Performance of basic arithmetic actions with complex numbers, which are presented in interval hyperbolic form

Complex Interval Arithmetic Using Polar Form

In this paper, the polar representation of complex numbers is extended to complex polar intervals or sectors; detailed algorithms are derived for performing basic arithmetic operations on sectors. While multiplication and division are exactly defined, addition and subtraction are not, and we seek to minimize the pessimism introduced by these operations. Addition is studied as an optimization pr...

Arithmetic With Complex Numbers

Trigonometric Form of Complex Numbers

One can prove the following propositions: (1) Let F be an add-associative right zeroed right complementable left distributive non empty double loop structure and x be an element of the carrier of F . Then 0F · x = 0F . (2) Let F be an add-associative right zeroed right complementable right distributive non empty double loop structure and x be an element of the carrier of F . Then x · 0F = 0F . ...

Actions of Certain Arithmetic Groups on Gromov Hyperbolic Spaces

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

New non-arithmetic complex hyperbolic lattices

We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne– Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for construc...