There are quaternions and octonions in https://github.com/forio/Quaternions.jl
Maybe have a look there? I guess the answer is that you should implement other numbers if you need them. And for them to be usable you need to implement some methods for them. On Fri, 2015-08-28 at 14:56, Pรกll Haraldsson <[email protected]> wrote: > On "quite long posts", yes. I'm trying not to do that and the pendulum, may > have swung too far in the other direction.. I was actually trying to not > have many questions - be to the point, but was a little hasty and the > interesting point was maybe too implicit. But there was A question: > > > "Should you use ::Real at every point to not get those [runtime errors] > with Complex [eliminated]?" > > > Trying again: > > A. "[higher generalizations of] numbers are not supported, but are they > [available] in libraries or needed? > > Not available, I think. Needed? Maybe not, as they are just very obscure > concepts (at least sedenions), but my general question applies even just to > complex numbers, that is in the standard library: > > > B. Is Julia, being a generic language, a good fit for them (and higher > math/numbers) because it is generic, by default? > > A manifest typed language has no "problem" with numbers and new types. At > least they just work and do not produce runtime errors. In a generic > language you are writing code, you can't check even theoretically, as the > code is generic and you expect it to work for even code not yet written.. > That just seems not possible.. You will, however, not get wrong answers, > just runtime exceptions. I guess that is a good thing. People advocating > static languages, with separate compilatin, regard it as a good thing, that > the compiler shakes out the bugs AND avoid runtime errors. > > > > C. Do all these generalization of numbers belong, or fit well, in a > language like Julia? Or at least in packages. Sedenions, seem just very > obscure. :) > > [I do not even know what "multiplicative normedness" is..] > > commutativity and associativity are common concepts you usually associate > (and order) with numbers/reals (but a pitfall for floating point..). I > wander when Julia knows that "rules" like these, I assume, like in C etc. > they just know to special case floating point. Would "multiplicative > normedness" trip Julia up? I do not even know if an operator applies to > that.. > > > Some context, that I maybe should have quoted, not just the linked: > > http://math.stackexchange.com/questions/86434/what-lies-beyond-the-sedenions > "Reals" โ "Complex" โ "Quaternions" โ "Octonions" โ "Sedenions" > > With the following "properties": > > From R to C you gain "algebraic-closure"-ness (but you throw away ordering). > From C to H we throw away commutativity. > From H to O we throw away associativity. > From O to S we throw away multiplicative normedness. > > > Is it clear now? It is longer..
