Implementace násobení na neasociativních (nekomutativních) algebrách

Abstract

Tato prace uvede ctenare do problematiky neasociativnich algeber a superalgeber, coz jsou matematicke struktury (mnoziny s nejakymi operacemi na nich). Predstavi take koncept volnych (super)algeber, ktere definuji identity a superidentity variet. Pote se soustredi na jednu volnou alternativni niln super-algebru s jednim lichym generatorem, pro kterou byla v teto praci vyvinuta interaktivni aplikace pro pocitani s prvky baze teto superalgebry. Aplikace take umi v teto superalgebre vyhodnotit niln superidentitu pro pevne stanovene n. Aplikace podporuje vystup ve formatu Wolfram Mathematica a pro pohodli uzivatele i vystup ve formatu LaTeX.

This bachelor's thesis introduces the reader to the subject of nonassociative algebras and superalgebras, which are mathematical structures (sets equipped with some operations on them). It also presents to the reader the concept of free (super)algebras that define identities and superidentities of varieties. The second part of this thesis focuses on one alternative niln superalgebra on one odd generator for which an interactive computer program has been developed. This program can evaluate any arithmetic expression in said superalgebra. For a fixed n it can also evaluate the niln superidentity in this superalgebra. The program supports output in the Wolfram Mathematica format and for greater user convenience even in LaTeX.