cycle

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cycle

$\begin{usage} cycle(f,v)\\ cycle(A,v) \end{usage}$

$\begin{signatures} cycle: & (\htmlref{\texttt{Vector}}{Vector} R $\to$\ \htmlr... ...Vector} R) $\to$\ (\htmlref{\texttt{Vector}}{Vector} R, M)\\\end{signatures}$

$\begin{params} {\em f} & \htmlref{\texttt{Vector}}{Vector} R $\to$\ \htmlref{\... ...ef{\texttt{Vector}}{Vector} R & A vector whose cycle is wanted\\\end{params}$

$\begin{retval} Returns $([a_0,\dots,a_n], m)$\ where \begin{displaymath} \sum_... ...umns of $m$\ are $v,f(v),\dots,f^n(v)$(resp.~$v,Av,\dots,A^n v$).\end{retval}$

$\begin{remarks} The relation is as small as possible, meaning that $v,f(v),\do... ...he iterates of $v$\ under $f$\ must all have the same dimension.\end{remarks}$

See Also

firstDependence

Manuel Bronstein 2000-12-13