# You must make sure to run all cells in sequence using shift + enter or you might encounter errors
from pykubegrader.initialize import initialize_assignment

responses = initialize_assignment("15_sympy_q", "week_3", "readings", assignment_points = 23.0, assignment_tag = 'week3-readings')

# Initialize Otter
import otter
grader = otter.Notebook("15_sympy_q.ipynb")

❓ ❌ Eliminate or ✅ Evaluate: Surviving the Sympy 🦑 Challenge!

# Run this block of code by pressing Shift + Enter to display the question
from questions._15_sympy_q import Question1
Question1().show()

# Run this block of code by pressing Shift + Enter to display the question
from questions._15_sympy_q import Question2
Question2().show()

# Run this block of code by pressing Shift + Enter to display the question
from questions._15_sympy_q import Question3
Question3().show()

Dalgona Cookie Break Equation

Instructions:

In the “Dalgona Cookie Challenge,” the break strength of the cookie is modeled by the equation \(x^2 + y^2 = 1\). Use SymPy to:

1. Solve the equation for \(x\) and \(y\) over the real numbers.

2. Return the symbolic solution. You can do this by using the Eq() function. Please assign the equation to the variable equation

3. Plot the circle function \(x^2 + y^2 = 1\) over the range \([-1.5, 1.5]\).

Your solution must include:

1. The import statements for Sympy – you can use the * wildcard to import all functions.

2. In the function solve_cookie_circle() provided for you:

   • Defines the equation for a circle. Using the ‘Eq()’ function.

# Add the correct imports for SymPy
...

# define the symbols x and y
...

def solve_cookie_circle():
    # Define the equation for the circle
    ...
    
    return equation

# DO NOT CHANGE THE CODE BELOW
# This code is used to plot the circle

def plot_circle():
    equation = solve_cookie_circle()
    p = plot_implicit(
        equation,
        (x, -1.5, 1.5),
        (y, -1.5, 1.5),
        title="Circle Shape: Cookie Break",
        xlabel="x",
        ylabel="y",
    )
    return p


# Example test case
equation = solve_cookie_circle()
print(f"Equation for Cookie Circle: {equation}")
plot_circle()

grader.check("cookie-break-equation")

Ddakji Flip Card System Analysis

Instructions:

In Ddakji the “Flip Card” game, a nonlinear system of equations models the flipping dynamics:

\[[ xy = 1, \ x - 2 = 0 ]\]

Use SymPy to:

1. Solve the nonlinear system of equations.

2. Return the symbolic solution.

Your solution must include:

1. A function analyze_flip_card() that:

   • Define the needed symbols for the variables x and y.

   • Defines the system of equations to the variable equations. To do this, you should solve each expression such that it equals zero. equations should be a list of the two equations.

   • Solves it using nonlinsolve. If you need help use the help() function. Assign the solution to the variable solution. You can pass a list of symbols as the second argument to nonlinsolve.

   • Returns the solution. We have provided the return statement for you.

# Import SymPy
...

def analyze_flip_card():
    # Define the SymPy symbols
    ...
    
    # Define the equations for the Flip Card System
    ...
    
    # Solve the equations using non-linear solver nonlinsolve
    ...
    return solution


# Example test case
solution = analyze_flip_card()
print(f"Flip Card System Solution: {solution}")

grader.check("Ddakji-Flip-Card-System-Analysis")

Submitting Assignment

Please run the following block of code using shift + enter to submit your assignment, you should see your score.

from pykubegrader.submit.submit_assignment import submit_assignment

submit_assignment("week3-readings", "15_sympy_q")