The degree spectrum of a countable structure is the set of all Turing degrees of presentations of that structure. We show that every nonlow Turing degree lies in the spectrum of some differentially closed field (of characteristic 0, with a single derivation) whose spectrum does not contain the computable degree 0. Indeed, this is an equivalence, for we also show that every such field of low deg...

We develop an algorithm for computing isomorphisms and automorphisms of algebraic function fields of transcendence degree one in characteristic zero and positive characteristic.

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...

We show how to perform basic operations (arithmetic, square roots, computing isomorphisms) over finite fields of the form F q2 in essentially linear time. Mathematics Subject Classification 2010. Primary 11Y16, 12Y05, Secondary 68W30.

Our aim in this paper is to complete some results given in [15] on the classification of symmetric bilinear forms of height 2 and degree d = 1 or 2 over fields of characteristic 2, i.e., those whose anisotropic parts over their own function fields are similar to d-fold bilinear Pfister forms.