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

## Synopsis

• Function: monoid
• Usage:
monoid R
• Inputs:
• Optional inputs:
• Constants (missing documentation) => ..., default value false,
• DegreeGroup (missing documentation) => ..., default value null,
• 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:
• , 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