The ContinuedFractionPolynomial(p, n) command computes simple continued fraction expansions for the real roots of p, up to the nth term.

For ContinuedFractionPolynomial(p), the simple continued fraction expansions for the real roots of p are calculated up to the $10$th term.

If rootopt is not given, then an expansion for each real root is returned. If rootopt is given, then only the expansion for rootopt is returned.

$\mathrm{with}\left(\mathrm{NumberTheory}\right)\:$

$\mathrm{ContinuedFractionPolynomial}\left(x^4-x^3-4x^2+4x+1\,20\right)$

$\left[\left[\mathrm{-2}\,22\,1\,7\,2\,1\,1\,2\,1\,2\,1\,17\,4\,4\,1\,1\,4\,2\,18\,1\,10\right]\,\left[\mathrm{-1}\,1\,3\,1\,3\,1\,1\,1\,1\,1\,1\,4\,1\,1\,1\,4\,1\,2\,4\,5\,18\right]\,\left[1\,2\,1\,21\,1\,7\,2\,1\,1\,2\,1\,2\,1\,17\,4\,4\,1\,1\,4\,2\,18\right]\,\left[1\,1\,4\,1\,3\,1\,1\,1\,1\,1\,1\,4\,1\,1\,1\,4\,1\,2\,4\,5\,18\right]\right]$

$\mathrm{ContinuedFractionPolynomial}\left(x^2-2\right)$

$\left[\left[\mathrm{-2}\,1\,1\,2\,2\,2\,2\,2\,2\,2\,2\right]\,\left[1\,2\,2\,2\,2\,2\,2\,2\,2\,2\,2\right]\right]$

$\mathrm{ContinuedFractionPolynomial}\left(x^2-2\,\mathrm{root}=\mathrm{sqrt}\left(2\right)\right)$

$\left[1\,2\,2\,2\,2\,2\,2\,2\,2\,2\,2\right]$

The NumberTheory[ContinuedFractionPolynomial] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.