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# MonomialSubalgebra -- class of monomial subalgebras

## Description

A monomial subalgebra is a subalgebra of a polynomial ring generated by monomials. In other words, it is a monoid algebra. A new monomial subalgebra can be created using createMonomialSubalgebra.

    i1 : R=ZZ/37[x,y,z];

    i2 : S=createMonomialSubalgebra {x^2*y, x*z, z^3}

    o2 = MonomialSubalgebra{cache => CacheTable{}       }
                                            2         3
                            generators => {x y, x*z, z }
                            ring => R

    o2 : MonomialSubalgebra of R

    i3 : ring S

    o3 = R

    o3 : PolynomialRing

    i4 : gens S

           2         3
    o4 = {x y, x*z, z }

    o4 : List

## See also

- createMonomialSubalgebra -- creates a monomial subalgebra

## Methods that use a monomial subalgebra:

- generators(MonomialSubalgebra) -- generators of a monomial subalgebra
- intclToricRing(MonomialSubalgebra) -- integral closure of a toric ring
- normalToricRing(MonomialSubalgebra) -- normalization of a toric ring
- numgens(MonomialSubalgebra) -- number of generators of a monomial subalgebra
- ring(MonomialSubalgebra) -- surrounding ring of a monomial subalgebra
- vars(MonomialSubalgebra) -- row matrix of the generators of a monomial subalgebra

## For the programmer

The object MonomialSubalgebra is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Normaliz.m2:840:0.