In [ ]:

```
from sympy import *
init_printing()
```

For each exercise, fill in the function according to its docstring.

What will be the output of the following code?

```
x = 3
y = symbols('y')
a = x + y
y = 5
print(a)
```

Replace `???`

in the below code with what you think the value of `a`

will be. Remember to define any Symbols you need!

In [ ]:

```
def symbols_exercise():
"""
>>> def testfunc():
... x = 3
... y = symbols('y')
... a = x + y
... y = 5
... return a
>>> symbols_exercise() == testfunc()
True
"""
y = symbols('y')
return 3 + y
```

In [ ]:

```
def testfunc():
x = 3
y = symbols('y')
a = x + y
y = 5
return a
symbols_exercise() == testfunc()
```

Write a function that takes two expressions as input, and returns a tuple of two booleans. The first if they are equal symbolically, and the second if they are equal mathematically.

In [ ]:

```
def equality_exercise(a, b):
"""
Determine if a = b symbolically and mathematically.
Returns a tuple of two booleans. The first is True if a = b symbolically,
the second is True if a = b mathematically. Note the second may be False
but the two still equal if SymPy is not powerful enough.
Examples
========
>>> x = symbols('x')
>>> equality_exercise(x, 2)
(False, False)
>>> equality_exercise((x + 1)**2, x**2 + 2*x + 1)
(False, True)
>>> equality_exercise(2*x, 2*x)
(True, True)
"""
return (a == b, simplify(a - b) == 0)
```

In [ ]:

```
x = symbols('x')
```

In [ ]:

```
equality_exercise(x, 2)
```

In [ ]:

```
equality_exercise((x + 1)**2, x**2 + 2*x + 1)
```

In [ ]:

```
equality_exercise(2*x, 2*x)
```

`^`

and `/`

¶Correct the following functions

In [ ]:

```
def operator_exercise1():
"""
>>> operator_exercise1()
x**2 + 2*x + 1/2
"""
x = symbols('x')
return x**2 + 2*x + Rational(1, 2)
```

In [ ]:

```
operator_exercise1()
```

In [ ]:

```
def operator_exercise2():
"""
>>> operator_exercise2()
(x**2/2 + 2*x + 3/4)**(3/2)
"""
x = symbols('x')
return (x**2/2 + 2*x + Rational(3, 4))**Rational(3, 2)
```

In [ ]:

```
operator_exercise2()
```

In [ ]:

```
```