Publication detail
On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb
BYRTUS, R. DEREVIANKO, A. VAŠÍK, P. HILDENBRAND, D. STEINMETZ, C.
English title
On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb
Type
journal article in Web of Science
Language
en
Original abstract
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.
English abstract
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.
Keywords in English
Conformal geometric algebra; Geometric algebra; Clifford algebra; Conic intersection
Released
01.02.2022
Publisher
SPRINGER BASEL AG
Location
BASEL
ISSN
0188-7009
Volume
32
Number
1
Pages from–to
1–21
Pages count
21
BIBTEX
@article{BUT175046,
author="Roman {Byrtus} and Anna {Derevianko} and Petr {Vašík} and Dietmar {Hildenbrand} and Christian {Steinmetz},
title="On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb",
year="2022",
volume="32",
number="1",
month="February",
pages="1--21",
publisher="SPRINGER BASEL AG",
address="BASEL",
issn="0188-7009"
}