#!/usr/bin/env python
# coding: utf-8

# # Gotchas Solutions

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from sympy import *
init_printing()


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

# ## Symbols

# 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!

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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


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

symbols_exercise() == testfunc()


# ## Equality

# 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.

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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)


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x = symbols('x')


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equality_exercise(x, 2)


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


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equality_exercise(2*x, 2*x)


# ## `^` and `/`

# Correct the following functions

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


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operator_exercise1()


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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)


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operator_exercise2()


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