# monoid(...,Degrees=>...) -- specify the degrees of the variables

## Synopsis

• Usage:
monoid[x,y,z, Degrees => {d1, d2, d3}]
monoid[x,y,z, DegreeRank => r]

## Description

The Degrees option specifies the degrees of the variables in the monoid. If provided, the value must be a list or sequence with as many entries (after splicing and flattening) as there are variables. Each degree is an integers or a list of integers. Degrees provided as integers will be converted into multidegrees of length 1.

 i1 : QQ[x,y,z, Degrees => {2:1, 2}] o1 = QQ[x..z] o1 : PolynomialRing i2 : degrees oo o2 = {{1}, {1}, {2}} o2 : List i3 : QQ[x,y, Degrees => {{1,0}, {0,1}}] o3 = QQ[x..y] o3 : PolynomialRing i4 : degrees oo o4 = {{1, 0}, {0, 1}} o4 : List

The DegreeRank option specifies the degree length of the monoid. If provided, the value must be an integer. If the Degrees option is not provided, the degrees of the variables are determined similar to this example.

 i5 : QQ[a..f, DegreeRank => 3] o5 = QQ[a..f] o5 : PolynomialRing i6 : transpose matrix degrees oo o6 = | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 1 1 1 1 | 3 6 o6 : Matrix ZZ <--- ZZ

This option may also be used when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.

## Further information

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