Faulhaber's triangle: Difference between revisions
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=={{header|Python}}== |
=={{header|Python}}== |
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{{trans|Haskell}} |
{{trans|Haskell}} |
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{{Works with|Python|3.7}} |
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<lang python>from itertools import (accumulate, count, islice, starmap) |
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<lang python>'''Faulhaber's triangle''' |
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from itertools import (accumulate, count, islice, starmap) |
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from fractions import (Fraction) |
from fractions import (Fraction) |
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# faulhaber :: Integer -> Integer -> Integer |
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def faulhaber(p, n): |
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"""Sum of the p-th powers of the first n positive integers""" |
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return sum( |
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list(starmap( |
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lambda x, y: y * (n ** x), |
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zip(count(1), faulhaberTriangle(p)[-1]) |
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)) |
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) |
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# faulhaberTriangle :: Int -> [[Fraction]] |
# faulhaberTriangle :: Int -> [[Fraction]] |
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def faulhaberTriangle(m): |
def faulhaberTriangle(m): |
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'''List of rows of Faulhaber fractions.''' |
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def go(rs, n): |
def go(rs, n): |
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xs = list(starmap( |
xs = list(starmap( |
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zip(islice(count(2), m), rs) |
zip(islice(count(2), m), rs) |
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)) |
)) |
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return [1 - sum(xs)] + xs |
return [Fraction(1 - sum(xs), 1)] + xs |
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return list(accumulate( |
return list(accumulate( |
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[[]] + list(islice(count(0), 1 + m)), |
[[]] + list(islice(count(0), 1 + m)), |
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go |
go |
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))[1:] |
))[1:] |
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# faulhaberSum :: Integer -> Integer -> Integer |
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def faulhaberSum(p, n): |
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'''Sum of the p-th powers of the first n |
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positive integers. |
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''' |
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return sum( |
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list(starmap( |
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lambda x, y: y * (n ** x), |
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zip(count(1), faulhaberTriangle(p)[-1]) |
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)) |
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) |
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# TEST ---------------------------------------------------- |
# TEST ---------------------------------------------------- |
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def main(): |
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'''Tests''' |
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fs = ( |
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fmap(fmap(showRatio(4)(2)))( |
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lambda ln: list(map( |
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faulhaberTriangle(9) |
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lambda r: str(r.numerator).rjust(2, ' ') + ( |
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) |
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'/' + str(r.denominator).ljust(5, ' ') if ( |
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) |
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r.denominator > 1 |
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print( |
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) else ' ' |
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) |
fTable(__doc__ + ':\n')(str)(str)( |
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lambda x: ''.join(fs[x]) |
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) |
)(range(0, len(fs))) |
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) |
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print('') |
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) |
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print( |
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faulhaberSum(17, 1000) |
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) |
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for row in faulhabers: |
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# DISPLAY ------------------------------------------------- |
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print (''.join(row)) |
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print ('') |
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# fTable :: String -> (a -> String) -> |
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print ( |
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# (b -> String) -> (a -> b) -> [a] -> String |
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faulhaber(17, 1000) |
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def fTable(s): |
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)</lang> |
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'''Heading -> x display function -> fx display function -> |
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f -> xs -> tabular string. |
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''' |
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def go(xShow, fxShow, f, xs): |
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ys = [xShow(x) for x in xs] |
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w = max(map(len, ys)) |
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return s + '\n' + '\n'.join(map( |
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lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)), |
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xs, ys |
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)) |
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return lambda xShow: lambda fxShow: lambda f: lambda xs: go( |
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xShow, fxShow, f, xs |
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) |
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# GENERIC ------------------------------------------------- |
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# showRatio :: Int -> Ratio -> String |
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def showRatio(m): |
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'''Aligned string representation |
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of the ratio r. |
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''' |
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def go(n, r): |
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d = r.denominator |
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return str(r.numerator).rjust(m, ' ') + ( |
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('/' + str(d).ljust(n, ' ')) if 1 != d else ( |
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' ' * (1 + n) |
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) |
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) |
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return lambda n: lambda r: go(n, r) |
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# fmap :: (a -> b) -> [a] -> [b] |
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def fmap(f): |
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'''fmap over a list. |
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f lifted to a function over a list. |
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''' |
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return lambda xs: list(map(f, xs)) |
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if __name__ == '__main__': |
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main()</lang> |
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{{Out}} |
{{Out}} |
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<pre> |
<pre>Faulhaber's triangle: |
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1/2 1/2 |
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0 -> 1 |
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1 -> 1/2 1/2 |
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- |
2 -> 1/6 1/2 1/3 |
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3 -> 0 1/4 1/2 1/4 |
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4 -> -1/30 0 1/3 1/2 1/5 |
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5 -> 0 -1/12 0 5/12 1/2 1/6 |
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- |
6 -> 1/42 0 -1/6 0 1/2 1/2 1/7 |
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7 -> 0 1/12 0 -7/24 0 7/12 1/2 1/8 |
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8 -> -1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9 |
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9 -> 0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10 |
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56056972216555580111030077961944183400198333273050000</pre> |
56056972216555580111030077961944183400198333273050000</pre> |
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