monoid(Ring) -- make or retrieve a monoid

• Function: monoid

• Usage:

  monoid R

• Inputs:
  • R, a ring,
• Optional inputs:
  • Constants => ..., default value false, specify how to handle degrees in the coefficient ring
  • DegreeGroup => ..., default value null, specify the degrees of the variables
  • 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:
  • a monoid, the monoid of monomials in the polynomial ring R

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