CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

PARALLEL ALGORITHMS PROJECT
automorphism called relator. This leads to the concept of an organ which broadens for Computation
the classical notion of an additive abelian group in Mathematics. By framing an organ into a euclidean
metric space, we obtain a metric cloth which allows us to perform weaving computations. This novel
concept accounts for the emergence of meaning from a rich noneuclidean geometry. See [ALG46] for more
information. The report [ALG42] shows how Einstein’s relativistic addition (1905) in R 3 is connected to
and may modify computation in the quaternionic field ∼ = R 4 . We also indicate that the complex versions of
Einstein’s addition and Poincaré’s hyperbolic translation (1880, 1907) are identical when they are based on
the same reference value. With the choice of 1 as reference value, they both represent all automorphisms of
the complex unit disk in C n other than unitary maps.
In addition, some work has been done in 2010 for the book [ALG1]. An additional chapter has been prepared
in 2011 for the republication of ”Eigenvalues of Matrices” (Wiley, 1993) in the SIAM Classics in Applied
Mathematics Series to appear in 2012.
CERFACS ACTIVITY REPORT 23