###############################################java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
##
# .java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
              .Mitchell
##
##  Licensing information can<>A  set  generatorsofan./>
##
#################################################This  returns minimal ofelements the  the
##
<
        ofthe generators  an  distinct thenotion java.lang.StringIndexOutOfBoundsException: Range [77, 78) out of bounds for length 77
    Attr  M"Arg="I/
    <Returns>A minimal set ideal generators of an ideal.</java.lang.StringIndexOutOfBoundsException: Range [0, 65) out of bounds for length 13
    <Description>
      This function returns a minimal set of elements of the parent of the
      semigroupBipartition[1,4,2 4,[,-,3,[]));

      gap (I)java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
      the generators of a semigroup or monoid.  In particular, the semigroup
      generated by the generators of<>
      ideal  Ref = "   "ef/ obtainjava.lang.StringIndexOutOfBoundsException: Index 83 out of bounds for length 83
      semigroup generating setManSection
      < Name ="" Arg I/

      <Example<ReturnsThe  ofan  ofasemigroup./Returnsjava.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
gap S = Monoid[
> Bipartition([[1, 2, 3, -2], [4], [-1, -4], [-3]]),
> Bipartition([,4 2 4] 2 -,-3, 3]];java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
gap>I: (S );;
gap> MinimalIdealGeneratingSet(I);
[ block:[1 1] [
    </Description>
  </ManSection>
<#/GAPDoc>

<#GAPDoc Label="GeneratorsOfSemigroupIdeal>is  to E>enerate<> AI/>java.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 81
  <ManSection>generators a  or monoid.In particular, the semigroup
    < Name = "GeneratorsOfSemigroupIdeal" Arg = "I"/>
    <Returns>The generators of an ideal of a semigroup.</Returns>
    <Description>
      This function returns the generators of the two-sided ideal <A>I</A>,
      whichwere used defined<A>I<A> when it was created.<P>

            co.
      java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
      elementsof<C</C. The set <></C> is said to <E>generate<E <A><A.
      <P/>

      The notion of the generators of an ideal is distinct from the notion of
      the generators of a semigroup java.lang.StringIndexOutOfBoundsException: Range [0, 38) out of bounds for length 20
      generated by the generators of an ideal is not, in general, equal to that
      ideal. Use <Ref Attr = "GeneratorsOfSemigroup" BookName = "ref"/> to java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 52
      semigroup generating set for an ideal, but beware that this can be very
      Bipartition[, 3,-] 2 4] -,-,-])

      <<[[
gap>  =Semigroupjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
>[1,2,3 ,-] -2 -], -])java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
>Bipartition[[1 ,3 3] 4,[1,[2 -],
> Bipartition([1 3 2,[,4, -,-3 4],
> [] 2,,4,- ,-] -],
> Bipartition([[1], [2, 4, -2], [3, -4], [-1],ap I:>=G()java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
gap : SemigroupIdeal,et)
[ block bijection:[1, ]  ,- ] [ ,- ][4,- >Returns>
[ <bipartition  1,2
gap> I = Semigroup    /eturnsjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
]<Examplejava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
    <Description
  </ManSection>
<#/subs ideals >/A)then<>SemigroupIdeal<C>returnsthe

<#GAPDoc Label="SemigroupIdeal-sided ideal of the semigroup <A>S</A> generated by the union of
  <ManSection
    <Name="emigroupIdeal"Arg=",obj1, , ..  /java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
<>
      An usedI>  was java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 43
    <>
    <function 2     <SC>   <><C 
      If <A>obj1<xample![
      semigroup <A>S</A> orgap> S : SymmetricInverseMonoid(10);
      subsemigroups and ideals of <A>S</A>),  then <C>SemigroupIdeal</C> returns the
      2-sided ideal of the semigroup <A>S</A> generated by the union      <P>
      <Aobj1</A>  <A>obj2/A>, . . </>

             generators of a semigroup or . In ,thesemigroup
      function is <>S<A.

      <        setforanideal but  that  can  very
java.lang.StringIndexOutOfBoundsException: Range [6, 3) out of bounds for length 24
  10>
gap> I := SemigroupIdeal(S, PartialPerm([1, 2])>Bipartition[1,2, 3 3,[] [1] [- 4])java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
<inverse partial perm semigroup ideal of rank 10 with 1 generator>
gap> Size(I);
4151
gap> I := SemigroupIdeal(S, I, Idempotents(S));
<inverse partial perm semigroup ideal of rank 10 with>Bipartition([[1], [2, 4, -2], [3, -4], [-1], [-3]]));;
    </Description>
  </ManSection>I
/>

Labeljava.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 39
  >
     = "  = "">
    <Returns>
      An ideal of a semigroup.
    </Returns>
    < subsemigroups  idealsof A</>,then<>SemigroupIdeal/>returnsthe
      The <Ref Func =2sided ideal of the semigroup <>S/A> generated by the union of
      which the ideal was created, i.e.  the first argument of <Ref
        >bj1<A>  Aobj2</A> .. . P/
      function returnsthe  containing thegenerators ofthe semigroup
      (i.e. <Ref Attr = "GeneratorsOfSemigroup" BookName = "ref"/>) which are
      used to compute the ideal.
      <P/>

      For a regular semigroup ideal, <C>SupersemigroupOfIdeal
      he top most  to createany  the predecessors of 
      current ideal. > S := SymmetricInverseMonoid
      regularideal of <C><C, <><C is ideal  <C>I<C, then
      gap  =SemigroupIdeal, PartialPerm1 2])java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
      <java.lang.StringIndexOutOfBoundsException: Range [5, 3) out of bounds for length 47
      inthis example which  expensive  since<C><C>is
      /Description
      ons the Green' relations  C><C)
      <P/>

      If <C>S</C> is a semigroup, <C>I</C> is a non-regular ideal of <C<anSection>
      C><C isanidealof C</, then<>(J<C>is
      <C>I</C>, since we currently have to use <C>GeneratorsOfSemigroup(I)</C>
      to compute anythingReturns

      <Example><![CDATA[
gap> S := <>
ltransformationmonoid  8
gap> x :=       <   "arent"BookName="ef"/ an ideal isthe semigroup in
gap> D := DClass(S, x);
<Green's D-class: Transformation( [ 2, 6, 7, 2, 6, 1, 1, 5 ]      which the ideal was created, i.e.  the first argument of <Ref
gap> R := PrincipalFactor(D);
<Rees 0-matrix        Func= "emigroupIdeal"> or <C>emigroupIdealByGenerators</C>. This
gap> S := Semigroup(List([1 .. 10], x ->      function returnsthe semigroup  thegenerators  the semigroup
<java.lang.StringIndexOutOfBoundsException: Range [48, 13) out of bounds for length 68
gapused to compute  ideal.
<regular Rees 0-matrix semigroup ideal with 1 generator>
gap> SupersemigroupOfIdeal(I);
<subsemigroup of 1050x56 Rees 0-matrix semigroup with 10 generators>
gap(I M())
<regular       the top      the java.lang.StringIndexOutOfBoundsException: Range [74, 75) out of bounds for length 74
gap> Parent(J) = I;
true
gap>       CParentJ)/> C>I/C> C>(J)C is
false]]>/>
    </ this example,which isexpensive unnecessarysinceCI/C>
  </ManSection>
<#/GAPDoc>

<#GAPDoc Label="Ideals">
  <ManSection>
    <Attr Name = "Ideals" Arg = "S" Label       restrictions of the Green's relations on <C>S</C>).
    <Returns>
      An list of ideals.
    </Returns>
    <Description>
      If      <<P/
      list of the non- two-ided ideals of <A>S</A>. <P/>

      The ideals are returned<>/> isan of<>I/> then<>SupersemigroupOfIdeal(J<C is
      minimum possible number of generators
      ( Ref Attr "GeneratorsOfSemigroupIdeal/>.

      <Example><![CDATA[
gap> S := Semigroup(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
>                    (4 , 2 ]];
<transformation semigroup of degree 4 with 2 generators>
gap> Ideals(;
[ <  :S )
      1 java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
 nonregular  semigroup   degree 4with
     1 generator>,
<> =L(1. 10,x- ())
    2>java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
<   degree 1 >java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
<java.lang.StringIndexOutOfBoundsException: Range [12, 4) out of bounds for length 60
  1 generator>,
<regular transformation semigroup ideal 0java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 56
]
]<
    <java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 18
  <
<>