from cake import Expression

expr = Expression("-b (+|-) sqrt((b ** 2) - 4(a)(c))")
# Top layer of the formula

# (+|-) will return 2 solutions as stated in the documentation
# Its one of the many ways of implements plus or minus

expr.wrap_all("/", "2(a)")
# Puts the entire current formula into brackets and divides by 2a

print(expr.substitute(a=10, b=-20, c=5))

# Results: (1.70711, 0.292893)

from cake import Expression
from cake.simultaneous import Circle

# Since `=` will raise a syntax error and will mess with the python syntax
# We settled on using the `==` operator
# What this is saying `Expression == something`, which returns an Eqaution instead of bool
# This is unpythonic but it still makes sense with what it does
# You should never do `if Expr == ...`. This will always be True
# Instead try `if (Expr == ...).solve(*args, **kwargs) == ...`

circle = Expression("x ** 2 + y ** 2") == 16
line = Expression("x + y") == 4

eq = Circle(circle, line)
eq.solve_by_sub()
# Result: ((4, 0), (0, 4))

from cake import Matrix
# We define the matrix structure using standard 2D array syntax
y = Matrix([10, 10, 10], [10, 10, 10])
x = Matrix([1, 2, 3], [4, 5, 6])

# As we have modified the addition method for the Matrix object
# we can simply add the two matrices together
print(x + y)
# Result = ([11, 12, 13], [14, 15, 16])

# The same logic applies to subtraction operations
print(y - x)
# Result = ([9, 8, 7], [6, 5, 4])