def conjclasses(self):
if 'conjclasses' in self._data:
return self._data['conjclasses']
g = self.gapgroupnt()
n = self.n()
gap.set(
'cycletype',
'function(el, n) local ct; ct := CycleLengths(el, [1..n]); ct := ShallowCopy(ct); Sort(ct); ct := Reversed(ct); return(ct); end;'
)
cc = g.ConjugacyClasses()
ccn = [x.Size() for x in cc]
ccc = [x.Representative() for x in cc]
if int(n) == 1:
cc2 = [[1]]
cc = ['()']
else:
cc = ccc
cc2 = [x.cycletype(n) for x in cc]
cc2 = [str(x) for x in cc2]
cc2 = [re.sub(r"\[", '', x) for x in cc2]
cc2 = [re.sub(r"\]", '', x) for x in cc2]
ans = [[cc[j], ccc[j].Order(), ccn[j], cc2[j]]
for j in range(len(ccn))]
self._data['conjclasses'] = ans
return ans
def factor_perm_repn(self, nfgg=None):
if 'artincoefs' in self._data:
return self._data['artincoefs']
try:
if nfgg is not None:
self._data["nfgg"] = nfgg
else:
if "nfgg" not in self._data:
from artin_representations.math_classes import NumberFieldGaloisGroup
nfgg = NumberFieldGaloisGroup(self._data['coeffs'])
self._data["nfgg"] = nfgg
else:
nfgg = self._data["nfgg"]
cc = nfgg.conjugacy_classes()
# cc is list, each has methods group, size, order, representative
ccreps = [x.representative() for x in cc]
ccns = [int(x.size()) for x in cc]
ccreps = [x.cycle_string() for x in ccreps]
ccgen = '[' + ','.join(ccreps) + ']'
ar = nfgg.artin_representations() # list of artin reps from db
arfull = nfgg.artin_representations_full_characters(
) # list of artin reps from db
gap.set(
'fixed',
'function(a,b) if a*b=a then return 1; else return 0; fi; end;'
)
g = gap.Group(ccgen)
h = g.Stabilizer('1')
rc = g.RightCosets(h)
# Permutation character for our field
permchar = [gap.Sum(rc, 'j->fixed(j,' + x + ')') for x in ccreps]
charcoefs = [0 for x in arfull]
# list of lists (inner are giving char values
ar2 = [x[0] for x in arfull]
for j in range(len(ar)):
fieldchar = int(arfull[j][1])
zet = CyclotomicField(fieldchar).gen()
ar2[j] = [psum(zet, x) for x in ar2[j]]
for j in range(len(ar)):
charcoefs[j] = 0
for k in range(len(ccns)):
charcoefs[j] += int(permchar[k]) * ccns[k] * ar2[j][k]
charcoefs = [x / int(g.Size()) for x in charcoefs]
self._data['artincoefs'] = charcoefs
return charcoefs
except AttributeError:
return []
return []
def conjclasses(g, n):
gap.set('cycletype', 'function(el, n) local ct; ct := CycleLengths(el, [1..n]); ct := ShallowCopy(ct); Sort(ct); ct := Reversed(ct); return(ct); end;')
cc = g.ConjugacyClasses()
ccn = [x.Size() for x in cc]
ccc = [x.Representative() for x in cc]
if int(n) == 1:
cc2 = [[1]]
cc = ['()']
else:
cc = ccc
cc2 = [x.cycletype(n) for x in cc]
cc2 = [str(x) for x in cc2]
cc2 = map(lambda x: re.sub("\[", '', x), cc2)
cc2 = map(lambda x: re.sub("\]", '', x), cc2)
ans = [[cc[j], ccc[j].Order(), ccn[j], cc2[j]] for j in range(len(ccn))]
return(ans)
def factor_perm_repn(self, nfgg=None):
if 'artincoefs' in self._data:
return self._data['artincoefs']
try:
if nfgg is not None:
self._data["nfgg"] = nfgg
else:
if "nfgg" not in self._data:
from artin_representations.math_classes import NumberFieldGaloisGroup
nfgg = NumberFieldGaloisGroup(self._data['coeffs'])
self._data["nfgg"] = nfgg
else:
nfgg = self._data["nfgg"]
cc = nfgg.conjugacy_classes()
# cc is list, each has methods group, size, order, representative
ccreps = [x.representative() for x in cc]
ccns = [int(x.size()) for x in cc]
ccreps = [x.cycle_string() for x in ccreps]
ccgen = '['+','.join(ccreps)+']'
ar = nfgg.artin_representations() # list of artin reps from db
arfull = nfgg.artin_representations_full_characters() # list of artin reps from db
gap.set('fixed', 'function(a,b) if a*b=a then return 1; else return 0; fi; end;');
g = gap.Group(ccgen)
h = g.Stabilizer('1')
rc = g.RightCosets(h)
# Permutation character for our field
permchar = [gap.Sum(rc, 'j->fixed(j,'+x+')') for x in ccreps]
charcoefs = [0 for x in arfull]
# list of lists (inner are giving char values
ar2 = [x[0] for x in arfull]
for j in range(len(ar)):
fieldchar = int(arfull[j][1])
zet = CyclotomicField(fieldchar).gen()
ar2[j] = [psum(zet, x) for x in ar2[j]]
for j in range(len(ar)):
charcoefs[j] = 0
for k in range(len(ccns)):
charcoefs[j] += int(permchar[k])*ccns[k]*ar2[j][k]
charcoefs = [x/int(g.Size()) for x in charcoefs]
self._data['artincoefs'] = charcoefs
return charcoefs
except AttributeError:
return []
return []
