On Mon, Apr 07, 2025 at 08:45:26AM -0700, Kurt Pagani wrote:
>
>
> On Monday, 7 April 2025 at 16:06:42 UTC+2 Waldek Hebisch wrote:
>
> On Sun, Apr 06, 2025 at 06:38:32PM +0200, Waldek Hebisch wrote:
> > On Sun, Apr 06, 2025 at 07:11:03AM -0700, Kurt Pagani wrote:
> > > Either my understanding of lquo/rquo (Category XFreeAlgebra) is wrong
> or
> > > there is a bug in the implementation of these functions in
> > > XDistributedPolynomial (XDPOLY).
> > >
> > > p1:= 3*x*y*x*z --> 3 x y x z
> > > lquo(p1,3*x*y) --> 9 x z (expected: x z)
> > >
> > > I think that by "left simplification" is meant mult by a left
> > > inverse/recip, similiar as in group theory, although there is no
> leftRecip
> > > of 3*x*y in XDPOLY, of course. Am I off the track?
> >
> > Current definition of 'lquo' looks odd, I have noticed this some
> > time ago. OTOH there are some odd looking operations on XFreeAlgebra-s
> > which actually make a lot of sense. So, it requires some investigative
> > work to decide if this is a bug or an unfortunate name of operation
> > needed elsewhere.
>
> A little update: this does not look like a bug, there are two different
> implementations in 'xpoly.spad' and similar implementation in
> 'xlpoly.spad'. There are also similar implementations of 'rquo'.
>
> I do not know why 'lquo' and 'rquo' are defined in this way. One
> possible explanation could be that in Lie case there are multiple
> possibilities for "base" words and maybe the definition tries do
> do something for words expressed in different basis.
>
>
> Ralf showed me another weird result:
>
> %%% (15) -> lquo(x*y, x*y+x)
>
> (15) 1 + y
>
>
>
>
> AFAICS strange definitions of 'lquo' and 'rquo' are not used by
> other code, so in principle we could remove them the reduce
> confusion.
>
>
> Yes, as long as there is no reasonable definition I would advocate for
> removal.
What about:
lquo : (%, %) -> %
++ \spad{lquo(x, y)} is a bilinear extention of \spad{lquo} from
++ words to \spad{%}.
--
Waldek Hebisch
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