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# monoid(...,Variables=>...) -- specify the names of the indeterminates

## Synopsis

• Usage:
monoid[Variables => L]
monoid[Variables => n, VariableBaseName => s]

## Description

When given a list or sequence, Variables => L specifies the variables to be used as generators of the monoid.

 i1 : QQ[Variables => vars(0..3)] o1 = QQ[a..d] o1 : PolynomialRing i2 : QQ[Variables => x_(0,0)..x_(3,3)] o2 = QQ[x ..x ] 0,0 3,3 o2 : PolynomialRing

When given a number, Variables => n specifies number of indexed variables to create with base name provided by VariableBaseName => s, where s may be either a symbol or string. The default base name is p.

 i3 : QQ[Variables => 2] o3 = QQ[p ..p ] 0 1 o3 : PolynomialRing i4 : QQ[Variables => 3, VariableBaseName => v] o4 = QQ[v ..v ] 0 2 o4 : PolynomialRing i5 : QQ[Variables => 4, VariableBaseName => "e"] o5 = QQ[e ..e ] 0 3 o5 : PolynomialRing i6 : class baseName e_0 o6 = IndexedVariable o6 : Type i7 : class e o7 = IndexedVariableTable o7 : Type

This option is also useful when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.

 i8 : R = QQ[x, y, Degrees => {1, 2}] o8 = R o8 : PolynomialRing i9 : newRing(R, Variables => {a,b}) o9 = QQ[a..b] o9 : PolynomialRing i10 : degrees oo o10 = {{1}, {2}} o10 : List i11 : tensor(R, R, Variables => t_(0,0)..t_(1,1)) o11 = QQ[t ..t ] 0,0 1,1 o11 : PolynomialRing i12 : degrees oo o12 = {{1, 0}, {2, 0}, {0, 1}, {0, 2}} o12 : List i13 : symmetricAlgebra(R^3, Variables => s_0..s_2) o13 = R[s ..s ] 0 2 o13 : PolynomialRing

## Further information

• Default value: null
• Function: monoid -- make or retrieve a monoid
• Option key: Variables -- an optional argument