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# degreeMA -- Degree of a monomial algebra.

## Synopsis

• Usage:
degreeMA R
degreeMA B
degreeMA 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.
• B, ,
• Optional inputs:
• Verbose => ..., default value 0, Option to print intermediate results.
• Outputs:

## 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 :

• degreeMA(List)
• degreeMA(MonomialAlgebra)
• degreeMA(PolynomialRing)

## For the programmer

The object degreeMA is .