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Kernel: SageMath 9.8
from lie_algebra_tools import calculatePartition, calculateMultiplicity, findAltSet, printPartitions
print(findAltSet("C2", [2,1],[1,0]))
#print(calculatePartition("A2", [2,1]))
#print(calculatePartition("C2", [2,1], q_analog=True))
print(calculatePartition("A3", [2,1,1]))
print(calculateMultiplicity("C2", [2,1], [1,0], True))
#printPartitions("A2", [4,0,-4], "simple.tex", simple=True, simple_weight=False)
[1, s2] 4 q^2 
print(findAltSet("A4", [1,1,1,1], [-1,-1,-1,-1]))
#print(calculatePartition("A2", [-1,0]))
print(calculateMultiplicity("A4", [1,1,1,1], [-1,-1,-1,-1], True))
[1, s1, s2, s3, s4, s3*s1, s4*s1, s2*s3, s4*s2, s3*s2, s2*s3*s2] q^8 + q^7 - q^4 
print(calculateMultiplicity("A6", [1,1,1,1,1,1], [0,1,1,0,0,0], True))
print(findAltSet("A6", [1,1,1,1,1,1], [0,1,1,0,0,0]))
q^4 [1, s4, s5] 
A=print(len(findAltSet("A6", [1,1,1,1,1,1], [0,0,0,0,0,-1])))
#print(calculateMultiplicity("A4", [1,1,1,1], [-1,-1,-1,-1], True))
13 
print(calculateMultiplicity("D4", [1,1,1,1], [1,0,0,0], True))
0 
print(findAltSet("C4", [2,2,2,1],[1,0,0,0]))
print(calculateMultiplicity("C4", [2,2,2,1], [1,0,0,0], True))
[1, s2, s3, s4, s2*s3, s4*s2, s3*s2, s2*s3*s2] q^6 
print(findAltSet("C5", [2,2,2,2,1],[1,0,0,0,0]))
print(calculateMultiplicity("C5", [2,2,2,2,1], [1,0,0,0,0], True))
[1, s2, s3, s4, s5, s2*s3, s4*s2, s5*s2, s3*s2, s3*s4, s5*s3, s4*s3, s2*s3*s2, s5*s2*s3, s4*s2*s3, s5*s3*s2, s3*s4*s3, s5*s2*s3*s2] q^8 
    print(findAltSet("C6", [2,2,2,2,2,1],[0,0,0,1,1,1]))
print(calculateMultiplicity("C6", [2,2,2,2,2,1], [0,0,0,1,1,1], True))
[1, s2, s3, s4, s5, s2*s3, s4*s2, s5*s2, s3*s2, s3*s4, s5*s3, s2*s3*s2, s5*s2*s3, s5*s3*s2, s5*s2*s3*s2] q^8 
print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,-1,-1,-1,-1,0,0]))

print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1]))
print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1], True))
[1, s2, s4, s6, s4*s2, s6*s2, s6*s4, s6*s4*s2] q^3 - 3*q^2 + 3*q - 1 
print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,1,1,0,0,0,0,0,0]))
print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,0,0,1,1,0,0]))

print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[0,1,1,0,0,0,0,0,0], True))
print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,0,0,1,1,0,0], True))
[1, s4, s5, s6, s7, s8, s6*s4, s7*s4, s8*s4, s7*s5, s8*s5, s8*s6, s8*s6*s4] [1, s2, s3, s4, s5, s8, s4*s2, s5*s2, s8*s2, s5*s3, s8*s3, s8*s4, s8*s5, s8*s4*s2, s8*s5*s2, s8*s5*s3] q^7 q^7 
print(findAltSet("A10", [1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0]))
print(calculateMultiplicity("A10", [1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0], True))
[1, s2, s4, s6, s4*s2, s6*s2, s6*s4, s6*s4*s2] q^4 - 3*q^3 + 3*q^2 - q 
print(findAltSet("A11", [1,1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0,0]))
print(calculateMultiplicity("A11", [1,1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0,0], True))
[1, s2, s4, s6, s10, s4*s2, s6*s2, s10*s2, s6*s4, s10*s4, s10*s6, s6*s4*s2, s10*s4*s2, s10*s6*s2, s10*s6*s4, s10*s6*s4*s2] q^5 - 3*q^4 + 3*q^3 - q^2 
print(findAltSet("A6", [1,1,1,1,1,1],[0,1,1,0,0,0]))
#print(calculatePartition("A2", [2,1]))
#print(calculatePartition("C2", [2,1], q_analog=True))
print(calculatePartition("A3", [2,1,1]))
print(calculateMultiplicity("A6", [1,1,1,1,1,1],[0,1,1,0,0,0], True))
[1, s4, s5] 4 q^4 


















11-8
3






print(calculateMultiplicity("A5",[4,6,8,9,10],[2,4,6,8,10], q_analog=True))
q^7 + q^6 + 2*q^5 + q^4 + q^3 






print(calculatePartition("A2", [2,1], q_analog=True))
q^3 + q^2 


calculateMultiplicity("A2", [-1, 0],[2,1], q_analog=True)
0
calculateMultiplicity("A2", [5,5],[2,1], q_analog=True)
q^7 + q^6 + q^5 + q^4
calculateMultiplicity("A2", [5,5],[-1,1], q_analog=True)
q^10 + q^9 + q^8 + q^7 + q^6 - q^4
calculateMultiplicity("A2", [5,5],[-1,0], q_analog=True)
q^11 + q^10 + q^9 + q^8 + q^7 + q^6 - q^5
calculateMultiplicity("A2", [5,5],[-3,-4], q_analog=True)
q^17 + q^16 + q^15 + q^14 + q^13 + q^12 - q^11 - q^10 - q^9 - q^8
calculateMultiplicity("A2", [4,4],[-1,-1],q_analog=True)
q^10 + q^9 + q^8 + q^7 + q^6 - q^5
calculateMultiplicity("A2", [4,2],[1,0],q_analog=True)
q^5
calculateMultiplicity("A2", [2,4],[1,0],q_analog=True)
q^5


calculateMultiplicity("A2", [2,0],[-1,-1], q_analog=True)
-q^5
calculateMultiplicity("A2", [9,3],[1,0],q_analog=True)
-q^13 - q^12
calculateMultiplicity("A2", [3,9],[1,0],q_analog=True)
-q^13 - q^12
calculateMultiplicity("A2", [-1,-1],[0,0],q_analog=True)
0
calculateMultiplicity("A2", [7,3],[2,1],q_analog=True)
0
calculateMultiplicity("A2", [3,1],[-1,-1],q_analog=True)
0
calculateMultiplicity("A2", [11,5],[1,0],q_analog=True)
0
calculateMultiplicity("A2", [0,-1],[0,-1],q_analog=True)
-q + 1
calculateMultiplicity("A2", [3,1],[-5,-5],q_analog=True)
0
calculateMultiplicity("A2", [-1,0],[-1,-1],q_analog=True)
-q^2
calculateMultiplicity("A2", [1,2],[1,0],q_analog=True)
q^2
calculateMultiplicity("A2", [-1,0],[-1,0],q_analog=True)
-q + 1
calculateMultiplicity("A2", [-1,0],[-1,-1],q_analog=True)
-q^2
calculateMultiplicity("A2", [-1,0],[-1,-2],q_analog=True)
-q^3 + q^2 + q - 1
calculateMultiplicity("A2", [1,1],[-1,-2],q_analog=True)
q^5 + q^4 - q^3 - q^2


calculateMultiplicity("A2", [1,1],[-2,-1],q_analog=True)
q^5 + q^4 - q^3 - q^2
calculateMultiplicity("A2", [1,2],[-2,-1],q_analog=True)
q^6
calculateMultiplicity("A2", [4,3],[-2,-1],q_analog=True)
q^10 + q^9 + q^8 - q^4
calculateMultiplicity("A2", [1,1],[1,1],q_analog=True)
1
calculatePartition("G2", [1,1])
2


findAltSet("A9", [1,1,1,1,1,1,1,1,1],[1,0,0,0,0,0,0,0,0])
[1, s2, s3, s4, s5, s6, s7, s8, s4*s2, s5*s2, s6*s2, s7*s2, s8*s2, s5*s3, s6*s3, s7*s3, s8*s3, s6*s4, s7*s4, s8*s4, s7*s5, s8*s5, s8*s6, s6*s4*s2, s7*s4*s2, s8*s4*s2, s7*s5*s2, s8*s5*s2, s8*s6*s2, s7*s5*s3, s8*s5*s3, s8*s6*s3, s8*s6*s4, s8*s6*s4*s2]


print(findAltSet("A4",[1,1,1,1],[1,1,1,1]))
[1] 
print(calculateMultiplicity("A3",[1,1,1],[1,0,0], q_analog=True))
q^2