Eisenstein primes: Difference between revisions

=={{header|Wren}}==

{{libheader|DOME}}

{{libheader|Wren-plot}}

{{libheader|Wren-iterate}}

{{libheader|Wren-complex}}

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

<syntaxhighlight lang="ecmascript">import "dome" for Window

import "graphics" for Canvas, Color

import "./plot" for Axes

import "./iterate" for Stepped

import "./complex" for Complex

import "./math2" for Math, Int

import "./fmt" for Fmt

var OMEGA = Complex.new(-0.5, 3.sqrt * 0.5)

class Eisenstein {

construct new(a, b) {

_a = a

_b = b

_n = OMEGA * b + a

}

a { _a }

b { _b }

n { _n }

real { _n.real }

imag { _n.imag }

norm { _a *_a - _a * _b + _b * _b }

isPrime {

if (_a == 0 || _b == 0 || _a == _b) {

var c = Math.max(_a.abs, _b.abs)

return Int.isPrime(c) && c % 3 == 2

}

return Int.isPrime(norm)

}

toString { _n.toString }

}

var eprimes = []

for (a in -100..100) {

for (b in -100..100) {

var e = Eisenstein.new(a, b)

if (e.isPrime) eprimes.add(e)

}

}

// try to replicate Julia sort order for easy comparison

eprimes.sort { |e1, e2|

if (e1.norm < e2.norm) return true

if (e1.norm == e2.norm) {

if (e1.imag < e2.imag) return true

if (e1.imag == e2.imag) return e1.real < e2.real

return false

}

return false

}

// convert to Complex numbers for easy display

eprimes = eprimes.map { |e| e.n }

// display first 100 to terminal

System.print("First 100 Eisenstein primes nearest zero:")

Fmt.tprint("$ 6.4z ", eprimes.take(100), 4)

// generate points for the plot

var Pts = eprimes.map { |e| [e.real, e.imag] }.toList

class Main {

construct new() {

Window.title = "Eisenstein primes with norm <= 100 (%(Pts.count) points)"

Canvas.resize(1000, 600)

Window.resize(1000, 600)

Canvas.cls(Color.white)

var axes = Axes.new(100, 500, 800, 400, -160..160, -100..100)

axes.draw(Color.black, 2)

var xMarks = Stepped.new(-150..150, 50)

var yMarks = Stepped.new(-75..75, 25)

axes.mark(xMarks, yMarks, Color.black, 2)

axes.label(xMarks, yMarks, Color.black, 2, Color.black)

axes.plot(Pts, Color.black, "·") // uses interpunct character 0xb7

}

init() {}

update() {}

draw(alpha) {}

}

var Game = Main.new()</syntaxhighlight>

{{out}}

Terminal output:

<pre>

First 100 Eisenstein primes nearest zero:

0.0000 - 1.7321i -1.5000 - 0.8660i 1.5000 - 0.8660i -1.5000 + 0.8660i

1.5000 + 0.8660i 0.0000 + 1.7321i -1.0000 - 1.7321i 1.0000 - 1.7321i

-2.0000 + 0.0000i 2.0000 + 0.0000i -1.0000 + 1.7321i 1.0000 + 1.7321i

-0.5000 - 2.5981i 0.5000 - 2.5981i -2.0000 - 1.7321i 2.0000 - 1.7321i

-2.5000 - 0.8660i 2.5000 - 0.8660i -2.5000 + 0.8660i 2.5000 + 0.8660i

-2.0000 + 1.7321i 2.0000 + 1.7321i -0.5000 + 2.5981i 0.5000 + 2.5981i

-1.0000 - 3.4641i 1.0000 - 3.4641i -2.5000 - 2.5981i 2.5000 - 2.5981i

-3.5000 - 0.8660i 3.5000 - 0.8660i -3.5000 + 0.8660i 3.5000 + 0.8660i

-2.5000 + 2.5981i 2.5000 + 2.5981i -1.0000 + 3.4641i 1.0000 + 3.4641i

-0.5000 - 4.3301i 0.5000 - 4.3301i -3.5000 - 2.5981i 3.5000 - 2.5981i

-4.0000 - 1.7321i 4.0000 - 1.7321i -4.0000 + 1.7321i 4.0000 + 1.7321i

-3.5000 + 2.5981i 3.5000 + 2.5981i -0.5000 + 4.3301i 0.5000 + 4.3301i

-2.5000 - 4.3301i 2.5000 - 4.3301i -5.0000 + 0.0000i 5.0000 + 0.0000i

-2.5000 + 4.3301i 2.5000 + 4.3301i -2.0000 - 5.1962i 2.0000 - 5.1962i

-3.5000 - 4.3301i 3.5000 - 4.3301i -5.5000 - 0.8660i 5.5000 - 0.8660i

-5.5000 + 0.8660i 5.5000 + 0.8660i -3.5000 + 4.3301i 3.5000 + 4.3301i

-2.0000 + 5.1962i 2.0000 + 5.1962i -0.5000 - 6.0622i 0.5000 - 6.0622i

-5.0000 - 3.4641i 5.0000 - 3.4641i -5.5000 - 2.5981i 5.5000 - 2.5981i

-5.5000 + 2.5981i 5.5000 + 2.5981i -5.0000 + 3.4641i 5.0000 + 3.4641i

-0.5000 + 6.0622i 0.5000 + 6.0622i -2.5000 - 6.0622i 2.5000 - 6.0622i

-4.0000 - 5.1962i 4.0000 - 5.1962i -6.5000 - 0.8660i 6.5000 - 0.8660i

-6.5000 + 0.8660i 6.5000 + 0.8660i -4.0000 + 5.1962i 4.0000 + 5.1962i

-2.5000 + 6.0622i 2.5000 + 6.0622i -0.5000 - 7.7942i 0.5000 - 7.7942i

-6.5000 - 4.3301i 6.5000 - 4.3301i -7.0000 - 3.4641i 7.0000 - 3.4641i

-7.0000 + 3.4641i 7.0000 + 3.4641i -6.5000 + 4.3301i 6.5000 + 4.3301i

</pre>

[[File:Eisenstein_primes_wren.png|500px|thumb|center]]