#UM(alpha,beta,gamma,delta)

#that implements box 1.1. on p. 20 of the The Nielsen-Chuang book #[Note the superflous comma]

#For random alpha, beta, gamma, delta apply it to IsUM(A).


UM:=proc(alpha, beta, gamma, delta)
A:=Matrix([[e^(-i*beta/2), 0],[0,e^(i*beta/2)]]):
B:=Matrix([[cos(gamma/2), -sin(gamma/2)],[sin(gamma/2), cos(gamma/2)]]):
C:=Matrix([[e^(i*delta/2), 0],[0, e^(i*delta/2)]]):

U:=e^(ia)* Multiply(Multiply(A,B), C):
U:

end:

#no time to prove!