{{{id=3|
# replace /home/tom/maths/free_sigma/ with the path to cutjoin.sage on your computer
load "/home/tom/maths/free_sigma/cutjoin.sage"
load "/home/tom/maths/oneloop/correlator.sage"
///
}}}

{{{id=1|
# find the matrix of the projection to sym(alpha)
alpha = Permutation([2,3,4,1])

# set sum=0 for matrix
sum = symmetrica.odg([2,2],range(1,5)) - symmetrica.odg([2,2],range(1,5))

for perm in sym_group(alpha):
    sum += symmetrica.odg([2,2],perm)
print sum
///
[       3 -sqrt(3)]
[-sqrt(3)        1]
}}}

{{{id=2|
# Collect D^\L_{11}(\sigma) into a list LambdaList; multiply by 2 so we have only integers

LambdaList=[]
for perm in Permutations(4):
    print symmetrica.odg([2,2],perm)[1,1]
    LambdaList.append(Integer(symmetrica.odg([2,2],perm)[1,1]*2))

print LambdaList
///
1
1
-1/2
-1/2
-1/2
-1/2
1
1
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
1
1
-1/2
-1/2
-1/2
-1/2
1
1
[2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2]
}}}

{{{id=4|
## add up the elements of the trace basis

n=4
alpha = Permutation([2,3,4,1])
Lambda = [2,2]
fields = ['X','X','Y','Y']
fieldContent = [2,2]
array = []
counter = -1
for p in Permutations(n):
    counter = counter+1
    addSAGEArray([[LambdaList[counter],p*alpha*p.inverse()]],array,fieldContent)

  
printSAGEArray(array,fields)
///
2^3 XXYY
-1 * 2^3 XYXY
}}}