# codimMA -- Codimension of a monomial algebra.

## Synopsis

• Usage:
codimMA R
codimMA B
codimMA M
• Inputs:
• R, , with B = degrees R and K = coefficientRing R, or
• B, a list, with the generators of an affine semigroup in \mathbb{N}^d.
• M, ,
• Outputs:

## 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 .