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

Synopsis

• Usage:

  monoid[Variables => L]

  monoid[Variables => n, VariableBaseName => s]

Description

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

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

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

See also

• vars -- variables
• baseName -- the base name of a generator
• IndexedVariable -- the class of all indexed variables
• IndexedVariableTable
• monoid -- make or retrieve a monoid
• newRing -- make a copy of a ring, with some features changed
• tensor(Ring,Ring) -- tensor product of monoids
• symmetricAlgebra -- the symmetric algebra of a module

Functions with optional argument named Variables :

• basis(...,Variables=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
• coefficients(...,Variables=>...) -- see coefficients -- monomials and their coefficients
• monoid(...,Variables=>...) -- specify the names of the indeterminates
• monomials(...,Variables=>...) -- specify variables
• newRing(...,Variables=>...) -- see newRing -- make a copy of a ring, with some features changed
• symmetricAlgebra(...,Variables=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
• tensor(Monoid,Monoid,Variables=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
• tensor(Ring,Ring,Variables=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids