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# monoid(Ring) -- make or retrieve a monoid

- Function: monoid
- Usage:
    `monoid R`
- Inputs:
  - R, a ring,
- Optional inputs:
  - Constants => ..., default value false, specify how to handle degrees in the coefficient ring
  - DegreeGroup => ..., default value null, specify the degrees of the variables
  - DegreeLift => ..., default value null, specify maps between degree groups
  - DegreeMap => ..., default value null, specify maps between degree groups
  - DegreeRank => ..., default value null, specify the degrees of the variables
  - Degrees => ..., default value null, specify the degrees of the variables
  - Global => ..., default value true, specify local or global monomial order
  - Heft => ..., default value null, specify a heft vector
  - Inverses => ..., default value false, allow negative exponents in monomials
  - Join => ..., default value null, specify how to handle degrees in the coefficient ring
  - Local => ..., default value false, specify local or global monomial order
  - MonomialOrder => ..., default value {GRevLex, Position => Up}, specify the monomial ordering
  - MonomialSize => ..., default value 32, specify the bit-length of monomial exponents in the ring
  - SkewCommutative => ..., default value {}, specify skew commuting variables in the ring
  - VariableBaseName => ..., default value "p", specify the names of the indeterminates
  - Variables => ..., default value null, specify the names of the indeterminates
  - Weights => ..., default value {}, specify weights of the variables
  - WeylAlgebra => ..., default value {}, specify differential operators in the ring
- Outputs:
  - a monoid, the monoid of monomials in the polynomial ring R

## Description

If R is a quotient ring of a polynomial ring S, then the monoid of S is returned.

    i1 : R = QQ[a..d, Weights=>{1,2,3,4}]

    o1 = R

    o1 : PolynomialRing

    i2 : M = monoid R

    o2 = M

    o2 : GeneralOrderedMonoid

    i3 : use M

    o3 = M

    o3 : GeneralOrderedMonoid

    i4 : class a

    o4 = M

    o4 : GeneralOrderedMonoid

## Ways to use this method:

- monoid(Ring) -- make or retrieve a monoid

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/monoid-doc.m2:563:0.