degreeMA -- Degree of a monomial algebra.

Synopsis

Usage:

degreeMA R

degreeMA B

degreeMA M
Inputs:
- R, a polynomial ring, with B = degrees R and K = coefficientRing R, or
- B, a list, with the generators of an affine semigroup in \mathbb{N}^d.
- B, a MonomialAlgebra,
Optional inputs:
- Verbose => ..., default value 0, Option to print intermediate results.
Outputs:
- an integer,

Description

Compute the degree of the homogeneous monomial algebra K[B].

As the result is independent of K it is possible to specify just B.

i1 : B={{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1, 3, 1}}

o1 = {{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1,
     ------------------------------------------------------------------------
     3, 1}}

o1 : List

i2 : R=QQ[x_1..x_(#B),Degrees=>B]

o2 = R

o2 : PolynomialRing

i3 : degreeMA R

o3 = 6

i4 : B={{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1, 3, 1}}

o4 = {{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1,
     ------------------------------------------------------------------------
     3, 1}}

o4 : List

i5 : M=monomialAlgebra B

      ZZ
o5 = ---[x ..x ]
     101  0   6

o5 : MonomialAlgebra generated by {{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1, 3, 1}}

i6 : degreeMA M

o6 = 6

Ways to use degreeMA :

degreeMA(List)
degreeMA(MonomialAlgebra)
degreeMA(PolynomialRing)

For the programmer

The object degreeMA is a method function with options.