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Faulhaber's triangle: Difference between revisions

Faulhaber's triangle (view source)

Revision as of 16:13, 16 January 2022

14,902 bytes added ,  2 years ago
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→‎{{header|Phix}}: added syntax colouring, marked p2js compatible
m (→‎{{header|Phix}}: added syntax colouring, marked p2js compatible)
Line 2,251:
=={{header|Phix}}==
{{trans|C#}}
<!--<lang Phix>include builtins\pfrac.e -- (0.8.0+phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #000000;">pfrac</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #000080;font-style:italic;">-- (0.8.0+)</span>
function bernoulli(integer n)
sequence a = {}
<span style="color: #008080;">function</span> <span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
for m=0 to n do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
a = append(a,{1,m+1})
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
for j=m to 1 by -1 do
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
a[j] = frac_mul({j,1},frac_sub(a[j+1],a[j]))
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">m</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">({</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span><span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]))</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if n!=1 then return a[1] end if
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return frac_uminus(a[1])
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">frac_uminus</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function binomial(integer n, k)
if n<0 or k<0 or n<k then ?9/0 end if
<span style="color: #008080;">function</span> <span style="color: #000000;">binomial</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
if n=0 or k=0 then return 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">k</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
atom num = 1,
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
denom = 1
<span style="color: #004080;">atom</span> <span style="color: #000000;">num</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
for i=k+1 to n do
<span style="color: #000000;">denom</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
num *= i
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">num</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
for i=2 to n-k do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
denom *= i
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">denom</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
return num / denom
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">num</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">denom</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function faulhaber_triangle(integer p, bool asString=true)
sequence coeffs = repeat(frac_zero,p+1)
<span style="color: #008080;">function</span> <span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">asString</span><span style="color: #0000FF;">=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
for j=0 to p do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">coeffs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac_zero</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
frac coeff = frac_mul({binomial(p+1,j),p+1},bernoulli(j))
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">p</span> <span style="color: #008080;">do</span>
coeffs[p-j+1] = iff(asString?sprintf("%5s",{frac_sprint(coeff)}):coeff)
<span style="color: #000000;">frac</span> <span style="color: #000000;">coeff</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">({</span><span style="color: #000000;">binomial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">),</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span><span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">))</span>
end for
<span style="color: #000000;">coeffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">asString</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%5s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">frac_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">coeff</span><span style="color: #0000FF;">)}):</span><span style="color: #000000;">coeff</span><span style="color: #0000FF;">)</span>
return coeffs
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">coeffs</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
for i=0 to 9 do
printf(1,"%s\n",{join(faulhaber_triangle(i)," ")})
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
end for
<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;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)})</span>
puts(1,"\n")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
sequence row18 = faulhaber_triangle(17,false)
frac res = frac_zero
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
atom t1 = time()+1
<span style="color: #004080;">sequence</span> <span style="color: #000000;">row18</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">faulhaber_triangle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span>
integer lim = 1000
<span style="color: #000000;">frac</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_zero</span>
for k=1 to lim do
<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
bigatom nn = BA_ONE
<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</span>
for i=1 to length(row18) do
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span>
res = frac_add(res,frac_mul(row18[i],{nn,1}))
<span style="color: #000000;">bigatom</span> <span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">BA_ONE</span>
nn = ba_mul(nn,lim)
<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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row18</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">row18</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],{</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}))</span>
if time()>t1 then printf(1,"calculating, k=%d...\r",k) t1 = time()+1 end if
<span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ba_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"%s \n",{frac_sprint(res)})</lang>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">then</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;">"calculating, k=%d...\r"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</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: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s \n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">frac_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</lang>-->
{{out}}
<pre>
Line 2,321 ⟶ 2,326:
56056972216555580111030077961944183400198333273050000
</pre>
Note the extra credit takes about 90s, so I disabled it under pwa/p2js.
 
=={{header|Prolog}}==
Petelomax
7,813

edits

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