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Solving Linear Diophantine Equations
 REPORTS OF THE INSTITUTE OF CYBERNETICS
"... An overview of a family of methods for finding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead. ..."
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Cited by 2 (0 self)
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An overview of a family of methods for finding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead.
On minimal solutions of linear Diophantine equations
"... This paper investigates the region in which all the minimal solutions of a linear diophantine equation lie. We present best possible inequalities which must be satisfied by these solutions and thereby improve earlier results. ..."
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This paper investigates the region in which all the minimal solutions of a linear diophantine equation lie. We present best possible inequalities which must be satisfied by these solutions and thereby improve earlier results.
On systems of linear Diophantine equations
 Math. Mag
, 1996
"... Introduction Something happened to me recently I would wager has happened to many who read this note. Teaching a new topic, you cannot understand one of the proofs. Your first attempt to fill the gap fails. You look through your books for an answer. Next, you ask colleagues, go to the library, maybe ..."
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Cited by 8 (1 self)
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Introduction Something happened to me recently I would wager has happened to many who read this note. Teaching a new topic, you cannot understand one of the proofs. Your first attempt to fill the gap fails. You look through your books for an answer. Next, you ask colleagues, go to the library, maybe even use the interlibrary loan. All in vain. Then it strikes you that, in fact, you cannot answer an even more basic and seemingly more interesting question. You peruse the books
SYSTEMS OF LINEAR DIOPHANTINE EQUATIONS AND DISEQUATIONS COMPLEXITY
, 2015
"... Abstract: Series of problems concerning systems of linear Diophantine equations and disequations with explicitly given parameters are offered below. For every problem from a series the conditions upon the parameters under which the problem is NPcomplete are proved. ..."
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Abstract: Series of problems concerning systems of linear Diophantine equations and disequations with explicitly given parameters are offered below. For every problem from a series the conditions upon the parameters under which the problem is NPcomplete are proved.
Multivariate Discrete Splines And Linear Diophantine Equations
 Trans. Amer. Math. Soc.340:1(1993),179197
, 1993
"... In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessar ..."
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Cited by 7 (1 self)
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In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a
Solving Systems of Linear Diophantine Equations: An Algebraic Approach
 IN PROC. 16TH MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, WARSAW, LNCS 520
, 1991
"... We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satisfiability of an homogeneous syst ..."
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Cited by 20 (1 self)
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We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satisfiability of an homogeneous
Fast methods for solving linear diophantine equations
 Proceedings of the 6th Portuguese Conference on Artificial Intelligence, 727
, 1993
"... Abstract. We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From empirica ..."
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Cited by 7 (4 self)
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Abstract. We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From
Hilbert bases of cones related to simultaneous Diophantine approximations and linear Diophantine equations
, 1997
"... This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results. We also show that the elements of the minimal Hilbert basis of the dual cone of all ..."
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Cited by 2 (1 self)
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This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results. We also show that the elements of the minimal Hilbert basis of the dual cone of all
An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations
, 1994
"... In this paper, we describe an algorithm for solving systems of linear Diophantine equations based on a generalization of an algorithm for solving one equation due to Fortenbacher [3]. It can solve a system as a whole, or be used incrementally when the system is a sequential accumulation of several s ..."
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Cited by 36 (0 self)
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In this paper, we describe an algorithm for solving systems of linear Diophantine equations based on a generalization of an algorithm for solving one equation due to Fortenbacher [3]. It can solve a system as a whole, or be used incrementally when the system is a sequential accumulation of several
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