<p>Let <span class="Math">\varphi,\psi\colon G \to G</span> be endomorphisms such that <span class="Math">R(\varphi^n,\psi^n) < \infty</span> for all <span class="Math">n \in \mathbb{N}</span>. Then the <em>Reidemeister zeta function</em> <span class="Math">Z_{\varphi,\psi}(s)</span> of the pair <span class="Math">(\varphi,\psi)</span> is defined as</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReidemeisterZetaCoefficients</code>( <var class="Arg">endo1</var>[, <var class="Arg">endo2</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: two lists of integers.</p>
<p>For a finite group, the sequence of Reidemeister numbers of the iterates of <var class="Arg">endo1</var> and <var class="Arg">endo2</var>, i.e. the sequence <code class="code">R(<var class="Arg">endo1</var>,<var class="Arg">endo2</var>)</code>, <code class="code">R(<var class="Arg">endo1</var>^2,<var class="Arg">endo2</var>^2)</code>, ..., is eventually periodic. Thus there exist a periodic sequence <span class="Math">(P_n)_{n \in \mathbb{N}}</span> and an eventually zero sequence <span class="Math">(Q_n)_{n \in \mathbb{N}}</span> such that</p>
<p class="pcenter">\forall n \in \mathbb{N}: R(\varphi^n,\psi^n) = P_n + Q_n.</p>
<p>This function returns two lists: the first list contains one period of the sequence <span class="Math">(P_n)_{n \in \mathbb{N}}</span>, the second list contains <span class="Math">(Q_n)_{n \in \mathbb{N}}</span> up to the part where it becomes the constant zero sequence.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsRationalReidemeisterZeta</code>( <var class="Arg">endo1</var>[, <var class="Arg">endo2</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> if the Reidemeister zeta function of <var class="Arg">endo1</var> and <var class="Arg">endo2</var> is rational, otherwise <code class="keyw">false</code>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReidemeisterZeta</code>( <var class="Arg">endo1</var>[, <var class="Arg">endo2</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: the Reidemeister zeta function of <var class="Arg">endo1</var> and <var class="Arg">endo2</var> if it is rational, otherwise <code class="keyw">fail</code>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PrintReidemeisterZeta</code>( <var class="Arg">endo1</var>[, <var class="Arg">endo2</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a string describing the Reidemeister zeta function of <var class="Arg">endo1</var> and <var class="Arg">endo2</var>.</p>
<p>This is often more readable than evaluating <code class="func">ReidemeisterZeta</code> (<a href="chap6.html#X7959DBAF78CC4401"><span class="RefLink">6.1-3</span></a>) in an indeterminate, and does not require rationality.</p>
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