Eisenstein primes: Difference between revisions

Line 154:

</pre>

[[File:Plot eisenstein primes julia example.svg|center|Eisenstein primes]]

=={{header|Phix}}==

Note MARKSTYLE=DOT added for this task, 1.0.3 has not yet been released, and won't be until work this needs under pwa/p2js is finished.

requires("1.0.3")

include complex.e

constant OMEGA = {-0.5, sqrt(3)*0.5}

// try to replicate Wren sort order for easy comparison

enum NORM, IMAG, REAL, IS_PRIME, ELEN=$

function new_Eisenstein(integer a,b)

atom {real,imag} = complex_add(complex_mul(OMEGA,b),a)

integer norm = a*a-a*b+b*b, c = max(abs(a),abs(b))

bool p = iff(a=0 or b=0 or a=b?is_prime(c) and remainder(c,3)=2

:is_prime(norm))

return {norm,imag,real,p} -- nb in [NORM..IS_PRIME] order

end function

function Eisenstein()

sequence eprimes = {}

for a=-100 to 100 do

for b=-100 to 100 do

sequence e = new_Eisenstein(a, b)

if e[IS_PRIME] then

eprimes = append(eprimes,e)

end if

end for

eprimes = sort(eprimes)

sequence real = vslice(eprimes,REAL),

imag = vslice(eprimes,IMAG),

f100 = repeat("",100)

for i=1 to 100 do -- convert for display

integer pm = iff(imag[i]>=0?'+':'-')

f100[i] = sprintf("%7.4f %c%7.4fi",{real[i],pm,abs(imag[i])})

end for

return {f100,real,imag}

end function

sequence {f100,real,imag} = Eisenstein()

printf(1,"First 100 Eisenstein primes nearest zero:\n%s\n",join_by(f100,1,4," "))

include xpGUI.e

function get_data(gdx graph) return {{real,imag}} end function

gdx graph = gGraph(get_data,"XMIN=-150,XMAX=150,YMIN=-100,YMAX=100"),

dlg = gDialog(graph,"Eisenstein primes","SIZE=392x290")

gSetAttribute(graph,"GTITLE","with norm <= 100 (%d points)",{length(real)})

gSetAttributes(graph,"XTICK=50,YTICK=25,MARKSTYLE=DOT,GRID=NO")

gShow(dlg)

gMainLoop()

Output same as Wren.

=={{header|Wren}}==

@@ Line 154: / Line 154: @@
 </pre>
 [[File:Plot eisenstein primes julia example.svg|center|Eisenstein primes]]
+=={{header|Phix}}==
+Note MARKSTYLE=DOT added for this task, 1.0.3 has not yet been released, and won't be until work this needs under pwa/p2js is finished.
+<!--<syntaxhighlight lang="phix">(phixonline)-->
+ <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.3"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">include</span> <span style="color: #004080;">complex</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+ <span style="color: #008080;">constant</span> <span style="color: #000000;">OMEGA</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">}</span>
+ <span style="color: #000080;font-style:italic;">// try to replicate Wren sort order for easy comparison</span>
+ <span style="color: #008080;">enum</span> <span style="color: #000000;">NORM</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">IMAG</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">REAL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">IS_PRIME</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ELEN</span><span style="color: #0000FF;">=$</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">new_Eisenstein</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">real</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_add</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">OMEGA</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">norm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">-</span><span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span>
+     <span style="color: #004080;">bool</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">b</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">2</span>
+                                   <span style="color: #0000FF;">:</span><span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">norm</span><span style="color: #0000FF;">))</span>
+     <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">norm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">,</span><span style="color: #000000;">real</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- nb in [NORM..IS_PRIME] order</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">Eisenstein</span><span style="color: #0000FF;">()</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">eprimes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">100</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">100</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
+             <span style="color: #004080;">sequence</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">new_Eisenstein</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">[</span><span style="color: #000000;">IS_PRIME</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
+                 <span style="color: #000000;">eprimes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">eprimes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #000000;">eprimes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">eprimes</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">real</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">eprimes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">REAL</span><span style="color: #0000FF;">),</span>
+              <span style="color: #000000;">imag</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">eprimes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">IMAG</span><span style="color: #0000FF;">),</span>
+              <span style="color: #000000;">f100</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- convert for display</span>
+         <span style="color: #004080;">integer</span> <span style="color: #000000;">pm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]>=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">'+'</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">f100</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%7.4f %c%7.4fi"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">real</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">pm</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">f100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">real</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">}</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+ <span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">f100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">real</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Eisenstein</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;">"First 100 Eisenstein primes nearest zero:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"  "</span><span style="color: #0000FF;">))</span>
+ <span style="color: #008080;">include</span> <span style="color: #000000;">xpGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">get_data</span><span style="color: #0000FF;">(</span><span style="color: #004080;">gdx</span> <span style="color: #000000;">graph</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">real</span><span style="color: #0000FF;">,</span><span style="color: #000000;">imag</span><span style="color: #0000FF;">}}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+ <span style="color: #004080;">gdx</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">gGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_data</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XMIN=-150,XMAX=150,YMIN=-100,YMAX=100"</span><span style="color: #0000FF;">),</span>
+     <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">gDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Eisenstein primes"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"SIZE=392x290"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">gSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"GTITLE"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"with norm &lt;= 100  (%d points)"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">real</span><span style="color: #0000FF;">)})</span>
+ <span style="color: #7060A8;">gSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XTICK=50,YTICK=25,MARKSTYLE=DOT,GRID=NO"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">gShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">gMainLoop</span><span style="color: #0000FF;">()</span>
+<!--</syntaxhighlight>-->
+Output same as Wren.
 =={{header|Wren}}==