Clifford algebras in R^4: Computing zeros of polynomials

  • Date:
  • Time: 14:00 - 15:30
  • Address:
    Sokolovská 83, Praha
  • Room: K3
  • Speaker: Drahoslava Janovská

We focus on some results in different types of Clifford algebras in R^4. After the brief (pre)historical overview, we will give the basic definitions for quaternions and coquaternions and compare their basic properties. We may observe many similarities in other algebras in R^4. In particular we will consider tessarines, cotessarines, nectarines, conectarines, tangerines, and cotangerines. We study the linear equations in quaternions and coquaternions. Based on the theory of companion polynomials, an algorithm was developed to calculate all roots of simple quaternionic polynomials of degree n. In general, quaternionic coefficients can be located on both sides of the powers. If so, there are even 5 different zero classes, that are classified according to the rank of a certain real 4x4 matrix. All results can be extended to other Clifford algebras in R^4.