Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[ContinuedFractionPolynomial] instead.

The cfracpol function returns simple continued fraction expansions of all real roots of a rational polynomial pol. Each expansion is given in list form with at most $n+1$ quotients. If the second argument n is not present, it defaults to 10.

The command with(numtheory,cfracpol) allows the use of the abbreviated form of this command.

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

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

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

$\mathrm{cfracpol}\left(x^6-x^5-6x^4+6x^3+8x^2-8x+1\right)$

$\left[\mathrm{-2}\,44\,1\,3\,3\,1\,1\,1\,3\,2\,3\,\mathrm{...}\right],\left[\mathrm{-2}\,1\,1\,6\,1\,7\,34\,1\,12\,1\,5\,\mathrm{...}\right],\left[0\,6\,1\,2\,4\,3\,1\,1\,3\,1\,63\,\mathrm{...}\right],\left[0\,1\,2\,1\,2\,2\,16\,1\,1\,5\,11\,\mathrm{...}\right],\left[1\,1\,1\,1\,7\,6\,10\,2\,29\,20\,1\,\mathrm{...}\right],\left[1\,1\,10\,3\,1\,13\,1\,1\,3\,1\,4\,\mathrm{...}\right]$

$a≔-117260219x^6+139540883x^5+17033080x^4+800302x^3+18628x^2+216x+1\:$

$\mathrm{cfracpol}\left(a\right)$

$\left[\mathrm{-1}\,1\,41\,7\,1\,7\,34\,1\,12\,1\,5\,\mathrm{...}\right],\left[\mathrm{-1}\,1\,42\,1\,1\,6\,1\,2\,4\,3\,1\,\mathrm{...}\right],\left[\mathrm{-1}\,1\,42\,1\,1\,1\,2\,1\,2\,2\,16\,\mathrm{...}\right],\left[\mathrm{-1}\,1\,42\,1\,2\,1\,1\,1\,7\,6\,10\,\mathrm{...}\right],\left[\mathrm{-1}\,1\,42\,1\,2\,1\,10\,3\,1\,13\,1\,\mathrm{...}\right],\left[1\,3\,3\,1\,1\,1\,3\,2\,3\,4\,1\,\mathrm{...}\right]$

$\mathrm{cfracpol}\left(\left(232x+543\right)\left(x^6-x^5-6x^4+6x^3+8x^2-8x+1\right)\,10\right)$

$\left[\mathrm{-3}\,1\,1\,1\,14\,1\,4\right],\left[\mathrm{-2}\,44\,1\,3\,3\,1\,1\,1\,3\,2\,3\,\mathrm{...}\right],\left[\mathrm{-2}\,1\,1\,6\,1\,7\,34\,1\,12\,1\,5\,\mathrm{...}\right],\left[0\,6\,1\,2\,4\,3\,1\,1\,3\,1\,63\,\mathrm{...}\right],\left[0\,1\,2\,1\,2\,2\,16\,1\,1\,5\,11\,\mathrm{...}\right],\left[1\,1\,1\,1\,7\,6\,10\,2\,29\,20\,1\,\mathrm{...}\right],\left[1\,1\,10\,3\,1\,13\,1\,1\,3\,1\,4\,\mathrm{...}\right]$

$\mathrm{cfracpol}\left(x^6-3x^5+5x^3-3x+1\right)$