add documentation for IsRefinementKernelOfTransformation

doc/trans.xml

@@ -43,3 +43,40 @@ Transformation( [ 3, 5, 2, 2, 2 ] )]]></Example>
   </Description>
   </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="IsRefinementKernelOfTransformation">
+  <ManSection>
+    <Func Name = "IsRefinementKernelOfTransformation" Arg = "trans1, trans2, n"/>
+    <Returns>
+      True or False.
+    </Returns>
+    <Description>
+      If <A>trans1</A> and <A>trans2</A> are two transformations belonging
+      to a transformation semigroup of degree <C>n</C>, then 
+      <C>IsRefinementKernelOfTransformation</C> returns True if the kernel of 
+      <A>trans1</A> is a refinement of the kernel of <A>trans2</A> and returns
+      False otherwise.
+      An error message will be raised if <A>trans1</A> or <A>trans2</A> has degree
+      higher than <C>n</C> and hence cannot belong to a semigroup of degree
+      <C>n</C>.
+    <Example><![CDATA[
+gap> s := Transformation([2,2,3,2]);
+Transformation( [ 2, 2, 3, 2 ] )
+gap> t := Transformation([2,2,3,3]);
+Transformation( [ 2, 2, 3, 3 ] )
+gap> IsRefinementKernelOfTransformation(s, t, 4);
+false
+gap> a := Transformation([2,4,3,2]);
+Transformation( [ 2, 4, 3, 2 ] )
+gap> b := Transformation([3,3,1,3]);
+Transformation( [ 3, 3, 1, 3 ] )
+gap> IsRefinementKernelOfTransformation(a, b, 4);
+false
+gap> IsRefinementKernelOfTransformation(b, a, 4);
+true
+gap> IsRefinementKernelOfTransformation(b, a, 3);
+Error, Degree of the first transformation greater than 3.
+Expecting a degree at most n, found 4 instead.]]></Example>
+  </Description>
+  </ManSection>
+<#/GAPDoc>

doc/z-chap11.xml

@@ -210,6 +210,7 @@
     <#Include Label = "SmallestElementSemigroup">
     <#Include Label = "CanonicalTransformation">
     <#Include Label = "IsConnectedTransformationSemigroup">
+    <#Include Label = "IsRefinementKernelOfTransformation">
 
   </Section>