def checkprimes(label): Fdata = get_Fdata(label) gen_name = findvar(Fdata['ideals']) WebF = get_WNF(label, gen_name) F = WebF.K() ideals = niceideals(F, Fdata['ideals']) primes = niceideals(F, Fdata['primes']) F = HilbertNumberField(label) L = [] for prhnf, prideal, prlabel in primes: ideal = F.ideal(prlabel) if ideal != prideal: L.append(prlabel) return L
def checkprimes(label): Fdata = get_Fdata(label) gen_name = findvar(Fdata['ideals']) WebF = get_WNF(label, gen_name) F = WebF.K() ideals = niceideals(F, Fdata['ideals']) primes = niceideals(F, Fdata['primes']) F = HilbertNumberField(label) L = [] for prhnf,prideal,prlabel in primes: ideal = F.ideal(prlabel) if ideal != prideal: L.append(prlabel) return L
def fldlabel2conjdata(label): data = {} Fdata = get_Fdata(label) gen_name = findvar(Fdata['ideals']) WebF = get_WNF(label, gen_name) F = WebF.K() data['F'] = F auts = F.automorphisms() if len(auts) == 1: #no nontrivial automorphism, nothing to do return None auts = [g for g in auts if not g.is_identity()] data['auts'] = auts ideals = niceideals(F, Fdata['ideals']) data['ideals'] = ideals cideals = conjideals(ideals, auts) data['conjideals'] = cideals primes = niceideals(F, Fdata['primes']) data['primes'] = primes cprimes = conjideals(primes, auts) data['conjprimes'] = cprimes return data
def fldlabel2conjdata(label): data = {} Fdata = get_Fdata(label) gen_name = findvar(Fdata['ideals']) WebF = get_WNF(label, gen_name) F = WebF.K() data['F'] = F auts = F.automorphisms() if len(auts) == 1: #no nontrivial automorphism, nothing to do return None auts = [g for g in auts if not g.is_identity()] data['auts'] = auts ideals = niceideals(F, Fdata['ideals']) data['ideals'] = ideals cideals = conjideals(ideals, auts) data['conjideals'] = cideals primes = niceideals(F, Fdata['primes']) data['primes'] = primes cprimes = conjideals(primes, auts) data['conjprimes'] = cprimes return data