-- -*- M2-comint -*- hash: 15944975140525308242

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x+y+z,x*y+x*z+y*z,x*y*z)

o2 = ideal (x + y + z, x*y + x*z + y*z, x*y*z)

o2 : Ideal of R

i3 : S3 = symmetricGroupActors R

o3 = {| y z x |, | y x z |, | x y z |}

o3 : List

i4 : A = action(R/I,S3)

o4 = QuotientRing with 3 actors

o4 : ActionOnGradedModule

i5 : a = character(A,0,3)

o5 = Character over R
      
     (0, {0}) => | 1 1 1 |
     (0, {1}) => | -1 0 2 |
     (0, {2}) => | -1 0 2 |
     (0, {3}) => | 1 -1 1 |

o5 : Character

i6 : sgn = character(R,3, hashTable { (0,{3}) => matrix{{1,-1,1}} })

o6 = Character over R
      
     (0, {3}) => | 1 -1 1 |

o6 : Character

i7 : dual(a,{1,2,3}) ** sgn === a

o7 = true

i8 : 
