GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<?xml version="1.0" encoding="UTF-8"?>
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<Section>
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                <Heading>
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                    Almost-symmetric numerical semigroups
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                </Heading>
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				A numerical semigroup is almost-symmetric (<Cite Key="BF97"></Cite>) if its genus is the arithmetic mean of its Frobenius number and type.
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				We use a procedure presented in <Cite Key="MR3169635"></Cite> to determine the set of all almost-symmetric numerical semigroups with given Frobenius
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				number. In order to do this, we first calculate the set of all almost-symmetric numerical semigroups that can be constructed from an irreducible
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				numerical semigroup.
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<P/>
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                <ManSection>
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                    <Func Arg="s" Name="AlmostSymmetricNumericalSemigroupsFromIrreducible"></Func>
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                    <Description>
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                        <A>s</A> is an irreducible numerical semigroup.  The output is the set of almost-symetric numerical semigroups that can be constructed
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						from <A>s</A> by removing some of its generators as explained in <Cite Key="MR3169635"></Cite>).
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                        <Example><![CDATA[
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gap> ns := NumericalSemigroup(5,8,9,11);;
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gap> AlmostSymmetricNumericalSemigroupsFromIrreducible(ns);
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[ <Numerical semigroup with 4 generators>,
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  <Numerical semigroup with 5 generators>,
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  <Numerical semigroup with 5 generators> ]
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gap> List(last,MinimalGeneratingSystemOfNumericalSemigroup);
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[ [ 5, 8, 9, 11 ], [ 5, 8, 11, 14, 17 ], [ 5, 9, 11, 13, 17 ] ]
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]]></Example>
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                    </Description>
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                </ManSection>
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                <ManSection>
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                  <Func Arg="s" Name="IsAlmostSymmetric"></Func>
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                    <Func Arg="s" Name="IsAlmostSymmetricNumericalSemigroup"></Func>
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                    <Description>
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                        <A>s</A> is a numerical semigroup.  The output is true if the numerical semigroup is almost symmetric.
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                        <Example><![CDATA[
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gap> IsAlmostSymmetricNumericalSemigroup(NumericalSemigroup(5,8,11,14,17));
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true
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]]></Example>
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                    </Description>
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                </ManSection>
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                <ManSection>
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                    <Func Arg="f" Name="AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber"></Func>
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                    <Description>
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                        <A>f</A> is an integer greater than or equal to -1. The output is the set of all almost symmetric
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                        numerical semigroups with Frobenius number <A>f</A>.
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                        <Example><![CDATA[
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gap> Length(AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber(12));
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gap> Length(IrreducibleNumericalSemigroupsWithFrobeniusNumber(12));
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2
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]]></Example>
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                    </Description>
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                </ManSection>
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</Section>
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