Applying Gröbner basis techniques to group theory
نویسندگان
چکیده
منابع مشابه
A Generalization of Gröbner Basis Algorithms to Polycyclic Group Rings
It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchber...
متن کاملProbabilistic Knowledge Representation Using Gröbner Basis Theory
An often used methodology for reasoning with probabilistic conditional knowledge bases is provided by the principle of maximum entropy (so-called MaxEnt principle) that realises an idea of informational economy. In this paper we exploit the fact that MaxEnt distributions can be computed by solving nonlinear equation systems that reflect the conditional logical structure of these distributions. ...
متن کاملGröbner Basis Techniques for Computing Actions of K - Categories ∗
This paper involves categories and computer science. Gröbner basis theory is a branch of computer algebra which has been usefully applied to a wide range of problems. Kan extensions are a key concept of category theory capable of expressing most algebraic structures. The paper combines the two, using Gröbner basis techniques to compute certain kinds of Kan extension.
متن کاملA new Gröbner basis conversion method based on stabilization techniques
We propose a new method for converting a Gröbner basis w.r.t. one term order into a Gröbner basis w.r.t. another term order by using the algorithm stabilization techniques proposed by Shirayanagi and Sweedler. First, we guess the support of the desired Gröbner basis from a floating-point Gröbner basis by exploiting the supportwise convergence property of the stabilized Buchberger’s algorithm. N...
متن کاملBlock Ciphers Sensitive to Gröbner Basis Attacks
We construct and analyze Feistel and SPN ciphers that have a sound design strategy against linear and differential attacks but for which the encryption process can be described by very simple polynomial equations. For a block and key size of 128 bits, we present ciphers for which practical Gröbner basis attacks can recover the full cipher key requiring only a minimal number of plaintext/ciphert...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2007
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2006.09.001