Faulhaber's triangle: Difference between revisions
→{{header|Perl}}
Line 1,646:
56056972216555580111030077961944183400198333273050000
</pre>
=={{header|Lua}}==
{{trans|C}}
<lang lua>function binomial(n,k)
if n<0 or k<0 or n<k then return -1 end
if n==0 or k==0 then return 1 end
local num = 1
for i=k+1,n do
num = num * i
end
local denom = 1
for i=2,n-k do
denom = denom * i
end
return num / denom
end
function gcd(a,b)
while b ~= 0 do
local temp = a % b
a = b
b = temp
end
return a
end
function makeFrac(n,d)
local result = {}
if d==0 then
result.num = 0
result.denom = 0
return result
end
if n==0 then
d = 1
elseif d < 0 then
n = -n
d = -d
end
local g = math.abs(gcd(n, d))
if g>1 then
n = n / g
d = d / g
end
result.num = n
result.denom = d
return result
end
function negateFrac(f)
return makeFrac(-f.num, f.denom)
end
function subFrac(lhs, rhs)
return makeFrac(lhs.num * rhs.denom - lhs.denom * rhs.num, rhs.denom * lhs.denom)
end
function multFrac(lhs, rhs)
return makeFrac(lhs.num * rhs.num, lhs.denom * rhs.denom)
end
function equalFrac(lhs, rhs)
return (lhs.num == rhs.num) and (lhs.denom == rhs.denom)
end
function lessFrac(lhs, rhs)
return (lhs.num * rhs.denom) < (rhs.num * lhs.denom)
end
function printFrac(f)
local str = tostring(f.num)
if f.denom ~= 1 then
str = str.."/"..f.denom
end
for i=1, 7 - string.len(str) do
io.write(" ")
end
io.write(str)
return nil
end
function bernoulli(n)
if n<0 then
return {num=0, denom=0}
end
local a = {}
for m=0,n do
a[m] = makeFrac(1, m+1)
for j=m,1,-1 do
a[j-1] = multFrac(subFrac(a[j-1], a[j]), makeFrac(j, 1))
end
end
if n~=1 then
return a[0]
end
return negateFrac(a[0])
end
function faulhaber(p)
local q = makeFrac(1, p+1)
local sign = -1
local coeffs = {}
for j=0,p do
sign = -1 * sign
coeffs[p-j] = multFrac(multFrac(multFrac(q, makeFrac(sign, 1)), makeFrac(binomial(p + 1, j), 1)), bernoulli(j))
end
for j=0,p do
printFrac(coeffs[j])
end
print()
return nil
end
-- main
for i=0,9 do
faulhaber(i)
end</lang>
{{out}}
<pre> 1
1/2 1/2
1/6 1/2 1/3
-0 1/4 1/2 1/4
-1/30 -0 1/3 1/2 1/5
-0 -1/12 -0 5/12 1/2 1/6
1/42 -0 -1/6 -0 1/2 1/2 1/7
-0 1/12 -0 -7/24 -0 7/12 1/2 1/8
-1/30 -0 2/9 -0 -7/15 -0 2/3 1/2 1/9
-0 -3/20 -0 1/2 -0 -7/10 -0 3/4 1/2 1/10</pre>
=={{header|Perl}}==
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