> with(linalg);

Warning, the protected names norm and trace have been redefined and unprotected

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...

> A:=matrix([[1,0,-5/6,0,0,0,-1,0],[0,0,1,0,-9/20,0,-1,0],[-13/42,0,0,0,1,0,-1,0],[0,1,-7/12,-7/12,0,0,0,0],[0,0,0,1,-9/20,-9/20,0,0],[0,0,0,0,0,1,-11/30,-11/30],[-13/42,-13/42,0,0,0,0,0,1]]);

A := matrix([[1, 0, (-5)/6, 0, 0, 0, -1, 0], [0, 0, 1, 0, (-9)/20, 0, -1, 0], [(-13)/42, 0, 0, 0, 1, 0, -1, 0], [0, 1, (-7)/12, (-7)/12, 0, 0, 0, 0], [0, 0, 0, 1, (-9)/20, (-9)/20, 0, 0], [0, 0, 0, 0,...

> nullspace(A);

{vector([246821/83710, 17158/8371, 1243419/585970, 815541/585970, 367903/175791, 1, 125739/106540, 1813071/1171940])}

> BasicSol:=evalm(nullspace(A)[1]*3*1171940);

BasicSol := vector([10366482, 7206360, 7460514, 4893246, 7358060, 3515820, 4149387, 5439213])

>

> ifactor(BasicSol[1]+BasicSol[3]);

(2)^2*(3)*(11)*(29)*(4657)

> ifactor(3*11*29*4657*(BasicSol[5]+BasicSol[7]));

(3)*(7)*(11)*(29)*(353)*(4657)^2

>

>