I am confused, what is the question? You seem to generally write quite long posts and it is hard to understand what the actual question is.
Usually, a short, to the point, example followed with the question makes it easier to get good answers. On Friday, August 28, 2015 at 11:50:45 AM UTC+2, Pรกll Haraldsson wrote: > > Mostly about math (that I do not know to well, this advanced, above > complex numbers), just seems relevant to generic programming..: > > In e.g.: > https://en.wikipedia.org/wiki/Complex_number > > in the template at the bottom: > > Real numbers and extensions: > > Real numbers (โ) Complex numbers (โ) Quaternions (โ) Octonions (๐) > Sedenions (๐) CayleyโDickson construction Dual numbers Split-complex > numbers Bicomplex numbers Hypercomplex numbers Superreal numbers Irrational > numbers Transcendental numbers Hyperreal numbers Levi-Civita field Surreal > numbers > > > http://math.stackexchange.com/questions/86434/what-lies-beyond-the-sedenions > > > I see that dual numbers are supported already with a library, and know > what Julia does support. > > > Since Julia IS a scientific language, I checked: > > julia> 1+0im < 2+0im > ERROR: `isless` has no method matching isless(::Complex{Int64}, > ::Complex{Int64}) > in < at operators.jl:32 > > that is the right thing. I wander what MATLAB does, since all numbers(?) > are stored as complex. 0im special cased? > > > real numbers have properties that floating point already doesn't support, > so loosing those properties with higher order numbers seems not to be an > issue, but is it for the even higher order numbers and those properties? I > assume not, as there are no operators/functions and even if there where > operators (really just functions), then they would just stop working. > > In a language where everything is typed (not generic), this might not be a > problem, but leads to run-time "ERROR"s/exceptions. Should you use ::Real > at every point to not get those with Complex? What about other possible > numbers? > > > Thanks in advance, > -- > Palli. > > >
