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MonomialAlgebras :: degreeMA

degreeMA -- Degree of a monomial algebra.

Synopsis

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 :

For the programmer

The object degreeMA is a method function with options.