Since this is a golf exercize, reducing number of characters, why use the
reduction form when infix is shorter?
squish(sort [X[&({$^a**$^b+$b**$a})]] 2..31,2..31) # from original
squish(sort 2..31 X[&({$^a**$^b+$b**$a})] 2..31) # infix is 2-chars shorter
Also I am trying to do a little un-golf speed-optimizing, the Wiki page for
the sequence notes that requiring a<=b removes trivial duplicates. Let's
see what I can figure out in the near future...
-y
On Sun, Oct 11, 2020 at 5:55 PM Cezmi Pastirma <cezmisi...@yandex.com>
wrote:
> Wow, that's a very comprehensive explanation. I've just found out that I
> couldn't even comprehend the first reduction operator. I was thinking it
> was doing some magic operations. All it did was enable the cross op to act
> on the 2 lists without having to be between them. As simple as that. And
> surely I mis-took the second bracket as a second reduction. Now it's clear
> that it's for Nesting of metaoperators
> <https://docs.raku.org/language/operators#___top> Actually I was
> guessing this fine detail must have been documented in the Raku docs but I
> hadn't the faintest idea how to search for it in the huge docs of Raku :)
>
> The custom operator definition to separate the Cross from the Op is very
> welcome too. I haven't written any custom op in Raku so far and it's good
> to see it in action.
>
> Thank you for your time. Very much appreciated.
>
>
> 11.10.2020, 21:31, "Bruce Gray" <robertbrucegr...@gmail.com>:
>
> NOTE: 30 minutes from now is the start of the Raku Study Group of the San
> Francisco Perl Mongers.
> We can offer a "deep dive" into how the Leyland code works, if that would
> be helpful.
> 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)
>
>
