def _compute(self):
WebHecke._compute(self)
self.number = self.label2number(self.numlabel)
assert len(self.number) == self.G.ngens()
self.chi = HeckeChar(self.H, self.number)
self.zetaorder = 0 # FIXME H.zeta_order()
def _compute(self):
WebHecke._compute(self)
self.number = self.label2number(self.numlabel)
assert len(self.number) == self.G.ngens()
self.chi = HeckeChar(self.H, self.number)
self.zetaorder = 0 # FIXME H.zeta_order()
class WebHeckeCharacter(WebChar, WebHecke):
def _compute(self):
WebHecke._compute(self)
self.number = self.label2number(self.numlabel)
assert len(self.number) == self.G.ngens()
self.chi = HeckeChar(self.H, self.number)
self.zetaorder = 0 # FIXME H.zeta_order()
@property
def codeinit(self):
kpol = self.k.polynomial()
return {
'sage': ['k.<a> = NumberField(%s)'%kpol,
'm = k.ideal(%s)'%self.modulus,
'G = RayClassGroup(k,m)',
'H = G.dual_group()',
'chi = H(%s)'%self.number],
'pari': ['k=bnfinit(%s)'%kpol,
'g=bnrinit(k,m,1)',
'chi = %s'%self.number]
}
@property
def title(self):
return r"Hecke Character: %s modulo %s" % (self.texname, self.modulus)
@property
def codecond(self):
return {
'sage': 'chi.conductor()',
'pari': 'bnrconductorofchar(G,chi)'
}
@property
def inducing(self):
#return lmfdb_hecke2tex(self.conductor(),self.indlabel())
return None
@property
def indlabel(self):
#return chi.primitive_character().number()
return None
@property
def genvalues(self):
logvals = self.chi.logvalues_on_gens()
return self.textuple( map(self.texlogvalue, logvals))
@property
def galoisorbit(self):
prim = self.isprimitive
return [ self._char_desc(c, prim=prim) for c in self.chi.galois_orbit() ]
def value(self, val):
chartex = self.char2tex(self.chi,val=val,tag=False)
val = self.label2group(val)
val = self.texlogvalue(self.chi.logvalue(val))
return '\(%s=%s\)'%(chartex,val)
def char4url(self, chi):
# FIXME: call url_character and only return (label, url)
if chi is None:
return ('', {})
label = self.char2tex(chi)
args = {'type': 'Hecke',
'number_field': self.nflabel,
'modulus': self.ideal2label(chi.modulus()),
'number': self.number2label(chi.exponents())}
return (label, args)
@property
def previous(self):
psi = self.chi.prev_character()
return self.char4url(psi)
@property
def next(self):
psi = self.chi.next_character()
return self.char4url(psi)
class WebHeckeCharacter(WebChar, WebHecke):
def _compute(self):
WebHecke._compute(self)
self.number = self.label2number(self.numlabel)
assert len(self.number) == self.G.ngens()
self.chi = HeckeChar(self.H, self.number)
self.zetaorder = 0 # FIXME H.zeta_order()
@property
def codeinit(self):
kpol = self.k.polynomial()
return {
'sage': [
'k.<a> = NumberField(%s)' % kpol,
'm = k.ideal(%s)' % self.modulus, 'G = RayClassGroup(k,m)',
'H = G.dual_group()',
'chi = H(%s)' % self.number
],
'pari': [
'k=bnfinit(%s)' % kpol, 'g=bnrinit(k,m,1)',
'chi = %s' % self.number
]
}
@property
def title(self):
return r"Hecke Character: %s modulo %s" % (self.texname, self.modulus)
@property
def codecond(self):
return {'sage': 'chi.conductor()', 'pari': 'bnrconductorofchar(G,chi)'}
@property
def inducing(self):
#return lmfdb_hecke2tex(self.conductor(),self.indlabel())
return None
@property
def indlabel(self):
#return chi.primitive_character().number()
return None
@property
def genvalues(self):
logvals = self.chi.logvalues_on_gens()
return self.textuple(map(self.texlogvalue, logvals))
@property
def galoisorbit(self):
prim = self.isprimitive
return [self._char_desc(c, prim=prim) for c in self.chi.galois_orbit()]
def value(self, val):
chartex = self.char2tex(self.chi, val=val, tag=False)
val = self.label2group(val)
val = self.texlogvalue(self.chi.logvalue(val))
return '\(%s=%s\)' % (chartex, val)
def char4url(self, chi):
# FIXME: call url_character and only return (label, url)
if chi is None:
return ('', {})
label = self.char2tex(chi)
args = {
'type': 'Hecke',
'number_field': self.nflabel,
'modulus': self.ideal2label(chi.modulus()),
'number': self.number2label(chi.exponents())
}
return (label, args)
@property
def previous(self):
psi = self.chi.prev_character()
return self.char4url(psi)
@property
def next(self):
psi = self.chi.next_character()
return self.char4url(psi)
