Status: Valid
Owner: ----
Labels: Type-Enhancement Priority-Medium NumberTheory
New issue 3937 by thilina....@gmail.com: Enhancements on continued fractions
http://code.google.com/p/sympy/issues/detail?id=3937
Currently SymPy only provides functionalities to find continued fraction
representation of rational fractions.
from sympy.physics.quantum.shor import continued_fraction
continued_fraction(4, 3)
[1,3]
It gives wrong results when a quadratic irrationality is given as an input.
continued_fraction(sqrt(5), 3)
[0,1,2]
But the correct answer should be 0,1,[2,1,12,1,2,2] with the terms inside
the bracket
repeating forever. I think this is due to the fact that current
implementation
assumes input is a rational fraction.
However it's good if we can create a class (or any abstraction) which can
find the
continued fraction representation of any rational or irrational number and
handle
all the arithmetic associated with continued fractions. At least we should
implement
this for quadratic irrationalities since they are very frequently used.
Lots of references can be found here:
http://www.numbertheory.org/ntw/N4.html#continued_fractions
Set of slides below gives a good introduction:
http://www.numbertheory.org/pdfs/CFquadratic.pdf
Here is an online calculator that can be used to verify the results:
http://www.numbertheory.org/php/surd.html
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