Publication result detail

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

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

Original Title

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

English Title

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Type

WoS Article

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

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

Key words in English

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

Authors

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

RIV year

2022

Released

01.02.2022

Publisher

SPRINGER BASEL AG

Location

BASEL

ISBN

0188-7009

Periodical

Advances in Applied Clifford Algebras

Volume

32

Number

1

State

Swiss Confederation

Pages from

1

Pages to

21

Pages count

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"
}