loadstgroups.py

password = open("password.txt", "r").readlines()[0].strip()
import pymongo
from urllib import quote
from base64 import b64encode

def load_histogram(file):
    return 'data:image/png;base64,'+quote(b64encode(open(file).read(1000000)))

conn = pymongo.Connection(host='localhost',port=int(37010))
conn.sato_tate_groups.authenticate('editor',password)
db = conn.sato_tate_groups
small_groups = [
{ 'label':'1.1', 'order':int(1), 'name':'C1', 'pretty':'C_1', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'2.1', 'order':int(2), 'name':'C2', 'pretty':'C_2', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'3.1', 'order':int(3), 'name':'C3', 'pretty':'C_3', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'4.1', 'order':int(4), 'name':'C4', 'pretty':'C_4', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'4.2', 'order':int(4), 'name':'C2^2', 'pretty':'C_2^2', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'5.1', 'order':int(5), 'name':'C5', 'pretty':'C_5', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'6.1', 'order':int(6), 'name':'S3', 'pretty':'S_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'6.2', 'order':int(6), 'name':'C6', 'pretty':'C_6', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'7.1', 'order':int(7), 'name':'C7', 'pretty':'C_7', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'8.1', 'order':int(8), 'name':'C8', 'pretty':'C_8', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'8.2', 'order':int(8), 'name':'C2*C4', 'pretty':'C_2\\times C_4', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'8.3', 'order':int(8), 'name':'D4', 'pretty':'D_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'8.4', 'order':int(8), 'name':'Q8', 'pretty':'Q_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'8.5', 'order':int(8), 'name':'C2^3', 'pretty':'C_2^3', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'9.1', 'order':int(9), 'name':'C9', 'pretty':'C_9', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'9.2', 'order':int(9), 'name':'C3^2', 'pretty':'C_3^2', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'10.1', 'order':int(10), 'name':'D5', 'pretty':'D_5', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'10.2', 'order':int(10), 'name':'C10', 'pretty':'C_{10}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'11.1', 'order':int(11), 'name':'C11', 'pretty':'C_{11}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'12.1', 'order':int(12), 'name':'C3:C4', 'pretty':'C_3:C_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'12.2', 'order':int(12), 'name':'C12', 'pretty':'C_{12}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'12.3', 'order':int(12), 'name':'A4', 'pretty':'A_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'12.4', 'order':int(12), 'name':'D6', 'pretty':'D_6', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'12.5', 'order':int(12), 'name':'C2*C6', 'pretty':'C_2\\times C_6', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'13.1', 'order':int(13), 'name':'C13', 'pretty':'C_{13}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'14.1', 'order':int(14), 'name':'D7', 'pretty':'D_7', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'14.2', 'order':int(14), 'name':'C14', 'pretty':'C_{14}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'15.1', 'order':int(15), 'name':'C15', 'pretty':'C_{15}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'16.1', 'order':int(16), 'name':'C16', 'pretty':'C_P16}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'16.2', 'order':int(16), 'name':'C4^2', 'pretty':'C_4^2', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'16.3', 'order':int(16), 'name':'C2^2:C4', 'pretty':'C_2^2:C_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.4', 'order':int(16), 'name':'C4:C4', 'pretty':'C_4:C_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.5', 'order':int(16), 'name':'C2*C8', 'pretty':'C_2\\times C_8', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'16.6', 'order':int(16), 'name':'OD16', 'pretty':'OD_{16}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.7', 'order':int(16), 'name':'D8', 'pretty':'D_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.8', 'order':int(16), 'name':'SD16', 'pretty':'SD_{16}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.9', 'order':int(16), 'name':'Q16', 'pretty':'Q_{16}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.10', 'order':int(16), 'name':'C2^2*C4', 'pretty':'C_2^2\\times C_4', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'16.11', 'order':int(16), 'name':'C2*D4', 'pretty':'C_2\\times D_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.12', 'order':int(16), 'name':'C2*Q8', 'pretty':'C_2\\times Q_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.13', 'order':int(16), 'name':'D4:C2', 'pretty':'D_4:C_2', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'16.14', 'order':int(16), 'name':'C2^4', 'pretty':'C_2^4', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'17.1', 'order':int(17), 'name':'C17', 'pretty':'C_{17}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'18.1', 'order':int(18), 'name':'D9', 'pretty':'D_9', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'18.2', 'order':int(18), 'name':'C18', 'pretty':'C_{18}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'18.3', 'order':int(18), 'name':'C3*S3', 'pretty':'C_3\\times S_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'18.4', 'order':int(18), 'name':'C3:S3', 'pretty':'C_3:S_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'18.5', 'order':int(18), 'name':'C3*C6', 'pretty':'C_3\\times C_6', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'19.1', 'order':int(19), 'name':'C19', 'pretty':'C_{19}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'20.1', 'order':int(20), 'name':'C5:C4', 'pretty':'C_5:C_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'20.2', 'order':int(20), 'name':'C20', 'pretty':'C_{20}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'20.3', 'order':int(20), 'name':'F5', 'pretty':'F_5', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'20.4', 'order':int(20), 'name':'D10', 'pretty':'D_{10}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'20.5', 'order':int(20), 'name':'C2*C10', 'pretty':'C_2\\times C_10', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'21.1', 'order':int(21), 'name':'C7:C3', 'pretty':'C_7:C_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'21.2', 'order':int(21), 'name':'C21', 'pretty':'C_{21}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'22.1', 'order':int(22), 'name':'D11', 'pretty':'D_{11}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'22.2', 'order':int(22), 'name':'C22', 'pretty':'C_{22}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'23.1', 'order':int(23), 'name':'C23', 'pretty':'C_{23}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'24.1', 'order':int(24), 'name':'C3:C8', 'pretty':'C_3:C_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.2', 'order':int(24), 'name':'C24', 'pretty':'C_{24}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(1)},
{ 'label':'24.3', 'order':int(24), 'name':'SL(2,3)', 'pretty':'\\mathrm{SL}(2,3)', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.4', 'order':int(24), 'name':'C3:Q8', 'pretty':'C_3:Q_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.5', 'order':int(24), 'name':'C4*S3', 'pretty':'C_4\\times S_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.6', 'order':int(24), 'name':'D12', 'pretty':'D_{12}', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.7', 'order':int(24), 'name':'C2*C3:C4', 'pretty':'C_2\\times C_3:C_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.8', 'order':int(24), 'name':'C3:D4', 'pretty':'C_3:D_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.9', 'order':int(24), 'name':'C2*C12', 'pretty':'C_2\\times C_{12}', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'24.10', 'order':int(24), 'name':'C3*D4', 'pretty':'C_3\\times D_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.11', 'order':int(24), 'name':'C3*Q8', 'pretty':'C_3\\times Q_8', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.12', 'order':int(24), 'name':'S4', 'pretty':'S_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.13', 'order':int(24), 'name':'C2*A4', 'pretty':'C_2\\times A_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.14', 'order':int(24), 'name':'C2^2*S3', 'pretty':'C_2^2\\times S_3', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
{ 'label':'24.15', 'order':int(24), 'name':'C2^2*C6', 'pretty':'C_2^2\\times C_6', 'solvable':bool(1), 'abelian':bool(1), 'cyclic':bool(0)},
{ 'label':'48.48', 'order':int(48), 'name':'C2*S4', 'pretty':'C_2\\times S_4', 'solvable':bool(1), 'abelian':bool(0), 'cyclic':bool(0)},
]
db.drop_collection("new_small_groups")
db.create_collection("new_small_groups")
db.new_small_groups.insert(small_groups)
db.new_small_groups.ensure_index('label')
db.new_small_groups.ensure_index('name')
db.new_small_groups.ensure_index('order')
db.drop_collection("old_small_groups")
db.small_groups.rename("old_small_groups")
db.new_small_groups.rename("small_groups")
st0_groups = [
{ 'label':'0.1.0', 'name':'SO(1)', 'pretty':'\\mathrm{SO}(1)', 'degree':int(1), 'real_dimension':int(0),'description':'\\mathrm{trivial}'},
{ 'label':'0.2.0', 'name':'SO(1)_2', 'pretty':'\\mathrm{SO}(1)_2', 'degree':int(2), 'real_dimension':int(0),'description':'\\mathrm{trivial}' },
{ 'label':'0.3.0', 'name':'SO(1)_3', 'pretty':'\\mathrm{SO}(1)_3', 'degree':int(3), 'real_dimension':int(0),'description':'\\mathrm{trivial}' },
{ 'label':'1.2.1', 'name':'U(1)', 'pretty':'\\mathrm{U}(1)', 'degree':int(2), 'real_dimension':int(1),
   'description':'\\left\\{\\begin{bmatrix}\\alpha&0\\\\0&\\bar\\alpha\\end{bmatrix}:\\alpha\\bar\\alpha = 1,\\ \\alpha\\in\\mathbb{C}\\right\\}' },
{ 'label':'1.2.3', 'name':'SU(2)', 'pretty':'\\mathrm{SU}(2)', 'degree':int(2), 'real_dimension':int(3),
   'description':'\\left\\{\\begin{bmatrix}\\alpha&\\beta\\\\-\\bar\\beta&\\bar\\alpha\\end{bmatrix}:\\alpha\\bar\\alpha+\\beta\\bar\\beta = 1,\\ \\alpha,\\beta\\in\\mathbb{C}\\right\\}' },
{ 'label':'1.4.1', 'name':'U(1)_2', 'pretty':'\\mathrm{U}(1)_2', 'degree':int(4), 'real_dimension':int(1),
  'description':'\\left\\{\\begin{bmatrix}\\mathrm{diag}_2(\\alpha)&0\\\\0&\\mathrm{diag}_2(\\bar\\alpha)\\end{bmatrix}: \\alpha\\bar\\alpha = 1,\\ \\alpha\\in\\mathbb{C}\\right\\},\\ \\mathrm{diag}_2(\\alpha):=\\begin{bmatrix}\\alpha&0\\\\0&\\alpha\\end{bmatrix}' },
{ 'label':'1.4.2', 'name':'U(1)xU(1)', 'pretty':'\\mathrm{U}(1)\\times\\mathrm{U}(1)', 'degree':int(4), 'real_dimension':int(2),
  'description':'\\left\\{\\begin{bmatrix}A&0\\\\0&B\\end{bmatrix}: A,B\\in \\mathrm{U}(1)\\right\\}' },
{ 'label':'1.4.3', 'name':'SU(2)_2', 'pretty':'\\mathrm{SU}(2)_2', 'degree':int(4), 'real_dimension':int(3),
  'description':'\\left\\{\\begin{bmatrix}A&0\\\\0&\\bar{A}\\end{bmatrix}: A\in \mathrm{SU}(2)\\right\\}'},
{ 'label':'1.4.4', 'name':'U(1)xSU(2)', 'pretty':'\\mathrm{U}(1)\\times\\mathrm{SU}(2)', 'degree':int(4), 'real_dimension':int(4),
  'description':'\\left\\{\\begin{bmatrix}A&0\\\\0&B\\end{bmatrix}: A\\in \\mathrm{U}(1),\\ B\\in\\mathrm{SU}(2)\\right\\}' },
{ 'label':'1.4.6', 'name':'SU(2)xSU(2)', 'pretty':'\\mathrm{SU}(2)\\times\\mathrm{SU}(2)', 'degree':int(4), 'real_dimension':int(6),
  'description':'\\left\\{\\begin{bmatrix}A&0\\\\0&B\\end{bmatrix}: A,B\\in\\mathrm{SU}(2)\\right\\}' },
{ 'label':'1.4.10', 'name':'USp(4)', 'pretty':'\\mathrm{USp}(4)', 'degree':int(4), 'real_dimension':int(10),
   'description':'\\Bigl\\{ A\\in \\mathrm{GL}_4(\\mathbb{C}):A^{-1}=\\bar{A^{\\mathrm{t}}},\\ A^{\\mathrm{t}}\\Omega A = \\Omega\\Bigr\\},\\ \\Omega:=\\begin{bmatrix}0&-I_2\\\\I_2&0\\end{bmatrix},\\ I_2:=\\begin{bmatrix}1&0\\\\0&1\\end{bmatrix}' },
]
db.drop_collection("new_st0_groups")
db.create_collection("new_st0_groups")
db.new_st0_groups.insert(st0_groups)
db.new_st0_groups.ensure_index('label')
db.new_st0_groups.ensure_index('name')
db.new_st0_groups.ensure_index('degree')
db.drop_collection("old_st0_groups")
db.st0_groups.rename("old_st0_groups")
db.new_st0_groups.rename("st0_groups")
st_groups = [
{ 'label':'0.1.0.1.1a', 'weight':0, 'degree':1, 'name':'C_1', 'pretty':'C_1', 'identity_component':'SO(1)', 'real_dimension':int(0), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':[],
  'moments':[['s_1','1','1','1','1','1','1','1','1','1','1','1']],
  'counts':[['s_1',[[int(1),int(1)]]]], 'trace_zero_density':'0' },
{ 'label':'0.2.0.1.1a', 'weight':0, 'degree':2, 'name':'C_1', 'pretty':'C_1', 'identity_component':'SO(1)_2', 'real_dimension':int(0), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['0.2.0.2.1a'],
  'moments':[['s_1','1','2','4','8','16','32','64','128','256','512','1024']],
  'counts':[['s_1',[[int(2),int(1)]]]], 'trace_zero_density':'0' },
{ 'label':'0.2.0.2.1a', 'weight':0, 'degree':2, 'name':'C_2', 'pretty':'C_2', 'identity_component':'SO(1)_2', 'real_dimension':int(0), 'components':int(2), 'component_group':'2.1',
  'gens':[[['0','1'],['1','0']]], 'subgroups':['0.2.0.1.1a'], 'supgroups':[],
   'moments':[['a_1','1','1','2','4','8','16','32','64','128','256','512']],
  'counts':[['a_1',[[int(0),int(1)],[int(2),int(1)]]]], 'trace_zero_density':'1/2' },
{ 'label':'0.3.0.1.1a', 'weight':0, 'degree':3, 'name':'C_1', 'pretty':'C_1', 'identity_component':'SO(1)_3', 'real_dimension':int(0), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['0.3.0.2.1a','0.3.0.3.1a'],
  'moments':[['s_1','1','3','9','27','81','243','729','2187','6561','19683','59049','177147','531441']],
  'counts':[['s_1',[[3,1]]]], 'trace_zero_density':'0'},
{ 'label':'0.3.0.2.1a', 'weight':0, 'degree':3, 'name':'C_2', 'pretty':'C_2', 'identity_component':'SO(1)_3', 'real_dimension':int(0), 'components':int(2), 'component_group':'2.1',
  'gens':[[['1','0','0'],['0','0','1'],['0','1','0']]] , 'subgroups':['0.3.0.1.1a'], 'supgroups':['0.3.0.6.1a'],
  'moments':[['s_1','1','2','5','14','41','122','365','1094','3281','9842','29525','88574','265721']],
  'counts':[['a_1',[[int(1),int(1)],[int(3),int(1)]]]], 'trace_zero_density':'0'},
{ 'label':'0.3.0.3.1a', 'weight':0, 'degree':3, 'name':'C_3', 'pretty':'C_3', 'identity_component':'SO(1)_3', 'real_dimension':int(0), 'components':int(3), 'component_group':'3.1',
  'gens':[[['0','1','0'],['0','0','1'],['1','0','0']]], 'subgroups':['0.3.0.1.1a'], 'supgroups':['0.3.0.6.1a'],
  'moments':[['a_1','1','1','3','9','27','81','243','729','2187','6561','19683','59049','177147']],
  'counts':[['a_1',[[int(0),int(2)],[int(3),int(1)]]]], 'trace_zero_density':'2/3' },
{ 'label':'0.3.0.6.1a', 'weight':0, 'degree':3, 'name':'S_3', 'pretty':'S_3', 'identity_component':'SO(1)_3', 'real_dimension':int(0), 'components':int(6), 'component_group':'6.1',
  'gens':[[['1','0','0'],['0','0','1'],['0','1','0']],[['0','1','0'],['0','0','1'],['1','0','0']]], 'subgroups':['0.3.0.2.1a','0.3.0.3.1a'], 'supgroups':[],
  'moments':[['s_1','1','1','2','5','14','41','122','365','1094','3281','9842','29525','88574']],
  'counts':[['a_1',[[int(0),int(2)],[int(1),int(3)],[int(3),int(1)]]]], 'trace_zero_density':'1/3' },
{ 'label':'1.2.1.1.1a', 'weight':1, 'degree':2, 'name':'U(1)', 'pretty':'\\mathrm{U}(1)', 'identity_component':'U(1)', 'real_dimension':int(1), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['1.2.1.2.1a'],
  'moments':[['a_1','1','0','2','0','6','0','20','0','70','0','252','0','924']],
  'counts':[], 'trace_zero_density':'0', 'trace_histogram':load_histogram('1.2.U(1).png')  },
{ 'label':'1.2.1.2.1a', 'weight':1, 'degree':2, 'name':'N(U(1))', 'pretty':'N(\\mathrm{U}(1))', 'identity_component':'U(1)', 'real_dimension':int(1), 'components':int(2), 'component_group':'2.1',
  'gens':[[['0','1'],['1','0']]], 'subgroups':['1.2.1.1.1a'], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','3','0','10','0','35','0','126','0','462']],
  'counts':[['a_1',[[int(0),int(1)]]]], 'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.2.N(U(1)).png')  },
{ 'label':'1.2.3.1.1a', 'weight':1, 'degree':2, 'name':'SU(2)', 'pretty':'\\mathrm{SU}(2)', 'identity_component':'SU(2)', 'real_dimension':int(3), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','2','0','5','0','14','0','42','0','132']],
  'counts':[], 'trace_zero_density':'0', 'trace_histogram':load_histogram('1.2.SU(2).png') },
{ 'label':'1.4.1.1.1a', 'weight':1, 'degree':4, 'name':'C_1', 'pretty':'C_1', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':[ '1.4.1.2.1a', '1.4.1.2.1b', '1.4.1.2.1c', '1.4.1.3.1a' ],
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  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.C_1.png') },
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  'counts':[['a_1',[[int(0),int(5)]]],['a_2',[[int(2),int(4)]]]],'trace_zero_density':'5/8', 'trace_histogram':load_histogram('1.4.D_{4,2}.png') },
{ 'label':'1.4.1.12.4d', 'weight':1, 'degree':4, 'name':'D_{6,2}', 'pretty':'D_{6,2}', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(12), 'component_group':'12.4',
  'gens':[], 'subgroups':[ '1.4.1.4.2c', '1.4.1.6.1b', '1.4.1.6.2a' ], 'supgroups':[ '1.4.1.24.14a' ],
  'moments':[['a_1','1','0','2','0','18','0','200','0','2450','0','31752','0','427812'],['a_2','1','2','6','20','82','372','1825','9326','49026','262628','1427641','7851846','43609857']],
  'counts':[['a_1',[[int(0),int(7)]]],['a_2',[[int(2),int(6)]]]],'trace_zero_density':'7/12', 'trace_histogram':load_histogram('1.4.D_{6,2}.png') },
{ 'label':'1.4.1.12.3a', 'weight':1, 'degree':4, 'name':'T', 'pretty':'T', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(12), 'component_group':'12.3',
  'gens':[], 'subgroups':[ '1.4.1.3.1a', '1.4.1.4.2a' ], 'supgroups':[ '1.4.1.24.12a', '1.4.1.24.12b', '1.4.1.24.13a' ],
  'moments':[['a_1','1','0','2','0','12','0','120','0','1540','0','21672','0','316008'],['a_2','1','1','4','12','52','236','1202','6378','35044','195924','1108834','6323978','36271314']],
  'counts':[['a_1',[[int(0),int(3)]]]],'trace_zero_density':'1/4', 'trace_histogram':load_histogram('1.4.T.png') },
{ 'label':'1.4.1.24.12a', 'weight':1, 'degree':4, 'name':'O', 'pretty':'O', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(24), 'component_group':'24.12',
  'gens':[], 'subgroups':[ '1.4.1.6.1a', '1.4.1.8.3a','1.4.1.12.3a' ], 'supgroups':[ '1.4.1.48.48a' ],
  'moments':[['a_1','1','0','2','0','12','0','100','0','1050','0','12852','0','172788'],['a_2','1','1','4','11','45','181','837','4047','20757','110117','600669','3338347','18811927']],
  'counts':[['a_1',[[int(0),int(9)]]]],'trace_zero_density':'3/8', 'trace_histogram':load_histogram('1.4.O.png') },
{ 'label':'1.4.1.24.12b', 'weight':1, 'degree':4, 'name':'O_1', 'pretty':'O_1', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(24), 'component_group':'24.12',
  'gens':[], 'subgroups':[ '1.4.1.6.1b', '1.4.1.8.3b', '1.4.1.12.3a' ], 'supgroups':[ '1.4.1.48.48a' ],
  'moments':[['a_1','1','0','1','0','6','0','60','0','770','0','10836','0','158004'],['a_2','1','1','3','8','30','126','617','3221','17586','98090','554673','3162501','18136681']],
  'counts':[['a_1',[[int(0),int(15)]]],['a_2',[[int(0),int(6)],[int(2),int(6)]]]],'trace_zero_density':'5/8', 'trace_histogram':load_histogram('1.4.O_1.png') },
{ 'label':'1.4.1.24.13a', 'weight':1, 'degree':4, 'name':'J(T)', 'pretty':'J(T)', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(24), 'component_group':'24.13',
  'gens':[], 'subgroups':[ '1.4.1.6.2b', '1.4.1.8.5a', '1.4.1.12.3a' ], 'supgroups':[ '1.4.1.48.48a' ],
  'moments':[['a_1','1','0','1','0','6','0','60','0','770','0','10836','0','158004'],['a_2','1','1','3','7','29','121','612','3200','17565','98005','554588','3162160','18136340']],
  'counts':[['a_1',[[int(0),int(15)]]],['a_2',[[int(-2),int(1)],[int(1),int(8)],[int(2),int(3)]]]],'trace_zero_density':'5/8', 'trace_histogram':load_histogram('1.4.J(T).png') },
{ 'label':'1.4.1.48.48a', 'weight':1, 'degree':4, 'name':'J(O)', 'pretty':'J(O)', 'identity_component':'U(1)_2', 'real_dimension':int(1), 'components':int(48), 'component_group':'48.48',
  'gens':[], 'subgroups':[ '1.4.1.12.4b', '1.4.1.24.13a', '1.4.1.16.11a', '1.4.1.24.12b', '1.4.1.24.12a' ], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','6','0','50','0','525','0','6426','0','86394'],['a_2','1','1','3','7','26','96','432','2045','10432','55144','300548','1669515','9406817']],
  'counts':[['a_1',[[int(0),int(33)]]],['a_2',[[int(-2),int(1)],[int(0),int(6)],[int(1),int(8)],[int(2),int(9)]]]],'trace_zero_density':'11/16', 'trace_histogram':load_histogram('1.4.J(O).png') },
{ 'label':'1.4.3.1.1a', 'weight':1, 'degree':4, 'name':'E_1', 'pretty':'E_1', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['1.4.3.2.1a', '1.4.3.2.1b', '1.4.3.3.1a' ],
  'moments':[['a_1','1','0','4','0','32','0','320','0','3584','0','43008','0','540672'],['a_2','1','3','10','37','150','654','3012','14445','71398','361114','1859628','9716194','51373180']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.E_1.png') },
{ 'label':'1.4.3.2.1a', 'weight':1, 'degree':4, 'name':'E_2', 'pretty':'E_2', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(2), 'component_group':'2.1',
  'gens':[], 'subgroups':[ '1.4.3.1.1a' ], 'supgroups':[ '1.4.3.4.1a', '1.4.3.4.2a', '1.4.3.6.2a' ],
  'moments':[['a_1','1','0','2','0','16','0','160','0','1792','0','21504','0','270336'],['a_2','1','1','6','17','78','322','1516','7205','35734','180494','929940','4857866','25687052']],
  'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.E_2.png') },
{ 'label':'1.4.3.3.1a', 'weight':1, 'degree':4, 'name':'E_3', 'pretty':'E_3', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(3), 'component_group':'3.1',
  'gens':[], 'subgroups':[ '1.4.3.1.1a' ], 'supgroups':[ '1.4.3.6.1a', '1.4.3.6.2a' ],
  'moments':[['a_1','1','0','2','0','12','0','110','0','1204','0','14364','0','180312'],['a_2','1','1','4','13','52','222','1014','4839','23860','120526','620278','3239788','17127202']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.E_3.png') },
{ 'label':'1.4.3.4.1a', 'weight':1, 'degree':4, 'name':'E_4', 'pretty':'E_4', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(4), 'component_group':'4.1',
  'gens':[], 'subgroups':[ '1.4.3.2.1a' ], 'supgroups':[ '1.4.3.8.3a' ],
  'moments':[['a_1','1','0','2','0','12','0','100','0','1008','0','11424','0','139392'],['a_2','1','1','4','11','46','182','824','3817','18582','92678','473368','2458326','12947532']],
  'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/4', 'trace_histogram':load_histogram('1.4.E_4.png') },
{ 'label':'1.4.3.6.2a', 'weight':1, 'degree':4, 'name':'E_6', 'pretty':'E_6', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(6), 'component_group':'6.2',
  'gens':[], 'subgroups':[ '1.4.3.2.1a', '1.4.3.3.1a' ], 'supgroups':[ '1.4.3.12.4a' ],
  'moments':[['a_1','1','0','2','0','12','0','100','0','980','0','10584','0','122232'],['a_2','1','1','4','11','44','172','754','3397','16020','77516','384578','1944626','9997970']],
  'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/6', 'trace_histogram':load_histogram('1.4.E_6.png') },
{ 'label':'1.4.3.2.1b', 'weight':1, 'degree':4, 'name':'J(E_1)', 'pretty':'J(E_1)', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(2), 'component_group':'2.1', 'gens':[], 'subgroups':[], 'supgroups':[],
  'gens':[], 'subgroups':[ '1.4.3.1.1a' ], 'supgroups':[ '1.4.3.4.2a', '1.4.3.6.1a' ],
  'moments':[['a_1','1','0','2','0','16','0','160','0','1792','0','21504','0','270336'],['a_2','1','2','6','20','78','332','1516','7240','35734','180620','929940','4858328','25687052']],
  'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.J(E_1).png') },
{ 'label':'1.4.3.4.2a', 'weight':1, 'degree':4, 'name':'J(E_2)', 'pretty':'J(E_2)', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(4), 'component_group':'4.2',
  'gens':[], 'subgroups':[ '1.4.3.2.1a', '1.4.3.2.1b' ], 'supgroups':[ '1.4.3.8.3a', '1.4.3.12.4a' ],
  'moments':[['a_1','1','0','1','0','8','0','80','0','896','0','10752','0','135168'],['a_2','1','1','4','10','42','166','768','3620','17902','90310','465096','2429164','12843988']],
  'counts':[['a_1',[[int(0),int(3)]]]],'trace_zero_density':'3/4', 'trace_histogram':load_histogram('1.4.J(E_2).png') },
{ 'label':'1.4.3.6.1a', 'weight':1, 'degree':4, 'name':'J(E_3)', 'pretty':'J(E_3)', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(6), 'component_group':'6.1',
  'gens':[], 'subgroups':[ '1.4.3.2.1b','1.4.3.3.1a' ], 'supgroups':[ '1.4.3.12.4a' ],
  'moments':[['a_1','1','0','1','0','6','0','55','0','602','0','7182','0','90156'],['a_2','1','1','3','8','29','116','517','2437','11965','60326','310265','1620125','8564063']],
  'counts':[['a_1',[[int(0),int(3)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.J(E_3).png') },
{ 'label':'1.4.3.8.3a', 'weight':1, 'degree':4, 'name':'J(E_4)', 'pretty':'J(E_4)', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(8), 'component_group':'8.3',
  'gens':[], 'subgroups':[ '1.4.3.4.1a', '1.4.3.4.2a' ], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','6','0','50','0','504','0','5712','0','69696'],['a_2','1','1','3','7','26','96','422','1926','9326','46402','236810','1229394','6474228']],
  'counts':[['a_1',[[int(0),int(5)]]]],'trace_zero_density':'5/8', 'trace_histogram':load_histogram('1.4.J(E_4).png') },
{ 'label':'1.4.3.12.4a', 'weight':1, 'degree':4, 'name':'J(E_6)', 'pretty':'J(E_6)', 'identity_component':'SU(2)_2', 'real_dimension':int(3), 'components':int(12), 'component_group':'12.4',
  'gens':[], 'subgroups':[ '1.4.3.4.2a', '1.4.3.6.1a', '1.4.3.6.2a' ], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','6','0','50','0','490','0','5292','0','61116'],['a_2','1','1','3','7','25','91','387','1716','8045','38821','192415','972544','4999447']],
  'counts':[['a_1',[[int(0),int(7)]]]],'trace_zero_density':'7/12', 'trace_histogram':load_histogram('1.4.J(E_6).png') },
{ 'label':'1.4.2.1.1a', 'weight':1, 'degree':4, 'name':'F', 'pretty':'F', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[ '1.4.2.2.1a', '1.4.2.2.1b' ], 'supgroups':[],
  'moments':[['a_1','1','0','4','0','36','0','400','0','4900','0','63504','0','853776'],['a_2','1','2','8','32','148','712','3584','18496','97444','521096','2820448','15414016','84917584']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.F.png') },
{ 'label':'1.4.2.2.1a', 'weight':1, 'degree':4, 'name':'F_a', 'pretty':'F_a', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(2), 'component_group':'2.1', 'gens':[], 'subgroups':[], 'supgroups':[],
  'moments':[['a_1','1','0','3','0','21','0','210','0','2485','0','31878','0','427350'],['a_2','1','2','6','20','82','372','1824','9312','48850','260804','1410736','7708032','42460840']],
  'counts':[['a_2',[[int(2),int(1)]]]],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.F_a.png') },
#{ 'label':'1.4.2.2.1a', 'weight':1, 'degree':4, 'name':'F_c', 'pretty':'F_c', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(2), 'component_group':'2.1', 'gens':[], 'subgroups':[], 'supgroups':[],
#  'moments':[['a_1','1','0','2','0','18','0','200','0','2450','0','31752','0','426888'],['a_2','1','1','5','16','77','356','1802','9248','48757','260548','1410350','7707008','42459254']], 'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.F_c.png') },
{ 'label':'1.4.2.2.1b', 'weight':1, 'degree':4, 'name':'F_{ab}', 'pretty':'F_{ab}', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(2), 'component_group':'2.1', 'gens':[], 'subgroups':[], 'supgroups':[],
  'moments':[['a_1','1','0','2','0','18','0','200','0','2450','0','31752','0','426888'],['a_2','1','2','6','20','82','372','1824','9312','48850','260804','1410736','7708032','42460840']],
  'counts':[['a_1',[[int(0),int(1)]]],['a_2',[[int(2),int(1)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.F_{ab}.png') },
{ 'label':'1.4.2.4.1a', 'weight':1, 'degree':4, 'name':'F_{ac}', 'pretty':'F_{ac}', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(4), 'component_group':'4.1',
  'gens':[], 'subgroups':[ '1.4.2.2.1a' ], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','9','0','100','0','1225','0','15876','0','213444'],['a_2','1','1','3','10','41','186','912','4656','24425','130402','705368','3854016','21230420']],
  'counts':[['a_1',[[int(0),int(3)]]],['a_2',[[int(0),int(2)],[int(2),int(1)]]]],'trace_zero_density':'3/4', 'trace_histogram':load_histogram('1.4.F_{ac}.png') },
{ 'label':'1.4.2.4.2a', 'weight':1, 'degree':4, 'name':'F_{a,b}', 'pretty':'F_{a,b}', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(4), 'component_group':'4.2',
  'gens':[], 'subgroups':[ '1.4.2.2.1a' '1.4.2.2.1b'], 'supgroups':[],
  'moments':[['a_1','1','0','2','0','12','0','110','0','1260','0','16002','0','213906'],['a_2','1','2','5','14','49','202','944','4720','24553','130658','705880','3855040','21232468']],
  'counts':[['a_1',[[int(0),int(1)]]],['a_2',[[int(2),int(3)]]]],'trace_zero_density':'1/4', 'trace_histogram':load_histogram('1.4.F_{a,b}.png') },
#{ 'label':'1.4.2.4.2a', 'weight':1, 'degree':4, 'name':'F_{ab,c}', 'pretty':'F_{ab,c}', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(4), 'component_group':'4.2', 'gens':[], 'subgroups':[], 'supgroups':[],
#  'moments':[['a_1','1','0','1','0','9','0','100','0','1225','0','15876','0','213444'],['a_2','1','1','4','10','44','186','922','4656','24460','130402','705494','3854016','21230882']], 'counts':[['a_1',[[int(0),int(3)]]],['a_2',[[int(2),int(1)]]]],'trace_zero_density':'3/4' },
#{ 'label':'1.4.2.8.3a', 'weight':1, 'degree':4, 'name':'F_{a,b,c}', 'pretty':'F_{a,b,c}', 'identity_component':'U(1)xU(1)', 'real_dimension':int(2), 'components':int(8), 'component_group':'8.3', 'gens':[], 'subgroups':[], 'supgroups':[],
#  'moments':[['a_1','1','0','1','0','6','0','55','0','630','0','8001','0','106953'],['a_2','1','1','3','7','26','101','477','2360','12294','65329','353003','1927520','10616465']], 'counts':[['a_1',[[int(0),int(5)]]],['a_2',[[int(0),int(2)],[int(2),int(3)]]]],'trace_zero_density':'5/8' },
{ 'label':'1.4.4.1.1a', 'weight':1, 'degree':4, 'name':'G_{1,3}', 'pretty':'G_{1,3}', 'identity_component':'U(1)xSU(2)', 'real_dimension':int(4), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['1.4.4.2.1a'],
  'moments':[['a_1','1','0','3','0','20','0','175','0','1764','0','19404','0','226512'],['a_2','1','2','6','20','76','312','1364','6232','29460','142952','708328','3570096','18251248']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.G_{1,3}.png') },
{ 'label':'1.4.4.2.1a', 'weight':1, 'degree':4, 'name':'N(G_{1,3})', 'pretty':'N(G_{1,3})', 'identity_component':'U(1)xSU(2)', 'real_dimension':int(4), 'components':int(2), 'component_group':'2.1',
  'gens':[], 'subgroups':['1.4.4.1.1a'], 'supgroups':[],
  'moments':[['a_1','1','0','2','0','11','0','90','0','889','0','9723','0','113322'],['a_2','1','2','5','14','46','172','714','3180','14858','71732','354676','1786072','9127672']],
  'counts':[['a_2',[[int(2),int(1)]]]],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.N(G_{1,3}).png') },
{ 'label':'1.4.6.1.1a', 'weight':1, 'degree':4, 'name':'G_{3,3}', 'pretty':'G_{3,3}', 'identity_component':'SU(2)xSU(2)', 'real_dimension':int(6), 'components':int(1), 'component_group':'1.1',
  'gens':[], 'subgroups':[], 'supgroups':['1.4.6.2.1a'],
  'moments':[['a_1','1','0','2','0','10','0','70','0','588','0','5544','0','56628'],['a_2','1','2','5','14','44','152','569','2270','9524','41576','187348','866296','4092400']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.G_{3,3}.png') },
{ 'label':'1.4.6.2.1a', 'weight':1, 'degree':4, 'name':'N(G_{3,3})', 'pretty':'N(G_{3,3})', 'identity_component':'SU(2)xSU(2)', 'real_dimension':int(6), 'components':int(2), 'component_group':'2.1',
  'gens':[], 'subgroups':['1.4.6.1a'], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','5','0','35','0','294','0','2772','0','28314'],['a_2','1','1','3','7','23','76','287','1135','4769','20788','93695','433148','2046266']],
  'counts':[['a_1',[[int(0),int(1)]]]],'trace_zero_density':'1/2', 'trace_histogram':load_histogram('1.4.N(G_{3,3}).png') },
{ 'label':'1.4.10.1.1a', 'weight':1, 'degree':4, 'name':'USp(4)', 'pretty':'\mathrm{USp}(4)', 'identity_component':'USp(4)', 'real_dimension':int(10), 'components':int(1), 'component_group':'1.1', 'gens':[], 'subgroups':[], 'supgroups':[],
  'moments':[['a_1','1','0','1','0','3','0','14','0','84','0','594','0','4719'],['a_2','1','1','2','4','10','27','82','268','940','3476','13448','53968','223412']],
  'counts':[],'trace_zero_density':'0', 'trace_histogram':load_histogram('1.4.USp(4).png') },
]
db.drop_collection("new_st_groups")
db.create_collection("new_st_groups")
db.new_st_groups.insert(st_groups)
db.new_st_groups.ensure_index('label')
db.new_st_groups.ensure_index('name')
db.new_st_groups.ensure_index('weight')
db.new_st_groups.ensure_index('degree')
db.new_st_groups.ensure_index([('weight',int(1)),('degree',int(1)),('real_dimension',int(1)),('components',int(1))])
db.drop_collection("old_st_groups")
db.st_groups.rename("old_st_groups")
db.new_st_groups.rename("st_groups")