```python
from sympy.core.symbol import symbols
from sympy.solvers.solveset import nonlinsolve
```


```python
x, y, z = symbols('x, y, z', real=True)
nonlinsolve([x*y - 1, 4*x**2 + y**2 - 5], [x, y])
```




    {(-1, -1), (-1/2, -2), (1/2, 2), (1, 1)}




```python
from sympy.solvers import solve, nonlinsolve
from sympy import Symbol, symbols
from sympy import sin, cos, limit
from mpmath import *
from sympy import *
```


```python
x = Symbol('x')
eq = x**2 - 1
solve([x >= 0.5, x <= 3, eq ], x)
```




    Eq(x, 1.00000000000000)




```python
x, theta, gamma = symbols('x, theta, gamma', real=True)

eq1 = sin(theta)/x

solve(eq1, [x, theta])
```




    [{theta: 0}, {theta: pi}]




```python
# theta = 0 --> cos(0) = 1
eq2 = 1 + gamma * (1 - x)

# theta = pi --> cos(pi) = -1
eq3 = -1 + gamma * (1 - x)


print(solve(eq2, [x, gamma]))
print('\n')
print(solve(eq3, [x, gamma]))
```

    [{x: (gamma + 1)/gamma}]
    
    
    [{x: (gamma - 1)/gamma}]



```python
sol3 = solve(eq3, [x, gamma])
```


```python
sol3[0][x].evalf(subs={gamma:3})
```




    0.666666666666667




```python

```

002527d8731fb49fbfa4f42c3582c20e0a1545ab
ipynb
Jupyter Notebook
FixedPoints-Sympy.ipynb
Camilo-HG/Exercises_Book
164eed0bf4a5be49994de15f05dc48242408d8c9
MIT
FixedPoints-Sympy.ipynb
Camilo-HG/Exercises_Book
164eed0bf4a5be49994de15f05dc48242408d8c9
MIT
FixedPoints-Sympy.ipynb
Camilo-HG/Exercises_Book
164eed0bf4a5be49994de15f05dc48242408d8c9
MIT
Qwen/Qwen-72B
1. YES
2. YES