Magma supports the following categories of semigroups:
The generic free structures are created by the functions FreeSemigroup(n) and FreeMonoid(n), where n is the number of generators. One may create any semigroup by creating one of these structures and then forming the required quotient semigroup, using the syntax
quo< SEMIGROUP | RELATIONS >
To abbreviate this process, these constructors apply:
Semigroup< GENERATORS | RELATIONS >
Monoid< GENERATORS | RELATIONS >
> M<x, y>:=Monoid< x, y | x^2, y^2, (x*y)^2 >;
> print M;
Finitely presented monoid
Relations
x^2 = Id(M)
y^2 = Id(M)
(x * y)^2 = Id(M)
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