Pisano period: Difference between revisions

{{trans|Nim}}

R m I/ gcd(m, n) * n

print(‘pisano(n) for integers 'n' from 1 to 180 are:’)

L(n) 1..180

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=={{header|Factor}}==

{{works with|Factor|0.99 2020-01-23}}

math.primes math.primes.factors math.ranges sequences ;

"n pisano for integers 'n' from 2 to 180:" print

2 180 [a,b] [ pisano ] map 15 group

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<pre style="height:45ex">

=={{header|Go}}==

import "fmt"

}

fmt.Println()

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=={{header|Haskell}}==

main = do

pisanoConjecture m = foldl1 lcm . map (uncurry pisanoPrime') $ factor m

where

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<pre>PisanoPrime(p,2) for prime p lower than 15

Use efficient algorithm to calculate period.

import java.util.ArrayList;

import java.util.Collections;

}

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<pre>

=={{header|Julia}}==

const pisanos = Dict{Int, Int}()

println("\nPisano(n) for n from 2 to 180:\n", [pisano(i) for i in 2:180])

println("\nPisano(n) using pisanoPrime for n from 2 to 180:\n", [pisanotask(i) for i in 2:180])

<pre>

pisanoPrime(2, 2) = 6

=={{header|Nim}}==

{{trans|Go}}

func primes(n: Positive): seq[int] =

echo "pisano(n) for integers 'n' from 1 to 180 are:"

for n in 1..180:

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{{trans|Sidef}}

{{libheader|ntheory}}

use warnings;

use feature 'say';

say "Pisano periods for squares of primes p <= 50:\n", display( map { pisano_period_pp($_, 2) } @{primes(1, 50)} ),

"\nPisano periods for primes p <= 180:\n", display( map { pisano_period_pp($_, 1) } @{primes(1, 180)} ),

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<pre>Pisano periods for squares of primes p <= 50:

=={{header|Phix}}==

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">pisano_period</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"pisano(1..180):\n"</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p180</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_IntFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntCh</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">})</span>

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<pre>

Uses the [[wp:SymPy|SymPy]] library.

from functools import reduce

print("\nPisano period (p) for integers 1 to 180")

for i in range(1, 181):

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{{works with|Rakudo|2020.02}}

Didn't bother making two differently named routines, just made a multi that will auto dispatch to the correct candidate.

constant @fib := 1,1,*+*…*;

put "\nPisano period (p, 1) for integers 1 to 180";

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<pre>Pisano period (p, 2) for primes less than 50

=={{header|REXX}}==

numeric digits 500 /*ensure enough decimal digits for Fib.*/

parse arg lim.1 lim.2 lim.3 . /*obtain optional arguments from the CL*/

end /*k*/; @.m= k; return k

/*──────────────────────────────────────────────────────────────────────────────────────*/

{{out|output|text=&nbsp; when using the default inputs:}}

=={{header|Sidef}}==

assert(k.is_pos, "k = #{k} must be positive")

say "\nPisano periods for integers n from 1 to 180:"

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<pre>

By assuming that '''Wall-Sun-Sun primes''' do not exist, we can compute the Pisano period more efficiently, as illustrated below on Fermat numbers '''F_n = 2^(2^n) + 1''':

(p - kronecker(5, p)).divisors.first_by {|d| fibmod(d, p) == 0 } * p**(k-1)

}

for k in (1..8) {

say ("Pisano(F_#{k}) = ", pisano_period(2**(2**k) + 1))

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<pre>

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

import "/fmt" for Fmt

if (n != 1 && n%15 == 0) System.print()

}

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=={{header|zkl}}==

{{libheader|GMP}} GNU Multiple Precision Arithmetic Library for prime testing

fcn pisanoPeriod(p){

_assert_(BI(p).probablyPrime(), "%s is not a prime number".fmt(p));

pisanoPeriod(p.pow(k))

[1..50].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(2))

.concat(" "," ").println();

println("Pisano period (p, 1) for primes less than 180:");

[1..180].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(1))

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<pre>

256 130 276 46 148 50 316 328 336 348 178

</pre>

primeFactors(m).pump(Dictionary().incV) //18 --> (2,3,3) --> ("2":1, "3":2)

.reduce(fcn(z,[(k,v])){ lcm(z,pisanoPrime(k.toInt(),v)) },1)

if(n!=m) acc.append(n/m); // opps, missed last factor

else acc;

[1..180].pump(List, pisano, "%4d".fmt)

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<pre>