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Geometric Algebra and Quaternion Techniques in Computer Algebra Systems for Describing Rotations in Eucledean Space
AbstractTensor formalism (and its special case—vector formalism) is a mathematical technique that is widely used in physical and engineering...
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Analytical Study of Cubature Formulas on a Sphere in Computer Algebra Systems
AbstractThe problem of finding the weights and nodes of cubature formulas of a given order on a unit sphere that are invariant under the icosahedral...
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Design of Low-Artifact Interpolation Kernels by Means of Computer Algebra
We present a number of new piecewise-polynomial kernels for image interpolation. The kernels are constructed by optimizing a measure of interpolation...
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Can I Bring My Calculator to the Exam? Some Reflections on the Abstraction Level of Computer Algebra Systems
The author began working with computer algebra systems (CAS) in the 80s to perform effective computations for his Ph.D Thesis in algebra. He thought...
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A New Course “Algebra + Computer Science”: What Should Be Its Outcomes and Where It Should Start
AbstractThe words “Programming is the second literacy” were coined more than 40 years ago [13], but never came to life. The paper develops and...
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Python in Computer Algebra
SymPy (for Symbolic Python) is a Python program package for the symbolic solution of mathematical problems. In the area of computer algebra, the...
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Investigation of the Dynamics of Two Connected Bodies in the Plane of a Circular Orbit Using Computer Algebra Methods
Computer algebra methods are used to investigate the equilibrium orientations of a system of two bodies connected by a spherical hinge that moves...
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Disaster Incident Analysis via Algebra Stories
Disaster management requires detailed data from past disasters for policy planning as well as for the generation of disaster exercises and...
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Computer Algebra Methods for Searching the Stationary Motions of the Connected Bodies System Moving in Gravitational Field
Computer algebra methods were used to find the stationary motions of the system of two bodies connected by a spherical hinge, that moves along a...
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Algebra
Die elementare Algebra nimmt traditionell einen großen Teil der Unterrichtszeit in der Sekundarstufe I ein. Medien können den Umgang mit abstrakten...
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Introduction to Geometric Algebra
Geometric algebra was initiated by W.K. Clifford over 140 years ago. It unifies all branches of physics, and has found rich applications in robotics,...
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Computer Experiment in Teaching Mathematics
AbstractA mathematical experiment has always been a key source for a mathematical discovery. Over the past 50 years, thanks to digital technologies,...
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Research into the Dynamics of a System of Two Connected Bodies Moving in the Plane of a Circular Orbit by Applying Computer Algebra Methods
AbstractComputer algebra methods are used to determine the equilibrium orientations of a system of two bodies connected by a spherical hinge that...
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Computer assisted investigation of alienness of linear functional equations
In this paper, a computer program developed in the computer algebra system Maple is presented, which investigates alienness and strong alienness of...
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Is Computer Algebra Ready for Conjecturing and Proving Geometric Inequalities in the Classroom?
We introduce an experimental version of GeoGebra that successfully conjectures and proves a large scale of geometric inequalities by providing an...
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Study of Secular Perturbations in the Restricted Three-Body Problem of Variable Masses Using Computer Algebra
AbstractA nonstationary restricted three-body problem for variable masses is considered taking into account the reactive forces arising due to...
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Computer Algebra Systems and Dynamic Geometry for Mathematical Thinking
For more than three decades, the use of Computer Algebra Systems (CAS) and Dynamic Geometry Environments (DGE) has introduced new possibilities in...
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Linear Algebra
Linear algebra introduces students to abstract concepts associated with vectors and matrices. Some students may have already worked with matrices at...
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Introduction to Computer Algebra
Before we discuss mathematical algorithms and their programming, we want to show the capabilities of a general computer algebra system such as...