  In this paper we propose some very promissing results in interval arithmetics
which permit to build well-defined arithmetics including distributivity of
multiplication and division according addition and substraction. Thus, it
allows to build all algebraic operations and functions on intervals. This will
avoid completely the wrapping effects and data dependance. Some simple
applications for matrix eigenvalues calculations, inversion of symmetric
matrices and finally optimization are exhibited in the object-oriented
programming language python.
