Advanced Expression Manipulation



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from sympy import *
x, y, z = symbols('x y z')

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

Creating expressions from classes

Create the following objects without using any mathematical operators like +, -, *, /, or ** by explicitly using the classes Add, Mul, and Pow. You may use x instead of Symbol('x') and 4 instead of Integer(4).

$$x^2 + 4xyz$$$$x^{(x^y)}$$$$x - \frac{y}{z}$$



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def explicit_classes1():
    """
    Returns the expression x**2 + 4*x*y*z, built using SymPy classes explicitly.

    >>> explicit_classes1()
    x**2 + 4*x*y*z
    """



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def explicit_classes2():
    """
    Returns the expression x**(x**y), built using SymPy classes explicitly.

    >>> explicit_classes2()
    x**(x**y)
    """



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def explicit_classes3():
    """
    Returns the expression x - y/z, built using SymPy classes explicitly.

    >>> explicit_classes3()
    x - y/z
    """

Nested args



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expr = x**2 - y*(2**(x + 3) + z)

Use nested .args calls to get the 3 in expr.



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def nested_args():
    """
    Get the 3 in the above expression.

    >>> nested_args()
    3
    """

Traversal

Write a post-order traversal function that prints each node.



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def post(expr):
    """
    Post-order traversal

    >>> expr = x**2 - y*(2**(x + 3) + z)
    >>> post(expr)
    -1
    y
    2
    3
    x
    x + 3
    2**(x + 3)
    z
    2**(x + 3) + z
    -y*(2**(x + 3) + z)
    x
    2
    x**2
    x**2 - y*(2**(x + 3) + z)
    """



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for i in postorder_traversal(expr):
    print(i)