def checkerA12inE8(l,basis,orderList):
print("Checking if conjugate to any of the complete ones:")
print(checker(l,basis,orderList))
#These are two two cases where we do not know lambda5: cases 28 and 29
l28=[(4,), (4,), (0,), (0,)]
l29=[(5,), (5,)]
L28=[]
L28=L28+concat([(0,)],wedge2(l28))
L28=L28+[(2,0)]
L29=[]
L29=L29+concat([(0,)],wedge2(l29))
L29=L29+[(2,0)]
basisTemp=[[(0)]]
basisTemp.append(l)
print("Conjugate to case 28?")
print(classifyIncomplete(L28,basisTemp,orderList2))
if len(classifyIncomplete(L28,basisTemp,orderList2))>1:
print("YES")
print("Conjugate to case 29?")
print(classifyIncomplete(L29,basisTemp,orderList2))
if len(classifyIncomplete(L29,basisTemp,orderList2))>1:
print("YES")
def diagA1(L,index1,index2):
n=len(L[0])
sol=[]
ind1=index1-1
ind2=index2-1
for i in range(0,len(L)):
#print("i= "+str(i))
x=tensor([(L[i][ind1],)],[(L[i][ind2],)])
#print("this is x:")
#print(x)
temp2=[]
for t in range(0,len(x)):
temp2.append((x[t],))
#for t in range(0,len(x)):
# x=[(x[0],)]
#print("This is temp2:")
#print(temp2)
s=()
for j in range(0,n):
if j!=ind1 and j!=ind2:
s=s+(L[i][j],)
#print("this is s:")
#print(s)
temp=[]
temp.append(s)
a=concat(temp2,temp)
#print(a)
for t in range(0,len(a)):
sol.append(a[t])
#sol.append(a)
return(sol)
#What is the spin here?
lambda1.append([(5,), (5,)])
lambda5.append(expand("[(8,)^2/(4,)^2/(0,)^4]"))
for i in range(1,len(lambda1)):
lambda2.append(wedge2(lambda1[i]))
#print(dimChecker(lambda2[i]))
orderList2=order(2)
L=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
for i in range(1,len(lambda1)):
L[i]=[]
L[i]=L[i]+concat([(0,)],lambda2[i])
L[i]=L[i]+[(2,0)]
L[i]=L[i]+concat([(1,)],lambda5[i])
x=checker(L[i],basisA12,orderList2)
# print("///////////////////////////////")
# print(i)
# print(x)
basisA12.append(L[i])
basisA12Lambda1.append(lambda1[i])
checker(L[i],basisA12,orderList2)
# if dimChecker(L[i])!=133:
# print("////////////////////////////////////")
# print(latex(lambda1[i]))
# print(dimChecker(L[i]))
# print(latex(L[i]))
# else:
# print("Match!")
#print(problems)
orderList5=order(5)
basisA15=[[0]]
for i in range(1,37):
#print(latex(lambda1[i]))
#print(latex(lambda2[i]))
#print(latex(lambda5[i]))
LE8[i]=[]
LE8[i]=concat([(1,1)],lambda1[i])
LE8[i]=LE8[i]+concat([(1,0)],lambda5[i])
LE8[i]=LE8[i]+[(2,0,0,0,0),(0,2,0,0,0)]
LE8[i]=LE8[i]+concat([(0,0)],lambda2[i])
LE8[i]=LE8[i]+concat([(0,1)],lambda5[i])
#print(latex(LE8[i]))
if dimChecker(LE8[i])!=248:
print("LE8 does not have dim 248 at i=")
print(i)
## print(latex(lambda1[i]))
## print(latex(lambda2[i]))
## print(latex(lambda5[i]))
temp=checker(LE8[i],basisA15,orderList5)
#if temp!=-1:
# print("problem two of the LE8 are equal")
lambda4.append(expand("[(8,)^2/(4,)^2/(0,)^4]"))
for i in range(1,len(lambda1)):
lambda2.append(wedge2(lambda1[i]))
#print(dimChecker(lambda2[i]))
orderList3=order(3)
basisA13=[[0]]
basisA13Lambda1=[[0]]
for i in range(1,38):
print("case i")
LE8[i]=[]
LE8[i]=concat([(1,1)],lambda1[i])
LE8[i]=LE8[i]+concat([(1,0)],lambda4[i])
LE8[i]=LE8[i]+[(2,0,0),(0,2,0)]
LE8[i]=LE8[i]+concat([(0,0)],lambda2[i])
LE8[i]=LE8[i]+concat([(0,1)],lambda5[i])
if dimChecker(LE8[i])!=248:
print("LE8 does not have dim 248 at i=")
print(i)
temp=checker(LE8[i],basisA13,orderList3)
print(temp)
if temp==-1:
print("New element, added to basis")
basisA13.append(LE8[i])
basisA13Lambda1.append(lambda1[i])
else:
l1[13]=expand("[(1,1,0,0)/(0,0,1,1)/(0,0,0,1)^2]")
l5[13]=expand("[(1,0,1,0)^2/(1,0,0,2)/(1,0,0,0)/(0,1,1,1)/(0,1,0,1)^2]")
l5b[13]=expand("[(1,0,1,1)/(1,0,0,1)^2/(0,1,1,0)^2/(0,1,0,2)/(0,1,0,0)]")
l1[14]=expand("[(1,1,0,0)/(0,1,1,0)/(0,1,0,1)]")
l5[14]=expand("[(1,1,0,1)/(1,1,1,0)/(0,3,0,0)/(0,1,0,0)^2/(0,1,1,1)]")
l5b[14]=expand("[(1,2,0,0)/(1,0,0,0)/(1,0,1,1)/(0,2,0,1)/(0,0,0,1)/(0,2,1,0)/(0,0,1,0)]")
basis2=[[0]]
orderList6=order(6)
for i in range(1,15):
l2[i]=wedge2(l1[i])
for i in range(1,15):
temp=concat([(1,1)],l1[i])
temp = temp+concat([(1,0)],l5[i])
temp = temp+[(2,0,0,0,0,0),(0,2,0,0,0,0)]
temp=temp+concat([(0,0)],l2[i])
L[i] = temp+concat([(0,1)],l5[i])
#print("i= "+str(i))
#print(checker(L[i],basis2,orderList6))
basis2.append(L[i])
#print("MOVING ON TO CASE b")
for i in range(1,15):
temp=concat([(1,1)],l1[i])
temp = temp+concat([(1,0)],l5b[i])
temp = temp+[(2,0,0,0,0,0),(0,2,0,0,0,0)]
temp=temp+concat([(0,0)],l2[i])