Python HilbertNumberField.ideal方法代码示例

# 需要导入模块: from lmfdb.hilbert_modular_forms.hilbert_field import HilbertNumberField [as 别名]
# 或者: from lmfdb.hilbert_modular_forms.hilbert_field.HilbertNumberField import ideal [as 别名]
def check_ideal_labels(field_label='2.2.5.1', min_norm=0, max_norm=None, fix=False, verbose=False):
    r""" Go through all curves with the given field label, assumed totally
    real, check whether the ideal label agrees with the level_label of
    the associated Hilbert Modular Form.
    """
    hmfs = conn.hmfs
    forms = hmfs.forms
    fields = hmfs.fields
    query = {}
    query['field_label'] = field_label
    query['conductor_norm'] = {'$gte' : int(min_norm)}
    if max_norm:
        query['conductor_norm']['$lte'] = int(max_norm)
    else:
        max_norm = 'infinity'
    cursor = nfcurves.find(query)
    nfound = 0
    nnotfound = 0
    K = HilbertNumberField(field_label)
    # NB We used to have 20 in the next line but that is insufficient
    # to distinguish the a_p for forms 2.2.12.1-150.1-a and
    # 2.2.12.1-150.1-b !
    primes = [P['ideal'] for P in K.primes_iter(30)]
    remap = {} # remap[old_label] = new_label

    for ec in cursor:
        fix_needed = False
        cond_label = ec['conductor_label']
        if cond_label in remap:
            new_cond_label = remap[cond_label]
            fix_needed=(cond_label!=new_cond_label)
            if not fix_needed:
                if verbose:
                    print("conductor label %s ok" % cond_label)
        else:
            conductor = make_conductor(ec,K)
            level = K.ideal(cond_label)
            new_cond_label = K.ideal_label(conductor)
            remap[cond_label] = new_cond_label
            fix_needed=(cond_label!=new_cond_label)

        if fix_needed:
            print("conductor label for curve %s is wrong, should be %s not %s" % (ec['label'],new_cond_label, cond_label))
            if fix:
                iso = ec['iso_label']
                num = str(ec['number'])
                newlabeldata = {}
                newlabeldata['conductor_label'] = new_cond_label
                newlabeldata['short_class_label'] = '-'.join([new_cond_label,iso])
                newlabeldata['short_label'] = ''.join([newlabeldata['short_class_label'],num])
                newlabeldata['class_label'] = '-'.join([field_label,
                                                        newlabeldata['short_class_label']])
                newlabeldata['label'] = '-'.join([field_label,
                                                  newlabeldata['short_label']])
                nfcurves.update({'_id': ec['_id']}, {"$set": newlabeldata}, upsert=True)
        else:
            if verbose:
                print("conductor label %s ok" % cond_label)

    return dict([(k,remap[k]) for k in remap if not k==remap[k]])

# 需要导入模块: from lmfdb.hilbert_modular_forms.hilbert_field import HilbertNumberField [as 别名]
# 或者: from lmfdb.hilbert_modular_forms.hilbert_field.HilbertNumberField import ideal [as 别名]
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']) # never used
    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

# 需要导入模块: from lmfdb.hilbert_modular_forms.hilbert_field import HilbertNumberField [as 别名]
# 或者: from lmfdb.hilbert_modular_forms.hilbert_field.HilbertNumberField import ideal [as 别名]
def export_magma_output(infilename, outfilename=None, verbose=False):
    r"""
    Convert Magma search output to a curves file.

    INPUT:

    - ``infilename`` (string) -- name of file containing Magma output

    - ``outfilename`` (string, default ``None``) -- name of output file

    - ``verbose`` (boolean, default ``False``) -- verbosity flag.
    """
    if outfilename:
        outfile = file(outfilename, mode="w")

    def output(L):
        if outfilename:
            outfile.write(L)
        if verbose:
            sys.stdout.write(L)

    K = None

    for field_label, cond_label, iso_label, num, cond_ideal, ai in magma_output_iter(infilename):
        ec = {}
        ec['field_label'] = field_label
        if not K:
            K = HilbertNumberField(field_label)
        ec['conductor_label'] = cond_label
        ec['iso_label'] = iso_label
        ec['number'] = num
        N = K.ideal(cond_label)
        norm = N.norm()
        hnf = N.pari_hnf()
        ec['conductor_ideal'] = cond_ideal
        ec['conductor_ideal'] = "[%i,%s,%s]" % (norm, hnf[1][0], hnf[1][1])
        ec['conductor_norm'] = norm
        ec['ainvs'] = [[str(c) for c in list(a)] for a in ai]
        ec['cm'] = '?'
        ec['base_change'] = []
        output(make_curves_line(ec) + "\n")

# 需要导入模块: from lmfdb.hilbert_modular_forms.hilbert_field import HilbertNumberField [as 别名]
# 或者: from lmfdb.hilbert_modular_forms.hilbert_field.HilbertNumberField import ideal [as 别名]
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, label=None, outfilename=None, verbose=False, effort=500):
    r""" Go through all Hilbert Modular Forms with the given field label,
    assumed totally real, for level norms in the given range, test
    whether an elliptic curve exists with the same label; if not, find
    the curves using Magma; output these to a file.
    """
    print("Checking forms over {}, norms from {} to {}".format(field_label,min_norm,max_norm))
    if outfilename:
        print("Output of curves found to {}".format(outfilename))
    else:
        print("No curve search or output, just checking")
    query = {}
    query['field_label'] = field_label
    if fields.find({'label': field_label}).count() == 0:
        if verbose:
            print("No HMF data for field %s" % field_label)
        return None

    query['dimension'] = 1  # only look at rational newforms
    if label:
        print("looking for {} only".format(label))
        query['short_label'] = label # e.g. '91.1-a'
    else:
        query['level_norm'] = {'$gte': int(min_norm)}
        if max_norm:
            query['level_norm']['$lte'] = int(max_norm)
    cursor = forms.find(query)
    cursor.sort([('level_norm', pymongo.ASCENDING)])
    labels = [f['label'] for f in cursor]
    nfound = 0
    nnotfound = 0
    nok = 0
    missing_curves = []
    K = HilbertNumberField(field_label)
    primes = [P['ideal'] for P in K.primes_iter(1000)]
    curve_ap = {}  # curve_ap[conductor_label] will be a dict iso -> ap
    form_ap = {}  # form_ap[conductor_label]  will be a dict iso -> ap

    # Step 1: look at all newforms, check that there is an elliptic
    # curve of the same label, and if so compare ap-lists.  The
    # dicts curve_ap and form_ap store these when there is
    # disagreement: e.g. curve_ap[conductor_label][iso_label] =
    # aplist.

    for curve_label in labels:
        # We find the forms again since otherwise the cursor might timeout during the loop.
        f = forms.find_one({'label': curve_label})
        ec = nfcurves.find_one({'field_label': field_label, 'class_label': curve_label, 'number': 1})
        if ec:
            if verbose:
                print("curve with label %s found in the database" % curve_label)
            nfound += 1
            ainvsK = parse_ainvs(K.K(), ec['ainvs'])
            E = EllipticCurve(ainvsK)
            good_flags = [E.has_good_reduction(P) for P in primes]
            good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
            aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes]
            f_aplist = [int(a) for a in f['hecke_eigenvalues']]
            f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag]
            nap = min(len(aplist), len(f_aplist))
            if aplist[:nap] == f_aplist[:nap]:
                nok += 1
                if verbose:
                    print("Curve {} and newform agree! (checked {} ap)".format(ec['short_label'],nap))
            else:
                print("Curve {} does NOT agree with newform".format(ec['short_label']))
                if verbose:
                    for P,aPf,aPc in zip(good_primes[:nap], f_aplist[:nap], aplist[:nap]):
                        if aPf!=aPc:
                            print("P = {} with norm {}".format(P,P.norm().factor()))
                            print("ap from curve: %s" % aPc)
                            print("ap from  form: %s" % aPf)
                if not ec['conductor_label'] in curve_ap:
                    curve_ap[ec['conductor_label']] = {}
                    form_ap[ec['conductor_label']] = {}
                curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
                form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
        else:
            if verbose:
                print("No curve with label %s found in the database!" % curve_label)
            missing_curves.append(f['short_label'])
            nnotfound += 1

    # Report progress:

    n = nfound + nnotfound
    if nnotfound:
        print("Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound))
    else:
        print("Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound))
    if nfound == nok:
        print("All curves agree with matching newforms")
    else:
        print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok))
    if nnotfound:
        print("%s missing curves" % len(missing_curves))
    else:
        return

    # Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()
#.........这里部分代码省略.........

# 需要导入模块: from lmfdb.hilbert_modular_forms.hilbert_field import HilbertNumberField [as 别名]
# 或者: from lmfdb.hilbert_modular_forms.hilbert_field.HilbertNumberField import ideal [as 别名]
def find_curves(field_label='2.2.5.1', min_norm=0, max_norm=None, outfilename=None, verbose=False):
    r""" Go through all Hilbert Modular Forms with the given field label,
    assumed totally real, for level norms in the given range, test
    whether an elliptic curve exists with the same label; if not, find
    the curves using Magma; output these to a file.
    """
    query = {}
    query['field_label'] = field_label
    if fields.find({'label': field_label}).count() == 0:
        if verbose:
            print("No HMF data for field %s" % field_label)
        return None

    query['dimension'] = 1  # only look at rational newforms
    query['level_norm'] = {'$gte': int(min_norm)}
    if max_norm:
        query['level_norm']['$lte'] = int(max_norm)
    else:
        max_norm = 'infinity'
    cursor = forms.find(query)
    cursor.sort([('level_norm', pymongo.ASCENDING)])
    labels = [f['label'] for f in cursor]
    nfound = 0
    nnotfound = 0
    nok = 0
    missing_curves = []
    K = HilbertNumberField(field_label)
    primes = [P['ideal'] for P in K.primes_iter(100)]
    curve_ap = {}  # curve_ap[conductor_label] will be a dict iso -> ap
    form_ap = {}  # form_ap[conductor_label]  will be a dict iso -> ap

    # Step 1: look at all newforms, check that there is an elliptic
    # curve of the same label, and if so compare ap-lists.  The
    # dicts curve_ap and form_ap store these when there is
    # disagreement: e.g. curve_ap[conductor_label][iso_label] =
    # aplist.

    for curve_label in labels:
        # We find the forms again since otherwise the cursor might timeout during the loop.
        f = forms.find_one({'label': curve_label})
        ec = nfcurves.find_one({'field_label': field_label, 'class_label': curve_label, 'number': 1})
        if ec:
            if verbose:
                print("curve with label %s found in the database" % curve_label)
            nfound += 1
            ainvsK = [K.K()([QQ(str(c)) for c in ai]) for ai in ec['ainvs']]
            E = EllipticCurve(ainvsK)
            good_flags = [E.has_good_reduction(P) for P in primes]
            good_primes = [P for (P, flag) in zip(primes, good_flags) if flag]
            aplist = [E.reduction(P).trace_of_frobenius() for P in good_primes[:30]]
            f_aplist = [int(a) for a in f['hecke_eigenvalues'][:40]]
            f_aplist = [ap for ap, flag in zip(f_aplist, good_flags) if flag][:30]
            if aplist == f_aplist:
                nok += 1
                if verbose:
                    print("Curve %s and newform agree!" % ec['short_label'])
            else:
                print("Curve %s does NOT agree with newform" % ec['short_label'])
                if verbose:
                    print("ap from curve: %s" % aplist)
                    print("ap from  form: %s" % f_aplist)
                if not ec['conductor_label'] in curve_ap:
                    curve_ap[ec['conductor_label']] = {}
                    form_ap[ec['conductor_label']] = {}
                curve_ap[ec['conductor_label']][ec['iso_label']] = aplist
                form_ap[ec['conductor_label']][f['label_suffix']] = f_aplist
        else:
            if verbose:
                print("No curve with label %s found in the database!" % curve_label)
            missing_curves.append(f['short_label'])
            nnotfound += 1

    # Report progress:

    n = nfound + nnotfound
    if nnotfound:
        print("Out of %s newforms, %s curves were found in the database and %s were not found" % (n, nfound, nnotfound))
    else:
        print("Out of %s newforms, all %s had curves with the same label and ap" % (n, nfound))
    if nfound == nok:
        print("All curves agree with matching newforms")
    else:
        print("%s curves agree with matching newforms, %s do not" % (nok, nfound - nok))
    if nnotfound:
        print("%s missing curves" % len(missing_curves))
    else:
        return

    # Step 2: for each newform for which there was no curve, call interface to Magma's EllipticCurveSearch()

    if outfilename:
        outfile = file(outfilename, mode="w")
    def output(L):
        if outfilename:
            outfile.write(L)
        if verbose:
            sys.stdout.write(L)

    for nf_label in missing_curves:
        if verbose:
#.........这里部分代码省略.........