# Please do not post
# Omar Aceval Garcia, due 2/09/2025. Assignment 4

# UM(alpha, beta, gamma, delta)
# Here is code that gives a unitary 2 by 2 matrix from four given real values, alpha through delta
# This comes from taking the decomposition given by the book and doing the matrix multiplications:
UMabgd := proc(alpha, beta, gamma, delta):
return [
	[exp(I*(alpha - (beta + delta)/2))*cos(gamma/2), -exp(I*(alpha - (beta + delta)/2))*sin(gamma/2)],
	[exp(I*(alpha + (beta - delta)/2))*sin(gamma/2),  exp(I*(alpha + (beta - delta)/2))*cos(gamma/2)]
       ]:
end:

# I checked IsUM(UMabgd(1,2,3,4)) and got back false, but upon adding a "simplify()" to the procedure of IsUM() it returned true. Hooray.