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

- Usage:
    `isNormalMA R`
    `isNormalMA B`
    `isNormalMA M`
- Inputs:
  - R, a polynomial ring, with B = degrees R and K = coefficientRing R, or
  - B, a list, with the generators of an affine semigroup in \mathbb{N}^d.
  - M, a MonomialAlgebra,
- Outputs:
  - a Boolean value,

## 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 a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MonomialAlgebras.m2:1980:0.