See https://code.jsoftware.com/wiki/Vocabulary/pdot#multinomial
(<_3 ]\ 7 2 3 4 1 0 9 0 0) p. 1 1,:2 2
20 241
Henry Rich
On 1/5/2023 3:43 PM, Raul Miller wrote:
On Thu, Jan 5, 2023 at 7:07 AM Ak O <akin...@gmail.com> wrote:
The point I mean to highlight is the represention (for the purpose of
calculation).
It's probably worth noting here that J's p. verb does not, by itself,
support polynomials like 7x^2y^3 + 4x^1y^0 - 9x^0y^0. And without a
representation for the polynomial we don't have a representation for
degrees of that polynomial.
Also...
To implement that, in a general case form, I guess you'd need a verb
which matched dimensions on the left with items on the right (and, for
efficiency purposes, the left argument would need to be a sparse
array. So in recent versions of J we'd be limited to at most 63
variables -- arrays of at most 63 items in the right hand argument.
That said, we'd also want improved sparse array handling.
This concept might be motivating for a re-implementation of J's type
and rank system, with several details changing:
(1) The sparse system itself could be made more efficient and general
(currently we can't put sparse arrays in boxes),
(2) The implementation of the type and rank system could be made more
space efficient (allowing for higher ranked arrays of numeric types at
the expense of no rank support for certain syntactic types which are
not exposed to the user), and
(3) The sparse system -- where something other than location in memory
is used to represent "array index" -- could be extended to support
something other than a fixed length list of numbers as an index (in
other words: the system could support a "dictionary type").
This is getting to be a bit of a reach, from where we currently stand.
And, there's still some important missing pieces which would need
careful thought before this sketch could be turned into something
practical. But it's interesting to think about...
Also... computers do have limits, so it's always going to be the case
that a person could invent mathematical structures which strain (or
break) a particular implementation of some math concepts.
Thanks,
--
Raul
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