Consider a system of equations in variables for which we
look for integral solutions.
is a matrix and is a vector of order .
In the homogeneous space, the equation is where
To solve such a sytems, first the rows of are rearranged in such a way that the first rows of are the ones which contribute to the rank. This is done with:
Then the function SolveDiophantine for solving the equation can be used. If a solution exists, the procedure returns , otherwise it returns .
Generally this functions is used in connection with operations on lattices because a lattice can be seen as a solution of a Diophantine equation.