Re: #matr~ vs ##matr (and: arity, questenian and !!)

On Fri, Feb 05, 2021 at 05:54:48AM -0800, Ilya Zakharevich wrote:
> On Fri, Feb 05, 2021 at 05:46:43AM -0800, Ilya Zakharevich wrote:
> >   Is not it desirable to implement ##matr as an (optimized) synonym for #matr~?
> > 
> > If the answer to the second question is positive, then one can maybe
> > improve things by returning a special value (such as -1) for scalars…
> 
> Well, to get things yet simpler, one can make ###x to return 0 for
> scalars, 1 for vectors/lists and 2 for matrices.

Taking all these things together, I think that in the best of the
worlds one would have these:

  #mattr~   optimized in the compiler to (an equivalent to) (matsize(mattr))[1]

  ##object  return “the arity” of the object: 2/1/0 for matrices/vectors/scalars 
  	    (and maybe -1 for the “tricky” cases, when/if an object may
  	     be used as a scalar AND as a vector/matrix/etc.).

Hope this helps,
Ilya

  P.S.  I wonder what is the purpose of implementing extra-obscure¹⁾
  	num# when PARI cannot even calculate 3!! right?!

	  ¹⁾ IIRC, Steinhaus has been denoting this as
	     	     num?
	     (“questenian”???).  If so, then num?? would have been
	     more appropriate in PARI.