Splitting full matrix algebras over algebraic number fields

Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.) As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.Comment: 15 pages; Theorem 2 and Lemma 8 correcte

Basis of Quartic Splines over Triangulation

Abstract. The modeling of complex shapes usually requires a well-based space of splines. The aim of this work is to give the construction method of such spline space basis over the chosen class of triangulations. This basis has several useful properties — local minimal support, low degree of polynomials. We also present several problems, that arise in lower-degree polynomials

i

Ich erkläre an Eides statt, dass ich die vorliegende Dissertation selbstständig un