Computation in multivariate quaternionic polynomial ring

In this paper we study on division algorithm and Gröbner bases in the multivariate quaternionic polynomial ring

EULER CHARACTERISTIC OF TANGO BUNDLES

We are interested in a vector bundle constructed by Tango (1976). The Tango bundle is an indecomposable vector bundle of rank n-1 on the complex projective space P^n. In particular, we show that the Euler characteristic of the Tango bundle on P^n is equal to 2n-1

A characterization of the algebraic degree in semidefinite programming

In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to use the theory of symmetric polynomials to obtain many interesting results of Nie, Ranestad and Sturmfels in a simpler way.Comment: 14 page