numtheory(deprecated)/cfracpol - Maple Help

numtheory(deprecated)

 cfracpol
 compute simple continued fraction expansions for all real roots of a rational polynomial

 Calling Sequence cfracpol(pol, n) cfracpol(pol)

Parameters

 pol - rational polynomial n - integer (n + 1 is the number of partial quotients)

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $\mathrm{cfracpol}\left({x}^{4}-{x}^{3}-4{x}^{2}+4x+1,20\right)$
 $\left[{-2}{,}{22}{,}{1}{,}{7}{,}{2}{,}{1}{,}{1}{,}{2}{,}{1}{,}{2}{,}{1}{,}{17}{,}{4}{,}{4}{,}{1}{,}{1}{,}{4}{,}{2}{,}{18}{,}{1}{,}{10}{,}{\mathrm{...}}\right]{,}\left[{-1}{,}{1}{,}{3}{,}{1}{,}{3}{,}{1}{,}{1}{,}{1}{,}{1}{,}{1}{,}{1}{,}{4}{,}{1}{,}{1}{,}{1}{,}{4}{,}{1}{,}{2}{,}{4}{,}{5}{,}{18}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{2}{,}{1}{,}{21}{,}{1}{,}{7}{,}{2}{,}{1}{,}{1}{,}{2}{,}{1}{,}{2}{,}{1}{,}{17}{,}{4}{,}{4}{,}{1}{,}{1}{,}{4}{,}{2}{,}{18}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{1}{,}{4}{,}{1}{,}{3}{,}{1}{,}{1}{,}{1}{,}{1}{,}{1}{,}{1}{,}{4}{,}{1}{,}{1}{,}{1}{,}{4}{,}{1}{,}{2}{,}{4}{,}{5}{,}{18}{,}{\mathrm{...}}\right]$ (1)
 > $\mathrm{cfracpol}\left({x}^{6}-{x}^{5}-6{x}^{4}+6{x}^{3}+8{x}^{2}-8x+1\right)$
 $\left[{-2}{,}{44}{,}{1}{,}{3}{,}{3}{,}{1}{,}{1}{,}{1}{,}{3}{,}{2}{,}{3}{,}{\mathrm{...}}\right]{,}\left[{-2}{,}{1}{,}{1}{,}{6}{,}{1}{,}{7}{,}{34}{,}{1}{,}{12}{,}{1}{,}{5}{,}{\mathrm{...}}\right]{,}\left[{0}{,}{6}{,}{1}{,}{2}{,}{4}{,}{3}{,}{1}{,}{1}{,}{3}{,}{1}{,}{63}{,}{\mathrm{...}}\right]{,}\left[{0}{,}{1}{,}{2}{,}{1}{,}{2}{,}{2}{,}{16}{,}{1}{,}{1}{,}{5}{,}{11}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{1}{,}{1}{,}{1}{,}{7}{,}{6}{,}{10}{,}{2}{,}{29}{,}{20}{,}{1}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{1}{,}{10}{,}{3}{,}{1}{,}{13}{,}{1}{,}{1}{,}{3}{,}{1}{,}{4}{,}{\mathrm{...}}\right]$ (2)
 > $a≔-117260219{x}^{6}+139540883{x}^{5}+17033080{x}^{4}+800302{x}^{3}+18628{x}^{2}+216x+1:$
 > $\mathrm{cfracpol}\left(a\right)$
 $\left[{-1}{,}{1}{,}{41}{,}{7}{,}{1}{,}{7}{,}{34}{,}{1}{,}{12}{,}{1}{,}{5}{,}{\mathrm{...}}\right]{,}\left[{-1}{,}{1}{,}{42}{,}{1}{,}{1}{,}{6}{,}{1}{,}{2}{,}{4}{,}{3}{,}{1}{,}{\mathrm{...}}\right]{,}\left[{-1}{,}{1}{,}{42}{,}{1}{,}{1}{,}{1}{,}{2}{,}{1}{,}{2}{,}{2}{,}{16}{,}{\mathrm{...}}\right]{,}\left[{-1}{,}{1}{,}{42}{,}{1}{,}{2}{,}{1}{,}{1}{,}{1}{,}{7}{,}{6}{,}{10}{,}{\mathrm{...}}\right]{,}\left[{-1}{,}{1}{,}{42}{,}{1}{,}{2}{,}{1}{,}{10}{,}{3}{,}{1}{,}{13}{,}{1}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{3}{,}{3}{,}{1}{,}{1}{,}{1}{,}{3}{,}{2}{,}{3}{,}{4}{,}{1}{,}{\mathrm{...}}\right]$ (3)
 > $\mathrm{cfracpol}\left(\left(232x+543\right)\left({x}^{6}-{x}^{5}-6{x}^{4}+6{x}^{3}+8{x}^{2}-8x+1\right),10\right)$
 $\left[{-3}{,}{1}{,}{1}{,}{1}{,}{14}{,}{1}{,}{4}\right]{,}\left[{-2}{,}{44}{,}{1}{,}{3}{,}{3}{,}{1}{,}{1}{,}{1}{,}{3}{,}{2}{,}{3}{,}{\mathrm{...}}\right]{,}\left[{-2}{,}{1}{,}{1}{,}{6}{,}{1}{,}{7}{,}{34}{,}{1}{,}{12}{,}{1}{,}{5}{,}{\mathrm{...}}\right]{,}\left[{0}{,}{6}{,}{1}{,}{2}{,}{4}{,}{3}{,}{1}{,}{1}{,}{3}{,}{1}{,}{63}{,}{\mathrm{...}}\right]{,}\left[{0}{,}{1}{,}{2}{,}{1}{,}{2}{,}{2}{,}{16}{,}{1}{,}{1}{,}{5}{,}{11}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{1}{,}{1}{,}{1}{,}{7}{,}{6}{,}{10}{,}{2}{,}{29}{,}{20}{,}{1}{,}{\mathrm{...}}\right]{,}\left[{1}{,}{1}{,}{10}{,}{3}{,}{1}{,}{13}{,}{1}{,}{1}{,}{3}{,}{1}{,}{4}{,}{\mathrm{...}}\right]$ (4)
 > $\mathrm{cfracpol}\left({x}^{6}-3{x}^{5}+5{x}^{3}-3x+1\right)$