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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
