Comment #20 on issue 4122 by [email protected]: Egyptian fractions
http://code.google.com/p/sympy/issues/detail?id=4122
Sorry for taking so long to get back to you on this � I've been having
issues with my computer. They're pretty much resolved by now.
Given a fraction *p/q* in lowest terms, Graham-Jewett returns an expansion
of length *2**p - 1*. At large numerators, this will indeed take a lot of
time and memory.
Takenouchi starts by creating a list of length *p*, all the elements of
which are *q*, and then manipulates that list � when it finds a pair of
identical terms, it either combines them into one if they are even or
rewrites them in place if they are odd. It has better behavior than
Graham-Jewett (expansions are at most *p* terms long), but will also hog
resources on fractions with large numerators.
I'll have to do a bit of research to figure out the limiting behavior of
the other algorithms. I'll get back to you on that.
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