next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
MonomialAlgebras :: codimMA

codimMA -- Codimension of a monomial algebra.

Synopsis

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 :