Advanced Expression Manipulation Solutions



In [34]:

    
from sympy import *
x, y, z = symbols('x y z')
init_printing()
from IPython.display import display

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).

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



In [35]:

    
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
    """
    return Add(Pow(x, 2), Mul(4, x, y, z))



In [36]:

    
explicit_classes1()









    Out[36]:





$$x^{2} + 4 x y z$$



In [37]:

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

    >>> explicit_classes2()
    x**(x**y)
    """
    return Pow(x, Pow(x, y))



In [38]:

    
explicit_classes2()









    Out[38]:





$$x^{x^{y}}$$



In [39]:

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

    >>> explicit_classes3()
    x - y/z
    """
    return Add(x, Mul(-1, Mul(y, Pow(z, -1))))



In [40]:

    
explicit_classes3()









    Out[40]:





$$x - \frac{y}{z}$$

Nested args



In [41]:

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

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



In [42]:

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

    >>> nested_args()
    3
    """
    expr = x**2 - y*(2**(x + 3) + z)
    return expr.args[0].args[2].args[1].args[1].args[0]



In [43]:

    
nested_args()









    Out[43]:





$$3$$

Traversal

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



In [44]:

    
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)
    """
    for arg in expr.args:
        post(arg)
    display(expr)



In [45]:

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



In [46]:

    
post(expr)









    





$$-1$$






    





$$y$$






    





$$z$$






    





$$2$$






    





$$3$$






    





$$x$$






    





$$x + 3$$






    





$$2^{x + 3}$$






    





$$2^{x + 3} + z$$






    





$$- y \left(2^{x + 3} + z\right)$$






    





$$x$$






    





$$2$$






    





$$x^{2}$$






    





$$x^{2} - y \left(2^{x + 3} + z\right)$$