"Testing circexp"

clear

T = circexp(cos(x))
check(T = 1/2*exp(-i*x)+1/2*exp(i*x))
T = circexp(sin(x))
check(T = 1/2*i*exp(-i*x)-1/2*i*exp(i*x))
T = circexp(tan(x))
check(T = simplify(i*exp(-i*x)/(exp(-i*x)+exp(i*x))-i*exp(i*x)/(exp(-i*x)+exp(i*x))))
T = circexp(cosh(x))
check(T = 1/2*exp(x)+1/2*exp(-x))
T = circexp(sinh(x))
check(T = 1/2*exp(x)-1/2*exp(-x))
T = circexp(tanh(x))
check(T = -1/(1+exp(2*x))+exp(2*x)/(1+exp(2*x)))
T = circexp((cos(x),sin(x)))
check(T = (1/2*exp(-i*x)+1/2*exp(i*x),1/2*i*exp(-i*x)-1/2*i*exp(i*x)))
T = circexp(cos(x)*sin(x))-expcos(x)*expsin(x)
check(T = 0)

T = circexp(d(arctan(y/x),y))
check(T = x/(x^2+y^2))
T = circexp(d(arctan(y/x),x))
check(T = -y/(x^2+y^2))
T = circexp(1-sin(x)^2)
check(T = circexp(cos(x)^2))
T = circexp(1-cos(x)^2)
check(T = circexp(sin(x)^2))
T = circexp(sin(x)^2-1)
check(T = circexp(-cos(x)^2))
T = circexp(cos(x)^2-1)
check(T = circexp(-sin(x)^2))

T = circexp(-3 exp(-1/3 r + i phi) cos(theta) / sin(theta) + 3 exp(-1/3 r + i phi) cos(theta) sin(theta) + 3 exp(-1/3 r + i phi) cos(theta)^3 / sin(theta))
check(T = 0)
