kill(all);

van=facebook.com/LearningCalculus$

load("eigen")$

A(x,y,z,w):=matrix([1,1,1,1],[1,1,1,-1],[x,y,z,w],[y*z*w,0,0,0])$
X(x,y,z,w):=columnvector([x,y,z,w])$
B         : columnvector([4,1,13/3,125/144])$

AI(x,y,z,w):=fullratsimp(invert(A(x,y,z,w)))$
AI(x,y,z,w);

fullratsimp(AI(x,y,z,w).A(x,y,z,w));

S: X(x,y,z,w) = fullratsimp(AI(x,y,z,w).B)$
S: fullratsimp(AI(x,y,z,w).B)$
w: first(S[4]);

f(x,y,z):=x+y+z = 5/2$
g(x,y,z):=x^2+y^2+z^2 = 25/12$
h(x,y,z):=x*y*z = 125/216$

factors_of_125:[1, 5, 25, 125]$
factors_of_216:[1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216]$

is(f(5/6, 5/6, 5/6)) and is(g(5/6, 5/6, 5/6)) and is(h(5/6, 5/6, 5/6));