# %matplotlib inline

from sympy import *
from IPython.display import Latex
import matplotlib.pyplot as plt

plt.style.use('dark_background')
init_printing(use_latex=True)
_ = var('c k t x y z')
```


```python
lhs = sin(x)**2 + cos(x)**2
Eq(lhs, simplify(lhs))
```


```python
p = (x + 1)**2 - 1
p, solve(p, x)
```


```python
lhs = x**2 - 7*x + 12
Eq(lhs, factor(lhs))
```


```python
eqs = [
    Eq(x + y, 4),
    Eq(x - y, 2) ]
(eqs), solve(eqs)
```


```python
A = Matrix([[1, 1], [1, -1]])
b = Matrix([4, 2])
X = MatrixSymbol('x', 2, 1)
X = A.LUsolve(b)
Eq(MatMul(A, X), b)
```


```python
expr = Integral(exp(-x**2 - y**2), (x, -oo, oo), (y, -oo, oo))
Eq(expr, expr.doit())
```


```python
f = Function('f')
eq = Eq(f(x).diff(x), k * f(x))
eq, dsolve(eq)
```


```python
plot(sin(x)**2, (x, -3, 1))
```


```python
from sympy.plotting import plot3d
plot3d(sin(x*10)*cos(y*5) - x*y)
```

537774a9adbd733c60c8012e6801c17b84130f31
ipynb
Jupyter Notebook
py/jupyter/sympy_demo.ipynb
YodaEmbedding/experiments
567c6a1c18fac2d951fe2af54aaa4917b7d529d2
MIT
py/jupyter/sympy_demo.ipynb
YodaEmbedding/experiments
567c6a1c18fac2d951fe2af54aaa4917b7d529d2
MIT
py/jupyter/sympy_demo.ipynb
YodaEmbedding/experiments
567c6a1c18fac2d951fe2af54aaa4917b7d529d2
MIT
Qwen/Qwen-72B
1. YES
2. YES