On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F22%3APU142365" target="_blank" >RIV/00216305:26210/22:PU142365 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00006-021-01182-z" target="_blank" >https://link.springer.com/article/10.1007/s00006-021-01182-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00006-021-01182-z" target="_blank" >10.1007/s00006-021-01182-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ADV APPL CLIFFORD AL

ISSN

0188-7009

e-ISSN

1661-4909

Svazek periodika

32

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000721868000001

EID výsledku v databázi Scopus

2-s2.0-85119682824