john_sheu | I went off and tried to do some crap with exp^ix |

|Anubis | __snake: what is the small e symbol ? |

TRWBW | john_sheu: that works too |

john_sheu | well, in my case, evidently it didn't :-P |

xor | The number represented by each sequence is \sum^n_{i=0}{f_i*b^i} with each f_i < b |

__snake | anubis: greek letter called epsilon |

TRWBW | xor: well you can, you just have to be very careful |

__snake | anubis: use any favorite letter instead of it if you don't like it |

xor | TRWBW: I already knew that you can |

TRWBW | xor: 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 |

xor | ok, and... |

TRWBW | xor: 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 |

xor | ok Long division But I still don't know how to divide the 2 digit numbers |

TRWBW | xor: 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 |

xor | I can represent numbers up to any size, using sequences of digits but that doesn't help me divide |

TRWBW | xor: if your problem is not knowing how to divide, look up "long division" on the web |

xor | I know the long division algorithm |

TRWBW | xor: 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 |

xor | But I don't know how to divide the 2 digit remainder numbers |

TRWBW | xor: 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. |

xor | For example, 4 into 15 (base 10) |

TRWBW | 4*3=12, 15-12=3, 15=4*3+3 |

xor | Clearly. But how did you come up with those numbers? |

TRWBW | the largest digit 1..9 that times 4 is less than 15 is 3 |

xor | hardly efficient |

TRWBW | xor: didn't say it was, but after you have that, everything else is just effeciency improvements |

xor | There has to be a better way than brute force well, doesn't have to be, but it feels there should be |

TRWBW | xor: try a lookup table |

xor | The bases we are working with are 2^32 or 2^64 A lookup table wouldn't even fit in memory |

TRWBW | xor: then if it's on a computer, use the builtin division for 2^w your word size |