On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

We describe a possibility for geometric calculation of specific conics’ intersections in Geometric Algebra for Conics (GAC) using its operations that may be expressed as sums of products. The advantage is that no solver for a system of quadratic equations is needed and thus no numerical error is inv...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2022-02, Vol.32 (1), Article 2
Main Authors: Byrtus, Roman, Derevianko, Anna, Vašík, Petr, Hildenbrand, Dietmar, Steinmetz, Christian
Format: Article
Language:English
Subjects:
Applications of Mathematics
Conics
ENGAGE 2020 Geometric Algebra for Computing
Graphics & Engineering
Intersections
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quadratic equations
Theoretical
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Summary:We describe a possibility for geometric calculation of specific conics’ intersections in Geometric Algebra for Conics (GAC) using its operations that may be expressed as sums of products. The advantage is that no solver for a system of quadratic equations is needed and thus no numerical error is involved. We also describe specific conics connected to intersections of conics in a general mutual position. Then we show how symbolic operations may be calculated directly in GAALOPWeb software, that the basis coefficients may be read off in the appropriate basis and, moreover, the result may be immediately and truly visualized. We compare the functionality with Maple package Clifford.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-021-01182-z