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.
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)
.
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))
explicit_classes1()
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))
explicit_classes2()
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))))
explicit_classes3()
expr = x**2 - y*(2**(x + 3) + z)
Use nested .args
calls to get the 3 in expr.
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]
nested_args()
Write a post-order traversal function that prints each node.
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)
expr = x**2 - y*(2**(x + 3) + z)
post(expr)