<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DifferencesList</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function has been transferred from package <strong class="pkg">ResClasses</strong>.</p>
<p>It takes a list <span class="SimpleMath">L</span> of length <span class="SimpleMath">n</span> and outputs the list of length <span class="SimpleMath">n-1</span> containing all the differences <span class="SimpleMath">L[i]-L[i-1]</span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ QuotientsList</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FloatQuotientsList</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>These functions have been transferred from package <strong class="pkg">ResClasses</strong>.</p>
<p>They take a list <span class="SimpleMath">L</span> of length <span class="SimpleMath">n</span> and output the quotients <span class="SimpleMath">L[i]/L[i-1]</span> of consecutive entries in <span class="SimpleMath">L</span>. An error is returned if an entry is zero.</p>
/tr><>
<p>This function has p><a id="X7AE6EFC086C0EB3C="AE6EFC086C0EB3C"/><>
<p><code class="code">SearchCycle</code> is a tool to find likely cycles in lists. What< class""><span="tocline>spanclass="nocss>nbsp> href.htmlX7C3F1E7D878AAA651span"">Functions listsspana>
<div class="example"><pre>
spanclass"GAPprompt"gap;/> <span class"L: [1..20];; L[1]:=13;;
<span class="GAPprompt">gap></span> <span class="GAPinput">for i in [1..19] do </span>
<span class="GAPprompt">></span> <span class="GAPinput"> if IsOddInt(L[i]) then L[i+1]:=3*L[i]+1; else L[i+1]:=L[i]/2; fi;</span>
<span class="GAPprompt">></span> <span class="GAPinput"> od; </span>
<span class="GAPprompt">gap></span> <span class="GAPinput">L; </span>
[ 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">SearchCycle( L ); </span>
[ 1 ,2]
<span class="GAPprompt">gap></span> <span class="GAPinput">n := 1;; L := [n];;</span>
< class=GAPprompt></> <span="GAPinput> in 1..0]do n=n^+)mod109; (Ln; od;/panjava.lang.StringIndexOutOfBoundsException: Index 127 out of bounds for length 127 span="GAPprompt>apgt;/>
[ 1, 2, 5, 26, 677, 363, 610, 481, 739, 715, 795, 272, 754, 157, 604, 848,
100spanclass="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78105CAA847A888C">3.2-1 DistinctRepresentatives</a></span>
21, 80, 521 7,75 7,74 17 0,4,10, 7,1,82 2,
378, 795,<div<div
754, 157, 604, 84, 104 27,211 0,51 38 9,22 5,17 0,java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
848,104,27, 21, 82,51,37, 75,22,74,15, 6, 848, 1004,
271, 211, 802, 521, 378, 795, 272, 754, 157, 604, 848, 1004 ]
<div>
[ 157, 60<div>
<span="">gap></pan="">P : Positions L,17)<s>
[42,3,,2 4 8 8]
<span java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
12
[ 12, 12, 12, 12, 12, 12, 12 ]
</pre></div>
<p><a id="X7EF06CAD7F35245D" name="
This function has been transferred frompackage>ResClasses.
<h5.- </h5
< class"">gap;</span <span="GAPinput>List( [1..2,n-&;n^ ;/>
<> function been from <strong=pkg</strong<p>
<p> returns random < classSimpleMath/>-tuple distinct of
<div class="example"><pre>
<span=GAPprompt>> classD( last>
<span class="GAPprompt">gap , ,6
[ 2, 16, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</div="func"< class"" width"10">tr><d ="tdleft>codeclass""&82;/> var =Arg>L class=tdright>&;&;)/d>tr
/>
<p><a id="X82F443FF84B8FCE3" name="X82F443FF84B8FCE3"></a></p<> functions have been from < classpkg<strong/java.lang.StringIndexOutOfBoundsException: Range [98, 99) out of bounds for length 98
<h4>3.2 <span class="Heading">Distinct and Common Representatives</span></h4>
<p><< class"">gapgt;</span<pan="GAPinput>ist 0.1] n &;Factorial() )/panjava.lang.StringIndexOutOfBoundsException: Index 107 out of bounds for length 107
<h5>3.<pan="GAPprompt>&t;/pan>( last ;/panjava.lang.StringIndexOutOfBoundsException: Index 91 out of bounds for length 91
/div>
<p>These operations have been transferred from package <strong class="pkg">XMod</strong>.</p>
<p>They with of of < class"">[1... ]/span>and systems distinct representatives simple, combinatorial.</p
<p> <span="impleMath>k> subsetshas at least >istinctRepresentatives>.</pjava.lang.StringIndexOutOfBoundsException: Index 365 out of bounds for length 365
<<id =""><
<p>531- </h5
<divp> class"SearchCycle is a tool to find likely cycles in . What, precisely,a em>ycle/em> is,isdeliberately here, andmaypossibly even change The is the beginning of the may be anything,following same pattern to be repeated severaltimes order to berecognized as a cycle.
<span">>gap></span> <span class="GAPinput">K := [ [3,4], [1,2], [2,3], [2,3,4] ];;</span>
<span ="">></spanspan="">CommonRepresentatives>
[ [ 3, 3, 3, 1 ], [ 1, 3, 4, 2 ] ]
<span classspan="GAPprompt>> od;
Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])
<span class="GAPprompt"[13, 4, 20,1,5 6 ,4 ,1 4 ,1 ,2 14 ,1, java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
<span class="GAPprompt">gap></span> <span class="GAPinput">c4 := Subgroup( d16, [ d16.1^2 ] ); </span>
Group([ (1,3,5,7)(2,4,6,8) ])
<span class="GAPprompt">gap></span> <span class="GAPinput">SetName( c4, "c4" );</span>
<span<span class"GAPprompt"gap;</span < classGAPinput( L) </span>
[ RightCoset(c4,()), RightCoset(c4,(2,8)(3,7)(4,6)), RightCoset(c4,(1java.lang.StringIndexOutOfBoundsException: Index 89 out of bounds for length 89
3),(c4(,)(2,)(,6(,)
<span class=< class>>span class";/>
[ (), (2,8)(3,7)(4,6), (1,2,3,4,5,6,7,8), (1,2)(3,8)(4,7)(5,6) ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IsCommonTransversal( java.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 75
true
< class"< =func =10%"<><td="< =func"&87 BlankFreeString>(<var=""></var)><td=; td><></>
<p>This function has been transferred from package <strong class"gapgt; < =GAPinput"> =Positions,5;/>
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