[Haskell-cafe] expension of fractions

2007-07-25 Thread Tom Pledger 

Arie Groeneveld wrote:
 :
 | Looking at the result of my rewriting gives me the idea it isn't
 | Haskelly enough.
 |
 | Anyways, here's my interpretation:
 |
 | -- period m/n base = (period length, preperiod digits, period digits)
 | period :: Integer -> Integer -> Integer -> (Int, ([Integer], [Integer]))
 :


Haskelliness

I'd be inclined to try using a Rational (from Data.Ratio) and the  
properFraction function, instead of numerators and denominators and gcd.


You could do away with the parts where you subscript a linked list, if  
you did something with elem and zip and span instead of findIndex and  
splitAt.


Instead of translating Nothing to -1 and Just i to i, you could use  
the result of findIndex directly in a case expression.



Correctness

*Main> period 8 70 10
(6,([0],[5,7,1,4,2,8]))

That should be (6,([1],[1,4,2,8,5,7])).


Regards,
Tom


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[Haskell-cafe] expension of fractions

2007-07-24 Thread Arie Groeneveld 
Hi,

I don't know if this is the right place to post this, but here I go.

I translated a BC-program found on the home page of Keith Matthews,
http://www.numbertheory.org/keith.html.
It's about the expension of a (not necessarily reduced) fraction m/n in
base b.

Looking at the result of my rewriting gives me the idea it isn't
Haskelly enough.

Anyways, here's my interpretation:

-- period m/n base = (period length, preperiod digits, period digits)
period :: Integer -> Integer -> Integer -> (Int, ([Integer], [Integer]))
period m n base | m' >= n'  = error $ show m ++ " >= " ++ show  n
| m' < 1= error $ "m (" ++ show m ++ ") < 1"
| n' < 1= error $ "n (" ++ show n ++ ") < 1"
| base <= 1 = error $ "base (" ++ show base ++ ") < 2"
| otherwise = decimals [] [m']
where g = gcd m n
  m' = m `div` g
  n' = n `div` g
  decimals qs rs | i' /= -1 = (length rs - i', splitAt i' qsi)
  | otherwise = decimals qsi (rs++[ri])
 where (qi,ri) = divMod (base * last rs) n
   i = findIndex (==ri) rs
   i' = if i == Nothing then -1 else fromJust i
   qsi = qs++[qi]



Which comes from the BC program:
(Keith Matthews)

define period(m,n,b){
auto a[],g,i,p,j,c[]
   
g=gcd(m,n)
m=m/g;n=n/g
if(m>=n){"m>=n:"; return(0)}
if(m<1){"m<1:"; return(0)}
if(n<1){"n<1:"; return(0)}
if(b<=1){"b<=1:"; return(0)}
i=0
c[0]=m
flag=0
while(flag==0){
p=b*c[i]
i=i+1
c[i]=p%n
a[i]=p/n
/*print "a[",i,"]=",a[i],"\n" /* the i-th digit */
if(i==1000){
   print "limit of 1000 digits produced\n"
   return(0)
}
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