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I can find the continued fraction expansion of a value using Maple. Is there a simple way for finding the sequence of convergents (approximants) of the continued fraction expansion in Maple? Currently I successively truncate the continued fraction expansions to develop the convergents but this is time consuming. Any suggestions for making it quicker? Maybe other mathematics packages can do it better than Maple, but I don't know

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In Mathematica the relevant function is Convergents. Convergents[Pi, 3] gives {3, 22/7, 333/106}. – Sasha Jan 24 '13 at 5:28
> with(numtheory):
> cfrac(Pi,3,cvgts):
> cvgts;
                        333  355
              [3, 22/7, ---, ---, ...]
                        106  113


> with(numtheory):
> cfrac([3,7,15,1]);
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