2018-08-13-102452 subsetsum.sagews

var('w x y z')

(w, x, y, z)

signal = sin(w) + sin(x) + sin(y)  +sin(z)
secondorder = (signal)^2 
thirdorder = (signal)^3

secondorder.simplify_trig().expand_trig().reduce_trig()

-1/2*cos(2*w) - cos(w + x) - cos(w + y) - cos(w + z) + cos(-w + x) + cos(-w + y) + cos(-w + z) - 1/2*cos(2*x) - cos(x + y) - cos(x + z) + cos(-x + y) + cos(-x + z) - 1/2*cos(2*y) - cos(y + z) + cos(-y + z) - 1/2*cos(2*z) + 2

thirdorder.simplify_trig().expand_trig().reduce_trig()

-1/4*sin(3*w) - 3/4*sin(2*w + x) - 3/4*sin(2*w + y) - 3/4*sin(2*w + z) - 3/4*sin(w + 2*x) - 3/2*sin(w + x + y) - 3/2*sin(w + x + z) + 3/2*sin(w - x + y) + 3/2*sin(w - x + z) - 3/4*sin(w + 2*y) - 3/2*sin(w + y + z) + 3/2*sin(w - y + z) - 3/4*sin(w + 2*z) + 21/4*sin(w) + 3/4*sin(-w + 2*x) + 3/2*sin(-w + x + y) + 3/2*sin(-w + x + z) - 3/2*sin(-w - x + y) - 3/2*sin(-w - x + z) + 3/4*sin(-w + 2*y) + 3/2*sin(-w + y + z) - 3/2*sin(-w - y + z) + 3/4*sin(-w + 2*z) - 3/4*sin(-2*w + x) - 3/4*sin(-2*w + y) - 3/4*sin(-2*w + z) - 1/4*sin(3*x) - 3/4*sin(2*x + y) - 3/4*sin(2*x + z) - 3/4*sin(x + 2*y) - 3/2*sin(x + y + z) + 3/2*sin(x - y + z) - 3/4*sin(x + 2*z) + 21/4*sin(x) + 3/4*sin(-x + 2*y) + 3/2*sin(-x + y + z) - 3/2*sin(-x - y + z) + 3/4*sin(-x + 2*z) - 3/4*sin(-2*x + y) - 3/4*sin(-2*x + z) - 1/4*sin(3*y) - 3/4*sin(2*y + z) - 3/4*sin(y + 2*z) + 21/4*sin(y) + 3/4*sin(-y + 2*z) - 3/4*sin(-2*y + z) - 1/4*sin(3*z) + 21/4*sin(z)