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Galois field (GF) arithmetic is used to implement critical arithmetic components in communication and security-related hardware, and verification of such components is of prime importance. Current techniques for formally verifying such components are based on computer algebra methods that proved successful in verification of integer arithmetic circuits. However, these methods are sequential in nature...
The main theme of this paper is summarizing the results on examining regularity of functional equations with computer algebra systems. These methods can be found in the PhD thesis and partially in some articles of the author. Additionally it deals with some other applications of CAS. There were used Maple(ver 15.0) and Sage(several versions) systems.
This paper presents a system that automatically assesses multi-step answers to algebra questions. The system requires teacher involvement only during the question set-up stage. Two types of algebra questions are currently supported: questions with linear equations containing fractions, and questions with quadratic equations. The system evaluates each step of a student's answer and awards full/partial...
Matrices are important tools for many fields, and used in solving systems of linear equation. Technological tools are available to work with matrix operations, but still students avoid using matrices, specially in early stages. Moreover, they limit the use to solving linear equations. Using the field of electrical circuits, this paper introduces the advantage of looking at the systems of equations...
This paper presents the algorithm for the function minimization of multivalued i.e. Radix >2 digital system. The ternary digital system which radix=3 is considered here for the demonstration of proposed algorithm and computer program is developed based on algorithm in the form of ternary map. As the radix of system increases, the difficulties in the minimization or reduction of logic function is...
We present a computer program developed in the computer algebra system Maple, which determines the solutions of systems of linear functional equations of two variables.
This paper surveys a short study about using and applying symbolic processing to direct execution of the expectation-maximization algorithm. Formulas are derived in the manner defined by the expectation-maximization algorithm and how there are applied. Symbolic processing uses the set of equations on the same way that describe expectation maximization algorithm without any adaptation and loops of...
Intervals play a pivotal role in both theoretical mathematics and applied mathematics. As a consequence, interval computation is becoming increasingly used in several fields of Mathematics and other applied sciences. However, only a few computer programs include specialized tools and libraries for interval computation so far. In this paper we describe a new package for dealing with single-valued interval...
We can obtain degeneracy conditions of singularities and the singular-discriminant of the quartic curve by using the elimination theory of the polynomial ideal. In this paper, we show the calculation results.
We describe our approach in education of the course Digital and Analog Circuits, which belongs to curricula of the Informatics study program. For analysis of analog and simple digital circuits we use computer algebra system Mathematica, which minimizes the amount of routine, handy calculations. This fact enables focusing on the problem and solving more examples, which in turn provides better comprehension...
Searching for a new solution method and acquire new exact solutions of nonlinear evolution equations has become one of the hot research field. In this paper we using a new(G/G') method by using the computer algebra system of Mathematics to obtained rich exact solutions of the (2+1)-dimensional Broer-Kaup equations, this method can also be used to find other nonlinear evolution equations of new exact...
A kind of cubic algebraic trigonometric B-spline base functions with a shape control parameter is presented, and the corresponding curves are defined by the introduced base functions. The curves inherit some properties with traditional cubic B-spline curves and can interpolate directly some control points without solving system of equations or inserting some additional control points. The curves can...
The criteria of finding the optimal structure of the model as interval difference operator is carried out. It is shown that the formulated task of structure identification is a multicriteria optimization task with the discrete target functions and nonlinear constraints specified by interval system of nonlinear algebraic equations (ISNAE).
The new approach in this paper added role factor in the activity-section flow chart and proposed human-computer interactive, role-exchanged concept. It is used in a logistics system, remove the activity loops and reduce interactive times between sections or roles, so it is more suitable for electronic business process than before.
The algebraic structure determining the vector-matrix transformation in the discrete vector Boolean space for the analyzing information based on logical operations on associative data.
Programming via rewriting is a part of the declarative programming which is illustrated by the languages: OBJ, Maude, CafeOBJ, CASL and so on. Programming via rewriting is very close to the equational logic. In the equational logic a set Γ of axioms is given. Axioms are Horn clauses, called also conditional equations. We are looking for all universal quantified equalities which are consequences...
In this paper, a procedure for ambiguity groups determination both in linear and non linear circuits is proposed. Such procedure, based on the a priori identifiability concept, represents an improvement with respect to previous approaches, since allows one to greatly reduce the computational complexity of the evaluation of canonical ambiguity groups. The identifiability of the circuit under test is...
A new method for the parameterization of quadric surfaces is presented. To parameterize a general quadric implicit surface, the new method first translates the implicit surface to make it pass through the origin point, and then the parametric surface is obtained by substituting the coefficients of the implicit equation into the parameterization formula. As to the parameterization of a quadric implicit...
Elimination method is an effective method for solving non-linear polynomial equations. It mainly includes Wu's methods, Grobner base and resultant methods. Dixon resultant is more efficient than other resultant methods. But Dixon matrix enlarges greatly when the polynomial sets have higher rank. Pro.Fu Hongguang et al worked out the recursive algorithm for computing Dixon resultant polynomial, by...
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