Solve an non-homogeneous system of equations mod Z.

[Hongyi Zhao <hongyi.zhao@gmail.com>]

Hi here,

I've a set of matrices and vectors as follows:

mats:= [
[ [ -2, 0, 0 ], [ 0, -2, 0 ], [ 1, 1, 0 ] ],
[ [ -2, 0, 0 ], [ 0, 0, 0 ], [ 0, -1, -2 ] ],
[ [ 0, 1, 2 ], [ 1, -1, 0 ], [ -1, 0, -2 ] ],
[ [ -1, 1, 0 ], [ 1, -1, 0 ], [ -1, -1, -2 ] ],
[ [ -2, 0, 0 ], [ 0, -2, 0 ], [ 0, 0, -2 ] ]
];
vecs:=  [
[ -23/8, 17/8, -9/8 ],
[ 17/8, 1, -3 ],
[ 0, 0, 0 ],
[ 1, -2, -15/16 ],
[ 1/8, -23/8, 15/16 ]
];

I want to find a common set of solutions, a.k.a., x, for the above
matrices and their corresponding vectors, which satisfy the following
conditions:

  mat * x = vec  (mod Z). \forall mat \in mats, and \forall vec \in
vecs in the corresponding order.

Any tips for tackling this problem?

Regards,
Zhao
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao@gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province