codimMA -- Codimension of a monomial algebra.

Synopsis

Usage:

codimMA R

codimMA B

codimMA 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.
- M, a MonomialAlgebra,
Outputs:
- an integer,

Description

Compute the codimension 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 : codimMA B

o2 = 4

i3 : B={{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1, 3, 1}}

o3 = {{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1,
     ------------------------------------------------------------------------
     3, 1}}

o3 : List

i4 : M=monomialAlgebra B

      ZZ
o4 = ---[x ..x ]
     101  0   6

o4 : MonomialAlgebra generated by {{2, 2, 1}, {1, 1, 3}, {1, 2, 2}, {2, 0, 3}, {1, 4, 0}, {2, 3, 0}, {1, 3, 1}}

i5 : codimMA M

o5 = 4

Ways to use codimMA :

codimMA(List)
codimMA(MonomialAlgebra)
codimMA(PolynomialRing)

For the programmer

The object codimMA is a method function.