Solving the Forward Position Problem of an In-Parallel Planar Manipulator in the Gauss Plane

10.32920/ryerson.14639721.v1 ◽

2021 ◽

Author(s):

Sureyya Sahin

Keyword(s):

Computer Algebra ◽

Computer Algebra System ◽

Complex Numbers ◽

Single Variable ◽

Groebner Bases ◽

Active Joint ◽

Triangular Shape ◽

Revolute Joints ◽

Moving Platform ◽

Position Problem

We study determining the posture of an in-parallel planar manipulator, which has three connectors composed of revolute, prismatic and revolute joints, from specified active joint variables. We construct an ideal in the field of complex numbers, and we introduce self inversive polynomials. We provide results for an in-parallel planar manipulator, which has a base and moving platform in right triangular shape. Using Sage computer algebra system, we compute its Groebner bases. We illustrate that the single variable polynomials obtained from the Groebner bases are self reciprocal.

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An Implementation of Lipschitz Simple Functions in Computer Algebra System Singular

Complexity ◽

10.1155/2021/6695461 ◽

2021 ◽

Vol 2021 ◽

pp. 1-5

Author(s):

Yanan Liu ◽

Muhammad Ahsan Binyamin ◽

Adnan Aslam ◽

Minahal Arshad ◽

Chengmei Fan ◽

...

Keyword(s):

Normal Form ◽

Computer Algebra ◽

Computer Algebra System ◽

Complete Classification ◽

Simple Function ◽

Complex Numbers ◽

Lipschitz Equivalence

A complete classification of simple function germs with respect to Lipschitz equivalence over the field of complex numbers ℂ was given by Nguyen et al. The aim of this article is to implement a classifier in terms of easy computable invariants to compute the type of the Lipschitz simple function germs without computing the normal form in the computer algebra system Singular.

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Calculus and Digital Natives in Rendezvous: wxMaxima Impact

Education Sciences ◽

10.3390/educsci11090490 ◽

2021 ◽

Vol 11 (9) ◽

pp. 490

Author(s):

Natanael Karjanto

Keyword(s):

Computer Algebra ◽

Computer Algebra System ◽

Digital Natives ◽

Human Intervention ◽

Single Variable ◽

Qualitative Feedback ◽

Multivariable Calculus ◽

Technological Tool ◽

Mixed Reaction

This article covers how a computer algebra system (CAS) wxMaxima can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where wxMaxima can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and unsuccessfully. By soliciting qualitative feedback on students’ experience in exploiting the CAS, we gathered a mixed reaction. Although some students commented positively, the majority seemed to be resistant to embracing a new technological tool.

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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