Add Translations

doc/bibliography.xml

@@ -576,5 +576,46 @@
   <year>2021</year>
   <other type="arxiv">2108.08277</other>
 </article></entry>
+
+<entry id="Petrich1968aa"><article>
+  <author>
+    <name><first>Mario</first><last>Petrich</last></name>
+  </author>  
+  <title>The translational hull of a completely 0-simple semigroup</title>
+  <journal>Glasgow Mathematical Journal</journal>
+  <year>1968</year>
+  <volume>9</volume>
+  <number>1</number>
+  <pages>1--11</pages>
+</article></entry>
+
+<entry id="Petrich1970aa"><article>
+  <author>
+    <name><first>Mario</first><last>Petrich</last></name>
+  </author>  
+  <title>The translational hull in semigroups and rings</title>
+  <journal>Semigroup Forum</journal>
+  <year>1970</year>
+  <volume>1</volume>
+  <number>1</number>
+  <pages>283--360</pages>
+  <issn>1432-2137</issn>
+  <url>https://doi.org/10.1007/BF02573051</url>
+  <other type="doi">10.1007/BF02573051</other>
+</article></entry>
 
+<entry id="Clifford1977aa"><article>
+  <author>
+    <name><first>Alfred H.</first><last>Clifford</last></name>
+    <name><first>Mario</first><last>Petrich</last></name>
+  </author>  
+  <title>Some classes of completely regular semigroups</title>
+  <journal>Journal of Algebra</journal>
+  <year>1977</year>
+  <volume>46</volume>
+  <number>2</number>
+  <pages>462--480</pages>
+  <issn>0021-8693</issn>
+  <url>http://dx.doi.org/10.1016/0021-8693(77)90383-0</url>
+</article></entry>
 </file>

doc/z-chap08.xml

@@ -176,4 +176,8 @@
     <#Include Label = "McAlisterTripleSemigroupElement">
   </Section>
 
+
+  <!--**********************************************************************-->
+  <!--**********************************************************************-->
+
 </Chapter>

doc/z-chap14.xml

@@ -155,4 +155,30 @@
     </Subsection>
   </Section>
 
+  <!--**********************************************************************-->
+  <!--**********************************************************************-->
+
+  <Section>
+
+    <Heading>
+      Changing the representation of a semigroup
+    </Heading>
+
+    <#Include Label = "IsomorphismReesZeroMatrixSemigroup">
+
+  </Section>
+
+  <!--**********************************************************************-->
+  <!--**********************************************************************-->
+
+  <Section>
+
+    <Heading>
+      The Nambooripad partial order of a regular semigroup
+    </Heading>
+
+    <#Include Label = "NambooripadLeqRegularSemigroup">
+    <#Include Label = "NambooripadPartialOrder">
+
+  </Section>
 </Chapter>

gap/attributes/attr.gd

@@ -74,3 +74,8 @@ DeclareAttribute("NambooripadPartialOrder", IsSemigroup);
 
 DeclareOperation("LeftIdentity", [IsSemigroup, IsMultiplicativeElement]);
 DeclareOperation("RightIdentity", [IsSemigroup, IsMultiplicativeElement]);
+
+DeclareAttribute("MultiplicationTableWithCanonicalPositions",
+                 IsSemigroup and CanUseFroidurePin);
+DeclareAttribute("TransposedMultiplicationTableWithCanonicalPositions",
+                 IsSemigroup and CanUseFroidurePin);

gap/attributes/attr.gi

@@ -1104,3 +1104,25 @@ function(S, x)
   result := EvaluateWord(GeneratorsOfSemigroup(S), p[2]);
   return result ^ SmallestIdempotentPower(result);
 end);
+
+InstallMethod(MultiplicationTableWithCanonicalPositions,
+"for a semigroup with CanUseFroidurePin",
+[IsSemigroup and CanUseFroidurePin],
+function(S)
+  local n, sortedlist, t, tinv, M;
+  n          := Size(S);
+  sortedlist := AsSortedList(S);
+
+  t    := PermList(List([1 .. n], i -> PositionCanonical(S, sortedlist[i])));
+  tinv := t ^ -1;
+  M    := MultiplicationTable(S);
+
+  return List([1 .. n], i -> List([1 .. n], j -> M[i ^ tinv][j ^ tinv] ^ t));
+end);
+
+InstallMethod(TransposedMultiplicationTableWithCanonicalPositions,
+"for a semigroup with CanUseFroidurePin",
+[IsSemigroup and CanUseFroidurePin],
+function(S)
+  return TransposedMat(MultiplicationTableWithCanonicalPositions(S));
+end);

gap/attributes/rms-translat.gd

@@ -0,0 +1,39 @@
+############################################################################
+##
+# W  rms-translat.gd
+# Y  Copyright (C) 2015-22                                      Finn Smith
+##
+##  Licensing information can be found in the README file of this package.
+##
+#############################################################################
+##
+
+# The definitions in this file are internal, and hence not included in the
+# user documentation.
+DeclareCategory("_IsTranslationOfNormalRMS", IsSemigroupTranslation);
+DeclareCategory("_IsLeftTranslationOfNormalRMS",
+                _IsTranslationOfNormalRMS and IsLeftTranslation);
+DeclareCategory("_IsRightTranslationOfNormalRMS",
+                _IsTranslationOfNormalRMS and IsRightTranslation);
+DeclareCategory("_IsBitranslationOfNormalRMS", IsBitranslation);
+
+DeclareCategoryCollections("_IsTranslationOfNormalRMS");
+DeclareCategoryCollections("_IsLeftTranslationOfNormalRMS");
+DeclareCategoryCollections("_IsRightTranslationOfNormalRMS");
+DeclareCategoryCollections("_IsBitranslationOfNormalRMS");
+
+DeclareSynonym("_IsTranslationOfNormalRMSSemigroup", IsSemigroup and
+                _IsTranslationOfNormalRMSCollection);
+DeclareSynonym("_IsLeftTranslationOfNormalRMSSemigroup", IsSemigroup and
+                _IsLeftTranslationOfNormalRMSCollection);
+DeclareSynonym("_IsRightTranslationOfNormalRMSSemigroup", IsSemigroup and
+                _IsRightTranslationOfNormalRMSCollection);
+DeclareSynonym("_IsBitranslationOfNormalRMSSemigroup", IsSemigroup and
+                _IsBitranslationOfNormalRMSCollection);
+
+DeclareGlobalFunction("_LeftTranslationOfNormalRMS");
+DeclareGlobalFunction("_LeftTranslationOfNormalRMSNC");
+DeclareGlobalFunction("_RightTranslationOfNormalRMS");
+DeclareGlobalFunction("_RightTranslationOfNormalRMSNC");
+
+DeclareGlobalFunction("_BitranslationOfNormalRMSByTripleNC");