drab wrote:In version 0.5.1.48, everything is fine now except
2 × 1J∅
The answer should be ∅J∅.
drab wrote:One more thing ...
The monadic circle function pi times is usually defined as
○r ←→ pi × r
This is fine most of the time, but it becomes pretty useless if r is a hyper with any ∅ coefficients, because the formal result will always be a hyper with all ∅ coefficients.
So to keep it useful with partially NaN hypers, we only have to redefine the circle function as
○r ←→ < pi × >r
This is a really only a documentation change, since that is always the way it is implemented anyway.
I agree. The rules for using multiplication shortcuts are applied inconsistently and need to be codified.
BTW, there are two sets of such rules, one for infinity and one for NaN. The one for infinity uses 0×∞ ←→ 0
which is really an indeterminate. The one for NaN is determinate as in 0×∅ ←→ ∅
. Both rules are for Real numbers -- and because multiplication and division of Hypercomplex numbers are defined recursively down to the Real number level, those operations on HC numbers can also be well-defined.
I would very much like to avoid things like ○R ←/→ (○1)×R
. That is, the rules for monadic PSFs are the same as for dyadic PSFs, so that (for example) +∅J1
is either ∅J∅
You are the NaN guy -- what do you think?