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Theory of Systems of Linear Diophantine Equations
An Algorithm Based on Ideas of Rosser
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3-integer ALDES algorithm for solving algorithm LDSMKB algorithm LDSSBR Bachem's algorithm basis cell characteristic equation characteristic roots Cn(x codominance coefficient matrix corollary of Theorem denote det(H diagonal elements Diophantine system Ax dk(S elementary column operations elementary matrices equivalent Fn(k Fortran greatest common divisor Hence Hermite normal form identity matrix induction hypothesis integer programming integral linear combination integral vector Kannan and Bachem's l+(ln largest integer LDSSBR LDSMKB length Let a-j linear Diophantine equations linear Diophantine system linearly independent major loop n-vector non-negative non-null list non-singular matrix null list obtained Obviously order Fibonacci sequence particular solution polynomial positive integer pseudo-Hermite matrix quotient sequences r(m+n rank(A recurrence relation 4.2 remainder sequence repeat-loop rk+1 Rosser's algorithm row-sequence SAC-2 system Section sequence of elementary Smith normal form solution module systems of linear Theorem theorem is true thesis unimodular matrix unimodular transformation variables Vector of integers vectors in Zn VIUT