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

Functions with optional argument named Degrees :

monoid(...,Degrees=>...) -- specify the degrees of the variables
newRing(...,Degrees=>...) -- see newRing -- make a copy of a ring, with some features changed
symmetricAlgebra(...,Degrees=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
tensor(Monoid,Monoid,Degrees=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,Degrees=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids

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

Synopsis

Description

Further information

See also

Functions with optional argument named Degrees :