def codeinit(self):
self.exnum = self.galorbnums[0]
self.exchi = ConreyCharacter(self.modulus, self.exnum)
values_gens = db.char_dir_values.lookup(
"{}.{}".format(self.modulus, self.exnum),
projection='values_gens'
)
vals = [int(v) for g, v in values_gens]
sage_zeta_order = self.exchi.sage_zeta_order(self.order)
self._genvalues_for_code = get_sage_genvalues(self.modulus,
self.order, vals, sage_zeta_order)
return {
'sage': [
'from sage.modular.dirichlet import DirichletCharacter',
'H = DirichletGroup({}, base_ring=CyclotomicField({}))'.format(
self.modulus, sage_zeta_order),
'M = H._module',
'chi = DirichletCharacter(H, M([{}]))'.format(
','.join(str(val) for val in self._genvalues_for_code)
),
'chi.galois_orbit()'
],
'pari': [
'[g,chi] = znchar(Mod(%i,%i))' % (self.exnum, self.modulus),
'order = charorder(g,chi)',
'[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]'
]
}
def _set_generators_and_genvalues(self, values_data):
"""
The char_dir_values db collection contains `values_gens`, which
contains the generators for the unit group U(modulus) and the values
of the character on those generators.
"""
valuepairs = values_data['values_gens']
if self.modulus == 1:
self.generators = r"\(1\)"
self.genvalues = r"\(1\)"
else:
gens = [int(g) for g, v in valuepairs]
vals = [int(v) for g, v in valuepairs]
self._genvalues_for_code = get_sage_genvalues(self.modulus, self.order, vals, self.chi.sage_zeta_order(self.order))
self.generators = self.textuple([str(g) for g in gens])
self.genvalues = self.textuple([self._tex_value(v) for v in vals])