I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

s2 = HFloat(0.2828503247068887),

s3 = HFloat(0.29444713116943216),

t1 = HFloat(0.2646161774916062),

t2 = HFloat(0.28285032471998384),

t3 = HFloat(0.2944471311346344)], 2527]

191.133

Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw