[Purdue-pm] a Perl 6 quick example

[Mark Senn]

Mark Ward,

1.  I helped Dr. Wagstaff typeset a book having to do with factoring
large integers and haven't been sending him stuff because I think he's
already aware of anything I've ever heard of.  I will bcc this to him in
case he or he would like his students to use Perl 6 (I also recommend
Mathematica) to easily experiment with ideas without having to write
much code.

2.  Perl 6's is-prime sub/method uses the "Rabin-Miller" (also known as the
"Miller-Rabin") algorithm.  See
    http://examples.perl6.org/categories/99-problems/P36-ovid.html
for a simple example of how to factor integers using Perl 6.

Some more information about Perl 6:

    Another simplification that can be done to the code below.
        # "(2..*)" can be simplified to "2..*"
        (grep {.is-prime}, 2..*)[^3]
        (2 3 5)

    Type
        <<a "butterfly wings" c>>.permutations
    to print all permutations of "a", "butterfly wings", and c.)

Mark Senn




Cc: purdue-pm at pm.org
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From: Mark Daniel Ward <mdw at purdue.edu>
Subject: Re: [Purdue-pm] a Perl 6 quick example
Date: Wed, 14 Dec 2016 04:51:25 -0500
To: Mark Senn <mark at purdue.edu>
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Mark Daniel Ward <mdw at purdue.edu> wrote on 2016-12-14 at 0451:
Dear Mark,

Thank you again for your email.  This email alone might have finally
convinced me to consider moving from Perl 5 to Perl 6.

I have two things for you to consider.

1.  You might send your email to Sam Wagstaff, who is one of Purdue's
experts on primes and factoring.

2.  I am curious what kinds of algorithms that Perl 6 is using under the
hood, for its factoring algorithms.  Here is a classic kind of
challenge: if you give Perl 6 a 200 digit number that has only 2
factors, each of which are about 100 digits long, how does it know if
the 200 digit number is prime or not?  What algorthm(s) is Perl 6
trying, under the hood, to perform such a calculation?

I am genuinely curious to know.

Mark

> On Dec 14, 2016, at 12:59 AM, Mark Senn <mark at purdue.edu> wrote:
> 
> # The "is-prime" sub is defined in Perl 6.
> is-prime(5)
> True
> 
> # The parentheses are not needed.
> is-prime 5
> True
> 
> # The "is-prime" method is defined in Perl 6.
> 5.is-prime
> True
> 
> # Get all primes from 2 to 10.
> grep {$_.is-prime}, (2..10)
> (2 3 5 7)
> 
> # If an object is not specified, "$_" is assumed.
> grep {.is-prime}, (2..10)
> (2 3 5 7)
> 
> # Get first three primes---I know the third prime comes before 10.
> (grep {.is-prime}, (2..10))[0..2]
> (2 3 5)
> 
> # Using "^3" will give first three also---I think of "^3"
> # as from 0 up to but not including 3.
> (grep {.is-prime), (2..10))[^3]
> (2 3 5)
> 
> # Let Perl 6 generate as many candidate integers
> # as we need (from 2 to infinity) to test for
> # primality but stop after we get 3 primes.
> (grep {.is-prime}, (2..Inf))[^3]
> (2 3 5)
> 
> # Use "*" ("whatever") instead of "Inf".
> # Instead of 2 to infinity think of it
> # as 2 to whatever.
> (grep {.is-prime}, (2..*))[^3]
> (2 3 5)
> 
> # Exercise for the reader, do the previous
> # computation in Perl 5 but make the code
> # at least as clear as the Perl 6 solution.
> 
> # Perl 6 uses really big integers in software
> # if an integer is too big for machine computation.
> 10**1000 - 3
> 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!
 99!
> 99999999997
> 
> -mark
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