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The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are four known computational approaches to calculating this antipode. The main goal of this paper is to compare the computational performances of the three latest methods, two coproduct recursion methods and the...
In this paper, the solution of limit problems, which is an important subject of high school and university mathematics is presented by using JavaCC code generation tool and symbolic computation methods. Although JavaCC is generally used for generating programming language interpreters, in a similar way it can also be used in the evaluation of mathematical expressions. In this work, first the general...
To solve complex and large mathematical expression manually using pen and paper is a time taking task which in most cases ends up in an erroneous result. This is a major drawback which may lead to heavy losses to people dealing in numbers. Henceforth we have come up with a vision of Symbolic computation which provides a quick, efficient and user friendly environment to its users. Symbolic Computation...
Symbolic Computation (Mathematics Subject Classification 2000, 68W30) is often treated as just another subject in the wide field of special topics within mathematics, on the same level as mesh generation (65L50) or quasi-Frobenius rings (16L60). Here we want to argue that actually Symbolic Computation is not so much a topic in mathematics, but a relatively novel approach to mathematical epistemology,...
In this paper, the KP-type equation is considered. some new theta function periodic solutions for this equation are successfully obtained with the aid of symbolic computation for the first time. It is shown that the method we used is a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematics and physics.
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...
In this paper, theta functions and the auxiliary equation method is used to seek exact solutions for the the mKdV-ZK equation. As a result, some theta function solutions are successfully obtained with the aid of symbolic computation for the first time. It is shown that the auxiliary equation method is a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematics...
In this paper, the auxiliary equation method is used to seek exact solutions of a 3-dimensional KdV equation. As a result, topological 1-soliton solutions are successfully obtained with the aid of symbolic computation. It is shown that the auxiliary equation method is a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematics and physics.
In this paper, by applying a reversible linear transform and a near-identity transformation, we obtain a simplest normal form for a class vector fields with double bifurcation. We have implemented an algorithm in Maple 12 and obtained an example of the further reduced normal forms up to some finite order.
Symbolic computation has experienced a distinct evolutionary path than numerical computation and this has prevented its proliferation in engineering. This paper offers a contemporary look at how the historical elements in symbolic computation has lead to a renewed interest symbolic in engineering modeling and simulation today. In particular symbolic techniques are showing promise for the modernization...
Computational methods for manipulating sets of polynomial equations are becoming of greater importance due to the use of polynomial in various applications. Dixon resultant algorithm provides one of the most efficient methods for solving the system of polynomial equations or eliminating variables. When computing Dixon resultant, we first construct the Dixon polynomial for input polynomial system....
We investigate the integration of C implementation of fast arithmetic operations into MAPLE, focusing on triangular decomposition algorithms. We show substantial improvements over existing MAPLE implementations; our code also outperforms MAGMA on many examples. Profiling data show that data conversion can become a bottleneck for some algorithms, leaving room for further improvements.
Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are themselves integer-valued polynomials. This article extends the notion of univariate polynomial decomposition to symbolic polynomials and presents an algorithm to compute these decompositions. For example, the symbolic polynomial f(X) = 2Xn2+n - 4X...
Although the limit of a function at a point is one of the most important concepts in mathematics, to prove symbolically its formal definition is a challenging exercise that requires a certain level of expertise usually out of the capabilities of most students. This paper introduces a new mathematica package to prove symbolically the values of limits of functions in terms of delta and epsiv. In addition...
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