Cyclotomic polynomial: Difference between revisions

=={{header|C++}}==

{{trans|Java}}

#include <iostream>

#include <initializer_list>

#include <vector>

 

const int algorithm = 2;

int divisions = 0;

 

return 0;

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<pre>Task 1: cyclotomic polynomials for n <= 30:

CP[10465] has coefficient with magnitude = 10</pre>

 

{{trans|Java}}

{{works with|C sharp|8}}

using System.Collections;

using System.Collections.Generic;

};

}

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<pre>

=={{header|D}}==

{{trans|Kotlin}}

import std.exception;

import std.format;

}

}

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<pre>Task 1: cyclotomic polynomials for n <= 30:

CP[6545] has coefficient with magnitude = 9

CP[10465] has coefficient with magnitude = 10</pre>

 

=={{header|Go}}==

{{trans|Java}}

 

import (

}

}

 

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</pre>

<math>Insert formula here</math>

 

=={{header|Java}}==

import java.util.ArrayList;

import java.util.Collections;

 

}

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<pre>

CP[6545] has coefficient with magnitude = 9

CP[10465] has coefficient with magnitude = 10

</pre>

 

=={{header|Julia}}==

# memoize cache for recursive calls

println("The cyclotomic polynomial Φ(", abs(n), ") has a coefficient that is ", n < 0 ? -i : i)

end

<pre>

First 30 cyclotomic polynomials:

=={{header|Kotlin}}==

{{trans|Java}}

import kotlin.math.abs

import kotlin.math.pow

} else coefficient.toString() + "x^" + exponent

}

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<pre>Task 1: cyclotomic polynomials for n <= 30:

CP[6545] has coefficient with magnitude = 9

CP[10465] has coefficient with magnitude = 10</pre>

 

=={{header|Nim}}==

We use Java algorithm with ideas from C#, D, Go and Kotlin. We have kept only algorithm number 2 as other algorithms are much less efficient. We have also done some Nim specific improvements in order to get better performances.

 

 

type

echo &"Φ{'(' & $n & ')':7} has coefficient with magnitude = {i}"

dec n

 

{{out}}

Φ(6545) has coefficient with magnitude = 9

Φ(10465) has coefficient with magnitude = 10</pre>

 

=={{header|Perl}}==

Conveniently, the module <code>Math::Polynomial::Cyclotomic</code> exists to do all the work. An <code>exponent too large</code> error prevents reaching the 10th step of the 2nd part of the task.

use List::Util qw(first);

use Math::Polynomial::Cyclotomic qw(cyclo_poly_iterate);

$n++;

}

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<pre>First 30 cyclotomic polynomials:

{{trans|Julia}}

Uses several routines from [[Polynomial_long_division#Phix]], tweaked slightly to check remainder is zero and trim the quotient.

{{out}}

If you disable the cheating, and if in a particularly self harming mood replace it with n+=1, you will get exactly the same output, eventually.<br>

 

=={{header|Python}}==

from collections import deque

 

while want in c or -want in c:

print(f'C[{want}]: {n}')

{{out}}

Only showing first 10 polynomials to avoid clutter.

 

Uses the same library as Perl, so comes with the same caveats.

 

say 'First 30 cyclotomic polynomials:';

sub super ($str) {

$str.subst( / '^' (\d+) /, { $0.trans([<0123456789>.comb] => [<⁰¹²³⁴⁵⁶⁷⁸⁹>.comb]) }, :g)

<pre>First 30 cyclotomic polynomials:

Φ(1) = (x - 1)

 

=={{header|Sidef}}==

for k in (1..30) {

}

 

say "\nSmallest cyclotomic polynomial with n or -n as a coefficient:"

var k = (1..Inf -> first {|k|

})

say "Φ(#{k}) has coefficient with magnitude #{n}"

 

{{out}}

^C

</pre>

=={{header|Visual Basic .NET}}==

{{trans|C++}}

 

Module Module1

End Sub

 

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<pre>Task 1: cyclotomic polynomials for n <= 30:

CP[6545] has coefficient with magnitude = 9

CP[10465] has coefficient with magnitude = 10</pre>