# codimMA -- Codimension of a monomial algebra.

• Usage:
codimMA R
codimMA B
codimMA M
• Inputs:
• 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 , x , x , x , x , x ] 101 0 1 2 3 4 5 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)