Recent content by KevB

The application is programmed in Python as a new data type, with all the standard operators overridden. Python has a number of features, like portablility, unlimitted length integer computations, generator functions, and complete object oriented paradigm that makes it attractive. While Python...

Thank you for your suggestions and comments. I have looked at methods that use LLT and Mobius Transforms and incorporate many of those ideas into my system. I suppose you could say my system has two components, a computational engine (based on Gosper's algorithms), and a analytic system...

If you use standard simple continued fractions you see the termination problems that Bill Gosper also described in his write up. I use a hybrid between simple and nearest-integer continued fractions to address this problem. I still need to derive better algorithms for calculations of some...

By 'repeating CFs' I'm referring to continued fractions who's coefficients have an arithmetic progression. For example e ~ 2.718281828 = CF([2,1,2,1],[0,2,0]) = CF([2,1,2,1,1,4,1,1,6,1,1,...]). While quadratic surds have the form CF( [a_{0}, a_{1}, ..., a_{n} ] and [v_{0},v_{1},...,v_{m}])...

I've been playing with a computational system that represents numbers in their simple continued fraction form. That is, CF([a0,a1, ... , an]) =a0 + \frac{1}{ a_{1}+\frac{1}{a_{2}+\ddots\frac{1}{a_{n}}} }Considering what types of numbers such a system can represent, the finite CF's correspond to...

Learning about data structures and algorithms as suggested above is essential. Learning other languages, particularly object oriented languages like python, ruby or c# makes these concepts much easier. Spend some time playing with some of these languages, many of which are available for free...

I've recently started development on a continued fraction based exact arithmetic computational package. This is work based on Bill Gosper's HACMEM algorithm and Peter Potts' Mobius transforms with significant modifications. These algorithms have some remarkable properties and can be made much...

Any root of a whole number, or root of a rational for that mater will have a repeated continued fraction as you described. That's true for any quadratic surd ( http://en.wikipedia.org/wiki/Quadratic_surd ). The converse is also true, so if it has repeated coefficients it's of the form...

From the .doc image: x = [-2, -2, -2,...] = [-2],[0] = [-3, 1, 1, 2],[0] =-1 - \sqrt{}2 ~ -2.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727

If x = [a_{0} ; a_{1}, a_{2},...] 1/x = [ 0 ; a_{0}, a_{1}, a_{2}, ... ] \ when \ a_{0} \neq 0 \ \ \ \ \ \ = [ a_{1}; a_{2}, a_{3},... ] \ when \ a_{0} = 0

It's my understanding that algebraic numbers are the roots of polynomials with rational (or equivalently integer) coefficients. I know all surds have a simple repeating continued fraction representation Is it also the case that all simple repeating continued fractions are algebraic numbers...