<Section>
                <Heading>
                    Numerical semigroups with maximal embedding dimension
                </Heading>
                If <M>S</M> is a numerical semigroup and <M>m</M> is its multiplicity (the least 
                positive integer belonging to it), then the embedding dimension <M>e</M> of <M>S</M> (the 
                cardinality of the minimal system of generators of <M>S</M>) is less than or equal
                to <M>m</M>. We say that <M>S</M> has maximal embedding dimension (MED for short) when <M>e=m</M>. 
                The intersection of two numerical semigroups with the same multiplicity and maximal embedding 
                dimension is again of maximal embedding dimension. Thus we define the MED closure of a non-empty subset
                of positive integers <M>M=\{m &lt; m_1 &lt; \cdots &lt; m_n &lt;\cdots\}</M> with <M>\gcd(M)=1</M>
                as the intersection of all MED numerical semigroups with multiplicity <M>m</M>. 
                
                <P/> 
                Given a MED numerical semigroup <M>S</M>, we say that <M>M=\{m_1 &lt; \cdots&lt; m_k\}</M> is a MED system 
                of generators if the MED closure of <M>M</M> is <M>S</M>. Moreover, <M>M</M> is a minimal MED generating 
                system for <M>S</M> provided that every proper subset of <M>M</M> is not a MED system of generators 
                of <M>S</M>. Minimal MED generating systems are unique, and in general are smaller that the 
                classical minimal generating systems (see <Cite Key="RGGB03"></Cite>).
                
                
                <ManSection>
                    <Func Arg="S" Name="IsMEDNumericalSemigroup"></Func>
                    <Description>
                        <A>S</A> is a numerical semigroup.    
                        <P/>
                        Returns true if <A>S</A> is a MED numerical semigroup and false otherwise. 
                        <Example><![CDATA[
gap> IsMEDNumericalSemigroup(NumericalSemigroup(3,5,7)); 
true 
gap> IsMEDNumericalSemigroup(NumericalSemigroup(3,5)); 
false
]]>
                        </Example>          
                    </Description>
                </ManSection>
                
                
                <ManSection>
                    <Func Arg="S" Name="MEDNumericalSemigroupClosure"></Func>
                    <Description>
                        <A>S</A> is a numerical semigroup.    
                        <P/>
                        Returns the MED closure of <A>S</A>.
                        <Example><![CDATA[
gap> MEDNumericalSemigroupClosure(NumericalSemigroup(3,5)); 
<Numerical semigroup> 
gap> MinimalGeneratingSystemOfNumericalSemigroup(last); 
[ 3, 5, 7 ]
]]>
                        </Example>          
                    </Description>
                </ManSection>
                
                <ManSection>
                    <Func Arg="S" Name="MinimalMEDGeneratingSystemOfMEDNumericalSemigroup"></Func>
                    <Description>
                        <A>S</A> is a MED numerical semigroup.    
                        <P/>
                        Returns the minimal MED generating system of <A>S</A>.
                        <Example><![CDATA[
gap> MinimalMEDGeneratingSystemOfMEDNumericalSemigroup( 
> NumericalSemigroup(3,5,7)); 
[ 3, 5 ]
]]>
                        </Example>          
                    </Description>
                </ManSection>
                
            </Section>