#math - Wed 28 Mar 2007 between 00:12 and 00:29

NY Lost Funds



john_sheuI went off and tried to do some crap with exp^ix
|Anubis__snake: what is the small e symbol ?
TRWBWjohn_sheu: that works too
john_sheuwell, in my case, evidently it didn't :-P
xorThe number represented by each sequence is \sum^n_{i=0}{f_i*b^i}
with each f_i < b
__snakeanubis: greek letter called epsilon
TRWBWxor: well you can, you just have to be very careful
__snakeanubis: use any favorite letter instead of it if you don't like it
xorTRWBW: I already knew that you can
TRWBWxor: if it's a computer problem, and you only have native 32 bit numbers, you can work in base 32, you just need to sometimes represent a number as a pair of numbers for example
xorok, and...
TRWBWxor: not sure what you are asking. the simple description of a base b algorithm for division or addition or multiplication or such sometimes deals with numbers bigger than b
xor: you deal with it by sometimes using 2 numbers, for example in addition, an extra "carry number"
xor: that is 2 numbers to represent 1 number
xorok
Long division
But I still don't know how to divide the 2 digit numbers
TRWBWxor: all i'm saying is that working in numbers larger than b isn't an issue, because you can represent them using two numbers, which gives you numbers up to b^2-1, or more if you need too. in general that should be enough, just two digits for intermediate values
xorI can represent numbers up to any size, using sequences of digits
but that doesn't help me divide
TRWBWxor: if your problem is not knowing how to divide, look up "long division" on the web
xorI know the long division algorithm
TRWBWxor: i'm sure any of those will be a more detailed explaination than i would care to type in
xor: clearly not, if you can't do it
xorBut I don't know how to divide the 2 digit remainder numbers
TRWBWxor: either you have found a flaw in the long division algorithm, which would be pretty big news, or the long division works, and your inability to do it means you don't understand it. i don't see any possibly middle ground.
xorFor example, 4 into 15 (base 10)
TRWBW4*3=12, 15-12=3, 15=4*3+3
xorClearly.
But how did you come up with those numbers?
TRWBWthe largest digit 1..9 that times 4 is less than 15 is 3
xorhardly efficient
TRWBWxor: didn't say it was, but after you have that, everything else is just effeciency improvements
xorThere has to be a better way than brute force
well, doesn't have to be, but it feels there should be
TRWBWxor: try a lookup table
xorThe bases we are working with are 2^32 or 2^64
A lookup table wouldn't even fit in memory
TRWBWxor: then if it's on a computer, use the builtin division for 2^w your word size

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