Detail publikačního výsledku

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

BYRTUS, R.; DEREVIANKO, A.; VAŠÍK, P.; HILDENBRAND, D.; STEINMETZ, C.

Originální název

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Anglický název

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Conformal geometric algebra; Geometric algebra; Clifford algebra; Conic intersection

Klíčová slova v angličtině

Conformal geometric algebra; Geometric algebra; Clifford algebra; Conic intersection

Autoři

BYRTUS, R.; DEREVIANKO, A.; VAŠÍK, P.; HILDENBRAND, D.; STEINMETZ, C.

Rok RIV

2022

Vydáno

01.02.2022

Nakladatel

SPRINGER BASEL AG

Místo

BASEL

ISSN

0188-7009

Periodikum

Advances in Applied Clifford Algebras

Svazek

32

Číslo

1

Stát

Švýcarská konfederace

Strany od

1

Strany do

21

Strany počet

21

URL

https://link.springer.com/article/10.1007/s00006-021-01182-z

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",
  journal="Advances in Applied Clifford Algebras",
  year="2022",
  volume="32",
  number="1",
  pages="1--21",
  doi="10.1007/s00006-021-01182-z",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-021-01182-z"
}