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<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#contents">[Contents]</a> <a href="chap20.html">[Previous Chapter]</a> <a href="chap22.html">[Next Chapter]</a> </div>
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<div class="ChapSects"><a href="chap21.html#X7B256AE5780F140A">21 <span class="Heading">Lists</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X86B28F5B781FFD31">21.1 <span class="Heading">List Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C4CC4EA8299701E">21.1-1 IsList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X870AA9D8798C93DD">21.1-2 IsDenseList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C71596C82B6EF35">21.1-3 IsHomogeneousList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X80872FAF80EB5DF9">21.1-4 IsTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79581E0387F7F7A9">21.1-5 IsRectangularTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C84E16A85C99C8C">21.1-6 IsConstantTimeAccessList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7B202D147A5C2884">21.2 <span class="Heading">Basic Operations for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8297BBCD79642BE6"><code>21.2-1 <span>\</span>[<span>\</span>]</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7921047F83F5FA28">21.3 <span class="Heading">List Elements</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X78791B8B838A8BA0"><code>21.3-1 \{\}</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X8611EF768210625B">21.4 <span class="Heading">List Assignment</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X813FF1637F8D2B7F"><code>21.4-1 \{\}\:\=</code></a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X795EC9D67E34DAB0">21.4-2 Add</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E98B11B79BA9167">21.4-3 Remove</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79D7E96F80A2D7C0">21.4-4 CopyListEntries</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79E31DB27C82D6E1">21.4-5 Append</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7963C8E17EFF86DB">21.5 <span class="Heading">IsBound and Unbind for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79EC565A7DCEC938">21.5-1 IsBound</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X866F45D3797FDA00">21.5-2 GetWithDefault</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X78B72FDF7BD63C0B">21.5-3 Unbind</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7DD65BEA7EDB0CD7">21.6 <span class="Heading">Identical Lists</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7ED7C0738495556F">21.7 <span class="Heading">Duplication of Lists</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X808A207182B2F84F">21.8 <span class="Heading">Membership Test for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B914A287F88ED0A"><code>21.8-1 \in</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X84D6FC7E7E39ED33">21.9 <span class="Heading">Enlarging Internally Represented Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X78BF67A5802E93AD">21.9-1 EmptyPlist</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X8016D50F85147A77">21.10 <span class="Heading">Comparisons of Lists</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X845EEAF083D43CCE">21.11 <span class="Heading">Arithmetic for Lists</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X84D642967B8546B7">21.12 <span class="Heading">Filters Controlling the Arithmetic Behaviour of Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X87ABCEE9809585A0">21.12-1 IsGeneralizedRowVector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FBCA5B58308C158">21.12-2 IsMultiplicativeGeneralizedRowVector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7BAD12E67BFC90DE">21.12-3 IsListDefault</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8428E77B86722D52">21.12-4 NestingDepthA</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X84B383B97FD986CD">21.12-5 NestingDepthM</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7E6A1F66781BE923">21.13 <span class="Heading">Additive Arithmetic for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X86A85ADC85C451DC">21.13-1 <span class="Heading">Zero for lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B91CE4D814C2D08">21.13-2 <span class="Heading">AdditiveInverse for lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X842D123E7EE5E3DB">21.13-3 <span class="Heading">Addition of lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C3DC8BE78DEECDE">21.13-4 <span class="Heading">Subtraction of lists</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X782ED7F27D8C7FC1">21.14 <span class="Heading">Multiplicative Arithmetic for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79A8A5627FD42FA5">21.14-1 <span class="Heading">One for lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X78C6C1E2849D303A">21.14-2 <span class="Heading">Inverse for lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X84FDB95179BFE4CD">21.14-3 <span class="Heading">Multiplication of lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X82EA2A5B786181C7">21.14-4 <span class="Heading">Division of lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7A0FD70C80B95C00">21.14-5 <span class="Heading">mod for lists</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X84BB2DFB8432A1A4">21.14-6 <span class="Heading">Left quotients of lists</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X8676EFE67972FD06">21.15 <span class="Heading">Mutability Status and List Arithmetic</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X80FDB1457FF582E7">21.15-1 ListWithIdenticalEntries</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X8196FD4779BCCA0C">21.16 <span class="Heading">Finding Positions in Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79975EC6783B4293">21.16-1 Position</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FA9648883AE1B88">21.16-2 Positions</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B4B10AE81602D4E">21.16-3 PositionCanonical</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7D2B25B484591506">21.16-4 PositionNthOccurrence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7A122E848464E534">21.16-5 PositionSorted</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X820BA44D85930EBF">21.16-6 PositionSortedBy</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X78BFE9D78347C0DA">21.16-7 PositionSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FD9C1D37F300206">21.16-8 PositionMaximum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E6C763A82C6153B">21.16-9 PositionProperty</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7DA94D278304EC3D">21.16-10 PositionsProperty</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X86C9E5C3863B3C03">21.16-11 PositionBound</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X819F71047AABEA2F">21.16-12 PositionsBound</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X865EF45D87ED1384">21.16-13 PositionNot</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7F42E5AD87EC9D5A">21.16-14 PositionNonZero</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X87A8C62A867D6DA4">21.16-15 PositionSublist</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7865747A7CCF5812">21.17 <span class="Heading">Properties and Attributes for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X83F8EC7C7BF27EFC">21.17-1 IsMatchingSublist</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FA892828252BB3B">21.17-2 IsDuplicateFree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7BAA9B0E81D4A884">21.17-3 IsSortedList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X80CDAF45782E8DCB">21.17-4 IsSSortedList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X780769238600AFD1">21.17-5 Length</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B55FB967CDEF468">21.17-6 ConstantTimeAccessList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X83E558E37D1B44D4">21.18 <span class="Heading">Sorting Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FE4975F8166884D">21.18-1 Sort</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X791F2B2C7E9B9A46">21.18-2 SortParallel</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X87287FCA81E2B06A">21.18-3 Sortex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X800209E881E7CECB">21.18-4 SortingPerm</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X80ABC25582343910">21.19 <span class="Heading">Sorted Lists and Sets</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B16AD597CB12305"><code>21.19-1 \in</code></a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B4C0FEE7CDF6F2A">21.19-2 IsEqualSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X79B940567A849216">21.19-3 IsSubsetSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X832C23CC7FCD8892">21.19-4 AddSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FCA282E789A4F4B">21.19-5 RemoveSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B3469CD7EFC1A87">21.19-6 UniteSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8473AA657FEC3D4D">21.19-7 IntersectSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X80B427537EB07D09">21.19-8 SubtractSet</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7DF510F7848CBBFD">21.20 <span class="Heading">Operations for Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X840C55A77D1BB2E1">21.20-1 Concatenation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7CB0A6AF87C7FAF7">21.20-2 Compacted</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7ECE9056792F28BA">21.20-3 Collected</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8727F2928467C2F9">21.20-4 DuplicateFreeList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7F5D4DD87E4378AC">21.20-5 AsDuplicateFreeList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FA272D984EF82ED">21.20-6 Flat</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C4FDB007C3F54A1">21.20-7 Reversed</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8057372F83374193">21.20-8 Shuffle</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8075FBDE7B81B4C8">21.20-9 Apply</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7EF6E2BC81DBF6FB">21.20-10 Perform</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8763882A7D65F979">21.20-11 PermListList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X82CE0DE8828E4303">21.20-12 <span class="Heading">Maximum</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X82F133EC7F89665F">21.20-13 <span class="Heading">Minimum</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X842851EB7E0969F7">21.20-14 <span class="Heading">MaximumList and MinimumList</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E1593B979BDF2CD">21.20-15 <span class="Heading">Cartesian</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E76F5A782184823">21.20-16 <span class="Heading">IteratorOfCartesianProduct</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7B5A19098406347A">21.20-17 Permuted</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X86CB7DCE8510F977">21.20-18 List</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7C86D7F7795125F0">21.20-19 Filtered</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8179B13D80E935FC">21.20-20 Number</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X82801DFA84E11272">21.20-21 First</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E5B62E780421CE9">21.20-22 Last</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7F06961278166671">21.20-23 ForAll</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7AF82E747A8BDA75">21.20-24 ForAny</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7E5C72F27B657948">21.20-25 Product</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7A04B71C84CFCC2D">21.20-26 Sum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X834E4DF57F3A20F0">21.20-27 Iterated</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7D150C2881881139">21.20-28 ListN</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X805CA0B68029B47A">21.21 <span class="Heading">Advanced List Manipulations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8258477D7F72171B">21.21-1 ListX</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7AC321B87A2DCAF5">21.21-2 SetX</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X82B1411E7FBE925F">21.21-3 SumX</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7FB318B47D8783DA">21.21-4 ProductX</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X79596BDE7CAF8491">21.22 <span class="Heading">Ranges</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X86DDC2FF7A50FBEE">21.22-1 IsRange</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X83896BC481536B07">21.22-2 IsRangeRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7D22B2298167A58F">21.22-3 ConvertToRangeRep</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X7EA3ACE27E43D174">21.23 <span class="Heading">Enumerators</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X7BB462C17962647F">21.23-1 IsQuickPositionList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap21.html#X81ECC2077D88E112">21.24 <span class="Heading">Plain Lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X8438CB908367254C">21.24-1 PlainListCopy</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap21.html#X87BA4EBF80F16B72">21.24-2 IsPlistRep</a></span>
</div></div>
</div>
<h3>21 <span class="Heading">Lists</span></h3>
<p>Lists are the most important way to treat objects together. A <em>list</em> arranges objects in a definite order. So each list implies a partial mapping from the integers to the elements of the list. I.e., there is a first element of a list, a second, a third, and so on. Lists can occur in mutable or immutable form, see <a href="chap12.html#X7F0C119682196D65"><span class="RefLink">12.6</span></a> for the concept of mutability, and <a href="chap21.html#X7ED7C0738495556F"><span class="RefLink">21.7</span></a> for the case of lists.</p>
<p>This chapter deals mainly with the aspect of lists in <strong class="pkg">GAP</strong> as <em>data structures</em>. Chapter <a href="chap30.html#X8050A8037984E5B6"><span class="RefLink">30</span></a> tells more about the <em>collection</em> aspect of certain lists, and more about lists as <em>arithmetic objects</em> can be found in the chapters <a href="chap23.html#X82C7E6CF7BA03391"><span class="RefLink">23</span></a> and <a href="chap24.html#X812CCAB278643A59"><span class="RefLink">24</span></a>.</p>
<p>Lists are used to implement ranges (see <a href="chap21.html#X79596BDE7CAF8491"><span class="RefLink">21.22</span></a>), sets (see <a href="chap21.html#X80ABC25582343910"><span class="RefLink">21.19</span></a>), strings (see <a href="chap27.html#X7D28329B7EDB8F47"><span class="RefLink">27</span></a>), row vectors and matrices (see <a href="chap23.html#X82C7E6CF7BA03391"><span class="RefLink">23</span></a> and <a href="chap24.html#X812CCAB278643A59"><span class="RefLink">24</span></a>, but note that <strong class="pkg">GAP</strong> supports also linear algebra for objects which are <em>not</em> lists, see <a href="chap26.html#X856C23B87E50F118"><span class="RefLink">26</span></a>); boolean lists (see <a href="chap22.html#X7AC531DD79B6938E"><span class="RefLink">22</span></a>) are a further special kind of lists.</p>
<p>Several operations for lists, such as <code class="func">Intersection</code> (<a href="chap30.html#X851069107CACF98E"><span class="RefLink">30.5-2</span></a>) and <code class="func">Random</code> (<a href="chap30.html#X7FF906E57D6936F8"><span class="RefLink">30.7-1</span></a>), will be described in Chapter <a href="chap30.html#X8050A8037984E5B6"><span class="RefLink">30</span></a>, in particular see <a href="chap30.html#X7C3722DF8736FFDB"><span class="RefLink">30.3</span></a>.</p>
<p><a id="X86B28F5B781FFD31" name="X86B28F5B781FFD31"></a></p>
<h4>21.1 <span class="Heading">List Categories</span></h4>
<p>A list can be written by writing down the elements in order between square brackets <code class="code">[</code>, <code class="code">]</code>, and separating them with commas <code class="code">,</code>. An <em>empty list</em>, i.e., a list with no elements, is written as <code class="code">[]</code>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">[ 1, 2, 3 ]; # a list with three elements</span>
[ 1, 2, 3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">[ [], [ 1 ], [ 1, 2 ] ]; # a list may contain other lists</span>
[ [ ], [ 1 ], [ 1, 2 ] ]
</pre></div>
<p>Each list constructed this way is mutable (see <a href="chap12.html#X7F0C119682196D65"><span class="RefLink">12.6</span></a>).</p>
<p><a id="X7C4CC4EA8299701E" name="X7C4CC4EA8299701E"></a></p>
<h5>21.1-1 IsList</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsList</code>( <var class="Arg">obj</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>tests whether <var class="Arg">obj</var> is a list.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsList( [ 1, 3, 5, 7 ] ); IsList( 1 );</span>
true
false
</pre></div>
<p><a id="X870AA9D8798C93DD" name="X870AA9D8798C93DD"></a></p>
<h5>21.1-2 IsDenseList</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsDenseList</code>( <var class="Arg">obj</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>A list is <em>dense</em> if it has no holes, i.e., contains an element at every position up to the length. It is absolutely legal to have lists with holes. They are created by leaving the entry between the commas empty. Holes at the end of a list are ignored. Lists with holes are sometimes convenient when the list represents a mapping from a finite, but not consecutive, subset of the positive integers.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsDenseList( [ 1, 2, 3 ] );</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">l := [ , 4, 9,, 25,, 49,,,, 121 ];; IsDenseList( l );</span>
false
<span class="GAPprompt">gap></span> <span class="GAPinput">l[3];</span>
9
<span class="GAPprompt">gap></span> <span class="GAPinput">l[4];</span>
List Element: <list>[4] must have an assigned value
not in any function
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' after assigning a value to continue
<span class="GAPbrkprompt">brk></span> <span class="GAPinput">l[4] := 16;; # assigning a value</span>
<span class="GAPbrkprompt">brk></span> <span class="GAPinput">return; # to escape the break-loop</span>
16
gap>
</pre></div>
<p>Observe that requesting the value of <code class="code">l[4]</code>, which was not assigned, caused the entry of a <code class="keyw">break</code>-loop (see Section <a href="chap6.html#X8593B49F8705B486"><span class="RefLink">6.4</span></a>). After assigning a value and typing <code class="code">return;</code>, <strong class="pkg">GAP</strong> is finally able to comply with our request (by responding with <code class="code">16</code>).</p>
<p><a id="X7C71596C82B6EF35" name="X7C71596C82B6EF35"></a></p>
<h5>21.1-3 IsHomogeneousList</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsHomogeneousList</code>( <var class="Arg">obj</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>returns <code class="keyw">true</code> if <var class="Arg">obj</var> is a list and it is homogeneous, and <code class="keyw">false</code> otherwise.</p>
<p>A <em>homogeneous</em> list is a dense list whose elements lie in the same family (see <a href="chap13.html#X846063757EC05986"><span class="RefLink">13.1</span></a>). The empty list is homogeneous but not a collection (see <a href="chap30.html#X8050A8037984E5B6"><span class="RefLink">30</span></a>), a nonempty homogeneous list is also a collection.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsHomogeneousList( [ 1, 2, 3 ] ); IsHomogeneousList( [] );</span>
true
true
<span class="GAPprompt">gap></span> <span class="GAPinput">IsHomogeneousList( [ 1, false, () ] );</span>
false
</pre></div>
<p><a id="X80872FAF80EB5DF9" name="X80872FAF80EB5DF9"></a></p>
<h5>21.1-4 IsTable</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsTable</code>( <var class="Arg">obj</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>A <em>table</em> is a nonempty list of homogeneous lists which lie in the same family. Typical examples of tables are matrices (see <a href="chap24.html#X812CCAB278643A59"><span class="RefLink">24</span></a>).</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsTable( [ [ 1, 2 ], [ 3, 4 ] ] ); # in fact a matrix</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">IsTable( [ [ 1 ], [ 2, 3 ] ] ); # not rectangular but a table</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">IsTable( [ [ 1, 2 ], [ () , (1,2) ] ] ); # not homogeneous</span>
false
</pre></div>
<p><a id="X79581E0387F7F7A9" name="X79581E0387F7F7A9"></a></p>
<h5>21.1-5 IsRectangularTable</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsRectangularTable</code>( <var class="Arg">list</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>A list lies in <code class="code">IsRectangularTable</code> when it is nonempty and its elements are all homogeneous lists of the same family and the same length.</p>
<p><a id="X7C84E16A85C99C8C" name="X7C84E16A85C99C8C"></a></p>
<h5>21.1-6 IsConstantTimeAccessList</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsConstantTimeAccessList</code>( <var class="Arg">list</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>This category indicates whether the access to each element of the list <var class="Arg">list</var> will take roughly the same time. This is implied for example by <code class="code">IsList and IsInternalRep</code>, so all strings, Boolean lists, ranges, and internally represented plain lists are in this category.</p>
<p>But also other enumerators (see <a href="chap21.html#X7EA3ACE27E43D174"><span class="RefLink">21.23</span></a>) can lie in this category if they guarantee constant time access to their elements.</p>
<p><a id="X7B202D147A5C2884" name="X7B202D147A5C2884"></a></p>
<h4>21.2 <span class="Heading">Basic Operations for Lists</span></h4>
<p>The basic operations for lists are element access (see <a href="chap21.html#X7921047F83F5FA28"><span class="RefLink">21.3</span></a>), assignment of elements to a list (see <a href="chap21.html#X8611EF768210625B"><span class="RefLink">21.4</span></a>), fetching the length of a list (see <code class="func">Length</code> (<a href="chap21.html#X780769238600AFD1"><span class="RefLink">21.17-5</span></a>)), the test for a hole at a given position, and unbinding an element at a given position (see <a href="chap21.html#X7963C8E17EFF86DB"><span class="RefLink">21.5</span></a>).</p>
<p>The term basic operation means that each other list operation can be formulated in terms of the basic operations. (But note that often a more efficient method than this one is implemented.)</p>
<p>Any <strong class="pkg">GAP</strong> object <var class="Arg">list</var> in the category <code class="func">IsList</code> (<a href="chap21.html#X7C4CC4EA8299701E"><span class="RefLink">21.1-1</span></a>) is regarded as a list, and if methods for the basic list operations are installed for <var class="Arg">list</var> then <var class="Arg">list</var> can be used also for the other list operations.</p>
<p>For internally represented lists, kernel methods are provided for the basic list operations with positive integer indices. For other lists or other indices, it is possible to install appropriate methods for these operations. This permits the implementation of lists that do not need to store all list elements (see also <a href="chap21.html#X7EA3ACE27E43D174"><span class="RefLink">21.23</span></a>); for example, the elements might be described by an algorithm, such as the elements list of a group. For this reduction of space requirements, however, a price in access time may have to be paid (see <code class="func">ConstantTimeAccessList</code> (<a href="chap21.html#X7B55FB967CDEF468"><span class="RefLink">21.17-6</span></a>)).</p>
<p><a id="X8297BBCD79642BE6" name="X8297BBCD79642BE6"></a></p>
<h5><code>21.2-1 <span>\</span>[<span>\</span>]</code></h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ <span>\</span>[<span>\</span>]</code>( <var class="Arg">list</var>, <var class="Arg">ix</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">‣ IsBound<span>\</span>[<span>\</span>]</code>( <var class="Arg">list</var>, <var class="Arg">ix</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">‣ <span>\</span>[<span>\</span>]\:\=</code>( <var class="Arg">list</var>, <var class="Arg">pos</var>, <var class="Arg">ix</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">‣ Unbind<span>\</span>[<span>\</span>]</code>( <var class="Arg">list</var>, <var class="Arg">ix</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>These operations implement element access, test for element boundedness, list element assignment, and removal of the element with index <var class="Arg">ix</var>.</p>
<p>Note that the special characters <code class="code">[</code>, <code class="code">]</code>, <code class="code">:</code>, and <code class="code">=</code> must be escaped with a backslash <code class="code">\</code> (see <a href="chap4.html#X7E90E6607F4E4943"><span class="RefLink">4.3</span></a>); so <code class="func"><span>\</span>[<span>\</span>]</code> denotes the operation for element access in a list, whereas <code class="code">[]</code> denotes an empty list. (Maybe the variable names involving special characters look strange, but nevertheless they are quite suggestive.)</p>
<p><code class="code">\[\]( <var class="Arg">list</var>, <var class="Arg">ix</var> )</code> is equivalent to <code class="code"><var class="Arg">list</var>[ <var class="Arg">ix</var> ]</code>, which clearly will usually be preferred; the former is useful mainly if one wants to access the operation itself, for example if one wants to install a method for element access in a special kind of lists.</p>
<p>Similarly, <code class="func">IsBound<span>\</span>[<span>\</span>]</code> is used explicitly mainly in method installations. In other situations, one can simply call <code class="func">IsBound</code> (<a href="chap21.html#X79EC565A7DCEC938"><span class="RefLink">21.5-1</span></a>), which then delegates to <code class="func">IsBound<span>\</span>[<span>\</span>]</code> if the first argument is a list, and to <code class="func">IsBound\.</code> (<a href="chap29.html#X7821AC097821AC09"><span class="RefLink">29.7-3</span></a>) if the first argument is a record.</p>
<p>Analogous statements hold for <code class="func"><span>\</span>[<span>\</span>]\:\=</code> and <code class="func">Unbind<span>\</span>[<span>\</span>]</code>.</p>
<p><a id="X7921047F83F5FA28" name="X7921047F83F5FA28"></a></p>
<h4>21.3 <span class="Heading">List Elements</span></h4>
<p><code class="code"><var class="Arg">list</var>[ <var class="Arg">ix</var> ]</code></p>
<p>The above construct evaluates to the element of the list <var class="Arg">list</var> with index <var class="Arg">ix</var>. For built-in list types and collections, indexing is done with origin 1, i.e., the first element of the list is the element with index 1.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">l := [ 2, 3, 5, 7, 11, 13 ];; l[1]; l[2]; l[6];</span>
2
3
13
</pre></div>
<p>If <var class="Arg">list</var> is not a built-in list, or <var class="Arg">ix</var> does not evaluate to a positive integer, method selection is invoked to try and find a way of indexing <var class="Arg">list</var> with index <var class="Arg">ix</var>. If this fails, or the selected method finds that <code class="code"><var class="Arg">list</var>[<var class="Arg">ix</var>]</code> is unbound, an error is signalled.</p>
<p><code class="code"><var class="Arg">list</var>{ <var class="Arg">poss</var> }</code></p>
<p>The above construct evaluates to a new list <var class="Arg">new</var> whose first element is <code class="code"><var class="Arg">list</var>[<var class="Arg">poss</var>[1]]</code>, whose second element is <code class="code"><var class="Arg">list</var>[<var class="Arg">poss</var>[2]]</code>, and so on. However, it does not need to be sorted and may contain duplicate elements. If for any <span class="SimpleMath">i</span>, <code class="code"><var class="Arg">list</var>[ <var class="Arg">poss</var>[</code><span class="SimpleMath">i</span><code class="code">] ]</code> is unbound, an error is signalled.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">l := [ 2, 3, 5, 7, 11, 13, 17, 19 ];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">l{[4..6]}; l{[1,7,1,8]};</span>
[ 7, 11, 13 ]
[ 2, 17, 2, 19 ]
</pre></div>
<p>The result is a <em>new</em> list, that is not identical to any other list. The elements of that list, however, are identical to the corresponding elements of the left operand (see <a href="chap21.html#X7DD65BEA7EDB0CD7"><span class="RefLink">21.6</span></a>).</p>
<p>It is possible to nest such <em>sublist extractions</em>, as can be seen in the example below.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">m := [ [1,2,3], [4,5,6], [7,8,9], [10,11,12] ];; m{[1,2,3]}{[3,2]};</span>
[ [ 3, 2 ], [ 6, 5 ], [ 9, 8 ] ]
<span class="GAPprompt">gap></span> <span class="GAPinput">l := m{[1,2,3]};; l{[3,2]};</span>
[ [ 7, 8, 9 ], [ 4, 5, 6 ] ]
</pre></div>
<p>Note the difference between the two examples. The latter extracts elements 1, 2, and 3 from <var class="Arg">m</var> and then extracts the elements 3 and 2 from <em>this list</em>. The former extracts elements 1, 2, and 3 from <var class="Arg">m</var> and then extracts the elements 3 and 2 from <em>each of those element lists</em>.</p>
<p>To be precise: With each selector <code class="code">[<var class="Arg">pos</var>]</code> or <code class="code">{<var class="Arg">poss</var>}</code> we associate a <em>level</em> that is defined as the number of selectors of the form <code class="code">{<var class="Arg">poss</var>}</code> to its left in the same expression. For example</p>
<div class="example"><pre>
l[pos1]{poss2}{poss3}[pos4]{poss5}[pos6]
level 0 0 1 2 2 3
</pre></div>
<p>Then a selector <code class="code"><var class="Arg">list</var>[<var class="Arg">pos</var>]</code> of level <var class="Arg">level</var> is computed as <code class="code">ListElement(<var class="Arg">list</var>,<var class="Arg">pos</var>,<var class="Arg">level</var>)</code>, where <code class="code">ListElement</code> is defined as follows. (Note that <code class="code">ListElement</code> is <em>not</em> a <strong class="pkg">GAP</strong> function.)</p>
<div class="example"><pre>
ListElement := function ( list, pos, level )
if level = 0 then
return list[pos];
else
return List( list, elm -> ListElement(elm,pos,level-1) );
fi;
end;
</pre></div>
<p>and a selector <code class="code"><var class="Arg">list</var>{<var class="Arg">poss</var>}</code> of level <var class="Arg">level</var> is computed as <code class="code">ListElements(<var class="Arg">list</var>,<var class="Arg">poss</var>,<var class="Arg">level</var>)</code>, where <code class="code">ListElements</code> is defined as follows. (Note that <code class="code">ListElements</code> is <em>not</em> a <strong class="pkg">GAP</strong> function.)</p>
<div class="example"><pre>
ListElements := function ( list, poss, level )
if level = 0 then
return list{poss};
else
return List( list, elm -> ListElements(elm,poss,level-1) );
fi;
end;
</pre></div>
<p><a id="X78791B8B838A8BA0" name="X78791B8B838A8BA0"></a></p>
<h5><code>21.3-1 \{\}</code></h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ \{\}</code>( <var class="Arg">list</var>, <var class="Arg">poss</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>This operation implements <em>sublist access</em>. For any list, the default method is to loop over the entries in the list <var class="Arg">poss</var>, and to delegate to the element access operation. (For nested sublist extractions, cf. <a href="chap21.html#X7921047F83F5FA28"><span class="RefLink">21.3</span></a>. For the somewhat strange variable name, cf. <a href="chap21.html#X7B202D147A5C2884"><span class="RefLink">21.2</span></a>.)</p>
<p><a id="X8611EF768210625B" name="X8611EF768210625B"></a></p>
<h4>21.4 <span class="Heading">List Assignment</span></h4>
<p><code class="code"><var class="Arg">list</var>[ <var class="Arg">ix</var> ] := <var class="Arg">object</var>;</code></p>
<p>The list element assignment assigns the object <var class="Arg">object</var>, which can be of any type, to the list with index <var class="Arg">ix</var>, in the mutable (see <a href="chap12.html#X7F0C119682196D65"><span class="RefLink">12.6</span></a>) list <var class="Arg">list</var>. That means that accessing the <var class="Arg">ix</var>-th element of the list <var class="Arg">list</var> will return <var class="Arg">object</var> after this assignment.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">l := [ 1, 2, 3 ];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">l[1] := 3;; l; # assign a new object</span>
[ 3, 2, 3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">l[2] := [ 4, 5, 6 ];; l; # <object> may be of any type</span>
[ 3, [ 4, 5, 6 ], 3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">l[ l[1] ] := 10;; l; # <index> may be an expression</span>
[ 3, [ 4, 5, 6 ], 10 ]
</pre></div>
<p>If the index <var class="Arg">ix</var> is an integer larger than the length of the list <var class="Arg">list</var> (see <code class="func">Length</code> (<a href="chap21.html#X780769238600AFD1"><span class="RefLink">21.17-5</span></a>)), the list is automatically enlarged to make room for the new element. Note that it is possible to generate lists with holes that way.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">l[4] := "another entry";; l; # <list> is enlarged</span>
[ 3, [ 4, 5, 6 ], 10, "another entry" ]
<span class="GAPprompt">gap></span> <span class="GAPinput">l[ 10 ] := 1;; l; # now <list> has a hole</span>
[ 3, [ 4, 5, 6 ], 10, "another entry",,,,,, 1 ]
</pre></div>
<p>The function <code class="func">Add</code> (<a href="chap21.html#X795EC9D67E34DAB0"><span class="RefLink">21.4-2</span></a>) should be used if you want to add an element to the end of the list.</p>
<p>Note that assigning to a list changes the list, thus this list must be mutable (see <a href="chap12.html#X7F0C119682196D65"><span class="RefLink">12.6</span></a>). See <a href="chap21.html#X7DD65BEA7EDB0CD7"><span class="RefLink">21.6</span></a> for subtleties of changing lists.</p>
<p>If <var class="Arg">list</var> does not evaluate to a list, <var class="Arg">pos</var> does not evaluate to a positive integer, method selection is invoked to try and find a way of indexing <var class="Arg">list</var> with index <var class="Arg">pos</var>. If this fails, or the selected method finds that <code class="code"><var class="Arg">list</var>[<var class="Arg">pos</var>]</code> is unbound, or if <var class="Arg">object</var> is a call to a function which does not return a value (for example <code class="code">Print</code>) an error is signalled.</p>
<p><code class="code"><var class="Arg">list</var>{ <var class="Arg">poss</var> } := <var class="Arg">objects</var>;</code></p>
<p>The sublist assignment assigns the object <code class="code"><var class="Arg">objects</var>[1]</code>, which can be of any type, to the list <var class="Arg">list</var> at the position <code class="code"><var class="Arg">poss</var>[1]</code>, the object <code class="code"><var class="Arg">objects</var>[2]</code> to <code class="code"><var class="Arg">list</var>[<var class="Arg">poss</var>[2]]</code>, and so on. <var class="Arg">poss</var> must be a dense list of positive integers, it need, however, not be sorted and may contain duplicate elements. <var class="Arg">objects</var> must be a dense list and must have the same length as <var class="Arg">poss</var>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">l := [ 2, 3, 5, 7, 11, 13, 17, 19 ];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">l{[1..4]} := [10..13];; l;</span>
[ 10, 11, 12, 13, 11, 13, 17, 19 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">l{[1,7,1,10]} := [ 1, 2, 3, 4 ];; l;</span>
[ 3, 11, 12, 13, 11, 13, 2, 19,, 4 ]
</pre></div>
<p>The next example shows that it is possible to nest such sublist assignments.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">m := [ [1,2,3], [4,5,6], [7,8,9], [10,11,12] ];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">m{[1,2,3]}{[3,2]} := [ [11,12], [13,14], [15,16] ];; m;</span>
[ [ 1, 12, 11 ], [ 4, 14, 13 ], [ 7, 16, 15 ], [ 10, 11, 12 ] ]
</pre></div>
<p>The exact behaviour is defined in the same way as for list extractions (see <a href="chap21.html#X7921047F83F5FA28"><span class="RefLink">21.3</span></a>). Namely, with each selector <code class="code">[<var class="Arg">pos</var>]</code> or <code class="code">{<var class="Arg">poss</var>}</code> we associate a <em>level</em> that is defined as the number of selectors of the form <code class="code">{<var class="Arg">poss</var>}</code> to its left in the same expression. For example</p>
<div class="example"><pre>
l[pos1]{poss2}{poss3}[pos4]{poss5}[pos6]
level 0 0 1 1 1 2
</pre></div>
<p>Then a list assignment <code class="code"><var class="Arg">list</var>[<var class="Arg">pos</var>] := <var class="Arg">vals</var>;</code> of level <var class="Arg">level</var> is computed as <code class="code">ListAssignment( <var class="Arg">list</var>, <var class="Arg">pos</var>, <var class="Arg">vals</var>, <var class="Arg">level</var> )</code>, where <code class="code">ListAssignment</code> is defined as follows. (Note that <code class="code">ListAssignment</code> is <em>not</em> a <strong class="pkg">GAP</strong> function.)</p>
<div class="example"><pre>
ListAssignment := function ( list, pos, vals, level )
local i;
if level = 0 then
list[pos] := vals;
else
for i in [1..Length(list)] do
ListAssignment( list[i], pos, vals[i], level-1 );
od;
fi;
end;
</pre></div>
<p>and a list assignment <code class="code"><var class="Arg">list</var>{<var class="Arg">poss</var>} := <var class="Arg">vals</var></code> of level <var class="Arg">level</var> is computed as <code class="code">ListAssignments( <var class="Arg">list</var>, <var class="Arg">poss</var>, <var class="Ar | | |
