Bruce Gray <robertbrucegr...@gmail.com> wrote: > NOTE: 30 minutes from now is the start of the Raku Study Group of the San > Francisco Perl Mongers.
Thanks-- though now it's 3 minutes-- but that was the info for last week. The current one is: https://www.meetup.com/San-Francisco-Perl/events/273839687/ In general, you can start at the San Francisco Perl group to get the latest meeting info: https://www.meetup.com/San-Francisco-Perl > We can offer a "deep dive" into how the Leyland code works, if that would be > helpful. I'm glad *you're* offering, I was just looking at that one going uh, Leyland Numbers? I haven't even heard of "squish"... > Zoom details here: > https://mail.pm.org/pipermail/sanfrancisco-pm/2020-October/004726.html > > >> On Oct 11, 2020, at 10:39 AM, Cezmi Pastirma <cezmisi...@yandex.com> >> wrote: >> >> I've got a question about a Leyland-numbers-listing Raku code which I saw >> at codegolf.stackexchange.com at >> https://codegolf.stackexchange.com/a/83013/98132 >> >> I've slightly rearranged the code to make it print Leyland numbers up to 1 >> Billion: >> .say for grep {$_ < 1E11}, squish(sort [X[&({$^a**$^b+$b**$a})]] >> 2..32,2..32) >> >> The question in short is: >> >> How does the cross reduce work there? > > The reduction is a red herring to our understanding here. > Note that, when you are only [reducing] on two lists, `[any_op_here] @a, @b` > is the same as `@a any_op_here @b`. > These are equivalent: > say [X+] 2..4, 1..5; > say 2..4 X+ 1..5; > The operator need not be a meta-operator: > say [*] 3, 5; > say 3 * 5; > >> Extra info: >> >> That cross reduce section surely does what this half-pseudo code tries to >> do: >> map { $^a ** $^b + $b ** $a }, 2..32,32…2 > > If @c has 20 elements, and @d has 30 elements, then `@c X+ @d` has 600 > elements. > You cannot produce the equivalent with a simple `map`. > (You could with a flattened map-within-a-map) > > > Simplifying your "slightly rearranged” code: > .say for grep {$_ < 1E11}, squish(sort [X[&({$^a**$^b+$b**$a})]] > 2..32,2..32) > > ...to just the part you are curious about, we get: > say [X[&({$^a**$^b+$b**$a})]] 2..4,2..4; > (8 17 32 17 54 145 32 145 512) > > We are only [reducing] on two lists, so we can remove the reduction, and > just use the Xop: > say 2..4 X[&({$^a**$^b+$b**$a})] 2..4; > (8 17 32 17 54 145 32 145 512) > > >> The tricky part here is the use of reduce operators two times in a row, >> once before the cross operator, once before the & operator, which I guess >> donates a closure. How to interpret this usage of operators? >> > > The square brackets after the X, I think you mis-took as a second > reduction. > > Those brackets are just there to disambiguate the `op` that the `X` is > crossing on. > See: https://docs.raku.org/language/operators#Nesting_of_metaoperators > > These are equivalent: > .say for ^2 X+ ^2; > .say for ^2 X[+] ^2; > > > We can create our own operator, to further separate the Cross from the Op: > multi infix:<⨁> ($a, $b) { > $a ** $b > + $b ** $a > }; > say 2 ⨁ 3; > say 2..4 X⨁ 2..4; > 17 > (8 17 32 17 54 145 32 145 512) > > The `X` itself is the operator-form of the `cross` routine, well-documented > here: > https://docs.raku.org/routine/cross > > https://docs.raku.org/language/operators#index-entry-X_(cross_metaoperator) > > https://docs.raku.org/language/operators#index-entry-cross_product_operator > > If any part of this was lacking in clarity, please let me know where to > focus, and I will be glad to expound. > > -- > Hope this helps, > Bruce Gray (Util of Perlmonks) >
