# isNormalMA -- Test whether a simplicial monomial algebra is normal.

## Synopsis

• Usage:
isNormalMA R
isNormalMA B
isNormalMA 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

Test whether the simplicial monomial algebra K[B] is normal.

Note that this condition does not depend on K.

 i1 : B={{1,0,0},{0,2,0},{0,0,2},{1,0,1},{0,1,1}} o1 = {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} o1 : List i2 : R=QQ[x_0..x_4,Degrees=>B] o2 = R o2 : PolynomialRing i3 : isNormalMA R o3 = false i4 : isSeminormalMA R o4 = true

 i5 : B={{1,0,0},{0,2,0},{0,0,2},{1,0,1},{0,1,1}} o5 = {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} o5 : List i6 : M=monomialAlgebra B ZZ o6 = ---[x ..x ] 101 0 4 o6 : MonomialAlgebra generated by {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} i7 : isNormalMA M o7 = false i8 : isSeminormalMA M o8 = true

## Ways to use isNormalMA :

• "isNormalMA(List)"
• "isNormalMA(MonomialAlgebra)"
• "isNormalMA(PolynomialRing)"

## For the programmer

The object isNormalMA is .