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#SIXFORMAT GapDocGAP
HELPBOOKINFOSIXTMP := rec(
encoding := "UTF-8",
bookname := "Semigroups",
entries :=
[ [ "Title page", "0.0", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5"
],
[ "Abstract", "0.0-1", [ 0, 0, 1 ], 217, 2, "abstract", "X7AA6C5737B711C89"
],
[ "Copyright", "0.0-2", [ 0, 0, 2 ], 240, 2, "copyright",
"X81488B807F2A1CF1" ],
[ "Acknowledgements", "0.0-3", [ 0, 0, 3 ], 249, 2, "acknowledgements",
"X82A988D47DFAFCFA" ],
[ "Table of Contents", "0.0-4", [ 0, 0, 4 ], 285, 4, "table of contents",
"X8537FEB07AF2BEC8" ],
[
"\033[1X\033[33X\033[0;-2YThe \033[5XSemigroups\033[105X\033[101X\027\033[1\
X\027 package\033[133X\033[101X", "1", [ 1, 0, 0 ], 1, 8,
"the semigroups package", "X7D8D6DB37A0326BE" ],
[ "\033[1X\033[33X\033[0;-2YIntroduction\033[133X\033[101X", "1.1",
[ 1, 1, 0 ], 4, 8, "introduction", "X7DFB63A97E67C0A1" ],
[ "\033[1X\033[33X\033[0;-2YOverview\033[133X\033[101X", "1.2",
[ 1, 2, 0 ], 19, 8, "overview", "X8389AD927B74BA4A" ],
[
"\033[1X\033[33X\033[0;-2YInstalling \033[5XSemigroups\033[105X\033[101X\\
027\033[1X\027\033[133X\033[101X", "2", [ 2, 0, 0 ], 1, 10,
"installing semigroups", "X82398F3785F63754" ],
[ "\033[1X\033[33X\033[0;-2YFor those in a hurry\033[133X\033[101X", "2.1",
[ 2, 1, 0 ], 4, 10, "for those in a hurry", "X7DA3059C79842BF3" ],
[ "\033[1X\033[33X\033[0;-2YCompiling the kernel module\033[133X\033[101X",
"2.2", [ 2, 2, 0 ], 68, 11, "compiling the kernel module",
"X849F6196875A6DF5" ],
[ "\033[1X\033[33X\033[0;-2YRebuilding the documentation\033[133X\033[101X",
"2.3", [ 2, 3, 0 ], 105, 11, "rebuilding the documentation",
"X857CBE5484CF703A" ],
[ "\033[1X\033[33X\033[0;-2YTesting your installation\033[133X\033[101X",
"2.4", [ 2, 4, 0 ], 120, 12, "testing your installation",
"X7862D3F37C5BBDEF" ],
[
"\033[1X\033[33X\033[0;-2YMore information during a computation\033[133X\\
033[101X", "2.5", [ 2, 5, 0 ], 188, 13,
"more information during a computation", "X798CBC46800AB80F" ],
[ "\033[1X\033[33X\033[0;-2YBipartitions and blocks\033[133X\033[101X",
"3", [ 3, 0, 0 ], 1, 14, "bipartitions and blocks", "X7C18DB427C9C0917"
],
[
"\033[1X\033[33X\033[0;-2YThe family and categories of bipartitions\033[133\
X\033[101X", "3.1", [ 3, 1, 0 ], 93, 15,
"the family and categories of bipartitions", "X7850845886902FBF" ],
[ "\033[1X\033[33X\033[0;-2YCreating bipartitions\033[133X\033[101X",
"3.2", [ 3, 2, 0 ], 121, 16, "creating bipartitions",
"X85D77073820C7E72" ],
[
"\033[1X\033[33X\033[0;-2YChanging the representation of a bipartition\033[\
133X\033[101X", "3.3", [ 3, 3, 0 ], 301, 18,
"changing the representation of a bipartition", "X7C2C44D281A0D2C9" ],
[ "\033[1X\033[33X\033[0;-2YOperators for bipartitions\033[133X\033[101X",
"3.4", [ 3, 4, 0 ], 541, 22, "operators for bipartitions",
"X83F2C3C97E8FFA49" ],
[ "\033[1X\033[33X\033[0;-2YAttributes for bipartitons\033[133X\033[101X",
"3.5", [ 3, 5, 0 ], 635, 24, "attributes for bipartitons",
"X87F3A304814797CE" ],
[
"\033[1X\033[33X\033[0;-2YCreating blocks and their attributes\033[133X\\
033[101X", "3.6", [ 3, 6, 0 ], 1041, 30,
"creating blocks and their attributes", "X87684C148592F831" ],
[ "\033[1X\033[33X\033[0;-2YActions on blocks\033[133X\033[101X", "3.7",
[ 3, 7, 0 ], 1159, 32, "actions on blocks", "X7A45E0067F344683" ],
[ "\033[1X\033[33X\033[0;-2YSemigroups of bipartitions\033[133X\033[101X",
"3.8", [ 3, 8, 0 ], 1203, 33, "semigroups of bipartitions",
"X876C963F830719E2" ],
[
"\033[1X\033[33X\033[0;-2YPartitioned binary relations (PBRs)\033[133X\033[\
101X", "4", [ 4, 0, 0 ], 1, 36, "partitioned binary relations pbrs",
"X85A717D1790B7BB5" ],
[
"\033[1X\033[33X\033[0;-2YThe family and categories of PBRs\033[133X\033[10\
1X", "4.1", [ 4, 1, 0 ], 17, 36, "the family and categories of pbrs",
"X7C40DA67826FF873" ],
[ "\033[1X\033[33X\033[0;-2YCreating PBRs\033[133X\033[101X", "4.2",
[ 4, 2, 0 ], 42, 36, "creating pbrs", "X8758C4FB81D2C2A1" ],
[
"\033[1X\033[33X\033[0;-2YChanging the representation of a PBR\033[133X\\
033[101X", "4.3", [ 4, 3, 0 ], 144, 38, "changing the representation of a pbr"
, "X86B714987C01895F" ],
[ "\033[1X\033[33X\033[0;-2YOperators for PBRs\033[133X\033[101X", "4.4",
[ 4, 4, 0 ], 290, 41, "operators for pbrs", "X872B5817878660E5" ],
[ "\033[1X\033[33X\033[0;-2YAttributes for PBRs\033[133X\033[101X", "4.5",
[ 4, 5, 0 ], 306, 41, "attributes for pbrs", "X78EC8E597EB99730" ],
[ "\033[1X\033[33X\033[0;-2YSemigroups of PBRs\033[133X\033[101X", "4.6",
[ 4, 6, 0 ], 612, 46, "semigroups of pbrs", "X7ECD4BBD7A0E834E" ],
[ "\033[1X\033[33X\033[0;-2YMatrices over semirings\033[133X\033[101X",
"5", [ 5, 0, 0 ], 1, 48, "matrices over semirings", "X82D6B7FE7CAC0AFA"
],
[
"\033[1X\033[33X\033[0;-2YCreating matrices over semirings\033[133X\033[101\
X", "5.1", [ 5, 1, 0 ], 47, 49, "creating matrices over semirings",
"X7ECF673C7BE2384D" ],
[ "\033[1X\033[33X\033[0;-2YMatrix filters\033[133X\033[101X", "5.1-8",
[ 5, 1, 8 ], 364, 54, "matrix filters", "X782480C686F1A663" ],
[ "\033[1X\033[33X\033[0;-2YMatrix collection filters\033[133X\033[101X",
"5.1-9", [ 5, 1, 9 ], 395, 54, "matrix collection filters",
"X86233A3E86512493" ],
[
"\033[1X\033[33X\033[0;-2YOperators for matrices over semirings\033[133X\\
033[101X", "5.2", [ 5, 2, 0 ], 521, 57,
"operators for matrices over semirings", "X807E402687741CDA" ],
[ "\033[1X\033[33X\033[0;-2YBoolean matrices\033[133X\033[101X", "5.3",
[ 5, 3, 0 ], 540, 57, "boolean matrices", "X844A32A184E5EB75" ],
[ "\033[1X\033[33X\033[0;-2YMatrices over finite fields\033[133X\033[101X",
"5.4", [ 5, 4, 0 ], 1158, 67, "matrices over finite fields",
"X873822B6830CE367" ],
[ "\033[1X\033[33X\033[0;-2YMatrices over the integers\033[133X\033[101X",
"5.5", [ 5, 5, 0 ], 1219, 68, "matrices over the integers",
"X8770A88E82AA24B7" ],
[
"\033[1X\033[33X\033[0;-2YMax-plus and min-plus matrices\033[133X\033[101X"
, "5.6", [ 5, 6, 0 ], 1307, 70, "max-plus and min-plus matrices",
"X86BFFFBC87F2AB1E" ],
[ "\033[1X\033[33X\033[0;-2YMatrix semigroups\033[133X\033[101X", "5.7",
[ 5, 7, 0 ], 1391, 71, "matrix semigroups", "X79B614AA803BD103" ],
[ "\033[1X\033[33X\033[0;-2YMatrix semigroup filters\033[133X\033[101X",
"5.7-1", [ 5, 7, 1 ], 1417, 72, "matrix semigroup filters",
"X7DC6EB0680B3E4DD" ],
[ "\033[1X\033[33X\033[0;-2YMatrix monoid filters\033[133X\033[101X",
"5.7-2", [ 5, 7, 2 ], 1435, 72, "matrix monoid filters",
"X8616225581BC7414" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups and monoids defined by generating sets\
\033[133X\033[101X", "6", [ 6, 0, 0 ], 1, 74,
"semigroups and monoids defined by generating sets",
"X7995B4F18672DDB0" ],
[ "\033[1X\033[33X\033[0;-2YUnderlying algorithms\033[133X\033[101X",
"6.1", [ 6, 1, 0 ], 9, 74, "underlying algorithms", "X7A19D22B7A05CC2F"
], [ "\033[1X\033[33X\033[0;-2YActing semigroups\033[133X\033[101X",
"6.1-1", [ 6, 1, 1 ], 18, 74, "acting semigroups", "X7A3AC74C7FF85825" ]
,
[ "\033[1X\033[33X\033[0;-2YThe Froidure-Pin Algorithm\033[133X\033[101X",
"6.1-3", [ 6, 1, 3 ], 85, 75, "the froidure-pin algorithm",
"X7E2DE9767D5D82F7" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups represented by generators\033[133X\\
033[101X", "6.2", [ 6, 2, 0 ], 183, 77, "semigroups represented by generators"
, "X79BD00A682BDED7A" ],
[
"\033[1X\033[33X\033[0;-2YOptions when creating semigroups\033[133X\033[101\
X", "6.3", [ 6, 3, 0 ], 200, 77, "options when creating semigroups",
"X799EBA2F819D8867" ],
[
"\033[1X\033[33X\033[0;-2YSubsemigroups and supersemigroups\033[133X\033[10\
1X", "6.4", [ 6, 4, 0 ], 346, 79, "subsemigroups and supersemigroups",
"X87AA2EB6810B4631" ],
[
"\033[1X\033[33X\033[0;-2YChanging the representation of a semigroup\033[13\
3X\033[101X", "6.5", [ 6, 5, 0 ], 499, 82,
"changing the representation of a semigroup", "X82CCC1A781650878" ],
[ "\033[1X\033[33X\033[0;-2YRandom semigroups\033[133X\033[101X", "6.6",
[ 6, 6, 0 ], 1027, 91, "random semigroups", "X7C3F130B8362D55A" ],
[ "\033[1X\033[33X\033[0;-2YStandard examples\033[133X\033[101X", "7",
[ 7, 0, 0 ], 1, 94, "standard examples", "X7C76D1DC7DAF03D3" ],
[ "\033[1X\033[33X\033[0;-2YTransformation semigroups\033[133X\033[101X",
"7.1", [ 7, 1, 0 ], 7, 94, "transformation semigroups",
"X7E42E8337A78B076" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups of order-preserving transformations\\
033[133X\033[101X", "7.1-5", [ 7, 1, 5 ], 89, 95,
"semigroups of order-preserving transformations", "X80E80A0A83B57483" ],
[ "\033[1X\033[33X\033[0;-2YSemigroups of partial permutations\033[133X\033[\
101X", "7.2", [ 7, 2, 0 ], 199, 97, "semigroups of partial permutations",
"X862BA1C67AA1C77C" ],
[
"\033[1X\033[33X\033[0;-2YInverse monoids of order-preserving partial permu\
tations\033[133X\033[101X", "7.2-3", [ 7, 2, 3 ], 248, 98,
"inverse monoids of order-preserving partial permutations",
"X85D841AE83DF101C" ],
[ "\033[1X\033[33X\033[0;-2YSemigroups of bipartitions\033[133X\033[101X",
"7.3", [ 7, 3, 0 ], 302, 99, "semigroups of bipartitions",
"X876C963F830719E2" ],
[ "\033[1X\033[33X\033[0;-2YStandard PBR semigroups\033[133X\033[101X",
"7.4", [ 7, 4, 0 ], 698, 106, "standard pbr semigroups",
"X874C945E7C61A969" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups of matrices over a finite field\033[13\
3X\033[101X", "7.5", [ 7, 5, 0 ], 725, 106,
"semigroups of matrices over a finite field", "X857DBF537A9A9976" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups of boolean matrices\033[133X\033[101X"
, "7.6", [ 7, 6, 0 ], 798, 108, "semigroups of boolean matrices",
"X85BACB7F81660ECC" ],
[
"\033[1X\033[33X\033[0;-2YSemigroups of matrices over a semiring\033[133X\\
033[101X", "7.7", [ 7, 7, 0 ], 955, 110,
"semigroups of matrices over a semiring", "X7F3D0AEE79AA8C98" ],
[
"\033[1X\033[33X\033[0;-2YExamples in various representations\033[133X\033[\
101X", "7.8", [ 7, 8, 0 ], 1005, 111, "examples in various representations",
"X7ED2F2577CD6B578" ],
[ "\033[1X\033[33X\033[0;-2YFree bands\033[133X\033[101X", "7.9",
[ 7, 9, 0 ], 1353, 117, "free bands", "X7BB29A6779E8066A" ],
[ "\033[1X\033[33X\033[0;-2YOperators\033[133X\033[101X", "7.9-10",
[ 7, 9, 10 ], 1567, 120, "operators", "X7AD6F77E7D95C996" ],
[ "\033[1X\033[33X\033[0;-2YGraph inverse semigroups\033[133X\033[101X",
"7.10", [ 7, 10, 0 ], 1582, 120, "graph inverse semigroups",
"X850B10D783053100" ],
[ "\033[1X\033[33X\033[0;-2YFree inverse semigroups\033[133X\033[101X",
"7.11", [ 7, 11, 0 ], 1819, 124, "free inverse semigroups",
"X7E51292C8755DCF2" ],
[
"\033[1X\033[33X\033[0;-2YDisplaying free inverse semigroup elements\033[13\
3X\033[101X", "7.11-8", [ 7, 11, 8 ], 1977, 127,
"displaying free inverse semigroup elements", "X8073A2387A42B52D" ],
[
"\033[1X\033[33X\033[0;-2YOperators for free inverse semigroup elements\\
033[133X\033[101X", "7.11-9", [ 7, 11, 9 ], 2011, 128,
"operators for free inverse semigroup elements", "X7A55FD9A7DF21C60" ],
[ "\033[1X\033[33X\033[0;-2YStandard constructions\033[133X\033[101X", "8",
[ 8, 0, 0 ], 1, 129, "standard constructions", "X86EE8DC987BA646E" ],
[ "\033[1X\033[33X\033[0;-2YProducts of semigroups\033[133X\033[101X",
"8.1", [ 8, 1, 0 ], 8, 129, "products of semigroups",
"X79546641809113CE" ],
[ "\033[1X\033[33X\033[0;-2YDual semigroups\033[133X\033[101X", "8.2",
[ 8, 2, 0 ], 80, 130, "dual semigroups", "X7F035EC07AA7CD97" ],
[
"\033[1X\033[33X\033[0;-2YStrong semilattices of semigroups\033[133X\033[10\
1X", "8.3", [ 8, 3, 0 ], 213, 132, "strong semilattices of semigroups",
"X7BEA92E67A6D349A" ],
[ "\033[1X\033[33X\033[0;-2YMcAlister triple semigroups\033[133X\033[101X",
"8.4", [ 8, 4, 0 ], 350, 135, "mcalister triple semigroups",
"X7CC4F6FE87AFE638" ],
[ "\033[1X\033[33X\033[0;-2YIdeals\033[133X\033[101X", "9", [ 9, 0, 0 ], 1,
140, "ideals", "X83629803819C4A6F" ],
[ "\033[1X\033[33X\033[0;-2YCreating ideals\033[133X\033[101X", "9.1",
[ 9, 1, 0 ], 22, 140, "creating ideals", "X82D4D9A578A56A8D" ],
[ "\033[1X\033[33X\033[0;-2YAttributes of ideals\033[133X\033[101X", "9.2",
[ 9, 2, 0 ], 78, 141, "attributes of ideals", "X85D4E72B787B1C49" ],
[ "\033[1X\033[33X\033[0;-2YGreen's relations\033[133X\033[101X", "10",
[ 10, 0, 0 ], 1, 144, "greens relations", "X80C6C718801855E9" ],
[
"\033[1X\033[33X\033[0;-2YCreating Green's classes and representatives\033[\
133X\033[101X", "10.1", [ 10, 1, 0 ], 7, 144,
"creating greens classes and representatives", "X788D6753849BAD7C" ],
[ "\033[1X\033[33X\033[0;-2YXClassOfYClass\033[133X\033[101X", "10.1-1",
[ 10, 1, 1 ], 13, 144, "xclassofyclass", "X87558FEF805D24E1" ],
[ "\033[1X\033[33X\033[0;-2YGreensXClassOfElement\033[133X\033[101X",
"10.1-2", [ 10, 1, 2 ], 78, 145, "greensxclassofelement",
"X81B7AD4C7C552867" ],
[ "\033[1X\033[33X\033[0;-2YGreensXClassOfElementNC\033[133X\033[101X",
"10.1-3", [ 10, 1, 3 ], 117, 146, "greensxclassofelementnc",
"X7B44317786571F8B" ],
[ "\033[1X\033[33X\033[0;-2YGreensXClasses\033[133X\033[101X", "10.1-4",
[ 10, 1, 4 ], 185, 147, "greensxclasses", "X7D51218A80234DE5" ],
[ "\033[1X\033[33X\033[0;-2YXClassReps\033[133X\033[101X", "10.1-5",
[ 10, 1, 5 ], 285, 149, "xclassreps", "X865387A87FAAC395" ],
[ "\033[1X\033[33X\033[0;-2YMaximalXClasses\033[133X\033[101X", "10.1-7",
[ 10, 1, 7 ], 368, 150, "maximalxclasses", "X834172F4787A565B" ],
[ "\033[1X\033[33X\033[0;-2YNrXClasses\033[133X\033[101X", "10.1-9",
[ 10, 1, 9 ], 427, 151, "nrxclasses", "X7E45FD9F7BADDFBD" ],
[ "\033[1X\033[33X\033[0;-2YPartialOrderOfXClasses\033[133X\033[101X",
"10.1-10", [ 10, 1, 10 ], 508, 152, "partialorderofxclasses",
"X8140814084748101" ],
[
"\033[1X\033[33X\033[0;-2YIterators and enumerators of classes and represen\
tatives\033[133X\033[101X", "10.2", [ 10, 2, 0 ], 645, 155,
"iterators and enumerators of classes and representatives",
"X819CCBD67FD27115" ],
[ "\033[1X\033[33X\033[0;-2YIteratorOfXClassReps\033[133X\033[101X",
"10.2-1", [ 10, 2, 1 ], 651, 155, "iteratorofxclassreps",
"X8566F84A7F6D4193" ],
[ "\033[1X\033[33X\033[0;-2YIteratorOfXClasses\033[133X\033[101X",
"10.2-2", [ 10, 2, 2 ], 666, 155, "iteratorofxclasses",
"X867D7B8982915960" ],
[ "\033[1X\033[33X\033[0;-2YProperties of Green's classes\033[133X\033[101X"
, "10.3", [ 10, 3, 0 ], 744, 156, "properties of greens classes",
"X820EF2BA7D5D53B4" ],
[ "\033[1X\033[33X\033[0;-2YLess than for Green's classes\033[133X\033[101X"
, "10.3-1", [ 10, 3, 1 ], 750, 157, "less than for greens classes",
"X85F30ACF86C3A733" ],
[ "\033[1X\033[33X\033[0;-2YAttributes of Green's classes\033[133X\033[101X"
, "10.4", [ 10, 4, 0 ], 855, 158, "attributes of greens classes",
"X855723B17D4AAF8F" ],
[
"\033[1X\033[33X\033[0;-2YOperations for Green's relations and classes\033[\
133X\033[101X", "10.5", [ 10, 5, 0 ], 1178, 164,
"operations for greens relations and classes", "X802E2BC9828341A2" ],
[
"\033[1X\033[33X\033[0;-2YAttributes and operations for semigroups\033[133X\
\033[101X", "11", [ 11, 0, 0 ], 1, 166,
"attributes and operations for semigroups", "X7C75B1DB81C7779B" ],
[
"\033[1X\033[33X\033[0;-2YAccessing the elements of a semigroup\033[133X\\
033[101X", "11.1", [ 11, 1, 0 ], 8, 166,
"accessing the elements of a semigroup", "X7AE0630287B8A757" ],
[ "\033[1X\033[33X\033[0;-2YCayley graphs\033[133X\033[101X", "11.2",
[ 11, 2, 0 ], 119, 168, "cayley graphs", "X789D5E5A8558AA07" ],
[
"\033[1X\033[33X\033[0;-2YRandom elements of a semigroup\033[133X\033[101X"
, "11.3", [ 11, 3, 0 ], 149, 168, "random elements of a semigroup",
"X824184C785BF12FF" ],
[
"\033[1X\033[33X\033[0;-2YProperties of elements in a semigroup\033[133X\\
033[101X", "11.4", [ 11, 4, 0 ], 164, 169,
"properties of elements in a semigroup", "X80EB463F7E5D8920" ],
[
"\033[1X\033[33X\033[0;-2YOperations for elements in a semigroup\033[133X\\
033[101X", "11.5", [ 11, 5, 0 ], 227, 170,
"operations for elements in a semigroup", "X7A20EC348515E37B" ],
[
"\033[1X\033[33X\033[0;-2YExpressing semigroup elements as words in generat\
ors\033[133X\033[101X", "11.6", [ 11, 6, 0 ], 256, 170,
"expressing semigroup elements as words in generators",
"X81CEB3717E021643" ],
[ "\033[1X\033[33X\033[0;-2YGenerating sets\033[133X\033[101X", "11.7",
[ 11, 7, 0 ], 460, 174, "generating sets", "X7E4AA1437A6C7B40" ],
[
"\033[1X\033[33X\033[0;-2YMinimal ideals and multiplicative zeros\033[133X\\
033[101X", "11.8", [ 11, 8, 0 ], 798, 179,
"minimal ideals and multiplicative zeros", "X830E18747A0B5BED" ],
[
"\033[1X\033[33X\033[0;-2YGroup of units and identity elements\033[133X\\
033[101X", "11.9", [ 11, 9, 0 ], 952, 182,
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--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
]
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