Computer Algebra and Symbolic Computation

2002 ◽  
Author(s):  
Joel S. Cohen
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra

The TOPAS symbolic computation system

2011 ◽  
Vol 26 (S1) ◽  
pp. S22-S25 ◽  
Author(s):  
A. A. Coelho ◽  
J. Evans ◽  
I. Evans ◽  
A. Kern ◽  
S. Parsons
Keyword(s):  
Developmental Stage ◽  
Rietveld Refinement ◽  
Symbolic Computation ◽  
Computer Algebra ◽  
Symbolic System ◽  
Symbolic Form ◽  
Functional Changes ◽  
Low Level ◽  
Run Time

Computer algebra removes much of the drudgery from mathematics; it allows users to formulate models by using the language of mathematics and to have those models evaluated with little effort. This symbolic form of representation is often thought of as being separate to dedicated computational programs such as Rietveld refinement. These dedicated programs are often written in low level languages; they are relatively inflexible in what they do and modifying them to change functionality in a small manner is often a major programming task. This paper describes a symbolic system that is integrated into the dedicated Rietveld refinement program called TOPAS. The symbolic component allows large functional changes to be made at run time and with a relatively small amount of effort. In addition, the system as a whole reduces the programming complexity at the developmental stage.

scholarly journals Not Another Computer Algebra System: Highlighting wxMaxima in Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1317
Author(s):  
Natanael Karjanto ◽  
Husty Serviana Husain
Keyword(s):  
Secondary Teachers ◽  
Symbolic Computation ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Teaching And Learning ◽  
Tertiary Level ◽  
Software Developers ◽  
University Instructors ◽  
Mathematics Educators ◽  
Calculus Teaching

This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into classrooms to enhance students’ understanding of Calculus concepts. For many mathematics educators who have been using CAS, this material is of great interest, particularly for secondary teachers and university instructors who plan to introduce an alternative CAS into their classrooms. By highlighting both the strengths and limitations of the software, we hope that it will stimulate further debate not only among mathematics educators and software users but also also among symbolic computation and software developers.

scholarly journals Using Symbolic Computation to Prove Nonexistence of Distance-Regular Graphs

10.37236/7763 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Janoš Vidali
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra ◽  
Regular Graph ◽  
Computer Algebra System ◽  
Intersection Array ◽  
Regular Graphs ◽  
Distance Regular Graph ◽  
Triple Intersection ◽  
Distance Regular Graphs ◽  
Krein Condition

A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array$$\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\}  (r, t \geq 1),$$$\{135,\! 128,\! 16; 1,\! 16,\! 120\}$, $\{234,\! 165,\! 12; 1,\! 30,\! 198\}$ or $\{55,\! 54,\! 50,\! 35,\! 10; 1,\! 5,\! 20,\! 45,\! 55\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence. 

Moments and Parametrizing Construction for 3-Band Biorthogonal Scaling Coefficients

2013 ◽  
Vol 284-287 ◽  
pp. 3189-3193
Author(s):  
Li Hong Cui ◽  
Yan Zhou ◽  
Bin Huang ◽  
Jian Jun Sun
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra ◽  
Computation Method ◽  
Scaling Functions ◽  
Dual Scaling ◽  
Vanishing Moments ◽  
Compactly Supported ◽  
Orthonormal Wavelets ◽  
Discrete Moments ◽  
The Relationship

Regensburger and Scherzer described a symbolic computation method for moments and filter coefficients of scaling functions and obtained parametrizing compactly supported orthonormal wavelets. Following the idea, we are devoted to a study moments and parameterization construction for 3-band biorthogonal scaling coefficients with several vanishing moments. Firstly, we investigate the relations between filter lengths and symmetry. Then, we prove the relationship between dual continuous moments of 3-band biorthogonal scaling functions in theorem 2. This theorem reveals that the sum of continuous moments of dual scaling functions and is completely determined by the lower discrete moments. And we show the fact that the odd-indexed discrete moments are determined by the smaller even-indexed discrete moments. Finally, a family 3-band biorthogonal scaling coefficients with discrete moments as parameters are explicitly expressed based on computer algebra.

scholarly journals Groebner Bases Based Verification Solution for SystemVerilog Concurrent Assertions

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ning Zhou ◽  
Xinyan Gao ◽  
Jinzhao Wu ◽  
Jianchao Wei ◽  
Dakui Li
Keyword(s):  
Case Studies ◽  
Symbolic Computation ◽  
Computer Algebra ◽  
Polynomial Ring ◽  
Digital Circuit ◽  
Groebner Bases ◽  
Symbolic Representations ◽  
Polynomial Modeling ◽  
Algorithm Framework ◽  
Algebraic Representations

We introduce an approach exploiting the power of polynomial ring algebra to perform SystemVerilog assertion verification over digital circuit systems. This method is based on Groebner bases theory and sequential properties checking. We define a constrained subset of SVAs so that an efficient polynomial modeling mechanism for both circuit descriptions and assertions can be applied. We present an algorithm framework based on the algebraic representations using Groebner bases for concurrent SVAs checking. Case studies show that computer algebra can provide canonical symbolic representations for both assertions and circuit designs and can act as a novel solver engine from the viewpoint of symbolic computation.

Abstracts of recent doctoral dissertations in computer algebra

2021 ◽  
Vol 55 (3) ◽  
pp. 117-124
Author(s):  
CCA editors
Keyword(s):  
Symbolic Computation ◽  
Computer Algebra ◽  
The Past ◽  
Doctoral Dissertations

Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.

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