# expand given AB-polynomial written as vectors
# over the Hall basis

with(linalg):

matr6 := transpose([
[1,-5,0,10,0,0,0,-10,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,-1,0,4,0,0,0,-6,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,6,0,0,0,-4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,-3,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,6,0,0,0,-6,0,0,0,0,0,0,0,3,-3,0,3,0,0,0,-1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-6,0,0,0,0,0,0,0,0,0,6,0,0,0,-2,-2,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,0,0,0,0,0,0,0,10,0,0,0,-10,0,5,-1],
[0,0,0,0,-1,1,0,0,3,-3,0,0,0,0,0,0,-2,0,0,3,0,0,0,-1,0,0,0,0,0,0,0,0,0,2,0,-3,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0,2,0,0,0,-2,0,1,0,0,0,0,0,0,1,0,-2,0,0,0,2,0,0,-1,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-3,0,2,0,0,0,0,0,0,0,0,0,-1,0,0,0,3,0,0,-2,0,0,0,0,0,0,-3,3,0,0,1,-1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,-1,0,2,-1,0,0,0,0,2,0,-4,2,0,0,1,-2,0,1,0,0,0,0,0,0,-1,0,2,-1,0,0,-2,4,0,-2,0,0,0,0,1,-2,0,1,0,0,0,0,0,0,0,0,0,0]
]);

bn61:=[1,-5,0,10,0,0,0,-10,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
bn62:=[0,0,-1,0,2,2,0,0,0,-6,0,0,0,0,0,0,0,0,0,6,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
bn63:=[0,0,0,0,0,0,1,0,0,0,-3,0,3,-3,0,0,0,0,0,0,0,6,0,0,0,-6,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,3,0,0,0,-1,0,0,0,0,0,0];
bn64:=[0,0,-1,0,3,1,0,0,-3,-3,0,0,0,0,0,0,2,0,0,3,0,0,0,-1,0,0,0,0,0,0,0,0,0,-2,0,3,0,0,0,-3,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
bn65:=[0,0,0,0,0,0,1,0,0,0,-2,0,0,-1,0,0,0,0,-1,0,4,2,0,0,-1,-2,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,-4,0,0,0,0,0,0,0,1,0,2,0,0,0,-1,0,0,0,0,0,0];
bn66:=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,-10,0,0,0,10,0,-5,1];
bn67:=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,6,0,0,0,0,0,0,0,0,0,-6,0,0,0,2,2,0,-1,0,0];
bn68:=[0,0,0,0,0,0,-1,0,0,0,3,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,-6,0,0,0,6,0,0,0,0,0,0,0,-3,3,0,-3,0,0,0,1,0,0,0,0,0,0];
bn69:=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-3,0,0,0,3,0,-2,0,0,0,0,0,0,0,0,0,-1,0,0,0,3,0,0,2,0,0,0,0,0,0,-3,-3,0,0,1,3,0,-1,0,0];
bn610:=[0,0,0,0,0,0,-1,0,0,0,2,0,1,0,0,0,0,0,0,0,-4,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,-2,-1,0,0,2,4,0,-1,0,0,0,0,-1,0,0,-2,0,0,0,1,0,0,0,0,0,0];

for i from 1 to 10 do
linsolve(matr6,bn6||i);
od;