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# Linear Diophantine equations

Linear Diophantine equations are linear equations in which only integer solutions are allowed.

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:

static void RearrangeMatforSolveDio (Matrix *M)
: rearrange the matrix in order to solve a diofantine equation.

Then the function SolveDiophantine for solving the equation can be used. If a solution exists, the procedure returns , otherwise it returns .

int SolveDiophantine (Matrix *M, Matrix **U, Vector **X)
: solve Diophantine Equations

Generally this functions is used in connection with operations on lattices because a lattice can be seen as a solution of a Diophantine equation.    Next: Smith decomposition Up: Other tools Previous: Other tools   Contents
Sorin Olaru 2002-04-24