• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.519-529
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• 2002

We investigate implementation of the determinantal representation of generalized inverses for complex and rational matrices in the symbolic package MATHEMATICA. We also introduce an implementation which is applicable to sparse matrices.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.91-104
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• 2004

A modification of the gradient method of convex programming is introduced. Also, we describe symbolic implementation of the gradient method and its modification by means of the programming language MATHEMATICA. A few numerical examples are reported.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.133-142
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• 1998

A simple mathematical theory is developed on the periodicity of elementary polar functions. The periodicity plays an important role in efficient plotting of some closed polar curves, without the excessive use of plotting devices and materials. An efficient plotting algorithm utilizing the periodicity is proposed and its implementation by a Mathematica program is introduced for a family of closed polar functions.

• The Journal of Korean Association of Computer Education
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• v.21 no.6
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• pp.39-47
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• 2018

This paper dealt with investigating the number of minimal spanning ladders originated from ladder game and their properties as well as the related computational thinking aspects. The author modified the filtering techniques to enhance Mathematica project where a new type of graph was generated based on the algorithm using a generator of firstly found minimal spanning graph by repeatedly applying independent ladder operator to a subsequence of ladder sequence. The newly produced YC graphs had recursive and hierarchical graph structures and showed the properties of edge-symmetric. As the computational complexity increased the author divided the whole search space into the each floor of the newly generated minimal spanning graphs for the (5, 10) YC graph and the higher (6, 15) YC graph. It turned out that the computational thinking capabilities such as data visualization, abstraction, and parallel computing with Mathematica contributed to enumerating the new YC graphs in order to investigate their structures and properties.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.81-94
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• 2007

In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.5.3-5
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• 2003

The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map, Some properties on the geometry of the boundary are investigated including the root point, the cusp, the component center and the length as well as the area bounded by the boundary curve. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.35-46
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• 2006

The concept of convolution is a fundamental mathematical concept in a wide variety of disciplines and applications including probability, image processing, physics, and many more. The visualization of convolution for the continuous case is generally predetermined. On the other hand, the convolution structure embedded in the discrete case is often subtle and its visualization is non- trivial. This paper purports to develop the CAS techniques in visualizing the logical structure in the concept of a discrete convolution.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.43-57
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• 2003

The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map. Some properties on the geometry of the boundary are investigated including the root point, the cusp and the length as well as the area bounded by the boundary curve. The centroid of the area for the period-2 component was numerically found with high accuracy and compared with its center. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.267-281
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• 2022

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA^® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.