diff --git a/doc/.gitignore b/doc/.gitignore deleted file mode 100644 index 369c34e..0000000 --- a/doc/.gitignore +++ /dev/null @@ -1,4 +0,0 @@ -## {{{1 gitkeep -* -!.gitignore -## }}}1 diff --git a/doc/_AutoDocMainFile.xml b/doc/_AutoDocMainFile.xml new file mode 100644 index 0000000..17936be --- /dev/null +++ b/doc/_AutoDocMainFile.xml @@ -0,0 +1,4 @@ + + + +<#Include SYSTEM "_Chapter_smallantimagmas_automatic_generated_documentation.xml"> diff --git a/doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml b/doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml new file mode 100644 index 0000000..e8b049d --- /dev/null +++ b/doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml @@ -0,0 +1,586 @@ + + + + +smallantimagmas automatic generated documentation + +
+smallantimagmas automatic generated documentation of properties + + + + true or false + + + identifies whether magma M is antiassociative. +

+ IsAntiassociative(OneSmallGroup(16)); +false +gap> IsAntiassociative(OneSmallAntimagma(2)); +true +gap> IsAntiassociative(OneSmallAntimagma(3)); +true +]]> + + +

+ + + + + + + true or false + + + if magma is left cyclic m. + + + + + + + true or false + + + if magma is left cyclic m. + + + + + + + true or false + + + if magma is left cancellative m. +

+ M := SmallAntimagma(2, 1); + +gap> Display( MultiplicationTable(M) ); +[ [ 2, 1 ], + [ 2, 1 ] ] +gap> IsRightCancellative(M); +false +gap> IsLeftCancellative(M); +true +gap> List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M)); +[ true, false ] +]]> + + +

+ + + + + + + true or false + + + if magma is right cancellative m. +

+ List(AllSmallAntimagmas(2), M -> IsRightCancellative(M)); +[ false, true ] +]]> + + +

+ + + + + + + true or false + + + if magma is cancellative m. +

+ List(AllSmallAntimagmas(2), M -> IsCancellative(M)); +[ false, false ] +]]> + + +

+ + + + +

+ + +
+smallantimagmas automatic generated documentation of attributes + + + + + identifies associativity index of M. +

+ OneSmallAntimagma(2); + +gap> AssociativityIndex(OneSmallAntimagma(2)); +0 +gap> OneSmallGroup(4); + +gap> AssociativityIndex(OneSmallGroup(4)); +64 +gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3; +true +]]> + + +

+ + + + + + + + computes diaognal of multiplication table of M. +

+ List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M))); +[ [ 2, 1, 1 ], [ 2, 1, 1 ], + [ 2, 3, 2 ], [ 2, 1, 1 ], + [ 2, 1, 1 ], [ 2, 1, 2 ], + [ 2, 3, 2 ], [ 2, 1, 2 ], + [ 2, 3, 1 ], [ 2, 3, 1 ] +] +]]> + + +

+ + + + + + + + identifies commutativity index of M. +

+ + + +

+ + + + + + + + calculates anticommutativity index of M. +

+ + + +

+ + + + + + + + computes squares index of M so the order of \left\{ m^2 | m \in \right\}. +

+ List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) ); +[ [ m2, m1 ], [ m2, m1 ] ] +gap> List(AllSmallAntimagmas(2), M -> SquaresIndex(M )); +[ 2, 2 ] +gap> List(AllSmallAntimagmas(3), M -> SquaresIndex(M )); +[ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ] +]]> + + +

+ + + + + + + + identifies class of antiassociative magma M. +

+ IsAntiassociative(OneSmallGroup(16)); +false +gap> IsAntiassociative(OneSmallAntimagma(2)); +true +gap> IsAntiassociative(OneSmallAntimagma(3)); +true +]]> + + +

+ + + + + + + + returns a left order of element m. + + + + + + + + returns a right order of element m. + + + + + + + + returns a left order of element m. + + + + + + + + returns a left order of element m. + + + + +

+ + +
+smallantimagmas automatic generated documentation of global functions + + + + + builds a collection of non-isomorphic submagmas of M. +

+ AllSmallAntimagmas(2); +[ , ] +gap> List(AllSmallAntimagmas(2), M -> AllSubmagmas(M)); +[ [ ], [ ] ] +]]> + + +

+ + + + + + + + computes isomorphism invariants of M. + + + + + + + + identifies whether magmas M, N are isomorphic. +

+ M := SmallAntimagma(2, 1); + +gap> N := SmallAntimagma(2, 2); + +gap> T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]); + +gap> IsMagmaIsomorphic(M, M); +true +gap> IsMagmaIsomorphic(M, T); +true +gap> IsMagmaIsomorphic(M, N); +false +]]> + + +

+ + + + + + + + identifies whether magmas M, N are antiisomorphic. +

+ N := SmallAntimagma(2, 1); + +gap> M := SmallAntimagma(2, 1); + +gap> N := SmallAntimagma(2, 2); + +gap> IsMagmaAntiisomorphic(M, M); +false +gap> IsMagmaAntiisomorphic(M, N); +true +gap> IsMagmaAntiisomorphic(M, TransposedMagma(M)); +true +]]> + + +

+ + + + + + + + generates transposed magma M. +

+ M := SmallAntimagma(2, 1); + +gap> IsMagmaAntiisomorphic(M, TransposedMagma(M)); +true +gap> IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M))); +true +gap> M := SmallAntimagma(2, 1); + +gap> Display(MultiplicationTable(M)); +[ [ 2, 1 ], + [ 2, 1 ] ] +gap> Display(MultiplicationTable(TransposedMagma(M))); +[ [ 2, 2 ], + [ 1, 1 ] ] +]]> + + +

+ + + + + + + + returns a left k-power of element m. + + + + + + + + returns a right k-power of element m. + + + + + + + + returns all antiassociative magmas of specified size n (a number) +

+ AllSmallAntimagmas(2); +[ , ] +gap> AllSmallAntimagmas(3); +[ + , , , + , , , + , , + , +] +]]> + + +

+ + + + + + + + counts number of antiassociative magmas of specified size n (a number). +

+ NrSmallAntimagmas(2); +2 +gap> NrSmallAntimagmas(3); +10 +gap> NrSmallAntimagmas(4); +17780 +]]> + + +

+ + + + + + + + returns antiassociative magma of id [n, i]. +

+ SmallAntimagma(2, 1); + +gap> SmallAntimagma(4, 5); + +]]> + + +

+ + + + + + + + returns a random antiassociative magma of size n. +

+ OneSmallAntimagma(2); + + +gap> OneSmallAntimagma(3); + +]]> + + +

+ + + + + + + + returns really-all antiassociative magmas, isomorphic, of specified size n (a number) +

+ ReallyAllSmallAntimagmas(2); +[ , ] +]]> + + +

+ + + + + + + + counts number of antiassociative magmas of specified size n (a number) +

+ ReallyNrSmallAntimagmas(3); +52 +]]> + + +

+ + + + + + + + returns all possible diagonals of multiplication table for [n]-antimagma. +

+ AntimagmaGeneratorPossibleDiagonals(2); +[ [ 2, 1 ] ] +gap> AntimagmaGeneratorPossibleDiagonals(3); +[ + [ 2, 1, 1 ], [ 2, 1, 2 ], [ 2, 3, 1 ], [ 2, 3, 2 ], + [ 3, 1, 1 ], [ 3, 1, 2 ], [ 3, 3, 1 ], [ 3, 3, 2 ] +] +]]> + + +

+ + + + + + + + filters non-isomorphic magmas m. + + + + +

+ + +
+smallantimagmas automatic generated documentation of methods + + + + + computes an isomoprhism between magmas M, N. +

+ M := SmallAntimagma(2, 1); + +gap> N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]); + +gap> MagmaIsomorphism(M, N); + Domain([ m1, m2 ]) > +]]> + + +

+ + + + + + + + creates an antiisomoprhism between magmas M, N. +

+ M := SmallAntimagma(2, 1); + +gap> N := SmallAntimagma(2, 2); + +gap> MagmaAntiisomorphism(M, N); + Domain([ m1, m2 ]) > +]]> + + +

+ + + + +

+ + + + diff --git a/doc/_Chunks.xml b/doc/_Chunks.xml new file mode 100644 index 0000000..e69de29 diff --git a/doc/_entities.xml b/doc/_entities.xml new file mode 100644 index 0000000..529f621 --- /dev/null +++ b/doc/_entities.xml @@ -0,0 +1 @@ +smallantimagmas'> diff --git a/doc/chap0.html b/doc/chap0.html new file mode 100644 index 0000000..bbe289d --- /dev/null +++ b/doc/chap0.html @@ -0,0 +1,125 @@ + + + + + + +GAP (smallantimagmas) - Contents + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
 [Top of Book]  [Contents]   [Next Chapter] 
+ + +

+
+ +

smallantimagmas

+ + +

A fork of smallgrp package for small antiassociative magmas

+ +

+ 0.2.0

+ +

+ 28 August 2024 +

+ +
+

+ Kamil Zabielski + + + +
Address:
Department of Theoretical Computer Science
Białystok University of Technology
Wiejska 45A
15-325 Białystok
Poland
+

+ +

+

Copyright

+

© 2024 by Kamil Zabielski

+ +

smallantimagmas package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

+ +

+

Acknowledgements

+

We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by GAP users and developers.

+ +

+ +
+

Contents

+ +
1 smallantimagmas automatic generated documentation +
 1.1 smallantimagmas automatic generated documentation of properties + +
+
  1.1-1 IsAntiassociative +
  1.1-2 IsLeftCyclic +
  1.1-3 IsRightCyclic +
  1.1-4 IsLeftCancellative +
  1.1-5 IsRightCancellative +
  1.1-6 IsCancellative +
+
 1.2 smallantimagmas automatic generated documentation of attributes + +
+
  1.2-1 AssociativityIndex +
  1.2-2 DiagonalOfMultiplicationTable +
  1.2-3 CommutativityIndex +
  1.2-4 AnticommutativityIndex +
  1.2-5 SquaresIndex +
  1.2-6 IdSmallAntimagma +
  1.2-7 LeftOrder +
  1.2-8 RightOrder +
  1.2-9 LeftOrdersOfElements +
  1.2-10 RightOrdersOfElements +
+
 1.3 smallantimagmas automatic generated documentation of global functions + +
+
  1.3-1 AllSubmagmas +
  1.3-2 MagmaIsomorphismInvariantsMatch +
  1.3-3 IsMagmaIsomorphic +
  1.3-4 IsMagmaAntiisomorphic +
  1.3-5 TransposedMagma +
  1.3-6 LeftPower +
  1.3-7 RightPower +
  1.3-8 AllSmallAntimagmas +
  1.3-9 NrSmallAntimagmas +
  1.3-10 SmallAntimagma +
  1.3-11 OneSmallAntimagma +
  1.3-12 ReallyAllSmallAntimagmas +
  1.3-13 ReallyNrSmallAntimagmas +
  1.3-14 AntimagmaGeneratorPossibleDiagonals +
  1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas +
+
 1.4 smallantimagmas automatic generated documentation of methods + +
+
  1.4-1 MagmaIsomorphism +
  1.4-2 MagmaAntiisomorphism +
+
+
Index
+
+
+ +
 [Top of Book]  [Contents]   [Next Chapter] 
+ + +
Goto Chapter: Top 1 Ind
+ +
+

generated by GAPDoc2HTML

+ + diff --git a/doc/chap0.txt b/doc/chap0.txt new file mode 100644 index 0000000..fe9d891 --- /dev/null +++ b/doc/chap0.txt @@ -0,0 +1,83 @@ + + +  smallantimagmas  + + +  A fork of smallgrp package for small antiassociative magmas  + + + 0.2.0 + + + 28 August 2024 + + + Kamil Zabielski + + + + + ------------------------------------------------------- + Copyright + © 2024 by Kamil Zabielski + + smallantimagmas package is free software; you can redistribute it and/or + modify it under the terms of the GNU General Public License + (http://www.fsf.org/licenses/gpl.html) as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any later + version. + + + ------------------------------------------------------- + Acknowledgements + We appreciate very much all past and future comments, suggestions and + contributions to this package and its documentation provided by GAP users + and developers. + + + ------------------------------------------------------- + + + Contents (smallantimagmas) + + 1 smallantimagmas automatic generated documentation + 1.1 smallantimagmas automatic generated documentation of properties + 1.1-1 IsAntiassociative + 1.1-2 IsLeftCyclic + 1.1-3 IsRightCyclic + 1.1-4 IsLeftCancellative + 1.1-5 IsRightCancellative + 1.1-6 IsCancellative + 1.2 smallantimagmas automatic generated documentation of attributes + 1.2-1 AssociativityIndex + 1.2-2 DiagonalOfMultiplicationTable + 1.2-3 CommutativityIndex + 1.2-4 AnticommutativityIndex + 1.2-5 SquaresIndex + 1.2-6 IdSmallAntimagma + 1.2-7 LeftOrder + 1.2-8 RightOrder + 1.2-9 LeftOrdersOfElements + 1.2-10 RightOrdersOfElements + 1.3 smallantimagmas automatic generated documentation of global functions + 1.3-1 AllSubmagmas + 1.3-2 MagmaIsomorphismInvariantsMatch + 1.3-3 IsMagmaIsomorphic + 1.3-4 IsMagmaAntiisomorphic + 1.3-5 TransposedMagma + 1.3-6 LeftPower + 1.3-7 RightPower + 1.3-8 AllSmallAntimagmas + 1.3-9 NrSmallAntimagmas + 1.3-10 SmallAntimagma + 1.3-11 OneSmallAntimagma + 1.3-12 ReallyAllSmallAntimagmas + 1.3-13 ReallyNrSmallAntimagmas + 1.3-14 AntimagmaGeneratorPossibleDiagonals + 1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas + 1.4 smallantimagmas automatic generated documentation of methods + 1.4-1 MagmaIsomorphism + 1.4-2 MagmaAntiisomorphism + + +  diff --git a/doc/chap0_mj.html b/doc/chap0_mj.html new file mode 100644 index 0000000..359a701 --- /dev/null +++ b/doc/chap0_mj.html @@ -0,0 +1,128 @@ + + + + + + + +GAP (smallantimagmas) - Contents + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
 [Top of Book]  [Contents]   [Next Chapter] 
+ + +

+
+ +

smallantimagmas

+ + +

A fork of smallgrp package for small antiassociative magmas

+ +

+ 0.2.0

+ +

+ 28 August 2024 +

+ +
+

+ Kamil Zabielski + + + +
Address:
Department of Theoretical Computer Science
Białystok University of Technology
Wiejska 45A
15-325 Białystok
Poland
+

+ +

+

Copyright

+

© 2024 by Kamil Zabielski

+ +

smallantimagmas package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

+ +

+

Acknowledgements

+

We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by GAP users and developers.

+ +

+ +
+

Contents

+ +
1 smallantimagmas automatic generated documentation +
 1.1 smallantimagmas automatic generated documentation of properties + +
+
  1.1-1 IsAntiassociative +
  1.1-2 IsLeftCyclic +
  1.1-3 IsRightCyclic +
  1.1-4 IsLeftCancellative +
  1.1-5 IsRightCancellative +
  1.1-6 IsCancellative +
+
 1.2 smallantimagmas automatic generated documentation of attributes + +
+
  1.2-1 AssociativityIndex +
  1.2-2 DiagonalOfMultiplicationTable +
  1.2-3 CommutativityIndex +
  1.2-4 AnticommutativityIndex +
  1.2-5 SquaresIndex +
  1.2-6 IdSmallAntimagma +
  1.2-7 LeftOrder +
  1.2-8 RightOrder +
  1.2-9 LeftOrdersOfElements +
  1.2-10 RightOrdersOfElements +
+
 1.3 smallantimagmas automatic generated documentation of global functions + +
+
  1.3-1 AllSubmagmas +
  1.3-2 MagmaIsomorphismInvariantsMatch +
  1.3-3 IsMagmaIsomorphic +
  1.3-4 IsMagmaAntiisomorphic +
  1.3-5 TransposedMagma +
  1.3-6 LeftPower +
  1.3-7 RightPower +
  1.3-8 AllSmallAntimagmas +
  1.3-9 NrSmallAntimagmas +
  1.3-10 SmallAntimagma +
  1.3-11 OneSmallAntimagma +
  1.3-12 ReallyAllSmallAntimagmas +
  1.3-13 ReallyNrSmallAntimagmas +
  1.3-14 AntimagmaGeneratorPossibleDiagonals +
  1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas +
+
 1.4 smallantimagmas automatic generated documentation of methods + +
+
  1.4-1 MagmaIsomorphism +
  1.4-2 MagmaAntiisomorphism +
+
+
Index
+
+
+ +
 [Top of Book]  [Contents]   [Next Chapter] 
+ + +
Goto Chapter: Top 1 Ind
+ +
+

generated by GAPDoc2HTML

+ + diff --git a/doc/chap1.html b/doc/chap1.html new file mode 100644 index 0000000..35570e9 --- /dev/null +++ b/doc/chap1.html @@ -0,0 +1,578 @@ + + + + + + +GAP (smallantimagmas) - Chapter 1: smallantimagmas automatic generated documentation + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
+ + +

+
1 smallantimagmas automatic generated documentation +
 1.1 smallantimagmas automatic generated documentation of properties + +
+
  1.1-1 IsAntiassociative +
  1.1-2 IsLeftCyclic +
  1.1-3 IsRightCyclic +
  1.1-4 IsLeftCancellative +
  1.1-5 IsRightCancellative +
  1.1-6 IsCancellative +
+
 1.2 smallantimagmas automatic generated documentation of attributes + +
+
  1.2-1 AssociativityIndex +
  1.2-2 DiagonalOfMultiplicationTable +
  1.2-3 CommutativityIndex +
  1.2-4 AnticommutativityIndex +
  1.2-5 SquaresIndex +
  1.2-6 IdSmallAntimagma +
  1.2-7 LeftOrder +
  1.2-8 RightOrder +
  1.2-9 LeftOrdersOfElements +
  1.2-10 RightOrdersOfElements +
+
 1.3 smallantimagmas automatic generated documentation of global functions + +
+
  1.3-1 AllSubmagmas +
  1.3-2 MagmaIsomorphismInvariantsMatch +
  1.3-3 IsMagmaIsomorphic +
  1.3-4 IsMagmaAntiisomorphic +
  1.3-5 TransposedMagma +
  1.3-6 LeftPower +
  1.3-7 RightPower +
  1.3-8 AllSmallAntimagmas +
  1.3-9 NrSmallAntimagmas +
  1.3-10 SmallAntimagma +
  1.3-11 OneSmallAntimagma +
  1.3-12 ReallyAllSmallAntimagmas +
  1.3-13 ReallyNrSmallAntimagmas +
  1.3-14 AntimagmaGeneratorPossibleDiagonals +
  1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas +
+
 1.4 smallantimagmas automatic generated documentation of methods + +
+
  1.4-1 MagmaIsomorphism +
  1.4-2 MagmaAntiisomorphism +
+
+ +

1 smallantimagmas automatic generated documentation

+ +

+ +

1.1 smallantimagmas automatic generated documentation of properties

+ +

+ +
1.1-1 IsAntiassociative
+ +
‣ IsAntiassociative( M )( property )
+

Returns: true or false

+ +

identifies whether magma M is antiassociative.

+ + +
+gap> IsAntiassociative(OneSmallGroup(16));
+false
+gap> IsAntiassociative(OneSmallAntimagma(2));
+true
+gap> IsAntiassociative(OneSmallAntimagma(3));
+true
+
+ +

+ +
1.1-2 IsLeftCyclic
+ +
‣ IsLeftCyclic( M )( property )
+

Returns: true or false

+ +

if magma is left cyclic m.

+ +

+ +
1.1-3 IsRightCyclic
+ +
‣ IsRightCyclic( M )( property )
+

Returns: true or false

+ +

if magma is left cyclic m.

+ +

+ +
1.1-4 IsLeftCancellative
+ +
‣ IsLeftCancellative( M )( property )
+

Returns: true or false

+ +

if magma is left cancellative m.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> Display( MultiplicationTable(M) );
+[ [  2,  1 ],
+  [  2,  1 ] ]
+gap> IsRightCancellative(M);
+false
+gap> IsLeftCancellative(M);
+true
+gap> List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M));
+[ true, false ]
+
+ +

+ +
1.1-5 IsRightCancellative
+ +
‣ IsRightCancellative( M )( property )
+

Returns: true or false

+ +

if magma is right cancellative m.

+ + +
+gap> List(AllSmallAntimagmas(2), M -> IsRightCancellative(M));
+[ false, true ]
+
+ +

+ +
1.1-6 IsCancellative
+ +
‣ IsCancellative( M )( property )
+

Returns: true or false

+ +

if magma is cancellative m.

+ + +
+gap> List(AllSmallAntimagmas(2), M -> IsCancellative(M));
+[ false, false ]
+
+ +

+ +

1.2 smallantimagmas automatic generated documentation of attributes

+ +

+ +
1.2-1 AssociativityIndex
+ +
‣ AssociativityIndex( M )( attribute )
+

identifies associativity index of M.

+ + +
+gap> OneSmallAntimagma(2);
+<magma with 2 generators>
+gap> AssociativityIndex(OneSmallAntimagma(2));
+0
+gap> OneSmallGroup(4);
+<pc group of size 4 with 2 generators>
+gap> AssociativityIndex(OneSmallGroup(4));
+64
+gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3;
+true
+
+ +

+ +
1.2-2 DiagonalOfMultiplicationTable
+ +
‣ DiagonalOfMultiplicationTable( M )( attribute )
+

computes diaognal of multiplication table of M.

+ + +
+gap> List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M)));                
+[ [ 2, 1, 1 ], [ 2, 1, 1 ], 
+  [ 2, 3, 2 ], [ 2, 1, 1 ], 
+  [ 2, 1, 1 ], [ 2, 1, 2 ], 
+  [ 2, 3, 2 ], [ 2, 1, 2 ], 
+  [ 2, 3, 1 ], [ 2, 3, 1 ]
+]
+
+ +

+ +
1.2-3 CommutativityIndex
+ +
‣ CommutativityIndex( M )( attribute )
+

identifies commutativity index of M.

+ + +
+
+
+ +

+ +
1.2-4 AnticommutativityIndex
+ +
‣ AnticommutativityIndex( M )( attribute )
+

calculates anticommutativity index of M.

+ + +
+
+ +

+ +
1.2-5 SquaresIndex
+ +
‣ SquaresIndex( M )( attribute )
+

computes squares index of M so the order of \left\{ m^2 | m \in \right\}.

+ + +
+gap> List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) );                
+[ [ m2, m1 ], [ m2, m1 ] ]
+gap> List(AllSmallAntimagmas(2), M -> SquaresIndex(M ));
+[ 2, 2 ]
+gap> List(AllSmallAntimagmas(3), M -> SquaresIndex(M ));
+[ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]
+
+ +

+ +
1.2-6 IdSmallAntimagma
+ +
‣ IdSmallAntimagma( M )( attribute )
+

identifies class of antiassociative magma M.

+ + +
+gap> IsAntiassociative(OneSmallGroup(16));
+false
+gap> IsAntiassociative(OneSmallAntimagma(2));
+true
+gap> IsAntiassociative(OneSmallAntimagma(3));
+true
+
+ +

+ +
1.2-7 LeftOrder
+ +
‣ LeftOrder( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +
1.2-8 RightOrder
+ +
‣ RightOrder( [m] )( attribute )
+

returns a right order of element m.

+ +

+ +
1.2-9 LeftOrdersOfElements
+ +
‣ LeftOrdersOfElements( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +
1.2-10 RightOrdersOfElements
+ +
‣ RightOrdersOfElements( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +

1.3 smallantimagmas automatic generated documentation of global functions

+ +

+ +
1.3-1 AllSubmagmas
+ +
‣ AllSubmagmas( M )( function )
+

builds a collection of non-isomorphic submagmas of M.

+ + +
+gap> AllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+gap> List(AllSmallAntimagmas(2), M -> AllSubmagmas(M));
+[ [ <magma with 1 generator> ], [ <magma with 1 generator> ] ]
+
+ +

+ +
1.3-2 MagmaIsomorphismInvariantsMatch
+ +
‣ MagmaIsomorphismInvariantsMatch( M )( function )
+

computes isomorphism invariants of M.

+ +

+ +
1.3-3 IsMagmaIsomorphic
+ +
‣ IsMagmaIsomorphic( M, N )( function )
+

identifies whether magmas M, N are isomorphic.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
+<magma with 2 generators>
+gap> IsMagmaIsomorphic(M, M);
+true
+gap> IsMagmaIsomorphic(M, T);
+true
+gap> IsMagmaIsomorphic(M, N);
+false
+
+ +

+ +
1.3-4 IsMagmaAntiisomorphic
+ +
‣ IsMagmaAntiisomorphic( [M, N] )( function )
+

identifies whether magmas M, N are antiisomorphic.

+ + +
+gap> N := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> IsMagmaAntiisomorphic(M, M);
+false
+gap> IsMagmaAntiisomorphic(M, N);
+true
+gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
+true
+
+ +

+ +
1.3-5 TransposedMagma
+ +
‣ TransposedMagma( [M] )( function )
+

generates transposed magma M.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
+true
+gap> IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M)));
+true
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> Display(MultiplicationTable(M));
+[ [  2,  1 ],
+  [  2,  1 ] ]
+gap> Display(MultiplicationTable(TransposedMagma(M)));
+[ [  2,  2 ],
+  [  1,  1 ] ]
+
+ +

+ +
1.3-6 LeftPower
+ +
‣ LeftPower( [m, k] )( function )
+

returns a left k-power of element m.

+ +

+ +
1.3-7 RightPower
+ +
‣ RightPower( [m, k] )( function )
+

returns a right k-power of element m.

+ +

+ +
1.3-8 AllSmallAntimagmas
+ +
‣ AllSmallAntimagmas( n )( function )
+

returns all antiassociative magmas of specified size n (a number)

+ + +
+gap> AllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+gap> AllSmallAntimagmas(3);
+[ 
+  <magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>
+]
+
+ +

+ +
1.3-9 NrSmallAntimagmas
+ +
‣ NrSmallAntimagmas( n )( function )
+

counts number of antiassociative magmas of specified size n (a number).

+ + +
+gap> NrSmallAntimagmas(2);
+2
+gap> NrSmallAntimagmas(3);
+10
+gap> NrSmallAntimagmas(4);
+17780
+
+ +

+ +
1.3-10 SmallAntimagma
+ +
‣ SmallAntimagma( n, i )( function )
+

returns antiassociative magma of id [n, i].

+ + +
+gap> SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> SmallAntimagma(4, 5);
+<magma with 4 generators>
+
+ +

+ +
1.3-11 OneSmallAntimagma
+ +
‣ OneSmallAntimagma( n )( function )
+

returns a random antiassociative magma of size n.

+ + +
+gap> OneSmallAntimagma(2);
+<magma with 2 generators>
+
+gap> OneSmallAntimagma(3);
+<magma with 3 generators>
+
+ +

+ +
1.3-12 ReallyAllSmallAntimagmas
+ +
‣ ReallyAllSmallAntimagmas( n )( function )
+

returns really-all antiassociative magmas, isomorphic, of specified size n (a number)

+ + +
+gap> ReallyAllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+
+ +

+ +
1.3-13 ReallyNrSmallAntimagmas
+ +
‣ ReallyNrSmallAntimagmas( n )( function )
+

counts number of antiassociative magmas of specified size n (a number)

+ + +
+gap> ReallyNrSmallAntimagmas(3);
+52
+
+ +

+ +
1.3-14 AntimagmaGeneratorPossibleDiagonals
+ +
‣ AntimagmaGeneratorPossibleDiagonals( n )( function )
+

returns all possible diagonals of multiplication table for [n]-antimagma.

+ + +
+gap> AntimagmaGeneratorPossibleDiagonals(2);
+[ [ 2, 1 ] ]
+gap> AntimagmaGeneratorPossibleDiagonals(3);
+[ 
+  [ 2, 1, 1 ], [ 2, 1, 2 ], [ 2, 3, 1 ], [ 2, 3, 2 ], 
+  [ 3, 1, 1 ], [ 3, 1, 2 ], [ 3, 3, 1 ], [ 3, 3, 2 ] 
+]
+
+ +

+ +
1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas
+ +
‣ AntimagmaGeneratorFilterNonIsomorphicMagmas( Ms )( function )
+

filters non-isomorphic magmas m.

+ +

+ +

1.4 smallantimagmas automatic generated documentation of methods

+ +

+ +
1.4-1 MagmaIsomorphism
+ +
‣ MagmaIsomorphism( M, N )( operation )
+

computes an isomoprhism between magmas M, N.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
+<magma with 2 generators>
+gap> MagmaIsomorphism(M, N);
+<mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
+
+ +

+ +
1.4-2 MagmaAntiisomorphism
+ +
‣ MagmaAntiisomorphism( M, N )( operation )
+

creates an antiisomoprhism between magmas M, N.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> MagmaAntiisomorphism(M, N);
+<mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
+
+ + +
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
+ + +
Goto Chapter: Top 1 Ind
+ +
+

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+ + diff --git a/doc/chap1.txt b/doc/chap1.txt new file mode 100644 index 0000000..7a7bc52 --- /dev/null +++ b/doc/chap1.txt @@ -0,0 +1,429 @@ + + 1 smallantimagmas automatic generated documentation + + + 1.1 smallantimagmas automatic generated documentation of properties + + 1.1-1 IsAntiassociative + + IsAntiassociative( M )  property + Returns: true or false + + identifies whether magma M is antiassociative. + +  Example  + gap> IsAntiassociative(OneSmallGroup(16)); + false + gap> IsAntiassociative(OneSmallAntimagma(2)); + true + gap> IsAntiassociative(OneSmallAntimagma(3)); + true +  + + 1.1-2 IsLeftCyclic + + IsLeftCyclic( M )  property + Returns: true or false + + if magma is left cyclic m. + + 1.1-3 IsRightCyclic + + IsRightCyclic( M )  property + Returns: true or false + + if magma is left cyclic m. + + 1.1-4 IsLeftCancellative + + IsLeftCancellative( M )  property + Returns: true or false + + if magma is left cancellative m. + +  Example  + gap> M := SmallAntimagma(2, 1); +  + gap> Display( MultiplicationTable(M) ); + [ [ 2, 1 ], +  [ 2, 1 ] ] + gap> IsRightCancellative(M); + false + gap> IsLeftCancellative(M); + true + gap> List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M)); + [ true, false ] +  + + 1.1-5 IsRightCancellative + + IsRightCancellative( M )  property + Returns: true or false + + if magma is right cancellative m. + +  Example  + gap> List(AllSmallAntimagmas(2), M -> IsRightCancellative(M)); + [ false, true ] +  + + 1.1-6 IsCancellative + + IsCancellative( M )  property + Returns: true or false + + if magma is cancellative m. + +  Example  + gap> List(AllSmallAntimagmas(2), M -> IsCancellative(M)); + [ false, false ] +  + + + 1.2 smallantimagmas automatic generated documentation of attributes + + 1.2-1 AssociativityIndex + + AssociativityIndex( M )  attribute + + identifies associativity index of M. + +  Example  + gap> OneSmallAntimagma(2); +  + gap> AssociativityIndex(OneSmallAntimagma(2)); + 0 + gap> OneSmallGroup(4); +  + gap> AssociativityIndex(OneSmallGroup(4)); + 64 + gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3; + true +  + + 1.2-2 DiagonalOfMultiplicationTable + + DiagonalOfMultiplicationTable( M )  attribute + + computes diaognal of multiplication table of M. + +  Example  + gap> List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M)));  + [ [ 2, 1, 1 ], [ 2, 1, 1 ],  +  [ 2, 3, 2 ], [ 2, 1, 1 ],  +  [ 2, 1, 1 ], [ 2, 1, 2 ],  +  [ 2, 3, 2 ], [ 2, 1, 2 ],  +  [ 2, 3, 1 ], [ 2, 3, 1 ] + ] +  + + 1.2-3 CommutativityIndex + + CommutativityIndex( M )  attribute + + identifies commutativity index of M. + +  Example  +  +  + + 1.2-4 AnticommutativityIndex + + AnticommutativityIndex( M )  attribute + + calculates anticommutativity index of M. + +  Example  +  + + 1.2-5 SquaresIndex + + SquaresIndex( M )  attribute + + computes squares index of M so the order of \left\{ m^2 | m \in \right\}. + +  Example  + gap> List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) );  + [ [ m2, m1 ], [ m2, m1 ] ] + gap> List(AllSmallAntimagmas(2), M -> SquaresIndex(M )); + [ 2, 2 ] + gap> List(AllSmallAntimagmas(3), M -> SquaresIndex(M )); + [ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ] +  + + 1.2-6 IdSmallAntimagma + + IdSmallAntimagma( M )  attribute + + identifies class of antiassociative magma M. + +  Example  + gap> IsAntiassociative(OneSmallGroup(16)); + false + gap> IsAntiassociative(OneSmallAntimagma(2)); + true + gap> IsAntiassociative(OneSmallAntimagma(3)); + true +  + + 1.2-7 LeftOrder + + LeftOrder( [m] )  attribute + + returns a left order of element m. + + 1.2-8 RightOrder + + RightOrder( [m] )  attribute + + returns a right order of element m. + + 1.2-9 LeftOrdersOfElements + + LeftOrdersOfElements( [m] )  attribute + + returns a left order of element m. + + 1.2-10 RightOrdersOfElements + + RightOrdersOfElements( [m] )  attribute + + returns a left order of element m. + + + 1.3 smallantimagmas automatic generated documentation of global functions + + 1.3-1 AllSubmagmas + + AllSubmagmas( M )  function + + builds a collection of non-isomorphic submagmas of M. + +  Example  + gap> AllSmallAntimagmas(2); + [ , ] + gap> List(AllSmallAntimagmas(2), M -> AllSubmagmas(M)); + [ [ ], [ ] ] +  + + 1.3-2 MagmaIsomorphismInvariantsMatch + + MagmaIsomorphismInvariantsMatch( M )  function + + computes isomorphism invariants of M. + + 1.3-3 IsMagmaIsomorphic + + IsMagmaIsomorphic( M, N )  function + + identifies whether magmas M, N are isomorphic. + +  Example  + gap> M := SmallAntimagma(2, 1); +  + gap> N := SmallAntimagma(2, 2); +  + gap> T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]); +  + gap> IsMagmaIsomorphic(M, M); + true + gap> IsMagmaIsomorphic(M, T); + true + gap> IsMagmaIsomorphic(M, N); + false +  + + 1.3-4 IsMagmaAntiisomorphic + + IsMagmaAntiisomorphic( [M, N] )  function + + identifies whether magmas M, N are antiisomorphic. + +  Example  + gap> N := SmallAntimagma(2, 1); +  + gap> M := SmallAntimagma(2, 1); +  + gap> N := SmallAntimagma(2, 2); +  + gap> IsMagmaAntiisomorphic(M, M); + false + gap> IsMagmaAntiisomorphic(M, N); + true + gap> IsMagmaAntiisomorphic(M, TransposedMagma(M)); + true +  + + 1.3-5 TransposedMagma + + TransposedMagma( [M] )  function + + generates transposed magma M. + +  Example  + gap> M := SmallAntimagma(2, 1); +  + gap> IsMagmaAntiisomorphic(M, TransposedMagma(M)); + true + gap> IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M))); + true + gap> M := SmallAntimagma(2, 1); +  + gap> Display(MultiplicationTable(M)); + [ [ 2, 1 ], +  [ 2, 1 ] ] + gap> Display(MultiplicationTable(TransposedMagma(M))); + [ [ 2, 2 ], +  [ 1, 1 ] ] +  + + 1.3-6 LeftPower + + LeftPower( [m, k] )  function + + returns a left k-power of element m. + + 1.3-7 RightPower + + RightPower( [m, k] )  function + + returns a right k-power of element m. + + 1.3-8 AllSmallAntimagmas + + AllSmallAntimagmas( n )  function + + returns all antiassociative magmas of specified size n (a number) + +  Example  + gap> AllSmallAntimagmas(2); + [ , ] + gap> AllSmallAntimagmas(3); + [  +  , , , +  , , , +  , , +  ,  + ] +  + + 1.3-9 NrSmallAntimagmas + + NrSmallAntimagmas( n )  function + + counts number of antiassociative magmas of specified size n (a number). + +  Example  + gap> NrSmallAntimagmas(2); + 2 + gap> NrSmallAntimagmas(3); + 10 + gap> NrSmallAntimagmas(4); + 17780 +  + + 1.3-10 SmallAntimagma + + SmallAntimagma( n, i )  function + + returns antiassociative magma of id [n, i]. + +  Example  + gap> SmallAntimagma(2, 1); +  + gap> SmallAntimagma(4, 5); +  +  + + 1.3-11 OneSmallAntimagma + + OneSmallAntimagma( n )  function + + returns a random antiassociative magma of size n. + +  Example  + gap> OneSmallAntimagma(2); +  +  + gap> OneSmallAntimagma(3); +  +  + + 1.3-12 ReallyAllSmallAntimagmas + + ReallyAllSmallAntimagmas( n )  function + + returns really-all antiassociative magmas, isomorphic, of specified size n + (a number) + +  Example  + gap> ReallyAllSmallAntimagmas(2); + [ , ] +  + + 1.3-13 ReallyNrSmallAntimagmas + + ReallyNrSmallAntimagmas( n )  function + + counts number of antiassociative magmas of specified size n (a number) + +  Example  + gap> ReallyNrSmallAntimagmas(3); + 52 +  + + 1.3-14 AntimagmaGeneratorPossibleDiagonals + + AntimagmaGeneratorPossibleDiagonals( n )  function + + returns all possible diagonals of multiplication table for [n]-antimagma. + +  Example  + gap> AntimagmaGeneratorPossibleDiagonals(2); + [ [ 2, 1 ] ] + gap> AntimagmaGeneratorPossibleDiagonals(3); + [  +  [ 2, 1, 1 ], [ 2, 1, 2 ], [ 2, 3, 1 ], [ 2, 3, 2 ],  +  [ 3, 1, 1 ], [ 3, 1, 2 ], [ 3, 3, 1 ], [ 3, 3, 2 ]  + ] +  + + 1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas + + AntimagmaGeneratorFilterNonIsomorphicMagmas( Ms )  function + + filters non-isomorphic magmas m. + + + 1.4 smallantimagmas automatic generated documentation of methods + + 1.4-1 MagmaIsomorphism + + MagmaIsomorphism( M, N )  operation + + computes an isomoprhism between magmas M, N. + +  Example  + gap> M := SmallAntimagma(2, 1); +  + gap> N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]); +  + gap> MagmaIsomorphism(M, N); +  Domain([ m1, m2 ]) > +  + + 1.4-2 MagmaAntiisomorphism + + MagmaAntiisomorphism( M, N )  operation + + creates an antiisomoprhism between magmas M, N. + +  Example  + gap> M := SmallAntimagma(2, 1); +  + gap> N := SmallAntimagma(2, 2); +  + gap> MagmaAntiisomorphism(M, N); +  Domain([ m1, m2 ]) > +  + diff --git a/doc/chap1_mj.html b/doc/chap1_mj.html new file mode 100644 index 0000000..62785d9 --- /dev/null +++ b/doc/chap1_mj.html @@ -0,0 +1,581 @@ + + + + + + + +GAP (smallantimagmas) - Chapter 1: smallantimagmas automatic generated documentation + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
+ + +

+
1 smallantimagmas automatic generated documentation +
 1.1 smallantimagmas automatic generated documentation of properties + +
+
  1.1-1 IsAntiassociative +
  1.1-2 IsLeftCyclic +
  1.1-3 IsRightCyclic +
  1.1-4 IsLeftCancellative +
  1.1-5 IsRightCancellative +
  1.1-6 IsCancellative +
+
 1.2 smallantimagmas automatic generated documentation of attributes + +
+
  1.2-1 AssociativityIndex +
  1.2-2 DiagonalOfMultiplicationTable +
  1.2-3 CommutativityIndex +
  1.2-4 AnticommutativityIndex +
  1.2-5 SquaresIndex +
  1.2-6 IdSmallAntimagma +
  1.2-7 LeftOrder +
  1.2-8 RightOrder +
  1.2-9 LeftOrdersOfElements +
  1.2-10 RightOrdersOfElements +
+
 1.3 smallantimagmas automatic generated documentation of global functions + +
+
  1.3-1 AllSubmagmas +
  1.3-2 MagmaIsomorphismInvariantsMatch +
  1.3-3 IsMagmaIsomorphic +
  1.3-4 IsMagmaAntiisomorphic +
  1.3-5 TransposedMagma +
  1.3-6 LeftPower +
  1.3-7 RightPower +
  1.3-8 AllSmallAntimagmas +
  1.3-9 NrSmallAntimagmas +
  1.3-10 SmallAntimagma +
  1.3-11 OneSmallAntimagma +
  1.3-12 ReallyAllSmallAntimagmas +
  1.3-13 ReallyNrSmallAntimagmas +
  1.3-14 AntimagmaGeneratorPossibleDiagonals +
  1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas +
+
 1.4 smallantimagmas automatic generated documentation of methods + +
+
  1.4-1 MagmaIsomorphism +
  1.4-2 MagmaAntiisomorphism +
+
+ +

1 smallantimagmas automatic generated documentation

+ +

+ +

1.1 smallantimagmas automatic generated documentation of properties

+ +

+ +
1.1-1 IsAntiassociative
+ +
‣ IsAntiassociative( M )( property )
+

Returns: true or false

+ +

identifies whether magma M is antiassociative.

+ + +
+gap> IsAntiassociative(OneSmallGroup(16));
+false
+gap> IsAntiassociative(OneSmallAntimagma(2));
+true
+gap> IsAntiassociative(OneSmallAntimagma(3));
+true
+
+ +

+ +
1.1-2 IsLeftCyclic
+ +
‣ IsLeftCyclic( M )( property )
+

Returns: true or false

+ +

if magma is left cyclic m.

+ +

+ +
1.1-3 IsRightCyclic
+ +
‣ IsRightCyclic( M )( property )
+

Returns: true or false

+ +

if magma is left cyclic m.

+ +

+ +
1.1-4 IsLeftCancellative
+ +
‣ IsLeftCancellative( M )( property )
+

Returns: true or false

+ +

if magma is left cancellative m.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> Display( MultiplicationTable(M) );
+[ [  2,  1 ],
+  [  2,  1 ] ]
+gap> IsRightCancellative(M);
+false
+gap> IsLeftCancellative(M);
+true
+gap> List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M));
+[ true, false ]
+
+ +

+ +
1.1-5 IsRightCancellative
+ +
‣ IsRightCancellative( M )( property )
+

Returns: true or false

+ +

if magma is right cancellative m.

+ + +
+gap> List(AllSmallAntimagmas(2), M -> IsRightCancellative(M));
+[ false, true ]
+
+ +

+ +
1.1-6 IsCancellative
+ +
‣ IsCancellative( M )( property )
+

Returns: true or false

+ +

if magma is cancellative m.

+ + +
+gap> List(AllSmallAntimagmas(2), M -> IsCancellative(M));
+[ false, false ]
+
+ +

+ +

1.2 smallantimagmas automatic generated documentation of attributes

+ +

+ +
1.2-1 AssociativityIndex
+ +
‣ AssociativityIndex( M )( attribute )
+

identifies associativity index of M.

+ + +
+gap> OneSmallAntimagma(2);
+<magma with 2 generators>
+gap> AssociativityIndex(OneSmallAntimagma(2));
+0
+gap> OneSmallGroup(4);
+<pc group of size 4 with 2 generators>
+gap> AssociativityIndex(OneSmallGroup(4));
+64
+gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3;
+true
+
+ +

+ +
1.2-2 DiagonalOfMultiplicationTable
+ +
‣ DiagonalOfMultiplicationTable( M )( attribute )
+

computes diaognal of multiplication table of M.

+ + +
+gap> List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M)));                
+[ [ 2, 1, 1 ], [ 2, 1, 1 ], 
+  [ 2, 3, 2 ], [ 2, 1, 1 ], 
+  [ 2, 1, 1 ], [ 2, 1, 2 ], 
+  [ 2, 3, 2 ], [ 2, 1, 2 ], 
+  [ 2, 3, 1 ], [ 2, 3, 1 ]
+]
+
+ +

+ +
1.2-3 CommutativityIndex
+ +
‣ CommutativityIndex( M )( attribute )
+

identifies commutativity index of M.

+ + +
+
+
+ +

+ +
1.2-4 AnticommutativityIndex
+ +
‣ AnticommutativityIndex( M )( attribute )
+

calculates anticommutativity index of M.

+ + +
+
+ +

+ +
1.2-5 SquaresIndex
+ +
‣ SquaresIndex( M )( attribute )
+

computes squares index of M so the order of \(\left\{ m^2 | m \in \right\}\).

+ + +
+gap> List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) );                
+[ [ m2, m1 ], [ m2, m1 ] ]
+gap> List(AllSmallAntimagmas(2), M -> SquaresIndex(M ));
+[ 2, 2 ]
+gap> List(AllSmallAntimagmas(3), M -> SquaresIndex(M ));
+[ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]
+
+ +

+ +
1.2-6 IdSmallAntimagma
+ +
‣ IdSmallAntimagma( M )( attribute )
+

identifies class of antiassociative magma M.

+ + +
+gap> IsAntiassociative(OneSmallGroup(16));
+false
+gap> IsAntiassociative(OneSmallAntimagma(2));
+true
+gap> IsAntiassociative(OneSmallAntimagma(3));
+true
+
+ +

+ +
1.2-7 LeftOrder
+ +
‣ LeftOrder( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +
1.2-8 RightOrder
+ +
‣ RightOrder( [m] )( attribute )
+

returns a right order of element m.

+ +

+ +
1.2-9 LeftOrdersOfElements
+ +
‣ LeftOrdersOfElements( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +
1.2-10 RightOrdersOfElements
+ +
‣ RightOrdersOfElements( [m] )( attribute )
+

returns a left order of element m.

+ +

+ +

1.3 smallantimagmas automatic generated documentation of global functions

+ +

+ +
1.3-1 AllSubmagmas
+ +
‣ AllSubmagmas( M )( function )
+

builds a collection of non-isomorphic submagmas of M.

+ + +
+gap> AllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+gap> List(AllSmallAntimagmas(2), M -> AllSubmagmas(M));
+[ [ <magma with 1 generator> ], [ <magma with 1 generator> ] ]
+
+ +

+ +
1.3-2 MagmaIsomorphismInvariantsMatch
+ +
‣ MagmaIsomorphismInvariantsMatch( M )( function )
+

computes isomorphism invariants of M.

+ +

+ +
1.3-3 IsMagmaIsomorphic
+ +
‣ IsMagmaIsomorphic( M, N )( function )
+

identifies whether magmas M, N are isomorphic.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
+<magma with 2 generators>
+gap> IsMagmaIsomorphic(M, M);
+true
+gap> IsMagmaIsomorphic(M, T);
+true
+gap> IsMagmaIsomorphic(M, N);
+false
+
+ +

+ +
1.3-4 IsMagmaAntiisomorphic
+ +
‣ IsMagmaAntiisomorphic( [M, N] )( function )
+

identifies whether magmas M, N are antiisomorphic.

+ + +
+gap> N := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> IsMagmaAntiisomorphic(M, M);
+false
+gap> IsMagmaAntiisomorphic(M, N);
+true
+gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
+true
+
+ +

+ +
1.3-5 TransposedMagma
+ +
‣ TransposedMagma( [M] )( function )
+

generates transposed magma M.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
+true
+gap> IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M)));
+true
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> Display(MultiplicationTable(M));
+[ [  2,  1 ],
+  [  2,  1 ] ]
+gap> Display(MultiplicationTable(TransposedMagma(M)));
+[ [  2,  2 ],
+  [  1,  1 ] ]
+
+ +

+ +
1.3-6 LeftPower
+ +
‣ LeftPower( [m, k] )( function )
+

returns a left \(k\)-power of element m.

+ +

+ +
1.3-7 RightPower
+ +
‣ RightPower( [m, k] )( function )
+

returns a right \(k\)-power of element m.

+ +

+ +
1.3-8 AllSmallAntimagmas
+ +
‣ AllSmallAntimagmas( n )( function )
+

returns all antiassociative magmas of specified size n (a number)

+ + +
+gap> AllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+gap> AllSmallAntimagmas(3);
+[ 
+  <magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>,
+  <magma with 3 generators>, <magma with 3 generators>
+]
+
+ +

+ +
1.3-9 NrSmallAntimagmas
+ +
‣ NrSmallAntimagmas( n )( function )
+

counts number of antiassociative magmas of specified size n (a number).

+ + +
+gap> NrSmallAntimagmas(2);
+2
+gap> NrSmallAntimagmas(3);
+10
+gap> NrSmallAntimagmas(4);
+17780
+
+ +

+ +
1.3-10 SmallAntimagma
+ +
‣ SmallAntimagma( n, i )( function )
+

returns antiassociative magma of id [n, i].

+ + +
+gap> SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> SmallAntimagma(4, 5);
+<magma with 4 generators>
+
+ +

+ +
1.3-11 OneSmallAntimagma
+ +
‣ OneSmallAntimagma( n )( function )
+

returns a random antiassociative magma of size n.

+ + +
+gap> OneSmallAntimagma(2);
+<magma with 2 generators>
+
+gap> OneSmallAntimagma(3);
+<magma with 3 generators>
+
+ +

+ +
1.3-12 ReallyAllSmallAntimagmas
+ +
‣ ReallyAllSmallAntimagmas( n )( function )
+

returns really-all antiassociative magmas, isomorphic, of specified size n (a number)

+ + +
+gap> ReallyAllSmallAntimagmas(2);
+[ <magma with 2 generators>, <magma with 2 generators> ]
+
+ +

+ +
1.3-13 ReallyNrSmallAntimagmas
+ +
‣ ReallyNrSmallAntimagmas( n )( function )
+

counts number of antiassociative magmas of specified size n (a number)

+ + +
+gap> ReallyNrSmallAntimagmas(3);
+52
+
+ +

+ +
1.3-14 AntimagmaGeneratorPossibleDiagonals
+ +
‣ AntimagmaGeneratorPossibleDiagonals( n )( function )
+

returns all possible diagonals of multiplication table for [n]-antimagma.

+ + +
+gap> AntimagmaGeneratorPossibleDiagonals(2);
+[ [ 2, 1 ] ]
+gap> AntimagmaGeneratorPossibleDiagonals(3);
+[ 
+  [ 2, 1, 1 ], [ 2, 1, 2 ], [ 2, 3, 1 ], [ 2, 3, 2 ], 
+  [ 3, 1, 1 ], [ 3, 1, 2 ], [ 3, 3, 1 ], [ 3, 3, 2 ] 
+]
+
+ +

+ +
1.3-15 AntimagmaGeneratorFilterNonIsomorphicMagmas
+ +
‣ AntimagmaGeneratorFilterNonIsomorphicMagmas( Ms )( function )
+

filters non-isomorphic magmas m.

+ +

+ +

1.4 smallantimagmas automatic generated documentation of methods

+ +

+ +
1.4-1 MagmaIsomorphism
+ +
‣ MagmaIsomorphism( M, N )( operation )
+

computes an isomoprhism between magmas M, N.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
+<magma with 2 generators>
+gap> MagmaIsomorphism(M, N);
+<mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
+
+ +

+ +
1.4-2 MagmaAntiisomorphism
+ +
‣ MagmaAntiisomorphism( M, N )( operation )
+

creates an antiisomoprhism between magmas M, N.

+ + +
+gap> M := SmallAntimagma(2, 1);
+<magma with 2 generators>
+gap> N := SmallAntimagma(2, 2);
+<magma with 2 generators>
+gap> MagmaAntiisomorphism(M, N);
+<mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
+
+ + +
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+ + +
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+ +
+

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+ + diff --git a/doc/chapInd.html b/doc/chapInd.html new file mode 100644 index 0000000..0e0b98f --- /dev/null +++ b/doc/chapInd.html @@ -0,0 +1,73 @@ + + + + + + +GAP (smallantimagmas) - Index + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
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+ + +

+ +
+

Index

+ +AllSmallAntimagmas 1.3-8
+AllSubmagmas 1.3-1
+AnticommutativityIndex, for IsMagma 1.2-4
+AntimagmaGeneratorFilterNonIsomorphicMagmas 1.3-15
+AntimagmaGeneratorPossibleDiagonals 1.3-14
+AssociativityIndex, for IsMagma 1.2-1
+CommutativityIndex, for IsMagma 1.2-3
+DiagonalOfMultiplicationTable, for IsMagma 1.2-2
+IdSmallAntimagma, for IsMagma 1.2-6
+IsAntiassociative, for IsMagma 1.1-1
+IsCancellative, for IsMagma 1.1-6
+IsLeftCancellative, for IsMagma 1.1-4
+IsLeftCyclic, for IsMagma 1.1-2
+IsMagmaAntiisomorphic 1.3-4
+IsMagmaIsomorphic 1.3-3
+IsRightCancellative, for IsMagma 1.1-5
+IsRightCyclic, for IsMagma 1.1-3
+LeftOrder, for IsExtLElement 1.2-7
+LeftOrdersOfElements, for IsMagma 1.2-9
+LeftPower 1.3-6
+License .-1
+MagmaAntiisomorphism, for IsMagma, IsMagma 1.4-2
+MagmaIsomorphism, for IsMagma, IsMagma 1.4-1
+MagmaIsomorphismInvariantsMatch 1.3-2
+NrSmallAntimagmas 1.3-9
+OneSmallAntimagma 1.3-11
+ReallyAllSmallAntimagmas 1.3-12
+ReallyNrSmallAntimagmas 1.3-13
+RightOrder, for IsExtRElement 1.2-8
+RightOrdersOfElements, for IsMagma 1.2-10
+RightPower 1.3-7
+SmallAntimagma 1.3-10
+SquaresIndex, for IsMagma 1.2-5
+TransposedMagma 1.3-5
+

+
+ +
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+ + +
Goto Chapter: Top 1 Ind
+ +
+

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+ + diff --git a/doc/chapInd.txt b/doc/chapInd.txt new file mode 100644 index 0000000..0b4322d --- /dev/null +++ b/doc/chapInd.txt @@ -0,0 +1,41 @@ + + + Index + + AllSmallAntimagmas 1.3-8 + AllSubmagmas 1.3-1 + AnticommutativityIndex, for IsMagma 1.2-4 + AntimagmaGeneratorFilterNonIsomorphicMagmas 1.3-15 + AntimagmaGeneratorPossibleDiagonals 1.3-14 + AssociativityIndex, for IsMagma 1.2-1 + CommutativityIndex, for IsMagma 1.2-3 + DiagonalOfMultiplicationTable, for IsMagma 1.2-2 + IdSmallAntimagma, for IsMagma 1.2-6 + IsAntiassociative, for IsMagma 1.1-1 + IsCancellative, for IsMagma 1.1-6 + IsLeftCancellative, for IsMagma 1.1-4 + IsLeftCyclic, for IsMagma 1.1-2 + IsMagmaAntiisomorphic 1.3-4 + IsMagmaIsomorphic 1.3-3 + IsRightCancellative, for IsMagma 1.1-5 + IsRightCyclic, for IsMagma 1.1-3 + LeftOrder, for IsExtLElement 1.2-7 + LeftOrdersOfElements, for IsMagma 1.2-9 + LeftPower 1.3-6 + License 0.0-1 + MagmaAntiisomorphism, for IsMagma, IsMagma 1.4-2 + MagmaIsomorphism, for IsMagma, IsMagma 1.4-1 + MagmaIsomorphismInvariantsMatch 1.3-2 + NrSmallAntimagmas 1.3-9 + OneSmallAntimagma 1.3-11 + ReallyAllSmallAntimagmas 1.3-12 + ReallyNrSmallAntimagmas 1.3-13 + RightOrder, for IsExtRElement 1.2-8 + RightOrdersOfElements, for IsMagma 1.2-10 + RightPower 1.3-7 + SmallAntimagma 1.3-10 + SquaresIndex, for IsMagma 1.2-5 + TransposedMagma 1.3-5 + + + ------------------------------------------------------- diff --git a/doc/chapInd_mj.html b/doc/chapInd_mj.html new file mode 100644 index 0000000..4ec59b4 --- /dev/null +++ b/doc/chapInd_mj.html @@ -0,0 +1,76 @@ + + + + + + + +GAP (smallantimagmas) - Index + + + + + + + + + +
Goto Chapter: Top 1 Ind
+ +
 [Top of Book]  [Contents]   [Previous Chapter] 
+ + +

+ +
+

Index

+ +AllSmallAntimagmas 1.3-8
+AllSubmagmas 1.3-1
+AnticommutativityIndex, for IsMagma 1.2-4
+AntimagmaGeneratorFilterNonIsomorphicMagmas 1.3-15
+AntimagmaGeneratorPossibleDiagonals 1.3-14
+AssociativityIndex, for IsMagma 1.2-1
+CommutativityIndex, for IsMagma 1.2-3
+DiagonalOfMultiplicationTable, for IsMagma 1.2-2
+IdSmallAntimagma, for IsMagma 1.2-6
+IsAntiassociative, for IsMagma 1.1-1
+IsCancellative, for IsMagma 1.1-6
+IsLeftCancellative, for IsMagma 1.1-4
+IsLeftCyclic, for IsMagma 1.1-2
+IsMagmaAntiisomorphic 1.3-4
+IsMagmaIsomorphic 1.3-3
+IsRightCancellative, for IsMagma 1.1-5
+IsRightCyclic, for IsMagma 1.1-3
+LeftOrder, for IsExtLElement 1.2-7
+LeftOrdersOfElements, for IsMagma 1.2-9
+LeftPower 1.3-6
+License .-1
+MagmaAntiisomorphism, for IsMagma, IsMagma 1.4-2
+MagmaIsomorphism, for IsMagma, IsMagma 1.4-1
+MagmaIsomorphismInvariantsMatch 1.3-2
+NrSmallAntimagmas 1.3-9
+OneSmallAntimagma 1.3-11
+ReallyAllSmallAntimagmas 1.3-12
+ReallyNrSmallAntimagmas 1.3-13
+RightOrder, for IsExtRElement 1.2-8
+RightOrdersOfElements, for IsMagma 1.2-10
+RightPower 1.3-7
+SmallAntimagma 1.3-10
+SquaresIndex, for IsMagma 1.2-5
+TransposedMagma 1.3-5
+

+
+ +
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+ + +
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+ +
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Or one can append '?GAPDocStyle=mystyle' to the URL + when loading any file of the manual (so the style can be configured in + the GAP user preferences). + +*/ + +/* generic helper function */ +function deleteCookie(nam) { + document.cookie = nam+"=;Path=/;expires=Thu, 01 Jan 1970 00:00:00 GMT"; +} + +/* read a value from a "nam1=val1;nam2=val2;..." string (e.g., the search + part of an URL or a cookie */ +function valueString(str,nam) { + var cs = str.split(";"); + for (var i=0; i < cs.length; i++) { + var pos = cs[i].search(nam+"="); + if (pos > -1) { + pos = cs[i].indexOf("="); + return cs[i].slice(pos+1); + } + } + return 0; +} + +/* when a non-default style is chosen via URL or a cookie, then + the cookie is reset and the styles .js and .css files are read */ +function overwriteStyle() { + /* style in URL? */ + var style = valueString(window.location.search, "GAPDocStyle"); + /* otherwise check cookie */ + if (style == 0) + style = valueString(document.cookie, "GAPDocStyle"); + if (style == 0) + return; + if (style == "default") + deleteCookie("GAPDocStyle"); + else { + /* ok, we set the cookie for path "/" */ + var path = "/"; + /* or better like this ??? + var here = window.location.pathname.split("/"); + for (var i=0; i+3 < here.length; i++) + path = path+"/"+here[i]; + */ + document.cookie = "GAPDocStyle="+style+";Path="+path; + /* split into names of style files */ + var stlist = style.split(","); + /* read style's css and js files */ + for (var i=0; i < stlist.length; i++) { + document.writeln(''); + document.writeln(''); + } + } +} + +/* this adds a "[Style]" link next to the MathJax switcher */ +function addStyleLink() { + var line = document.getElementById("mathjaxlink"); + var el = document.createElement("a"); + var oncl = document.createAttribute("href"); + var back = window.location.protocol+"//" + if (window.location.protocol == "http:" || + window.location.protocol == "https:") { + back = back+window.location.host; + if (window.location.port != "") { + back = back+":"+window.location.port; + } + } + back = back+window.location.pathname; + oncl.nodeValue = "chooser.html?BACK="+back; + el.setAttributeNode(oncl); + var cont = document.createTextNode(" [Style]"); + el.appendChild(cont); + line.appendChild(el); +} + +var jscontentfuncs = new Array(); + +jscontentfuncs.push(addStyleLink); + +/* the default jscontent() only adds the [Style] link to the page */ +function jscontent () { + for (var i=0; i < jscontentfuncs.length; i++) + jscontentfuncs[i](); +} + diff --git a/doc/manual.lab b/doc/manual.lab new file mode 100644 index 0000000..1c2c390 --- /dev/null +++ b/doc/manual.lab @@ -0,0 +1,45 @@ +\GAPDocLabFile{smallantimagmas} +\makelabel{smallantimagmas:Title page}{}{X7D2C85EC87DD46E5} +\makelabel{smallantimagmas:Copyright}{}{X81488B807F2A1CF1} +\makelabel{smallantimagmas:Acknowledgements}{}{X82A988D47DFAFCFA} +\makelabel{smallantimagmas:Table of Contents}{}{X8537FEB07AF2BEC8} +\makelabel{smallantimagmas:smallantimagmas automatic 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+\makelabel{smallantimagmas:AntimagmaGeneratorPossibleDiagonals}{1.3.14}{X83FADDD185B26133} +\makelabel{smallantimagmas:AntimagmaGeneratorFilterNonIsomorphicMagmas}{1.3.15}{X8493D36B80E32C64} +\makelabel{smallantimagmas:MagmaIsomorphism for IsMagma, IsMagma}{1.4.1}{X87F3EA827FF3D302} +\makelabel{smallantimagmas:MagmaAntiisomorphism for IsMagma, IsMagma}{1.4.2}{X7AB3F3E37D8A5687} diff --git a/doc/manual.pdf b/doc/manual.pdf new file mode 100644 index 0000000..fee6e48 Binary files /dev/null and b/doc/manual.pdf differ diff --git a/doc/manual.six b/doc/manual.six new file mode 100644 index 0000000..a2b18e3 --- /dev/null +++ b/doc/manual.six @@ -0,0 +1,114 @@ +#SIXFORMAT GapDocGAP +HELPBOOKINFOSIXTMP := rec( +encoding := "UTF-8", +bookname := "smallantimagmas", +entries := +[ [ "Title page", "0.0", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" + ], + [ "Copyright", "0.0-1", [ 0, 0, 1 ], 21, 2, "copyright", + "X81488B807F2A1CF1" ], + [ "Acknowledgements", "0.0-2", [ 0, 0, 2 ], 32, 2, "acknowledgements", + "X82A988D47DFAFCFA" ], + [ "Table of Contents", "0.0-3", [ 0, 0, 3 ], 39, 3, "table of contents", + "X8537FEB07AF2BEC8" ], + [ + "\033[1X\033[33X\033[0;-2Ysmallantimagmas automatic generated documentation\ +\033[133X\033[101X", "1", [ 1, 0, 0 ], 1, 4, + "smallantimagmas automatic generated documentation", + "X7EB7BB817CC15891" ], + [ + "\033[1X\033[33X\033[0;-2Ysmallantimagmas automatic generated documentation\ + of properties\033[133X\033[101X", "1.1", [ 1, 1, 0 ], 4, 4, + "smallantimagmas automatic generated documentation of properties", + "X78F902077A6714C4" ], + [ + "\033[1X\033[33X\033[0;-2Ysmallantimagmas automatic generated documentation\ + of attributes\033[133X\033[101X", "1.2", [ 1, 2, 0 ], 82, 5, + "smallantimagmas automatic generated documentation of attributes", + "X839C88FC81394B14" ], + [ + "\033[1X\033[33X\033[0;-2Ysmallantimagmas automatic generated documentation\ + of global functions\033[133X\033[101X", "1.3", [ 1, 3, 0 ], 193, 7, + "smallantimagmas automatic generated documentation of global functions", + "X7A4C95527CCD8524" ], + [ + "\033[1X\033[33X\033[0;-2Ysmallantimagmas automatic generated documentation\ + of methods\033[133X\033[101X", "1.4", [ 1, 4, 0 ], 397, 11, + "smallantimagmas automatic generated documentation of methods", + "X8553DA53796C81EA" ], + [ "Index", "ind", [ "Ind", 0, 0 ], 1, 12, "index", "X83A0356F839C696F" ], + [ "License", "0.0-1", [ 0, 0, 1 ], 21, 2, "license", "X81488B807F2A1CF1" ], + [ "\033[2XIsAntiassociative\033[102X for IsMagma", "1.1-1", [ 1, 1, 1 ], 7, + 4, "isantiassociative for ismagma", "X7B8537C57970AE37" ], + [ "\033[2XIsLeftCyclic\033[102X for IsMagma", "1.1-2", [ 1, 1, 2 ], 23, 4, + "isleftcyclic for ismagma", "X8392BFEE78284DE1" ], + [ "\033[2XIsRightCyclic\033[102X for IsMagma", "1.1-3", [ 1, 1, 3 ], 30, 4, + "isrightcyclic for ismagma", "X7BE3D1C0801AE7EA" ], + [ "\033[2XIsLeftCancellative\033[102X for IsMagma", "1.1-4", [ 1, 1, 4 ], + 37, 4, "isleftcancellative for ismagma", "X7D994F7382127E77" ], + [ "\033[2XIsRightCancellative\033[102X for IsMagma", "1.1-5", [ 1, 1, 5 ], + 58, 5, "isrightcancellative for ismagma", "X85C01ECF83CD5484" ], + [ "\033[2XIsCancellative\033[102X for IsMagma", "1.1-6", [ 1, 1, 6 ], 70, + 5, "iscancellative for ismagma", "X7E58570787350F43" ], + [ "\033[2XAssociativityIndex\033[102X for IsMagma", "1.2-1", [ 1, 2, 1 ], + 85, 5, "associativityindex for ismagma", "X809A477180F2A0F6" ], + [ "\033[2XDiagonalOfMultiplicationTable\033[102X for IsMagma", "1.2-2", + [ 1, 2, 2 ], 104, 6, "diagonalofmultiplicationtable for ismagma", + "X802DA9B083E7F4A3" ], + [ "\033[2XCommutativityIndex\033[102X for IsMagma", "1.2-3", [ 1, 2, 3 ], + 120, 6, "commutativityindex for ismagma", "X87FED7267EB0A068" ], + [ "\033[2XAnticommutativityIndex\033[102X for IsMagma", "1.2-4", + [ 1, 2, 4 ], 130, 6, "anticommutativityindex for ismagma", + "X7D32B8F780294AEC" ], + [ "\033[2XSquaresIndex\033[102X for IsMagma", "1.2-5", [ 1, 2, 5 ], 139, 6, + "squaresindex for ismagma", "X85904967802C27B4" ], + [ "\033[2XIdSmallAntimagma\033[102X for IsMagma", "1.2-6", [ 1, 2, 6 ], + 154, 6, "idsmallantimagma for ismagma", "X783C01BD7B931A12" ], + [ "\033[2XLeftOrder\033[102X for IsExtLElement", "1.2-7", [ 1, 2, 7 ], 169, + 7, "leftorder for isextlelement", "X78BF96667D805695" ], + [ "\033[2XRightOrder\033[102X for IsExtRElement", "1.2-8", [ 1, 2, 8 ], + 175, 7, "rightorder for isextrelement", "X850894387AD0E717" ], + [ "\033[2XLeftOrdersOfElements\033[102X for IsMagma", "1.2-9", [ 1, 2, 9 ], + 181, 7, "leftordersofelements for ismagma", "X7CDCE61679BFD1F7" ], + [ "\033[2XRightOrdersOfElements\033[102X for IsMagma", "1.2-10", + [ 1, 2, 10 ], 187, 7, "rightordersofelements for ismagma", + "X84D8A5D88790F870" ], + [ "\033[2XAllSubmagmas\033[102X", "1.3-1", [ 1, 3, 1 ], 196, 7, + "allsubmagmas", "X8011AFA47C662D53" ], + [ "\033[2XMagmaIsomorphismInvariantsMatch\033[102X", "1.3-2", [ 1, 3, 2 ], + 209, 8, "magmaisomorphisminvariantsmatch", "X7BA7BE44861A8C51" ], + [ "\033[2XIsMagmaIsomorphic\033[102X", "1.3-3", [ 1, 3, 3 ], 215, 8, + "ismagmaisomorphic", "X7F7EAF23807EE984" ], + [ "\033[2XIsMagmaAntiisomorphic\033[102X", "1.3-4", [ 1, 3, 4 ], 236, 8, + "ismagmaantiisomorphic", "X807BD59180325341" ], + [ "\033[2XTransposedMagma\033[102X", "1.3-5", [ 1, 3, 5 ], 257, 8, + "transposedmagma", "X79BF9EB48562EF6C" ], + [ "\033[2XLeftPower\033[102X", "1.3-6", [ 1, 3, 6 ], 280, 9, "leftpower", + "X7FD21A58851687DF" ], + [ "\033[2XRightPower\033[102X", "1.3-7", [ 1, 3, 7 ], 286, 9, "rightpower", + "X788005DE7947D914" ], + [ "\033[2XAllSmallAntimagmas\033[102X", "1.3-8", [ 1, 3, 8 ], 292, 9, + "allsmallantimagmas", "X7DDB92C284197B0B" ], + [ "\033[2XNrSmallAntimagmas\033[102X", "1.3-9", [ 1, 3, 9 ], 310, 9, + "nrsmallantimagmas", "X7E5054007A985873" ], + [ "\033[2XSmallAntimagma\033[102X", "1.3-10", [ 1, 3, 10 ], 325, 10, + "smallantimagma", "X7903CEEA79DEBA73" ], + [ "\033[2XOneSmallAntimagma\033[102X", "1.3-11", [ 1, 3, 11 ], 338, 10, + "onesmallantimagma", "X804A623879A9AC7F" ], + [ "\033[2XReallyAllSmallAntimagmas\033[102X", "1.3-12", [ 1, 3, 12 ], 352, + 10, "reallyallsmallantimagmas", "X7D0A720279246D45" ], + [ "\033[2XReallyNrSmallAntimagmas\033[102X", "1.3-13", [ 1, 3, 13 ], 364, + 10, "reallynrsmallantimagmas", "X796637787C216BA1" ], + [ "\033[2XAntimagmaGeneratorPossibleDiagonals\033[102X", "1.3-14", + [ 1, 3, 14 ], 375, 11, "antimagmageneratorpossiblediagonals", + "X83FADDD185B26133" ], + [ "\033[2XAntimagmaGeneratorFilterNonIsomorphicMagmas\033[102X", "1.3-15", + [ 1, 3, 15 ], 391, 11, "antimagmageneratorfilternonisomorphicmagmas", + "X8493D36B80E32C64" ], + [ "\033[2XMagmaIsomorphism\033[102X for IsMagma, IsMagma", "1.4-1", + [ 1, 4, 1 ], 400, 11, "magmaisomorphism for ismagma ismagma", + "X87F3EA827FF3D302" ], + [ "\033[2XMagmaAntiisomorphism\033[102X for IsMagma, IsMagma", "1.4-2", + [ 1, 4, 2 ], 415, 11, "magmaantiisomorphism for ismagma ismagma", + "X7AB3F3E37D8A5687" ] ] +); diff --git 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randchar("cdef")+randchar(hexdigits)+ + randchar("cdef")+randchar(hexdigits)+ + randchar("cdef")+randchar(hexdigits) +} +function randdark() { + return randchar("012345789")+randchar(hexdigits)+ + randchar("012345789")+randchar(hexdigits)+ + randchar("102345789")+randchar(hexdigits) +} + +document.write('\n'); + + + diff --git a/doc/smallantimagmas.aux b/doc/smallantimagmas.aux new file mode 100644 index 0000000..5d2b0c0 --- /dev/null +++ b/doc/smallantimagmas.aux @@ -0,0 +1,98 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} 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0 +- -- 0 +* -- 0 +:= -- 0 +add.period$ -- 0 +call.type$ -- 0 +change.case$ -- 0 +chr.to.int$ -- 0 +cite$ -- 0 +duplicate$ -- 0 +empty$ -- 0 +format.name$ -- 0 +if$ -- 0 +int.to.chr$ -- 0 +int.to.str$ -- 0 +missing$ -- 0 +newline$ -- 0 +num.names$ -- 0 +pop$ -- 0 +preamble$ -- 0 +purify$ -- 0 +quote$ -- 0 +skip$ -- 0 +stack$ -- 0 +substring$ -- 0 +swap$ -- 0 +text.length$ -- 0 +text.prefix$ -- 0 +top$ -- 0 +type$ -- 0 +warning$ -- 0 +while$ -- 0 +width$ -- 0 +write$ -- 0 +(There were 3 error messages) diff --git a/doc/smallantimagmas.idx b/doc/smallantimagmas.idx new file mode 100644 index 0000000..ed727c5 --- /dev/null +++ b/doc/smallantimagmas.idx @@ -0,0 +1,34 @@ +\indexentry{License|hyperpage}{2} +\indexentry{IsAntiassociative@\texttt {IsAntiassociative}!for IsMagma|hyperpage}{4} +\indexentry{IsLeftCyclic@\texttt {IsLeftCyclic}!for IsMagma|hyperpage}{4} +\indexentry{IsRightCyclic@\texttt {IsRightCyclic}!for IsMagma|hyperpage}{4} +\indexentry{IsLeftCancellative@\texttt {IsLeftCancellative}!for IsMagma|hyperpage}{4} +\indexentry{IsRightCancellative@\texttt {IsRightCancellative}!for IsMagma|hyperpage}{5} +\indexentry{IsCancellative@\texttt {IsCancellative}!for IsMagma|hyperpage}{5} +\indexentry{AssociativityIndex@\texttt {AssociativityIndex}!for IsMagma|hyperpage}{5} +\indexentry{DiagonalOfMultiplicationTable@\texttt {DiagonalOfMultiplicationTable}!for IsMagma|hyperpage}{6} +\indexentry{CommutativityIndex@\texttt {CommutativityIndex}!for IsMagma|hyperpage}{6} +\indexentry{AnticommutativityIndex@\texttt {AnticommutativityIndex}!for IsMagma|hyperpage}{6} +\indexentry{SquaresIndex@\texttt {SquaresIndex}!for IsMagma|hyperpage}{6} +\indexentry{IdSmallAntimagma@\texttt {IdSmallAntimagma}!for IsMagma|hyperpage}{6} +\indexentry{LeftOrder@\texttt {LeftOrder}!for IsExtLElement|hyperpage}{7} +\indexentry{RightOrder@\texttt {RightOrder}!for IsExtRElement|hyperpage}{7} +\indexentry{LeftOrdersOfElements@\texttt {LeftOrdersOfElements}!for IsMagma|hyperpage}{7} +\indexentry{RightOrdersOfElements@\texttt {RightOrdersOfElements}!for IsMagma|hyperpage}{7} +\indexentry{AllSubmagmas@\texttt {AllSubmagmas}|hyperpage}{7} +\indexentry{MagmaIsomorphismInvariantsMatch@\texttt {MagmaIsomorphismInvariantsMatch}|hyperpage}{8} +\indexentry{IsMagmaIsomorphic@\texttt {IsMagmaIsomorphic}|hyperpage}{8} +\indexentry{IsMagmaAntiisomorphic@\texttt {IsMagmaAntiisomorphic}|hyperpage}{8} +\indexentry{TransposedMagma@\texttt {TransposedMagma}|hyperpage}{8} +\indexentry{LeftPower@\texttt {LeftPower}|hyperpage}{9} +\indexentry{RightPower@\texttt {RightPower}|hyperpage}{9} +\indexentry{AllSmallAntimagmas@\texttt {AllSmallAntimagmas}|hyperpage}{9} +\indexentry{NrSmallAntimagmas@\texttt {NrSmallAntimagmas}|hyperpage}{9} +\indexentry{SmallAntimagma@\texttt {SmallAntimagma}|hyperpage}{10} +\indexentry{OneSmallAntimagma@\texttt {OneSmallAntimagma}|hyperpage}{10} +\indexentry{ReallyAllSmallAntimagmas@\texttt {ReallyAllSmallAntimagmas}|hyperpage}{10} +\indexentry{ReallyNrSmallAntimagmas@\texttt {ReallyNrSmallAntimagmas}|hyperpage}{10} +\indexentry{AntimagmaGeneratorPossibleDiagonals@\texttt {AntimagmaGeneratorPossibleDiagonals}|hyperpage}{11} +\indexentry{AntimagmaGeneratorFilterNonIsomorphicMagmas@\texttt {Antimagma}\-\texttt {Generator}\-\texttt {Filter}\-\texttt {Non}\-\texttt {Isomorphic}\-\texttt {Magmas}|hyperpage}{11} +\indexentry{MagmaIsomorphism@\texttt {MagmaIsomorphism}!for IsMagma, IsMagma|hyperpage}{11} +\indexentry{MagmaAntiisomorphism@\texttt {MagmaAntiisomorphism}!for IsMagma, IsMagma|hyperpage}{11} diff --git a/doc/smallantimagmas.ilg b/doc/smallantimagmas.ilg new file mode 100644 index 0000000..3d236c7 --- /dev/null +++ b/doc/smallantimagmas.ilg @@ -0,0 +1,6 @@ +This is makeindex, version 2.15 [TeX Live 2022/dev] (kpathsea + Thai support). +Scanning input file smallantimagmas.idx....done (34 entries accepted, 0 rejected). +Sorting entries....done (186 comparisons). +Generating output file smallantimagmas.ind....done (87 lines written, 0 warnings). +Output written in smallantimagmas.ind. +Transcript written in smallantimagmas.ilg. diff --git a/doc/smallantimagmas.ind b/doc/smallantimagmas.ind new file mode 100644 index 0000000..9169daa --- /dev/null +++ b/doc/smallantimagmas.ind @@ -0,0 +1,87 @@ +\begin{theindex} + + \item \texttt {AllSmallAntimagmas}, \hyperpage{9} + \item \texttt {AllSubmagmas}, \hyperpage{7} + \item \texttt {AnticommutativityIndex} + \subitem for IsMagma, \hyperpage{6} + \item \texttt {Antimagma}\-\texttt {Generator}\-\texttt {Filter}\-\texttt {Non}\-\texttt {Isomorphic}\-\texttt {Magmas}, + \hyperpage{11} + \item \texttt {AntimagmaGeneratorPossibleDiagonals}, \hyperpage{11} + \item \texttt {AssociativityIndex} + \subitem for IsMagma, \hyperpage{5} + + \indexspace + + \item \texttt {CommutativityIndex} + \subitem for IsMagma, \hyperpage{6} + + \indexspace + + \item \texttt {DiagonalOfMultiplicationTable} + \subitem for IsMagma, \hyperpage{6} + + \indexspace + + \item \texttt {IdSmallAntimagma} + \subitem for IsMagma, \hyperpage{6} + \item \texttt {IsAntiassociative} + \subitem for IsMagma, \hyperpage{4} + \item \texttt {IsCancellative} + \subitem for IsMagma, \hyperpage{5} + \item \texttt {IsLeftCancellative} + \subitem for IsMagma, \hyperpage{4} + \item \texttt {IsLeftCyclic} + \subitem for IsMagma, \hyperpage{4} + \item \texttt {IsMagmaAntiisomorphic}, \hyperpage{8} + \item \texttt {IsMagmaIsomorphic}, \hyperpage{8} + \item \texttt {IsRightCancellative} + \subitem for IsMagma, \hyperpage{5} + \item \texttt {IsRightCyclic} + \subitem for IsMagma, \hyperpage{4} + + \indexspace + + \item \texttt {LeftOrder} + \subitem for IsExtLElement, \hyperpage{7} + \item \texttt {LeftOrdersOfElements} + \subitem for IsMagma, \hyperpage{7} + \item \texttt {LeftPower}, \hyperpage{9} + \item License, \hyperpage{2} + + \indexspace + + \item \texttt {MagmaAntiisomorphism} + \subitem for IsMagma, IsMagma, \hyperpage{11} + \item \texttt {MagmaIsomorphism} + \subitem for IsMagma, IsMagma, \hyperpage{11} + \item \texttt {MagmaIsomorphismInvariantsMatch}, \hyperpage{8} + + \indexspace + + \item \texttt {NrSmallAntimagmas}, \hyperpage{9} + + \indexspace + + \item \texttt {OneSmallAntimagma}, \hyperpage{10} + + \indexspace + + \item \texttt {ReallyAllSmallAntimagmas}, \hyperpage{10} + \item \texttt {ReallyNrSmallAntimagmas}, \hyperpage{10} + \item \texttt {RightOrder} + \subitem for IsExtRElement, \hyperpage{7} + \item \texttt {RightOrdersOfElements} + \subitem for IsMagma, \hyperpage{7} + \item \texttt {RightPower}, \hyperpage{9} + + \indexspace + + \item \texttt {SmallAntimagma}, \hyperpage{10} + \item \texttt {SquaresIndex} + \subitem for IsMagma, \hyperpage{6} + + \indexspace + + \item \texttt {TransposedMagma}, \hyperpage{8} + +\end{theindex} diff --git a/doc/smallantimagmas.log b/doc/smallantimagmas.log new file mode 100644 index 0000000..d7cd8f8 --- /dev/null +++ b/doc/smallantimagmas.log @@ -0,0 +1,671 @@ +This is 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+\definecolor{RoyalGreen}{rgb}{0.0236,0.6179,0.0894} +\definecolor{RoyalRed}{rgb}{0.6179,0.0236,0.0894} +\definecolor{LightBlue}{rgb}{0.8544,0.9511,1.0000} +\definecolor{Black}{rgb}{0.0,0.0,0.0} + +\definecolor{linkColor}{rgb}{0.0,0.0,0.554} +\definecolor{citeColor}{rgb}{0.0,0.0,0.554} +\definecolor{fileColor}{rgb}{0.0,0.0,0.554} +\definecolor{urlColor}{rgb}{0.0,0.0,0.554} +\definecolor{promptColor}{rgb}{0.0,0.0,0.589} +\definecolor{brkpromptColor}{rgb}{0.589,0.0,0.0} +\definecolor{gapinputColor}{rgb}{0.589,0.0,0.0} +\definecolor{gapoutputColor}{rgb}{0.0,0.0,0.0} + +%% for a long time these were red and blue by default, +%% now black, but keep variables to overwrite +\definecolor{FuncColor}{rgb}{0.0,0.0,0.0} +%% strange name because of pdflatex bug: +\definecolor{Chapter }{rgb}{0.0,0.0,0.0} +\definecolor{DarkOlive}{rgb}{0.1047,0.2412,0.0064} + + +\usepackage{fancyvrb} + +\usepackage{mathptmx,helvet} +\usepackage[T1]{fontenc} +\usepackage{textcomp} + + +\usepackage[ + pdftex=true, + bookmarks=true, + a4paper=true, + pdftitle={Written with GAPDoc}, + pdfcreator={LaTeX with hyperref package / GAPDoc}, + colorlinks=true, + backref=page, + breaklinks=true, + linkcolor=linkColor, + citecolor=citeColor, + filecolor=fileColor, + urlcolor=urlColor, + pdfpagemode={UseNone}, + ]{hyperref} + +\newcommand{\maintitlesize}{\fontsize{50}{55}\selectfont} + +% write page numbers to a .pnr log file for online help +\newwrite\pagenrlog +\immediate\openout\pagenrlog =\jobname.pnr +\immediate\write\pagenrlog{PAGENRS := [} +\newcommand{\logpage}[1]{\protect\write\pagenrlog{#1, \thepage,}} +%% were never documented, give conflicts with some additional packages + +\newcommand{\GAP}{\textsf{GAP}} + +%% nicer description environments, allows long labels +\usepackage{enumitem} +\setdescription{style=nextline} + +%% depth of toc +\setcounter{tocdepth}{1} + + + + + +%% command for ColorPrompt style examples +\newcommand{\gapprompt}[1]{\color{promptColor}{\bfseries #1}} +\newcommand{\gapbrkprompt}[1]{\color{brkpromptColor}{\bfseries #1}} +\newcommand{\gapinput}[1]{\color{gapinputColor}{#1}} + + +\begin{document} + +\logpage{[ 0, 0, 0 ]} +\begin{titlepage} +\mbox{}\vfill + +\begin{center}{\maintitlesize \textbf{ smallantimagmas \mbox{}}}\\ +\vfill + +\hypersetup{pdftitle= smallantimagmas } +\markright{\scriptsize \mbox{}\hfill smallantimagmas \hfill\mbox{}} +{\Huge \textbf{ A fork of smallgrp package for small antiassociative magmas \mbox{}}}\\ +\vfill + +{\Huge 0.2.0 \mbox{}}\\[1cm] +{ 28 August 2024 \mbox{}}\\[1cm] +\mbox{}\\[2cm] +{\Large \textbf{ Kamil Zabielski\\ + \mbox{}}}\\ +\hypersetup{pdfauthor= Kamil Zabielski\\ + } +\end{center}\vfill + +\mbox{}\\ +{\mbox{}\\ +\small \noindent \textbf{ Kamil Zabielski\\ + }\\ + Address: \begin{minipage}[t]{8cm}\noindent + Department of Theoretical Computer Science\\ + Bia{\l}ystok University of Technology\\ + Wiejska 45A\\ + 15\texttt{\symbol{45}}325 Bia{\l}ystok\\ + Poland\\ + \end{minipage} +}\\ +\end{titlepage} + +\newpage\setcounter{page}{2} +{\small +\section*{Copyright} +\logpage{[ 0, 0, 1 ]} + \index{License} {\copyright} 2024 by Kamil Zabielski + + \textsf{smallantimagmas} package is free software; you can redistribute it and/or modify it under the +terms of the \href{http://www.fsf.org/licenses/gpl.html} {GNU General Public License} as published by the Free Software Foundation; either version 2 of the License, +or (at your option) any later version. \mbox{}}\\[1cm] +{\small +\section*{Acknowledgements} +\logpage{[ 0, 0, 2 ]} + We appreciate very much all past and future comments, suggestions and +contributions to this package and its documentation provided by \textsf{GAP} users and developers. \mbox{}}\\[1cm] +\newpage + +\def\contentsname{Contents\logpage{[ 0, 0, 3 ]}} + +\tableofcontents +\newpage + + +\chapter{\textcolor{Chapter }{smallantimagmas automatic generated documentation}}\label{Chapter_smallantimagmas_automatic_generated_documentation} +\logpage{[ 1, 0, 0 ]} +\hyperdef{L}{X7EB7BB817CC15891}{} +{ + +\section{\textcolor{Chapter }{smallantimagmas automatic generated documentation of properties}}\label{Chapter_smallantimagmas_automatic_generated_documentation_Section_smallantimagmas_automatic_generated_documentation_of_properties} +\logpage{[ 1, 1, 0 ]} +\hyperdef{L}{X78F902077A6714C4}{} +{ + + +\subsection{\textcolor{Chapter }{IsAntiassociative (for IsMagma)}} +\logpage{[ 1, 1, 1 ]}\nobreak +\hyperdef{L}{X7B8537C57970AE37}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsAntiassociative({\mdseries\slshape M})\index{IsAntiassociative@\texttt{IsAntiassociative}!for IsMagma} +\label{IsAntiassociative:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + identifies whether magma \mbox{\texttt{\mdseries\slshape M}} is antiassociative. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallGroup(16));| + false + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallAntimagma(2));| + true + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallAntimagma(3));| + true +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{IsLeftCyclic (for IsMagma)}} +\logpage{[ 1, 1, 2 ]}\nobreak +\hyperdef{L}{X8392BFEE78284DE1}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsLeftCyclic({\mdseries\slshape M})\index{IsLeftCyclic@\texttt{IsLeftCyclic}!for IsMagma} +\label{IsLeftCyclic:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + if magma is left cyclic \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{IsRightCyclic (for IsMagma)}} +\logpage{[ 1, 1, 3 ]}\nobreak +\hyperdef{L}{X7BE3D1C0801AE7EA}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsRightCyclic({\mdseries\slshape M})\index{IsRightCyclic@\texttt{IsRightCyclic}!for IsMagma} +\label{IsRightCyclic:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + if magma is left cyclic \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{IsLeftCancellative (for IsMagma)}} +\logpage{[ 1, 1, 4 ]}\nobreak +\hyperdef{L}{X7D994F7382127E77}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsLeftCancellative({\mdseries\slshape M})\index{IsLeftCancellative@\texttt{IsLeftCancellative}!for IsMagma} +\label{IsLeftCancellative:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + if magma is left cancellative \mbox{\texttt{\mdseries\slshape m}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@Display( MultiplicationTable(M) );| + [ [ 2, 1 ], + [ 2, 1 ] ] + !gapprompt@gap>| !gapinput@IsRightCancellative(M);| + false + !gapprompt@gap>| !gapinput@IsLeftCancellative(M);| + true + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M));| + [ true, false ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{IsRightCancellative (for IsMagma)}} +\logpage{[ 1, 1, 5 ]}\nobreak +\hyperdef{L}{X85C01ECF83CD5484}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsRightCancellative({\mdseries\slshape M})\index{IsRightCancellative@\texttt{IsRightCancellative}!for IsMagma} +\label{IsRightCancellative:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + if magma is right cancellative \mbox{\texttt{\mdseries\slshape m}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> IsRightCancellative(M));| + [ false, true ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{IsCancellative (for IsMagma)}} +\logpage{[ 1, 1, 6 ]}\nobreak +\hyperdef{L}{X7E58570787350F43}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsCancellative({\mdseries\slshape M})\index{IsCancellative@\texttt{IsCancellative}!for IsMagma} +\label{IsCancellative:for IsMagma} +}\hfill{\scriptsize (property)}}\\ +\textbf{\indent Returns:\ } +\texttt{true} or \texttt{false} + + + + if magma is cancellative \mbox{\texttt{\mdseries\slshape m}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> IsCancellative(M));| + [ false, false ] +\end{Verbatim} + + + } + + } + + +\section{\textcolor{Chapter }{smallantimagmas automatic generated documentation of attributes}}\label{Chapter_smallantimagmas_automatic_generated_documentation_Section_smallantimagmas_automatic_generated_documentation_of_attributes} +\logpage{[ 1, 2, 0 ]} +\hyperdef{L}{X839C88FC81394B14}{} +{ + + +\subsection{\textcolor{Chapter }{AssociativityIndex (for IsMagma)}} +\logpage{[ 1, 2, 1 ]}\nobreak +\hyperdef{L}{X809A477180F2A0F6}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AssociativityIndex({\mdseries\slshape M})\index{AssociativityIndex@\texttt{AssociativityIndex}!for IsMagma} +\label{AssociativityIndex:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + identifies associativity index of \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@OneSmallAntimagma(2);| + + !gapprompt@gap>| !gapinput@AssociativityIndex(OneSmallAntimagma(2));| + 0 + !gapprompt@gap>| !gapinput@OneSmallGroup(4);| + + !gapprompt@gap>| !gapinput@AssociativityIndex(OneSmallGroup(4));| + 64 + !gapprompt@gap>| !gapinput@AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3;| + true +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{DiagonalOfMultiplicationTable (for IsMagma)}} +\logpage{[ 1, 2, 2 ]}\nobreak +\hyperdef{L}{X802DA9B083E7F4A3}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{DiagonalOfMultiplicationTable({\mdseries\slshape M})\index{DiagonalOfMultiplicationTable@\texttt{DiagonalOfMultiplicationTable}!for IsMagma} +\label{DiagonalOfMultiplicationTable:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + computes diaognal of multiplication table of \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M))); | + [ [ 2, 1, 1 ], [ 2, 1, 1 ], + [ 2, 3, 2 ], [ 2, 1, 1 ], + [ 2, 1, 1 ], [ 2, 1, 2 ], + [ 2, 3, 2 ], [ 2, 1, 2 ], + [ 2, 3, 1 ], [ 2, 3, 1 ] + ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{CommutativityIndex (for IsMagma)}} +\logpage{[ 1, 2, 3 ]}\nobreak +\hyperdef{L}{X87FED7267EB0A068}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{CommutativityIndex({\mdseries\slshape M})\index{CommutativityIndex@\texttt{CommutativityIndex}!for IsMagma} +\label{CommutativityIndex:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + identifies commutativity index of \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{AnticommutativityIndex (for IsMagma)}} +\logpage{[ 1, 2, 4 ]}\nobreak +\hyperdef{L}{X7D32B8F780294AEC}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AnticommutativityIndex({\mdseries\slshape M})\index{AnticommutativityIndex@\texttt{AnticommutativityIndex}!for IsMagma} +\label{AnticommutativityIndex:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + calculates anticommutativity index of \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{SquaresIndex (for IsMagma)}} +\logpage{[ 1, 2, 5 ]}\nobreak +\hyperdef{L}{X85904967802C27B4}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{SquaresIndex({\mdseries\slshape M})\index{SquaresIndex@\texttt{SquaresIndex}!for IsMagma} +\label{SquaresIndex:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + computes squares index of \mbox{\texttt{\mdseries\slshape M}} so the order of $\left\{ m^2 | m \in \right\}$. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) ); | + [ [ m2, m1 ], [ m2, m1 ] ] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> SquaresIndex(M ));| + [ 2, 2 ] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(3), M -> SquaresIndex(M ));| + [ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{IdSmallAntimagma (for IsMagma)}} +\logpage{[ 1, 2, 6 ]}\nobreak +\hyperdef{L}{X783C01BD7B931A12}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IdSmallAntimagma({\mdseries\slshape M})\index{IdSmallAntimagma@\texttt{IdSmallAntimagma}!for IsMagma} +\label{IdSmallAntimagma:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + identifies class of antiassociative magma \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallGroup(16));| + false + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallAntimagma(2));| + true + !gapprompt@gap>| !gapinput@IsAntiassociative(OneSmallAntimagma(3));| + true +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{LeftOrder (for IsExtLElement)}} +\logpage{[ 1, 2, 7 ]}\nobreak +\hyperdef{L}{X78BF96667D805695}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{LeftOrder({\mdseries\slshape [m]})\index{LeftOrder@\texttt{LeftOrder}!for IsExtLElement} +\label{LeftOrder:for IsExtLElement} +}\hfill{\scriptsize (attribute)}}\\ + + + returns a left order of element \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{RightOrder (for IsExtRElement)}} +\logpage{[ 1, 2, 8 ]}\nobreak +\hyperdef{L}{X850894387AD0E717}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{RightOrder({\mdseries\slshape [m]})\index{RightOrder@\texttt{RightOrder}!for IsExtRElement} +\label{RightOrder:for IsExtRElement} +}\hfill{\scriptsize (attribute)}}\\ + + + returns a right order of element \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{LeftOrdersOfElements (for IsMagma)}} +\logpage{[ 1, 2, 9 ]}\nobreak +\hyperdef{L}{X7CDCE61679BFD1F7}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{LeftOrdersOfElements({\mdseries\slshape [m]})\index{LeftOrdersOfElements@\texttt{LeftOrdersOfElements}!for IsMagma} +\label{LeftOrdersOfElements:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + returns a left order of element \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{RightOrdersOfElements (for IsMagma)}} +\logpage{[ 1, 2, 10 ]}\nobreak +\hyperdef{L}{X84D8A5D88790F870}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{RightOrdersOfElements({\mdseries\slshape [m]})\index{RightOrdersOfElements@\texttt{RightOrdersOfElements}!for IsMagma} +\label{RightOrdersOfElements:for IsMagma} +}\hfill{\scriptsize (attribute)}}\\ + + + returns a left order of element \mbox{\texttt{\mdseries\slshape m}}. } + + } + + +\section{\textcolor{Chapter }{smallantimagmas automatic generated documentation of global functions}}\label{Chapter_smallantimagmas_automatic_generated_documentation_Section_smallantimagmas_automatic_generated_documentation_of_global_functions} +\logpage{[ 1, 3, 0 ]} +\hyperdef{L}{X7A4C95527CCD8524}{} +{ + + +\subsection{\textcolor{Chapter }{AllSubmagmas}} +\logpage{[ 1, 3, 1 ]}\nobreak +\hyperdef{L}{X8011AFA47C662D53}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AllSubmagmas({\mdseries\slshape M})\index{AllSubmagmas@\texttt{AllSubmagmas}} +\label{AllSubmagmas} +}\hfill{\scriptsize (function)}}\\ + + + builds a collection of non\texttt{\symbol{45}}isomorphic submagmas of \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@AllSmallAntimagmas(2);| + [ , ] + !gapprompt@gap>| !gapinput@List(AllSmallAntimagmas(2), M -> AllSubmagmas(M));| + [ [ ], [ ] ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{MagmaIsomorphismInvariantsMatch}} +\logpage{[ 1, 3, 2 ]}\nobreak +\hyperdef{L}{X7BA7BE44861A8C51}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{MagmaIsomorphismInvariantsMatch({\mdseries\slshape M})\index{MagmaIsomorphismInvariantsMatch@\texttt{MagmaIsomorphismInvariantsMatch}} +\label{MagmaIsomorphismInvariantsMatch} +}\hfill{\scriptsize (function)}}\\ + + + computes isomorphism invariants of \mbox{\texttt{\mdseries\slshape M}}. } + + + +\subsection{\textcolor{Chapter }{IsMagmaIsomorphic}} +\logpage{[ 1, 3, 3 ]}\nobreak +\hyperdef{L}{X7F7EAF23807EE984}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsMagmaIsomorphic({\mdseries\slshape M, N})\index{IsMagmaIsomorphic@\texttt{IsMagmaIsomorphic}} +\label{IsMagmaIsomorphic} +}\hfill{\scriptsize (function)}}\\ + + + identifies whether magmas \mbox{\texttt{\mdseries\slshape M}}, \mbox{\texttt{\mdseries\slshape N}} are isomorphic. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@N := SmallAntimagma(2, 2);| + + !gapprompt@gap>| !gapinput@T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);| + + !gapprompt@gap>| !gapinput@IsMagmaIsomorphic(M, M);| + true + !gapprompt@gap>| !gapinput@IsMagmaIsomorphic(M, T);| + true + !gapprompt@gap>| !gapinput@IsMagmaIsomorphic(M, N);| + false +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{IsMagmaAntiisomorphic}} +\logpage{[ 1, 3, 4 ]}\nobreak +\hyperdef{L}{X807BD59180325341}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{IsMagmaAntiisomorphic({\mdseries\slshape [M, N]})\index{IsMagmaAntiisomorphic@\texttt{IsMagmaAntiisomorphic}} +\label{IsMagmaAntiisomorphic} +}\hfill{\scriptsize (function)}}\\ + + + identifies whether magmas \mbox{\texttt{\mdseries\slshape M}}, \mbox{\texttt{\mdseries\slshape N}} are antiisomorphic. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@N := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@N := SmallAntimagma(2, 2);| + + !gapprompt@gap>| !gapinput@IsMagmaAntiisomorphic(M, M);| + false + !gapprompt@gap>| !gapinput@IsMagmaAntiisomorphic(M, N);| + true + !gapprompt@gap>| !gapinput@IsMagmaAntiisomorphic(M, TransposedMagma(M));| + true +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{TransposedMagma}} +\logpage{[ 1, 3, 5 ]}\nobreak +\hyperdef{L}{X79BF9EB48562EF6C}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{TransposedMagma({\mdseries\slshape [M]})\index{TransposedMagma@\texttt{TransposedMagma}} +\label{TransposedMagma} +}\hfill{\scriptsize (function)}}\\ + + + generates transposed magma \mbox{\texttt{\mdseries\slshape M}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@IsMagmaAntiisomorphic(M, TransposedMagma(M));| + true + !gapprompt@gap>| !gapinput@IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M)));| + true + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@Display(MultiplicationTable(M));| + [ [ 2, 1 ], + [ 2, 1 ] ] + !gapprompt@gap>| !gapinput@Display(MultiplicationTable(TransposedMagma(M)));| + [ [ 2, 2 ], + [ 1, 1 ] ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{LeftPower}} +\logpage{[ 1, 3, 6 ]}\nobreak +\hyperdef{L}{X7FD21A58851687DF}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{LeftPower({\mdseries\slshape [m, k]})\index{LeftPower@\texttt{LeftPower}} +\label{LeftPower} +}\hfill{\scriptsize (function)}}\\ + + + returns a left $k$\texttt{\symbol{45}}power of element \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{RightPower}} +\logpage{[ 1, 3, 7 ]}\nobreak +\hyperdef{L}{X788005DE7947D914}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{RightPower({\mdseries\slshape [m, k]})\index{RightPower@\texttt{RightPower}} +\label{RightPower} +}\hfill{\scriptsize (function)}}\\ + + + returns a right $k$\texttt{\symbol{45}}power of element \mbox{\texttt{\mdseries\slshape m}}. } + + + +\subsection{\textcolor{Chapter }{AllSmallAntimagmas}} +\logpage{[ 1, 3, 8 ]}\nobreak +\hyperdef{L}{X7DDB92C284197B0B}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AllSmallAntimagmas({\mdseries\slshape n})\index{AllSmallAntimagmas@\texttt{AllSmallAntimagmas}} +\label{AllSmallAntimagmas} +}\hfill{\scriptsize (function)}}\\ + + + returns all antiassociative magmas of specified size \mbox{\texttt{\mdseries\slshape n}} (a number) + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@AllSmallAntimagmas(2);| + [ , ] + !gapprompt@gap>| !gapinput@AllSmallAntimagmas(3);| + [ + , , , + , , , + , , + , + ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{NrSmallAntimagmas}} +\logpage{[ 1, 3, 9 ]}\nobreak +\hyperdef{L}{X7E5054007A985873}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{NrSmallAntimagmas({\mdseries\slshape n})\index{NrSmallAntimagmas@\texttt{NrSmallAntimagmas}} +\label{NrSmallAntimagmas} +}\hfill{\scriptsize (function)}}\\ + + + counts number of antiassociative magmas of specified size \mbox{\texttt{\mdseries\slshape n}} (a number). + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@NrSmallAntimagmas(2);| + 2 + !gapprompt@gap>| !gapinput@NrSmallAntimagmas(3);| + 10 + !gapprompt@gap>| !gapinput@NrSmallAntimagmas(4);| + 17780 +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{SmallAntimagma}} +\logpage{[ 1, 3, 10 ]}\nobreak +\hyperdef{L}{X7903CEEA79DEBA73}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{SmallAntimagma({\mdseries\slshape n, i})\index{SmallAntimagma@\texttt{SmallAntimagma}} +\label{SmallAntimagma} +}\hfill{\scriptsize (function)}}\\ + + + returns antiassociative magma of id \mbox{\texttt{\mdseries\slshape [n, i]}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@SmallAntimagma(4, 5);| + +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{OneSmallAntimagma}} +\logpage{[ 1, 3, 11 ]}\nobreak +\hyperdef{L}{X804A623879A9AC7F}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{OneSmallAntimagma({\mdseries\slshape n})\index{OneSmallAntimagma@\texttt{OneSmallAntimagma}} +\label{OneSmallAntimagma} +}\hfill{\scriptsize (function)}}\\ + + + returns a random antiassociative magma of size \mbox{\texttt{\mdseries\slshape n}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@OneSmallAntimagma(2);| + + + !gapprompt@gap>| !gapinput@OneSmallAntimagma(3);| + +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{ReallyAllSmallAntimagmas}} +\logpage{[ 1, 3, 12 ]}\nobreak +\hyperdef{L}{X7D0A720279246D45}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{ReallyAllSmallAntimagmas({\mdseries\slshape n})\index{ReallyAllSmallAntimagmas@\texttt{ReallyAllSmallAntimagmas}} +\label{ReallyAllSmallAntimagmas} +}\hfill{\scriptsize (function)}}\\ + + + returns really\texttt{\symbol{45}}all antiassociative magmas, isomorphic, of +specified size \mbox{\texttt{\mdseries\slshape n}} (a number) + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@ReallyAllSmallAntimagmas(2);| + [ , ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{ReallyNrSmallAntimagmas}} +\logpage{[ 1, 3, 13 ]}\nobreak +\hyperdef{L}{X796637787C216BA1}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{ReallyNrSmallAntimagmas({\mdseries\slshape n})\index{ReallyNrSmallAntimagmas@\texttt{ReallyNrSmallAntimagmas}} +\label{ReallyNrSmallAntimagmas} +}\hfill{\scriptsize (function)}}\\ + + + counts number of antiassociative magmas of specified size \mbox{\texttt{\mdseries\slshape n}} (a number) + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@ReallyNrSmallAntimagmas(3);| + 52 +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{AntimagmaGeneratorPossibleDiagonals}} +\logpage{[ 1, 3, 14 ]}\nobreak +\hyperdef{L}{X83FADDD185B26133}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AntimagmaGeneratorPossibleDiagonals({\mdseries\slshape n})\index{AntimagmaGeneratorPossibleDiagonals@\texttt{AntimagmaGeneratorPossibleDiagonals}} +\label{AntimagmaGeneratorPossibleDiagonals} +}\hfill{\scriptsize (function)}}\\ + + + returns all possible diagonals of multiplication table for \mbox{\texttt{\mdseries\slshape [n]}}\texttt{\symbol{45}}antimagma. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@AntimagmaGeneratorPossibleDiagonals(2);| + [ [ 2, 1 ] ] + !gapprompt@gap>| !gapinput@AntimagmaGeneratorPossibleDiagonals(3);| + [ + [ 2, 1, 1 ], [ 2, 1, 2 ], [ 2, 3, 1 ], [ 2, 3, 2 ], + [ 3, 1, 1 ], [ 3, 1, 2 ], [ 3, 3, 1 ], [ 3, 3, 2 ] + ] +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{AntimagmaGeneratorFilterNonIsomorphicMagmas}} +\logpage{[ 1, 3, 15 ]}\nobreak +\hyperdef{L}{X8493D36B80E32C64}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{AntimagmaGeneratorFilterNonIsomorphicMagmas({\mdseries\slshape Ms})\index{AntimagmaGeneratorFilterNonIsomorphicMagmas@\texttt{Antimagma}\-\texttt{Generator}\-\texttt{Filter}\-\texttt{Non}\-\texttt{Isomorphic}\-\texttt{Magmas}} +\label{AntimagmaGeneratorFilterNonIsomorphicMagmas} +}\hfill{\scriptsize (function)}}\\ + + + filters non\texttt{\symbol{45}}isomorphic magmas \mbox{\texttt{\mdseries\slshape m}}. } + + } + + +\section{\textcolor{Chapter }{smallantimagmas automatic generated documentation of methods}}\label{Chapter_smallantimagmas_automatic_generated_documentation_Section_smallantimagmas_automatic_generated_documentation_of_methods} +\logpage{[ 1, 4, 0 ]} +\hyperdef{L}{X8553DA53796C81EA}{} +{ + + +\subsection{\textcolor{Chapter }{MagmaIsomorphism (for IsMagma, IsMagma)}} +\logpage{[ 1, 4, 1 ]}\nobreak +\hyperdef{L}{X87F3EA827FF3D302}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{MagmaIsomorphism({\mdseries\slshape M, N})\index{MagmaIsomorphism@\texttt{MagmaIsomorphism}!for IsMagma, IsMagma} +\label{MagmaIsomorphism:for IsMagma, IsMagma} +}\hfill{\scriptsize (operation)}}\\ + + + computes an isomoprhism between magmas \mbox{\texttt{\mdseries\slshape M}}, \mbox{\texttt{\mdseries\slshape N}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);| + + !gapprompt@gap>| !gapinput@MagmaIsomorphism(M, N);| + Domain([ m1, m2 ]) > +\end{Verbatim} + + + } + + + +\subsection{\textcolor{Chapter }{MagmaAntiisomorphism (for IsMagma, IsMagma)}} +\logpage{[ 1, 4, 2 ]}\nobreak +\hyperdef{L}{X7AB3F3E37D8A5687}{} +{\noindent\textcolor{FuncColor}{$\triangleright$\enspace\texttt{MagmaAntiisomorphism({\mdseries\slshape M, N})\index{MagmaAntiisomorphism@\texttt{MagmaAntiisomorphism}!for IsMagma, IsMagma} +\label{MagmaAntiisomorphism:for IsMagma, IsMagma} +}\hfill{\scriptsize (operation)}}\\ + + + creates an antiisomoprhism between magmas \mbox{\texttt{\mdseries\slshape M}}, \mbox{\texttt{\mdseries\slshape N}}. + + +\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] + !gapprompt@gap>| !gapinput@M := SmallAntimagma(2, 1);| + + !gapprompt@gap>| !gapinput@N := SmallAntimagma(2, 2);| + + !gapprompt@gap>| !gapinput@MagmaAntiisomorphism(M, N);| + Domain([ m1, m2 ]) > +\end{Verbatim} + + + } + + } + + } + + \def\indexname{Index\logpage{[ "Ind", 0, 0 ]} +\hyperdef{L}{X83A0356F839C696F}{} +} + +\cleardoublepage +\phantomsection +\addcontentsline{toc}{chapter}{Index} + + +\printindex + +\immediate\write\pagenrlog{["Ind", 0, 0], \arabic{page},} +\newpage +\immediate\write\pagenrlog{["End"], \arabic{page}];} +\immediate\closeout\pagenrlog +\end{document} diff --git a/doc/smallantimagmas.toc b/doc/smallantimagmas.toc new file mode 100644 index 0000000..031cf8c --- /dev/null +++ b/doc/smallantimagmas.toc @@ -0,0 +1,39 @@ +\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{smallantimagmas automatic generated documentation}}{4}{chapter.1}% +\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{smallantimagmas automatic generated documentation of properties}}{4}{section.1.1}% +\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{IsAntiassociative (for IsMagma)}}{4}{subsection.1.1.1}% +\contentsline {subsection}{\numberline {1.1.2}\textcolor {Chapter }{IsLeftCyclic (for IsMagma)}}{4}{subsection.1.1.2}% +\contentsline {subsection}{\numberline {1.1.3}\textcolor {Chapter }{IsRightCyclic (for IsMagma)}}{4}{subsection.1.1.3}% +\contentsline {subsection}{\numberline {1.1.4}\textcolor {Chapter }{IsLeftCancellative (for IsMagma)}}{4}{subsection.1.1.4}% +\contentsline {subsection}{\numberline {1.1.5}\textcolor {Chapter }{IsRightCancellative (for IsMagma)}}{5}{subsection.1.1.5}% +\contentsline {subsection}{\numberline {1.1.6}\textcolor {Chapter }{IsCancellative (for IsMagma)}}{5}{subsection.1.1.6}% +\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{smallantimagmas automatic generated documentation of attributes}}{5}{section.1.2}% +\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{AssociativityIndex (for IsMagma)}}{5}{subsection.1.2.1}% +\contentsline {subsection}{\numberline {1.2.2}\textcolor {Chapter }{DiagonalOfMultiplicationTable (for IsMagma)}}{6}{subsection.1.2.2}% +\contentsline {subsection}{\numberline {1.2.3}\textcolor {Chapter }{CommutativityIndex (for IsMagma)}}{6}{subsection.1.2.3}% +\contentsline {subsection}{\numberline {1.2.4}\textcolor {Chapter }{AnticommutativityIndex (for IsMagma)}}{6}{subsection.1.2.4}% +\contentsline {subsection}{\numberline {1.2.5}\textcolor {Chapter }{SquaresIndex (for IsMagma)}}{6}{subsection.1.2.5}% +\contentsline {subsection}{\numberline {1.2.6}\textcolor {Chapter }{IdSmallAntimagma (for IsMagma)}}{6}{subsection.1.2.6}% +\contentsline {subsection}{\numberline {1.2.7}\textcolor {Chapter }{LeftOrder (for IsExtLElement)}}{7}{subsection.1.2.7}% +\contentsline {subsection}{\numberline {1.2.8}\textcolor {Chapter }{RightOrder (for IsExtRElement)}}{7}{subsection.1.2.8}% +\contentsline {subsection}{\numberline {1.2.9}\textcolor {Chapter }{LeftOrdersOfElements (for IsMagma)}}{7}{subsection.1.2.9}% +\contentsline {subsection}{\numberline {1.2.10}\textcolor {Chapter }{RightOrdersOfElements (for IsMagma)}}{7}{subsection.1.2.10}% +\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{smallantimagmas automatic generated documentation of global functions}}{7}{section.1.3}% +\contentsline {subsection}{\numberline {1.3.1}\textcolor {Chapter }{AllSubmagmas}}{7}{subsection.1.3.1}% +\contentsline {subsection}{\numberline {1.3.2}\textcolor {Chapter }{MagmaIsomorphismInvariantsMatch}}{8}{subsection.1.3.2}% +\contentsline {subsection}{\numberline {1.3.3}\textcolor {Chapter }{IsMagmaIsomorphic}}{8}{subsection.1.3.3}% +\contentsline {subsection}{\numberline {1.3.4}\textcolor {Chapter }{IsMagmaAntiisomorphic}}{8}{subsection.1.3.4}% +\contentsline {subsection}{\numberline {1.3.5}\textcolor {Chapter }{TransposedMagma}}{8}{subsection.1.3.5}% +\contentsline {subsection}{\numberline {1.3.6}\textcolor {Chapter }{LeftPower}}{9}{subsection.1.3.6}% +\contentsline {subsection}{\numberline {1.3.7}\textcolor {Chapter }{RightPower}}{9}{subsection.1.3.7}% +\contentsline {subsection}{\numberline {1.3.8}\textcolor {Chapter }{AllSmallAntimagmas}}{9}{subsection.1.3.8}% +\contentsline {subsection}{\numberline {1.3.9}\textcolor {Chapter }{NrSmallAntimagmas}}{9}{subsection.1.3.9}% +\contentsline {subsection}{\numberline {1.3.10}\textcolor {Chapter }{SmallAntimagma}}{10}{subsection.1.3.10}% +\contentsline {subsection}{\numberline {1.3.11}\textcolor {Chapter }{OneSmallAntimagma}}{10}{subsection.1.3.11}% +\contentsline {subsection}{\numberline {1.3.12}\textcolor {Chapter }{ReallyAllSmallAntimagmas}}{10}{subsection.1.3.12}% +\contentsline {subsection}{\numberline {1.3.13}\textcolor {Chapter }{ReallyNrSmallAntimagmas}}{10}{subsection.1.3.13}% +\contentsline {subsection}{\numberline {1.3.14}\textcolor {Chapter }{AntimagmaGeneratorPossibleDiagonals}}{11}{subsection.1.3.14}% +\contentsline {subsection}{\numberline {1.3.15}\textcolor {Chapter }{AntimagmaGeneratorFilterNonIsomorphicMagmas}}{11}{subsection.1.3.15}% +\contentsline {section}{\numberline {1.4}\textcolor {Chapter }{smallantimagmas automatic generated documentation of methods}}{11}{section.1.4}% +\contentsline {subsection}{\numberline {1.4.1}\textcolor {Chapter }{MagmaIsomorphism (for IsMagma, IsMagma)}}{11}{subsection.1.4.1}% +\contentsline {subsection}{\numberline {1.4.2}\textcolor {Chapter }{MagmaAntiisomorphism (for IsMagma, IsMagma)}}{11}{subsection.1.4.2}% +\contentsline {chapter}{Index}{12}{section*.4}% diff --git a/doc/smallantimagmas.xml b/doc/smallantimagmas.xml new file mode 100644 index 0000000..614a9dc --- /dev/null +++ b/doc/smallantimagmas.xml @@ -0,0 +1,16 @@ + + + + +] +> + +<#Include SYSTEM "title.xml"> + + +<#Include SYSTEM "_AutoDocMainFile.xml"> + + + diff --git a/doc/times.css b/doc/times.css new file mode 100644 index 0000000..4262272 --- /dev/null +++ b/doc/times.css @@ -0,0 +1,6 @@ +/* times.css Frank Lübeck */ +/* Change default CSS to use Times font. */ + +body { + font-family: Times,Times New Roman,serif; +} diff --git a/doc/title.xml b/doc/title.xml new file mode 100644 index 0000000..cc3d22b --- /dev/null +++ b/doc/title.xml @@ -0,0 +1,44 @@ + + + + + + smallantimagmas + + + A fork of smallgrp package for small antiassociative magmas + + + 0.2.0 + + + Kamil Zabielski
 +
+Department of Theoretical Computer Science
+Białystok University of Technology
+Wiejska 45A
+15-325 Białystok
+Poland
+
+ + + + 28 August 2024 + + + License + ©right; 2024 by Kamil Zabielski

+ &smallantimagmas; package is free software; + you can redistribute it and/or modify it under the terms of the + http://www.fsf.org/licenses/gpl.html + as published by the Free Software Foundation; either version 2 of the License, + or (at your option) any later version. + + + + We appreciate very much all past and future comments, suggestions and + contributions to this package and its documentation provided by &GAP; + users and developers. + + + \ No newline at end of file diff --git a/doc/toggless.css b/doc/toggless.css new file mode 100644 index 0000000..88650cb --- /dev/null +++ b/doc/toggless.css @@ -0,0 +1,42 @@ +/* toggless.css Frank Lübeck */ + +/* Using javascript we change all div.ContSect to div.ContSectOpen or + div.ContSectClosed. This way the config for div.ContSect in manual.css + is no longer relevant. Here we add the CSS for the new elements. */ +/* This layout is based on an idea by Burkhard Höfling. */ + +div.ContSectClosed { + text-align: left; + margin-left: 1em; +} +div.ContSectOpen { + text-align: left; + margin-left: 1em; +} +div.ContSectOpen div.ContSSBlock { + display: block; + text-align: left; + margin-left: 1em; +} +div.ContSectOpen div.ContSSBlock a { + display: block; + width: 100%; + margin-left: 1em; +} +span.tocline a:hover { + display: inline; + background: #eeeeee; +} +span.ContSS a:hover { + display: inline; + background: #eeeeee; +} +span.toctoggle { + font-size: 80%; + display: inline-block; + width: 1.2em; +} +span.toctoggle:hover { + background-color: #aaaaaa; +} + diff --git a/doc/toggless.js b/doc/toggless.js new file mode 100644 index 0000000..b932d83 --- /dev/null +++ b/doc/toggless.js @@ -0,0 +1,65 @@ +/* toggless.js Frank Lübeck */ + +/* this file contains two functions: + mergeSideTOCHooks: this changes div.ContSect elements to the class + ContSectClosed and includes a hook to toggle between + ContSectClosed and ContSectOpen. + openclosetoc: this function does the toggling, the rest is done by + CSS +*/ + + + +closedTOCMarker = "▶ "; +openTOCMarker = "▼ "; +noTOCMarker = " "; +/* merge hooks into side toc for opening/closing subsections + with openclosetoc */ +function mergeSideTOCHooks() { + var hlist = document.getElementsByTagName("div"); + for (var i = 0; i < hlist.length; i++) { + if (hlist[i].className == "ContSect") { + var chlds = hlist[i].childNodes; + var el = document.createElement("span"); + var oncl = document.createAttribute("class"); + oncl.nodeValue = "toctoggle"; + el.setAttributeNode(oncl); + var cont; + if (chlds.length > 2) { + var oncl = document.createAttribute("onclick"); + oncl.nodeValue = "openclosetoc(event)"; + el.setAttributeNode(oncl); + cont = document.createTextNode(closedTOCMarker); + } else { + cont = document.createTextNode(noTOCMarker); + } + el.appendChild(cont); + hlist[i].firstChild.insertBefore(el, hlist[i].firstChild.firstChild); + hlist[i].className = "ContSectClosed"; + } + } +} + +function openclosetoc (event) { + /* first two steps to make it work in most browsers */ + var evt=window.event || event; + if (!evt.target) + evt.target=evt.srcElement; + + var markClosed = document.createTextNode(closedTOCMarker); + var markOpen = document.createTextNode(openTOCMarker); + + var par = evt.target.parentNode.parentNode; + if (par.className == "ContSectOpen") { + par.className = "ContSectClosed"; + evt.target.replaceChild(markClosed, evt.target.firstChild); + } + else if (par.className == "ContSectClosed") { + par.className = "ContSectOpen"; + evt.target.replaceChild(markOpen, evt.target.firstChild); + } +} + +/* adjust jscontent which is called onload */ +jscontentfuncs.push(mergeSideTOCHooks); +