|
|
Gröbner bases
Petržilková, Lenka ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
In this thesis we remind you of the basic Buchberger algorithm for com- puting the Gröbner base over commutative polynomial rings. We also observe uniqueness of the Gröbner base for the ideal. Next we research less known, but more effective (for some instances) Faugère F4 algorithm. At the end of the first chapter we compare these two algorithms. In the second chapter we analyze a generalization of the Buchberger algorithm for noncommutative rings both for free algebra and factor algebra. On the contary to the commu- tative case, Gröbner bases can be infinite in this case, even for some finitely generated ideals. Among other things, we investigate quasi-zero elements,i.e. such elements, that we get zero by multiplying them with an arbitrary term, and their role in the division of a polynom by set of polynoms. 1
|
|
| |
|
|
Group rings in coding theory
Horáček, Jan ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
This work is focused on linear error-correcting codes in group rings. The basic introduc- tion to group rings and to coding in group rings is given. By code we mean a R-submodul, which generalizes the definition of the code as an ideal. We describe unit-derived and zero- divisor codes. We test paramaters of unit-derived codes. The construction of LDPC codes without short cycles is explained. Except from the derivation of the generator and check matrix we focus on algebraic properties of codes and group rings. We also deal with the self-dual codes, reversible codes or number of units in a finite group algebra of a cyclic group. 1
|
|
|
The Ideal of Chivalrous Sovereign. The Case of Czech Medieval Alexandrian Epic
Rajterová, Petra ; Dvořáčková, Dana (advisor) ; Žemlička, Josef (referee)
My final thesis, based on study of primary and secondary sources, is focused on the idea of sovereign around 1300 AD. Old-Czech poem Alexandreida and German version Alexander of Ulrich von Etzenbach are used as primary repository of information. Thesis follows both of them and in their comparison shows, how the idea was formulated. Final thesis deals also with works of historians, literary historians and German studies related to its topic. The goal is not an linguistic analysis but to evaluate the poems as an historiographic source, on which we can study medieval notions of rulers and their role in society. Second main task for this final thesis is to reconstruct niveau of bohemian court surrounding King of Bohemia at the end of 13th century, where the poems were originally written. In the end, thesis describes so called "court culture" in the relation to both of Alexandrian poems and their influence in bohemia society.
|
|
| |
|
| |
|
|
The foundations of premonstratensian monasteries in the Central Europe until the beginning of the 13th Century. Filial foundations of Steinfeld and Dünnwald
Kremer, Jan ; Žemlička, Josef (advisor) ; Pařez, Jan (referee)
Presented diploma thesis is concerned with the foundation of the first czech premonstratensian houses in the 12th century, specially in relation to the central abbey of Prémontré, the premonstratensian general chapter and two mother houses of Steinfeld and Dünnwald in the Eifel region of Germany. The first chapter deals with the central role of the general chapter and the abbey of Prémontré. It describes the ways in which the general chapter has tried to control the other houses of the order. We can follow the contitutions of the order to the half of the 13th century. In the following text we are trying to describe the function of circaries and visitations. The second part is treating the life of the founder of Prémontré - Norbert of Xanten - whose life had a very strong influence on the whole order even after he was elected archbishop of Magdeburg in the year 1126. We are trying to explain how the abbey of Prémontré and its abbot Hugo of Fosse preserved the unity of the order in the following years. We are further concerned with the ideal of apostolic life in the order and with cura animarum, unity and diversity in the order. We are describing, how the premonstratensians spread across the whole Europe and what kind of places they inhabited. The following part is explaining the role of the women houses and...
|
|
|
The coronation ordines of Charles IV. as ritualized rulers programme
Žůrek, Václav ; Žemlička, Josef (advisor) ; Doležalová, Eva (referee)
The present diploma thesis is an attempt to find new ways of interpreting the Charles IV.'s coronation ordines text (Drdo ad coronandum regem Boemorum). The rudimentary analysis ofthis source was already accomplished by Josef Cibulka and it is precisely his work which served us as a basis. We attempted to take into account the contemporary medievalist literature which deals with coronation and intronization rituals in Europe abundantly. Even though the main topic of the contemporary works are rituals of the early Middle Ages, their conclusions can be helpful for our thesis as well. We have described the situation before Charles IV.' s acceSSlOn, especially the chronichlers' descriptions of the Přemyslid corronations. The analysis of these sources doesn't provide us sufficient information to decide whether a Přemysliďs coronation ordines text existed in the 13th century (surely not before) or not. Basing ourselves on the coronation ordines text analysis we have come to the conclusion that the Czech coronation ordines text was modeled on the ground of the Otonian coronation ordines text from the 10th century and was extended with several elements from the French ordines text from the 13th century which were created during the reign of Saint Louis IX. Beside the French inspiration, the Czech coronation ordines...
|
|
|
MQ problem
Středa, Adolf ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
The aim of this thesis is to describe a general MQ Problem with a focus on its variant called HFE, outline several attacks on a basic scheme based on HFE and describe a new attack on HFEz, a cryptosystem based on special polynomials over finite fields with a modification, which discards a portion of the output from the initial transformation. This ensures a dependency on more variables while keeping the same size of the field. The attack starts with a translation of HFE into HFE with branches, followed by a branch separating algorithm described in [Fel06]. The separation algorithm uses the public key to derive an operation, which induces (with addition) a non-associative algebra. Utilising some properties of non-associative algebras, a matrix, which can separate variables into distinct sets according to branches, is calculated. This leads to stripping off the HFEz modification and thus allowing us to attack directly the HFE polynomial. Powered by TCPDF (www.tcpdf.org)
|
|
|
Structure of division rings
Reichel, Tomáš ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
This bachelor thesis deals with a theorem and its proof, which allows construction of division ring from cyclic field extension which satisfies certain conditions. The reader is expected to have basic knowledge of linear algebra, ring and module theory. For using this theorem the reader also needs some skills in counting Galois groups. In this work there are also included two basic examples of usage the theorem. During the proof we introduce a structure of tensor product and Brauer group. Powered by TCPDF (www.tcpdf.org)
|
guest ::
RSS feed.