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Topic:
unitary (Egyptian) fractions
Replies:
17
Last Post:
Mar 31, 2000 6:38 AM




Re: unitary (Egyptian) fractions
Posted:
Mar 21, 2000 12:48 PM


I found an APL program to compute unit fraction that found the following answer shown below Dan Hoey wrote  By the way, I found that 732/733 has 2771 different seventerm representations. The largest denominator appears in the representation (2305193137933140 33397845 4484 45 7 3 2). The APL ans (2346193812419340 33397845 4484 45 7 3 2) Using PC FP good to about 15 places So largest number is only good to 2 places. The program used comes from a 1991 System Journal  the program is short and produces the result with no visable delay. On the other hand it produces one result not other ones that also are solutions. Array language APL program FUN [0] Z < T FUN X [1] * SYVESTER ALG [2] execute (X<=T)/ '> 0,0 reshape Z <iota 0' [3] Z < Z,T FUN X ÃÂÃÂ·Z < ceiling ÃÂÃÂ·X [4] * EX 1E16 FUN 335ÃÂÃÂ·336 * YIELDS 2 3 7 48 Comments line 0 function header line 1 a comment this is sylvester algorithm line 2 set up if X is less than or equal the tolerance set truth to 0 or 1 if false go to 0 which is function exit if true initalize Z to a null number since Z will be concatnated it has to have something in it to start  namely null line 3 execute right to left Z gets ceiling of recipical of X X  ÃÂÃÂ·Z call fun recursively and Z gets Z, FUN result comma is concatenate Left argument to FUN is the compare tolerance set to 1E16 line 4 a comment example call 1 E16 FUN 335ÃÂÃÂ·336 yeilds 2 3 7 48 which stands for 1/2 1/3 1/7 1/48
monadic divide ÃÂÃÂ· takes one over the each element in a vector In another post I was wrong about the period of 732/733 Helmut Richter has a web site which shows that it is 61 All rational fractions are finite repeating decimals
Dan Hoey wrote in message <20000320210410.11752.00002552@ngci1.aol.com>... >It took about 13 hours on a 296 Mhz Ultra. If a mips is a >Mhz, that's almost half a mipsyear. I don't how much of the >remaining speed difference is due to the programming language/system >and how much is due to the algorithm. > >By the way, I found that 732/733 has 2771 different seventerm >representations. The largest denominator appears in the >representation (2305193137933140 33397845 4484 45 7 3 2). The >smallest maximum denominator appears in (26388 20524 7330 45 7 3 2). > >Dan Hoey <haoyuep@aol.com> Posted and emailed >



