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<div class="ChapSects"><a href="chap3.html#X792305CC81E8606A">3 <span class="Heading">Collectors</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X800FD91386C08CD8">3.1 <span class="Heading">Constructing a Collector</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8382A4E78706DE65">3.1-1 FromTheLeftCollector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X79A308B28183493B">3.1-2 SetRelativeOrder</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7BC319BA8698420C">3.1-3 SetPower</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X86A08D887E049347">3.1-4 SetConjugate</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7B25997C7DF92B6D">3.1-5 SetCommutator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7E9903F57BC5CC24">3.1-6 UpdatePolycyclicCollector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8006790B86328CE8">3.1-7 IsConfluent</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X818484817C3BAAE6">3.2 <span class="Heading">Accessing Parts of a Collector</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X865160E07FA93E00">3.2-3 GetConjugate</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X79AEB3477800DC16">3.3 <span class="Heading">Special Features</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X82EE2ACD7B8C178B">3.3-1 IsWeightedCollector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7A1D7ED68334282C">3.3-2 AddHallPolynomials</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7BDFB55D7CB33543">3.3-9 USE_COMBINATORIAL_COLLECTOR</a></span>
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<h3>3 <span class="Heading">Collectors</span></h3>
<p>Let <span class="SimpleMath">G</span> be a group defined by a pc-presentation as described in the Chapter <a href="chap2.html#X792561B378D95B23"><span class="RefLink"><span class="Heading">Introduction to polycyclic presentations</span></span></a>.</p>
<p>The process for computing the collected form for an arbitrary word in the generators of <span class="SimpleMath">G</span> is called <em>collection</em>. The basic idea in collection is the following. Given a word in the defining generators, one scans the word for occurrences of adjacent generators (or their inverses) in the wrong order or occurrences of subwords <span class="SimpleMath">g_i^e_i</span> with <span class="SimpleMath">i∈ I</span> and <span class="SimpleMath">e_i</span> not in the range <span class="SimpleMath">0... r_i-1</span>. In the first case, the appropriate conjugacy relation is used to move the generator with the smaller index to the left. In the second case, one uses the appropriate power relation to move the exponent of <span class="SimpleMath">g_i</span> into the required range. These steps are repeated until a collected word is obtained.</p>
<p>There exist a number of different strategies for collecting a given word to collected form. The strategies implemented in this package are <em>collection from the left</em> as described by <a href="chapBib.html#biBLGS90">[LS90]</a> and <a href="chapBib.html#biBSims94">[Sim94]</a> and <em>combinatorial collection from the left</em> by <a href="chapBib.html#biBMVL90">[Vau90]</a>. In addition, the package provides access to Hall polynomials computed by Deep Thought for the multiplication in a nilpotent group, see <a href="chapBib.html#biBWWM97">[Mer97]</a> and <a href="chapBib.html#biBLGS98">[LS98]</a>.</p>
<p>The first step in defining a pc-presented group is setting up a data structure that knows the pc-presentation and has routines that perform the collection algorithm with words in the generators of the presentation. Such a data structure is called <em>a collector</em>.</p>
<p>To describe the right hand sides of the relations in a pc-presentation we use <em>generator exponent lists</em>; the word <span class="SimpleMath">g_i_1^e_1g_i_2^e_2... g_i_k^e_k</span> is represented by the generator exponent list <span class="SimpleMath">[i_1,e_1,i_2,e_2,...,i_k,e_k]</span>.</p>
<p><a id="X800FD91386C08CD8" name="X800FD91386C08CD8"></a></p>
<h4>3.1 <span class="Heading">Constructing a Collector</span></h4>
<p>A collector for a group given by a pc-presentation starts by setting up an empty data structure for the collector. Then the relative orders, the power relations and the conjugate relations are added into the data structure. The construction is finalised by calling a routine that completes the data structure for the collector. The following functions provide the necessary tools for setting up a collector.</p>
<p><a id="X8382A4E78706DE65" name="X8382A4E78706DE65"></a></p>
<h5>3.1-1 FromTheLeftCollector</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FromTheLeftCollector</code>( <var class="Arg">n</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns an empty data structure for a collector with <var class="Arg">n</var> generators. No generator has a relative order, no right hand sides of power and conjugate relations are defined. Two generators for which no right hand side of a conjugate relation is defined commute. Therefore, the collector returned by this function can be used to define a free abelian group of rank <var class="Arg">n</var>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">ftl := FromTheLeftCollector( 4 );</span>
<<from the left collector with 4 generators>>
<span class="GAPprompt">gap></span> <span class="GAPinput">PcpGroupByCollector( ftl );</span>
Pcp-group with orders [ 0, 0, 0, 0 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IsAbelian(last);</span>
true
</pre></div>
<p>If the relative order of a generators has been defined (see <code class="func">SetRelativeOrder</code> (<a href="chap3.html#X79A308B28183493B"><span class="RefLink">3.1-2</span></a>)), but the right hand side of the corresponding power relation has not, then the order and the relative order of the generator are the same.</p>
<p><a id="X79A308B28183493B" name="X79A308B28183493B"></a></p>
<h5>3.1-2 SetRelativeOrder</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetRelativeOrder</code>( <var class="Arg">coll</var>, <var class="Arg">i</var>, <var class="Arg">ro</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetRelativeOrderNC</code>( <var class="Arg">coll</var>, <var class="Arg">i</var>, <var class="Arg">ro</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>set the relative order in collector <var class="Arg">coll</var> for generator <var class="Arg">i</var> to <var class="Arg">ro</var>. The parameter <var class="Arg">coll</var> is a collector as returned by the function <code class="func">FromTheLeftCollector</code> (<a href="chap3.html#X8382A4E78706DE65"><span class="RefLink">3.1-1</span></a>), <var class="Arg">i</var> is a generator number and <var class="Arg">ro</var> is a non-negative integer. The generator number <var class="Arg">i</var> is an integer in the range <span class="SimpleMath">1,...,n</span> where <span class="SimpleMath">n</span> is the number of generators of the collector.</p>
<p>If <var class="Arg">ro</var> is <span class="SimpleMath">0,</span> then the generator with number <var class="Arg">i</var> has infinite order and no power relation can be specified. As a side effect in this case, a previously defined power relation is deleted.</p>
<p>If <var class="Arg">ro</var> is the relative order of a generator with number <var class="Arg">i</var> and no power relation is set for that generator, then <var class="Arg">ro</var> is the order of that generator.</p>
<p>The NC version of the function bypasses checks on the range of <var class="Arg">i</var>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">ftl := FromTheLeftCollector( 4 );</span>
<<from the left collector with 4 generators>>
<span class="GAPprompt">gap></span> <span class="GAPinput">for i in [1..4] do SetRelativeOrder( ftl, i, 3 ); od;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">G := PcpGroupByCollector( ftl );</span>
Pcp-group with orders [ 3, 3, 3, 3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IsElementaryAbelian( G );</span>
true
</pre></div>
<p><a id="X7BC319BA8698420C" name="X7BC319BA8698420C"></a></p>
<h5>3.1-3 SetPower</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetPower</code>( <var class="Arg">coll</var>, <var class="Arg">i</var>, <var class="Arg">rhs</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetPowerNC</code>( <var class="Arg">coll</var>, <var class="Arg">i</var>, <var class="Arg">rhs</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>set the right hand side of the power relation for generator <var class="Arg">i</var> in collector <var class="Arg">coll</var> to (a copy of) <var class="Arg">rhs</var>. An attempt to set the right hand side for a generator without a relative order results in an error.</p>
<p>Right hand sides are by default assumed to be trivial.</p>
<p>The parameter <var class="Arg">coll</var> is a collector, <var class="Arg">i</var> is a generator number and <var class="Arg">rhs</var> is a generators exponent list or an element from a free group.</p>
<p>The no-check (NC) version of the function bypasses checks on the range of <var class="Arg">i</var> and stores <var class="Arg">rhs</var> (instead of a copy) in the collector.</p>
<p><a id="X86A08D887E049347" name="X86A08D887E049347"></a></p>
<h5>3.1-4 SetConjugate</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetConjugate</code>( <var class="Arg">coll</var>, <var class="Arg">j</var>, <var class="Arg">i</var>, <var class="Arg">rhs</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetConjugateNC</code>( <var class="Arg">coll</var>, <var class="Arg">j</var>, <var class="Arg">i</var>, <var class="Arg">rhs</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>set the right hand side of the conjugate relation for the generators <var class="Arg">j</var> and <var class="Arg">i</var> with <var class="Arg">j</var> larger than <var class="Arg">i</var>. The parameter <var class="Arg">coll</var> is a collector, <var class="Arg">j</var> and <var class="Arg">i</var> are generator numbers and <var class="Arg">rhs</var> is a generator exponent list or an element from a free group. Conjugate relations are by default assumed to be trivial.</p>
<p>The generator number <var class="Arg">i</var> can be negative in order to define conjugation by the inverse of a generator.</p>
<p>The no-check (NC) version of the function bypasses checks on the range of <var class="Arg">i</var> and <var class="Arg">j</var> and stores <var class="Arg">rhs</var> (instead of a copy) in the collector.</p>
<p><a id="X7B25997C7DF92B6D" name="X7B25997C7DF92B6D"></a></p>
<h5>3.1-5 SetCommutator</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SetCommutator</code>( <var class="Arg">coll</var>, <var class="Arg">j</var>, <var class="Arg">i</var>, <var class="Arg">rhs</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>set the right hand side of the conjugate relation for the generators <var class="Arg">j</var> and <var class="Arg">i</var> with <var class="Arg">j</var> larger than <var class="Arg">i</var> by specifying the commutator of <var class="Arg">j</var> and <var class="Arg">i</var>. The parameter <var class="Arg">coll</var> is a collector, <var class="Arg">j</var> and <var class="Arg">i</var> are generator numbers and <var class="Arg">rhs</var> is a generator exponent list or an element from a free group.</p>
<p>The generator number <var class="Arg">i</var> can be negative in order to define the right hand side of a commutator relation with the second generator being the inverse of a generator.</p>
<p><a id="X7E9903F57BC5CC24" name="X7E9903F57BC5CC24"></a></p>
<h5>3.1-6 UpdatePolycyclicCollector</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UpdatePolycyclicCollector</code>( <var class="Arg">coll</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>completes the data structures of a collector. This is usually the last step in setting up a collector. Among the steps performed is the completion of the conjugate relations. For each non-trivial conjugate relation of a generator, the corresponding conjugate relation of the inverse generator is calculated.</p>
<p>Note that <code class="code">UpdatePolycyclicCollector</code> is automatically called by the function <code class="code">PcpGroupByCollector</code> (see <code class="func">PcpGroupByCollector</code> (<a href="chap4.html#X7C8FBCAB7F63FACB"><span class="RefLink">4.3-1</span></a>)).</p>
<p><a id="X8006790B86328CE8" name="X8006790B86328CE8"></a></p>
<h5>3.1-7 IsConfluent</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsConfluent</code>( <var class="Arg">coll</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>tests if the collector <var class="Arg">coll</var> is confluent. The function returns true or false accordingly.</p>
<p>Compare Chapter <a href="chap2.html#X792561B378D95B23"><span class="RefLink">2</span></a> for a definition of confluence.</p>
<p>Note that confluence is automatically checked by the function <code class="code">PcpGroupByCollector</code> (see <code class="func">PcpGroupByCollector</code> (<a href="chap4.html#X7C8FBCAB7F63FACB"><span class="RefLink">4.3-1</span></a>)).</p>
<p>The following example defines a collector for a semidirect product of the cyclic group of order <span class="SimpleMath">3</span> with the free abelian group of rank <span class="SimpleMath">2</span>. The action of the cyclic group on the free abelian group is given by the matrix</p>
<p class="pcenter">\pmatrix{ 0 & 1 \cr -1 & -1}.</p>
<p>This leads to the following polycyclic presentation:</p>
<p class="pcenter">\langle g_1,g_2,g_3 | g_1^3,
g_2^{g_1}=g_3,
g_3^{g_1}=g_2^{-1}g_3^{-1},
g_3^{g_2}=g_3\rangle.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">ftl := FromTheLeftCollector( 3 );</span>
<<from the left collector with 3 generators>>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetRelativeOrder( ftl, 1, 3 );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetConjugate( ftl, 2, 1, [3,1] );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetConjugate( ftl, 3, 1, [2,-1,3,-1] );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">UpdatePolycyclicCollector( ftl );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsConfluent( ftl );</span>
true
</pre></div>
<p>The action of the inverse of <span class="SimpleMath">g_1</span> on <span class="SimpleMath">⟨ g_2,g_2⟩</span> is given by the matrix</p>
<p class="pcenter">\pmatrix{ -1 & -1 \cr 1 & 0}.</p>
<p>The corresponding conjugate relations are automatically computed by <code class="code">UpdatePolycyclicCollector</code>. It is also possible to specify the conjugation by inverse generators. Note that you need to run <code class="code">UpdatePolycyclicCollector</code> after one of the set functions has been used.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetConjugate( ftl, 2, -1, [2,-1,3,-1] );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetConjugate( ftl, 3, -1, [2,1] );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsConfluent( ftl );</span>
Error, Collector is out of date called from
CollectWordOrFail( coll, ev1, [ j, 1, i, 1 ] ); called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
<span class="GAPbrkprompt">brk></span>
<span class="GAPprompt">gap></span> <span class="GAPinput">UpdatePolycyclicCollector( ftl );</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsConfluent( ftl );</span>
true
</pre></div>
<p><a id="X818484817C3BAAE6" name="X818484817C3BAAE6"></a></p>
<h4>3.2 <span class="Heading">Accessing Parts of a Collector</span></h4>
<p><a id="X7DD0DF677AC1CF10" name="X7DD0DF677AC1CF10"></a></p>
<h5>3.2-1 RelativeOrders</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RelativeOrders</code>( <var class="Arg">coll</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>returns (a copy of) the list of relative order stored in the collector <var class="Arg">coll</var>.</p>
<p><a id="X844C0A478735EF4B" name="X844C0A478735EF4B"></a></p>
<h5>3.2-2 GetPower</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GetPower</code>( <var class="Arg">coll</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GetPowerNC</code>( <var class="Arg">coll</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns a copy of the generator exponent list stored for the right hand side of the power relation of the generator <var class="Arg">i</var> in the collector <var class="Arg">coll</var>.</p>
<p>The no-check (NC) version of the function bypasses checks on the range of <var class="Arg">i</var> and does not create a copy before returning the right hand side of the power relation.</p>
<p><a id="X865160E07FA93E00" name="X865160E07FA93E00"></a></p>
<h5>3.2-3 GetConjugate</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GetConjugate</code>( <var class="Arg">coll</var>, <var class="Arg">j</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ GetConjugateNC</code>( <var class="Arg">coll</var>, <var class="Arg">j</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns a copy of the right hand side of the conjugate relation stored for the generators <var class="Arg">j</var> and <var class="Arg">i</var> in the collector <var class="Arg">coll</var> as generator exponent list. The generator <var class="Arg">j</var> must be larger than <var class="Arg">i</var>.</p>
<p>The no-check (NC) version of the function bypasses checks on the range of <var class="Arg">i</var> and <var class="Arg">j</var> and does not create a copy before returning the right hand side of the power relation.</p>
<p><a id="X7D6A26A4871FF51A" name="X7D6A26A4871FF51A"></a></p>
<h5>3.2-4 NumberOfGenerators</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NumberOfGenerators</code>( <var class="Arg">coll</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns the number of generators of the collector <var class="Arg">coll</var>.</p>
<p><a id="X873ECF388503E5DE" name="X873ECF388503E5DE"></a></p>
<h5>3.2-5 ObjByExponents</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ObjByExponents</code>( <var class="Arg">coll</var>, <var class="Arg">expvec</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns a generator exponent list for the exponent vector <var class="Arg">expvec</var>. This is the inverse operation to <code class="code">ExponentsByObj</code>. See <code class="func">ExponentsByObj</code> (<a href="chap3.html#X85BCB97B8021EAD6"><span class="RefLink">3.2-6</span></a>) for an example.</p>
<p><a id="X85BCB97B8021EAD6" name="X85BCB97B8021EAD6"></a></p>
<h5>3.2-6 ExponentsByObj</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ExponentsByObj</code>( <var class="Arg">coll</var>, <var class="Arg">genexp</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns an exponent vector for the generator exponent list <var class="Arg">genexp</var>. This is the inverse operation to <code class="code">ObjByExponents</code>. The function assumes that the generators in <var class="Arg">genexp</var> are given in the right order and that the exponents are in the right range.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">G := UnitriangularPcpGroup( 4, 0 );</span>
Pcp-group with orders [ 0, 0, 0, 0, 0, 0 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">coll := Collector ( G );</span>
<<from the left collector with 6 generators>>
<span class="GAPprompt">gap></span> <span class="GAPinput">ObjByExponents( coll, [6,-5,4,3,-2,1] );</span>
[ 1, 6, 2, -5, 3, 4, 4, 3, 5, -2, 6, 1 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">ExponentsByObj( coll, last );</span>
[ 6, -5, 4, 3, -2, 1 ]
</pre></div>
<p><a id="X79AEB3477800DC16" name="X79AEB3477800DC16"></a></p>
<h4>3.3 <span class="Heading">Special Features</span></h4>
<p>In this section we descibe collectors for nilpotent groups which make use of the special structure of the given pc-presentation.</p>
<p><a id="X82EE2ACD7B8C178B" name="X82EE2ACD7B8C178B"></a></p>
<h5>3.3-1 IsWeightedCollector</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsWeightedCollector</code>( <var class="Arg">coll</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>checks if there is a function <span class="SimpleMath">w</span> from the generators of the collector <var class="Arg">coll</var> into the positive integers such that <span class="SimpleMath">w(g) ≥ w(x)+w(y)</span> for all generators <span class="SimpleMath">x</span>, <span class="SimpleMath">y</span> and all generators <span class="SimpleMath">g</span> in (the normal of) <span class="SimpleMath">[x,y]</span>. If such a function does not exist, false is returned. If such a function exists, it is computed and stored in the collector. In addition, the default collection strategy for this collector is set to combinatorial collection.</p>
<p><a id="X7A1D7ED68334282C" name="X7A1D7ED68334282C"></a></p>
<h5>3.3-2 AddHallPolynomials</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddHallPolynomials</code>( <var class="Arg">coll</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>is applicable to a collector which passes <code class="code">IsWeightedCollector</code> and computes the Hall multiplication polynomials for the presentation stored in <var class="Arg">coll</var>. The default strategy for this collector is set to evaluating those polynomial when multiplying two elements.</p>
<p><a id="X81FB5BE27903EC32" name="X81FB5BE27903EC32"></a></p>
<h5>3.3-3 String</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ String</code>( <var class="Arg">coll</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>converts a collector <var class="Arg">coll</var> into a string.</p>
<p><a id="X7ED466B6807D16FE" name="X7ED466B6807D16FE"></a></p>
<h5>3.3-4 FTLCollectorPrintTo</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FTLCollectorPrintTo</code>( <var class="Arg">file</var>, <var class="Arg">name</var>, <var class="Arg">coll</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>stores a collector <var class="Arg">coll</var> in the file <var class="Arg">file</var> such that the file can be read back using the function 'Read' into <strong class="pkg">GAP</strong> and would then be stored in the variable <var class="Arg">name</var>.</p>
<p><a id="X789D9EB37ECFA9D7" name="X789D9EB37ECFA9D7"></a></p>
<h5>3.3-5 FTLCollectorAppendTo</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FTLCollectorAppendTo</code>( <var class="Arg">file</var>, <var class="Arg">name</var>, <var class="Arg">coll</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>appends a collector <var class="Arg">coll</var> in the file <var class="Arg">file</var> such that the file can be read back into <strong class="pkg">GAP</strong> and would then be stored in the variable <var class="Arg">name</var>.</p>
<p><a id="X808A26FB873A354F" name="X808A26FB873A354F"></a></p>
<h5>3.3-6 UseLibraryCollector</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UseLibraryCollector</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>this property can be set to <code class="keyw">true</code> for a collector to force a simple from-the-left collection strategy implemented in the <strong class="pkg">GAP</strong> language to be used. Its main purpose is to help debug the collection routines.</p>
<p><a id="X844E195C7D55F8BD" name="X844E195C7D55F8BD"></a></p>
<h5>3.3-7 USE_LIBRARY_COLLECTOR</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ USE_LIBRARY_COLLECTOR</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>this global variable can be set to <code class="keyw">true</code> to force all collectors to use a simple from-the-left collection strategy implemented in the <strong class="pkg">GAP</strong> language to be used. Its main purpose is to help debug the collection routines.</p>
<p><a id="X7945C6B97BECCDA8" name="X7945C6B97BECCDA8"></a></p>
<h5>3.3-8 DEBUG_COMBINATORIAL_COLLECTOR</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DEBUG_COMBINATORIAL_COLLECTOR</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>this global variable can be set to <code class="keyw">true</code> to force the comparison of results from the combinatorial collector with the result of an identical collection performed by a simple from-the-left collector. Its main purpose is to help debug the collection routines.</p>
<p><a id="X7BDFB55D7CB33543" name="X7BDFB55D7CB33543"></a></p>
<h5>3.3-9 USE_COMBINATORIAL_COLLECTOR</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ USE_COMBINATORIAL_COLLECTOR</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>this global variable can be set to <code class="keyw">false</code> in order to prevent the combinatorial collector to be used.</p>
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