Hermite normal form computation using modulo determinant arithmetic
Mathematics of Operations Research
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Exact Solution of Systems of Linear Equations with Polynomial Coefficients
Journal of the ACM (JACM)
Algorithm 287: matrix triangulation with integer arithmetic [F1]
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Integer matrices and Abelian groups (invited)
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Algorithms for the solution of systems of linear diophantine equations
Algorithms for the solution of systems of linear diophantine equations
Residual methods for computing hermite and smith normal forms (congruence, determinant, sparsity)
Residual methods for computing hermite and smith normal forms (congruence, determinant, sparsity)
A linear space algorithm for computing the hermite normal form
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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This paper extends the class of Hermite normal form solution procedures that use modulo determinant arithmetic. Given any relatively prime factorization of the determinant value, integral congruence relations are used to compute the Hermite normal form. A polynomial-time complexity bound that is a function of the length of the input string exists for this class of procedures. Computational results for this new approach are given.