- Tytuł:
- Algorithms for integral solutions of a class of diophantine equations
- Autorzy:
- Polak, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/206419.pdf
- Data publikacji:
- 2011
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
integral quadratic form
unit form
diophantine equations
roots
Euler bilinear form
Euclidean diagrams
mesh quiver
algorithm
Maple - Opis:
- In 1970 a negative solution to the tenth Hilbert problem, concerning the determination of integral solutions of diophantine equations, has been published by Y. W. Matiyasevich (see Matiyasevich, 1970). Despite this result, we can present algorithms to compute integral solutions (roots) for a wide class of quadratic diophantine equations of the form q(x) = d, where q : Zn → Z is a homogeneous quadratic form. We will focus on the roots of one (i.e., d = 1) of quadratic Euler forms of selected posets from Loupias list (see Loupias, 1975). In particular, we will describe the roots of positive definite quadratic forms and the roots of quadratic forms that are principal (see Simson, 2010a). The algorithms and results we present here are successfully used in the representation theory of finite groups and algebras.
- Źródło:
-
Control and Cybernetics; 2011, 40, 2; 491-514
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł