def queryUploadDatabase(filename, path, limit=0):
file = getDBConnection().upload.fs.files.find_one({
"metadata.related_to": path,
"filename": filename
})
upload_fs = GridFS(getDBConnection().upload)
return upload_fs.get(file['_id']).read(limit)
def profile(userid):
getDBConnection().knowledge.knowls.ensure_index('title')
user = LmfdbUser(userid)
bread = base_bread() + [
(user.name, url_for('.profile', userid=user.get_id()))
]
userknowls = getDBConnection().knowledge.knowls.find(
{
'authors': userid
}, fields=['title']).sort([('title', ASC)])
userfiles = getDBConnection().upload.fs.files.find({
'metadata.uploader_id':
userid,
'metadata.status':
'approved'
})
userfilesmod = getDBConnection().upload.fs.files.find({
'metadata.uploader_id':
userid,
'metadata.status':
'unmoderated'
})
return render_template("user-detail.html",
user=user,
title="%s" % user.name,
bread=bread,
userknowls=userknowls,
userfiles=userfiles,
userfilesmod=userfilesmod)
def updateMetadata():
db = getDBConnection().upload
id = request.values['id']
property = request.values['property']
value = request.values['value']
db.fs.files.update({"_id" : ObjectId(id)}, {"$set": {"metadata."+property : value}})
if property == "status":
db.fs.files.update({"metadata.parent_archive_id" : ObjectId(id)}, {"$set": {"metadata.status" : value+"child"}}, multi=1)
return getDBConnection().upload.fs.files.find_one({"_id" : ObjectId(id)})['metadata'][property]
def profile(userid):
getDBConnection().knowledge.knowls.ensure_index('title')
user = LmfdbUser(userid)
bread = base_bread() + [(user.name, url_for('.profile', userid=user.get_id()))]
userknowls = getDBConnection().knowledge.knowls.find({'authors' : userid}, fields=['title']).sort([('title', ASC)])
userfiles = getDBConnection().upload.fs.files.find({'metadata.uploader_id' : userid, 'metadata.status': 'approved'})
userfilesmod = getDBConnection().upload.fs.files.find({'metadata.uploader_id' : userid, 'metadata.status': 'unmoderated'})
return render_template("user-detail.html", user=user,
title="%s" % user.name, bread= bread, userknowls = userknowls, userfiles = userfiles, userfilesmod = userfilesmod)
def field_knowl(self):
from WebNumberField import nf_display_knowl
nfgg = self.number_field_galois_group()
if nfgg.url_for():
return nf_display_knowl(nfgg.label(), getDBConnection(), nfgg.polredabshtml())
else:
return nfgg.polredabshtml()
def __init__(self, dbname='', **kwds):
r"""
For 'one-dimensiona' data sets the second skip parameter does not have a meaning but should be present anyway...
"""
self._skip = kwds.get('skip', [])
self._limit = kwds.get('limit', [])
self._keys = kwds.get('keys', [])
self._db = getDBConnection()[dbname]
self._collection_name = kwds.get('collection', 'all')
self._collection = []
self._skip_rec = 0
self._props = {}
if self._limit and self._skip:
self._nrows = self._limit[0]
if len(self._limit) > 1:
self._ncols = self._limit[1]
else:
self._ncols = 1
if len(self._skip) == 2:
self._skip_rows = self._skip[0]
self._skip_cols = self._skip[1]
else:
self._skip_rec = self._skip[0]
self._table = dict()
self._is_set = False
self._set_collection()
self._row_heads = []
self._col_heads = []
def query(**kwargs):
C = getDBConnection()
degree = request.args.get("degree", 0, type=int)
level = request.args.get("level", 0, type=int)
first_zero_start = request.args.get("zerolowerbound", -1.0, type=float)
first_zero_end = request.args.get("zeroupperbound", -1.0, type=float)
sort = request.args.get("sort", "first_zero", type=str)
direction = request.args.get("direction", "up", type=str)
if sort not in ['degree', 'first_zero', 'level', 'coeffs']:
sort = "first_zero"
if direction not in ["up", "down"]:
direction = "up"
if direction == "up":
direction = pymongo.ASCENDING
else:
direction = pymongo.DESCENDING
filter = {}
if degree:
filter['degree'] = degree
if level:
filter['level'] = level
if first_zero_start != -1.0 or first_zero_end != -1.0:
filter['first_zero'] = {}
if first_zero_start != -1.0:
filter['first_zero']['$gte'] = float(first_zero_start)
if first_zero_end != -1.0:
filter['first_zero']['$lte'] = float(first_zero_end)
query = C.test.Lfunctions_test2.find(filter).sort(sort, direction)
pagination = LazyMongoDBPagination(query = query, per_page=50, page=request.args.get('page', 1), endpoint=".query", endpoint_params=dict(request.args))
return render_template('lf-list.html', pagination=pagination, title=title)
def alive():
try:
conn = getDBConnection()
assert conn.userdb.users.count()
except:
abort(503)
return "LMFDB!"
def admin_update():
db = getDBConnection().upload
fs = GridFS(db)
id = request.form['id']
if request.form.has_key('approve'):
db.fs.files.update({"_id": ObjectId(id)},
{"$set": {
"metadata.status": "approved"
}})
db.fs.files.update({"metadata.parent_archive_id": ObjectId(id)},
{"$set": {
"metadata.status": "approvedchild"
}},
multi=1)
flask.flash('Approved')
if request.form.has_key('disapprove'):
db.fs.files.update({"_id": ObjectId(id)},
{"$set": {
"metadata.status": "disapproved"
}})
db.fs.files.update({"metadata.parent_archive_id": ObjectId(id)},
{"$set": {
"metadata.status": "disapprovedchild"
}},
multi=1)
flask.flash('Disapproved')
return flask.redirect(url_for(".admin"))
def download(id, filename):
file = GridFS(getDBConnection().upload).get(ObjectId(id))
response = flask.Response(file.__iter__())
response.headers['content-type'] = file.metadata['content_type']
response.content_length = file.length
return response
def download(id, filename): file = GridFS(getDBConnection().upload).get(ObjectId(id)) response = flask.Response(file.__iter__()) response.headers['content-type'] = file.metadata['content_type'] response.content_length=file.length return response
def __init__(self,dbname='',**kwds):
r"""
For 'one-dimensiona' data sets the second skip parameter does not have a meaning but should be present anyway...
"""
self._skip = kwds.get('skip',[])
self._limit= kwds.get('limit',[])
self._keys= kwds.get('keys',[])
self._db = getDBConnection()[dbname]
self._collection_name=kwds.get('collection','all')
self._collection = []
self._skip_rec=0
self._props = {}
if self._limit and self._skip:
self._nrows = self._limit[0]
if len(self._limit)>1:
self._ncols = self._limit[1]
else:
self._ncols = 1
if len(self._skip)==2:
self._skip_rows=self._skip[0]
self._skip_cols=self._skip[1]
else:
self._skip_rec = self._skip[0]
self._table=dict()
self._is_set=False
self._set_collection()
self._row_heads=[]
self._col_heads=[]
def alive():
try:
conn = getDBConnection()
assert conn.userdb.users.count()
except:
abort(503)
return "LMFDB!"
def zero_search(**kwargs):
C = getDBConnection()
if not 'zero' in kwargs:
query = C.test.Lfunctions_test2.find().sort('first_zero')
else:
zero = float(kwargs['zero'])
query = C.test.Lfunctions_test2.find({
'first_zero': {
'$lt': zero + .1,
'$gt': zero - .1
}
}).sort('first_zero')
pagination = LazyMongoDBPagination(query=query,
per_page=50,
page=request.args.get('page', 1),
endpoint=".zero_search",
endpoint_params=kwargs)
#result_string = ""
#printed_arrow = False
#for x in L:
# if x['zero'] > zero and printed_arrow == False:
# result_string = result_string + "-------->"
# printed_arrow = True
# result_string = result_string + str(x['zero']) + " " + str(x['modulus']) + " " + str(x['character']) + "<br>\n"
#return result_string
return render_template('lf-list.html', pagination=pagination, title=title)
def updateMetadata():
db = getDBConnection().upload
id = request.values['id']
property = request.values['property']
value = request.values['value']
db.fs.files.update({"_id": ObjectId(id)},
{"$set": {
"metadata." + property: value
}})
if property == "status":
db.fs.files.update({"metadata.parent_archive_id": ObjectId(id)},
{"$set": {
"metadata.status": value + "child"
}},
multi=1)
return getDBConnection().upload.fs.files.find_one({"_id": ObjectId(id)
})['metadata'][property]
def field_knowl(self):
from WebNumberField import nf_display_knowl
nfgg = self.number_field_galois_group()
if nfgg.url_for():
return nf_display_knowl(nfgg.label(), getDBConnection(),
nfgg.polredabshtml())
else:
return nfgg.polredabshtml()
def download_hmf_magma(**args):
C = getDBConnection()
data = None
label = str(args['label'])
f = C.hmfs.forms.find_one({'label': label})
if f is None:
return "No such form"
F = WebNumberField(f['field_label'])
F_hmf = C.hmfs.fields.find_one({'label': f['field_label']})
outstr = 'P<x> := PolynomialRing(Rationals());\n'
outstr += 'g := P!' + str(F.coeffs()) + ';\n'
outstr += 'F<w> := NumberField(g);\n'
outstr += 'ZF := Integers(F);\n\n'
# outstr += 'ideals_str := [' + ','.join([st for st in F_hmf["ideals"]]) + '];\n'
# outstr += 'ideals := [ideal<ZF | {F!x : x in I}> : I in ideals_str];\n\n'
outstr += 'NN := ideal<ZF | {' + f["level_ideal"][1:-1] + '}>;\n\n'
outstr += 'primesArray := [\n' + ','.join(
[st for st in F_hmf["primes"]]).replace('],[', '],\n[') + '];\n'
outstr += 'primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];\n\n'
if f["hecke_polynomial"] != 'x':
outstr += 'heckePol := ' + f["hecke_polynomial"] + ';\n'
outstr += 'K<e> := NumberField(heckePol);\n'
else:
outstr += 'heckePol := x;\nK := Rationals(); e := 1;\n'
outstr += '\nheckeEigenvaluesArray := [' + ', '.join(
[st for st in f["hecke_eigenvalues"]]) + '];'
outstr += '\nheckeEigenvalues := AssociativeArray();\n'
outstr += 'for i := 1 to #heckeEigenvaluesArray do\n heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];\nend for;\n\n'
outstr += 'ALEigenvalues := AssociativeArray();\n'
for s in f["AL_eigenvalues"]:
outstr += 'ALEigenvalues[ideal<ZF | {' + s[0][1:-1] + '}>] := ' + s[
1] + ';\n'
outstr += '\n// EXAMPLE:\n// pp := Factorization(2*ZF)[1][1];\n// heckeEigenvalues[pp];\n\n'
outstr += '/* EXTRA CODE: recompute eigenform (warning, may take a few minutes or longer!):\n'
outstr += 'M := HilbertCuspForms(F, NN);\n'
outstr += 'S := NewSubspace(M);\n'
outstr += '// SetVerbose("ModFrmHil", 1);\n'
outstr += 'newspaces := NewformDecomposition(S);\n'
outstr += 'newforms := [Eigenform(U) : U in newspaces];\n'
outstr += 'ppind := 0;\n'
outstr += 'while #newforms gt 1 do\n'
outstr += ' pp := primes[ppind];\n'
outstr += ' newforms := [f : f in newforms | HeckeEigenvalue(f,pp) eq heckeEigenvalues[pp]];\n'
outstr += 'end while;\n'
outstr += 'f := newforms[1];\n'
outstr += '// [HeckeEigenvalue(f,pp) : pp in primes] eq heckeEigenvaluesArray;\n'
outstr += '*/\n'
return outstr
def render_hmf_webpage(**args):
C = getDBConnection()
data = None
if 'label' in args:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such field"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
field_info = C.numberfields.fields.find_one({'label': data['field_label']})
field_info['galois_group'] = str(field_info['galois_group'][3])
info['field_info'] = field_info
info['field_poly'] = pol_to_html(str(coeff_to_poly(field_info['coefficients'])))
data['field_label'] = field_pretty(data['field_label'])
info.update(data)
info['downloads_visible'] = True
info['downloads'] = [('worksheet (not yet)', '/')]
info['friends'] = [('L-function (not yet)', '/')]
# info['learnmore'] = [('Number Field labels', url_for("render_labels_page")), ('Galois group labels',url_for("render_groups_page")), ('Discriminant ranges',url_for("render_discriminants_page"))]
bread = [('Hilbert Modular Forms', url_for("hilbert_modular_form_render_webpage")),('%s'%data['label'],' ')]
t = "Hilbert Cusp Form %s" % info['label']
credit = 'L. Dembele, S. Donnelly and J. Voight'
eigs = eval(data['hecke_eigenvalues'])
primes = hmf_field['primes']
w = polygen(QQ,'w')
n = min(len(eigs),len(primes))
info['eigs'] = [{'eigenvalue': eigs[i],
'prime_ideal': primes[i],
'prime_norm': primes[i][0]} for i in range(n)]
properties = []
properties = ['<br>']
properties.extend('<table>')
properties.extend('<tr><td align=left>Field:<td align=left>%s</td>'%data["field_label"])
properties.extend('<tr><td align=left>Degree:<td align=left> %s</td>'%field_info['degree'])
properties.extend('<tr><td align=left>Discriminant:<td align=left>%s</td>'%field_info['discriminant'])
properties.extend('<tr><td align=left>Polynomial:<td align=left>%s</td>'%field_info['discriminant'])
properties.extend('<tr><td align=left>Class number:<td align=left>%s</td>'%field_info['class_number'])
properties.extend('<tr><td align=left>Galois group:<td align=left>%s</td>'%field_info['galois_group'])
properties.extend('</table>')
properties.extend('<hr>')
properties.extend('<table>')
properties.extend('<tr><td align=left>Weight:<td align=left>%s</td>'%data["weight"])
properties.extend('<tr><td align=left>Level:<td align=left> %s</td>'%data['level_ideal'])
properties.extend('<tr><td align=left>Level Norm:<td align=left>%s</td>'%data['level_norm'])
properties.extend('<tr><td align=left>Label:<td align=left>%s</td>'%data['label_suffix'])
properties.extend('</table>')
return render_template("hilbert_modular_form/hilbert_modular_form.html", info = info, properties=properties, credit=credit, title = t, bread=bread)
def database_list():
all_db = []
C = base.getDBConnection()
for db_name in C.database_names():
if db_name in ('admin', 'local'):
continue
db = getattr(C, db_name)
all_db.append((db_name, filter(is_safe, db.collection_names())))
return render_template("raw/index.html", all_db = all_db, title="Number Theory Database")
def upload():
stream = None
fn = None
content_type = None
if request.form['url'] != "":
stream = urlopen(request.form['url'])
fn = path.basename(urlparse(request.form['url']).path)
content_type = stream.info().gettype()
else:
stream = request.files['file']
fn = request.files['file'].filename
content_type = request.files['file'].content_type
metadata = {
"name": request.form['name'],
"full_description": request.form['full_description'],
"related_to": request.form['related_to'],
"data_format": request.form['data_format'],
"creator": request.form['creator'],
"reference": request.form['reference'],
"bibtex": request.form['bibtex'],
"comments": request.form['comments'],
"uploader": current_user.name,
"uploader_id": current_user.id,
"time": datetime.datetime.utcnow(),
"original_file_name": fn,
"status": "unmoderated",
"version": "1",
"file_url": request.form['url'],
"content_type": content_type
}
flask.flash("Received file '%s' and awaiting moderation from an administrator" % fn)
upload_db = getDBConnection().upload
upload_fs = GridFS(upload_db)
db_id = upload_fs.put(stream.read(), metadata = metadata, filename=fn)
logging.info("file '%s' receieved and data with id '%s' stored" % (fn, db_id))
if fn[-4:] == ".tgz" or fn[-4:] == ".tar" or fn[-7:] == ".tar.gz" :
child_index = []
tar = tarfile.open(fileobj=upload_fs.get(ObjectId(db_id)))
for tarinfo in tar:
if tarinfo.isfile():
metadata2 = copy.copy(metadata)
metadata2['parent_archive_id'] = db_id
metadata2['parent_archive_filename'] = fn
metadata2['status'] = "unmoderatedchild"
metadata2['original_file_name'] = fn+"/"+tarinfo.name
metadata2['related_to'] = ""
metadata2['content_type'] = ""
id = upload_fs.put( tar.extractfile(tarinfo).read(), metadata = metadata2, filename=fn+"/"+tarinfo.name )
child_index.append([id, tarinfo.name]);
upload_db.fs.files.update({"_id": db_id}, {"$set": {"metadata.child_index": child_index}})
return flask.redirect("/upload/view/"+str(db_id))
def viewAll():
db = getDBConnection().upload
fs = GridFS(db)
approved = [ fs.get(x['_id']) for x in db.fs.files.find({"metadata.status" : "approved"}) ]
unmoderated = [ fs.get(x['_id']) for x in db.fs.files.find({"metadata.status" : "unmoderated"}) ]
return render_template("upload-view.html", title = "Uploaded data", bread = get_bread(), approved=approved, unmoderated2=unmoderated)
def get_knowls():
_C = getDBConnection()
knowls = _C.knowledge.knowls
knowls.ensure_index('authors')
# _keywords is used for the full text search
knowls.ensure_index('title')
knowls.ensure_index('cat')
knowls.ensure_index('_keywords')
return knowls
def get_knowls():
_C = getDBConnection()
knowls = _C.knowledge.knowls
knowls.ensure_index('authors')
# _keywords is used for the full text search
knowls.ensure_index('title')
knowls.ensure_index('cat')
knowls.ensure_index('_keywords')
return knowls
def admin():
db = getDBConnection().upload
fs = GridFS(db)
unmoderated = [ fs.get(x['_id']) for x in db.fs.files.find({"metadata.status" : "unmoderated"}) ]
approved = [ fs.get(x['_id']) for x in db.fs.files.find({"metadata.status" : "approved"}) ]
disapproved = [ fs.get(x['_id']) for x in db.fs.files.find({"metadata.status" : "disapproved"}) ]
return render_template("upload-view.html", title = "Moderate uploaded data", bread = get_bread(), unmoderated=unmoderated)#, approved=approved, disapproved=disapproved)
def download_hmf_magma(**args):
C = getDBConnection()
data = None
label = str(args['label'])
f = C.hmfs.forms.find_one({'label': label})
if f is None:
return "No such form"
F = WebNumberField(f['field_label'])
F_hmf = C.hmfs.fields.find_one({'label': f['field_label']})
outstr = 'P<x> := PolynomialRing(Rationals());\n'
outstr += 'g := P!' + str(F.coeffs()) + ';\n'
outstr += 'F<w> := NumberField(g);\n'
outstr += 'ZF := Integers(F);\n\n'
# outstr += 'ideals_str := [' + ','.join([st for st in F_hmf["ideals"]]) + '];\n'
# outstr += 'ideals := [ideal<ZF | {F!x : x in I}> : I in ideals_str];\n\n'
outstr += 'NN := ideal<ZF | {' + f["level_ideal"][1:-1] + '}>;\n\n'
outstr += 'primesArray := [\n' + ','.join([st for st in F_hmf["primes"]]).replace('],[', '],\n[') + '];\n'
outstr += 'primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];\n\n'
if f["hecke_polynomial"] != 'x':
outstr += 'heckePol := ' + f["hecke_polynomial"] + ';\n'
outstr += 'K<e> := NumberField(heckePol);\n'
else:
outstr += 'heckePol := x;\nK := Rationals(); e := 1;\n'
outstr += '\nheckeEigenvaluesArray := [' + ', '.join([st for st in f["hecke_eigenvalues"]]) + '];'
outstr += '\nheckeEigenvalues := AssociativeArray();\n'
outstr += 'for i := 1 to #heckeEigenvaluesArray do\n heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];\nend for;\n\n'
outstr += 'ALEigenvalues := AssociativeArray();\n'
for s in f["AL_eigenvalues"]:
outstr += 'ALEigenvalues[ideal<ZF | {' + s[0][1:-1] + '}>] := ' + s[1] + ';\n'
outstr += '\n// EXAMPLE:\n// pp := Factorization(2*ZF)[1][1];\n// heckeEigenvalues[pp];\n\n'
outstr += '/* EXTRA CODE: recompute eigenform (warning, may take a few minutes or longer!):\n'
outstr += 'M := HilbertCuspForms(F, NN);\n'
outstr += 'S := NewSubspace(M);\n'
outstr += '// SetVerbose("ModFrmHil", 1);\n'
outstr += 'newspaces := NewformDecomposition(S);\n'
outstr += 'newforms := [Eigenform(U) : U in newspaces];\n'
outstr += 'ppind := 0;\n'
outstr += 'while #newforms gt 1 do\n'
outstr += ' pp := primes[ppind];\n'
outstr += ' newforms := [f : f in newforms | HeckeEigenvalue(f,pp) eq heckeEigenvalues[pp]];\n'
outstr += 'end while;\n'
outstr += 'f := newforms[1];\n'
outstr += '// [HeckeEigenvalue(f,pp) : pp in primes] eq heckeEigenvaluesArray;\n'
outstr += '*/\n'
return outstr
def author_links(self):
"""
Basically finds all full names for all the referenced authors.
(lookup for all full names in just *one* query, hence the or)
"""
a_query = [{'_id': _} for _ in self.authors]
a = []
if len(a_query) > 0:
users = getDBConnection().userdb.users
a = users.find({"$or" : a_query}, fields=["full_name"])
return a
def author_links(self):
"""
Basically finds all full names for all the referenced authors.
(lookup for all full names in just *one* query, hence the or)
"""
a_query = [{'_id': _} for _ in self.authors]
a = []
if len(a_query) > 0:
users = getDBConnection().userdb.users
a = users.find({"$or": a_query}, fields=["full_name"])
return a
def render_isogeny_class(iso_class):
info = {}
credit = 'John Cremona'
label = iso_class
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
if data is None:
return "No such isogeny class"
ainvs = [int(a) for a in data['ainvs_for_optimal_curve']]
E = EllipticCurve(ainvs)
info = {'label': label}
info['optimal_ainvs'] = ainvs
if 'imag' in data:
info['imag'] = data['imag']
if 'real' in data:
info['real'] = data['real']
info['rank'] = data['rank']
info['isogeny_matrix'] = latex(matrix(eval(data['isogeny_matrix'])))
info['modular_degree'] = data['degree']
#info['f'] = ajax_more(E.q_eigenform, 10, 20, 50, 100, 250)
info['f'] = web_latex(E.q_eigenform(10))
G = E.isogeny_graph()
n = G.num_verts()
G.relabel(range(1, n + 1)) # proper cremona labels...
info['graph_img'] = image_src(G.plot(edge_labels=True))
curves = data['label_of_curves_in_the_class']
info['curves'] = list(curves)
info['download_qexp_url'] = url_for('download_qexp',
limit=100,
ainvs=','.join([str(a)
for a in ainvs]))
info['download_all_url'] = url_for('download_all', label=str(label))
friends = [('Elliptic Curve %s' % l, "/EllipticCurve/Q/%s" % l)
for l in data['label_of_curves_in_the_class']]
friends.append(('Quadratic Twist', "/quadratic_twists/%s" % (label)))
friends.append(('Modular Form',
url_for("emf.render_classical_modular_form_from_label",
label="%s" % (label))))
info['friends'] = friends
t = "Elliptic Curve Isogeny Class %s" % info['label']
bread = [('Elliptic Curves ', url_for("rational_elliptic_curves")),
('isogeny class %s' % info['label'], ' ')]
return render_template("elliptic_curve/iso_class.html",
info=info,
bread=bread,
credit=credit,
title=t)
def hilbert_modular_form_search(**args):
C = getDBConnection()
info = to_dict(args) # what has been entered in the search boxes
if 'natural' in info:
return render_hmf_webpage({'label' : info['natural']})
query = {}
for field in ['field_label', 'weight', 'level_norm', 'dimension']:
if info.get(field):
if field == 'weight':
query[field] = parse_list(info[field])
else:
if field == 'field_label':
query[field] = parse_field_string(info[field])
else:
query[field] = info[field]
if info.get('count'):
try:
count = int(info['count'])
except:
count = 10
else:
info['count'] = 10
count = 10
info['query'] = dict(query)
# C.hmfs.forms.ensure_index([('label',pymongo.ASCENDING)])
res = C.hmfs.forms.find(query).sort([('label',pymongo.ASCENDING)]).limit(count)
nres = res.count()
info['forms'] = res
if nres>0:
info['field_pretty_name'] = field_pretty(res[0]['field_label'])
else:
info['field_pretty_name'] = ''
info['number'] = nres
if nres==1:
info['report'] = 'unique match'
else:
if nres>count:
info['report'] = 'displaying first %s of %s matches'%(count,nres)
else:
info['report'] = 'displaying all %s matches'%nres
# info['learnmore'] = [('Number Field labels', url_for("render_labels_page")), ('Galois group labels',url_for("render_groups_page")), ('Discriminant ranges',url_for("render_discriminants_page"))]
t = 'Hilbert Modular Form search results'
bread = [('Hilbert Modular Forms', url_for("hilbert_modular_form_render_webpage")),('Search results',' ')]
properties = []
return render_template("hilbert_modular_form/hilbert_modular_form_search.html", info = info, title=t, properties=properties, bread=bread)
def plot_ec(label):
C = base.getDBConnection()
data = C.ellcurves.curves.find_one({'label': label})
if data is None:
return "No such curve"
ainvs = [int(a) for a in data['ainvs']]
E = EllipticCurve(ainvs)
P = E.plot()
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def plot_ec(label):
C = base.getDBConnection()
data = C.ellcurves.curves.find_one({'label': label})
if data is None:
return "No such curve"
ainvs = [int(a) for a in data['ainvs']]
E = EllipticCurve(ainvs)
P = E.plot()
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def updateMappingRule():
id = request.form['id']
print id
rules = filter(lambda x: x.strip()!="", request.form['rule'].splitlines())
db = getDBConnection().upload
child_index = db.fs.files.find_one({"_id": ObjectId(id)})['metadata']['child_index']
for child in child_index:
url = ""
for i in range(len(rules)/2):
if re.search(rules[i+i], child[1]) is not None:
url = re.sub(rules[i+i], rules[i+i+1], child[1])
break
db.fs.files.update({"_id": child[0]}, {"$set": {"metadata.related_to": url}})
print child[0], child[1], url
return "resp"
def admin_update():
db = getDBConnection().upload
fs = GridFS(db)
id = request.form['id']
if request.form.has_key('approve'):
db.fs.files.update({"_id" : ObjectId(id)}, {"$set": {"metadata.status" : "approved"}})
db.fs.files.update({"metadata.parent_archive_id" : ObjectId(id)}, {"$set": {"metadata.status" : "approvedchild"}}, multi=1)
flask.flash('Approved')
if request.form.has_key('disapprove'):
db.fs.files.update({"_id" : ObjectId(id)}, {"$set": {"metadata.status" : "disapproved"}})
db.fs.files.update({"metadata.parent_archive_id" : ObjectId(id)}, {"$set": {"metadata.status" : "disapprovedchild"}}, multi=1)
flask.flash('Disapproved')
return flask.redirect(url_for(".admin"))
def getUploadedFor(path):
files = getDBConnection().upload.fs.files.find({
"metadata.related_to":
path,
"$or": [{
"metadata.status": "approved"
}, {
"metadata.status": "approvedchild"
}]
})
ret = [[x['metadata']['name'],
"/upload/view/%s" % x['_id']] for x in files]
ret.insert(0, [
"Upload your data here",
url_for("upload.index") + "?related_to=" + request.path
])
return ret
def poly_to_field_label(pol):
try:
pol=PolynomialRing(QQ,'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredabs())
except:
return None
coeffs = [int(c) for c in pol.coeffs()]
d = int(pol.degree())
query = {'degree': d, 'coefficients': coeffs}
import base
C = base.getDBConnection()
one = C.numberfields.fields.find_one(query)
if one:
return one['label']
return None
def poly_to_field_label(pol):
try:
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredabs())
except:
return None
coeffs = [int(c) for c in pol.coeffs()]
d = int(pol.degree())
query = {'degree': d, 'coefficients': coeffs}
import base
C = base.getDBConnection()
one = C.numberfields.fields.find_one(query)
if one:
return one['label']
return None
def zero_search(**kwargs):
C = getDBConnection()
if not 'zero' in kwargs:
query = C.test.Lfunctions_test2.find().sort('first_zero')
else:
zero = float(kwargs['zero'])
query = C.test.Lfunctions_test2.find({'first_zero' : {'$lt' : zero + .1, '$gt' : zero - .1 } }).sort('first_zero')
pagination = LazyMongoDBPagination(query = query, per_page=50, page=request.args.get('page', 1), endpoint=".zero_search", endpoint_params=kwargs)
#result_string = ""
#printed_arrow = False
#for x in L:
# if x['zero'] > zero and printed_arrow == False:
# result_string = result_string + "-------->"
# printed_arrow = True
# result_string = result_string + str(x['zero']) + " " + str(x['modulus']) + " " + str(x['character']) + "<br>\n"
#return result_string
return render_template('lf-list.html', pagination=pagination, title=title)
def download_Rub_data():
import gridfs
label = (request.args.get('label'))
limit = (request.args.get('limit'))
C = base.getDBConnection()
fs = gridfs.GridFS(C.quadratic_twists, 'isogeny')
isogeny = C.quadratic_twists.isogeny.files
filename = isogeny.find_one({'label': label})['filename']
d = fs.get_last_version(filename)
if limit is None:
response = flask.Response(d.__iter__())
response.headers['Content-disposition'] = 'attachment; filename=%s' % label
response.content_length = d.length
else:
limit = int(limit)
response = make_response(''.join(str(d.readline()) for i in srange(limit)))
response.headers['Content-type'] = 'text/plain'
return response
def inject_database(self, relevant_info, time_limit = None):
# relevant_methods are text strings
# desired_database_fields = [Lfunction.original_mathematical_object, Lfunction.level]
# also zeroes, degree, conductor, type, real_coeff, rational_coeff, algebraic_coeff, critical_value, value_at_1, sign
# ok_methods = [Lfunction.math_id, Lfunction.level]
#
# Is used to inject the data in relevant_fields
logger.info("Trying to inject")
import base
db = base.getDBConnection().Lfunctions
Lfunctions = db.full_collection
update_dict = dict([(method_name,get_attr_or_method(self,method_name)) for method_name in relevant_info])
logger.info("injecting " + str(update_dict))
search_dict = {"original_mathematical_object()": get_attr_or_method(self, "original_mathematical_object()")}
my_find_update(Lfunctions, search_dict, update_dict)
def download_Rub_data():
import gridfs
label = (request.args.get('label'))
limit = (request.args.get('limit'))
C = base.getDBConnection()
fs = gridfs.GridFS(C.quadratic_twists, 'isogeny')
isogeny = C.quadratic_twists.isogeny.files
filename = isogeny.find_one({'label': label})['filename']
d = fs.get_last_version(filename)
if limit is None:
response = flask.Response(d.__iter__())
response.headers['Content-disposition'] = 'attachment; filename=%s' % label
response.content_length = d.length
else:
limit = int(limit)
response = make_response(''.join(str(d.readline()) for i in srange(limit)))
response.headers['Content-type'] = 'text/plain'
return response
def download_all():
label=(request.args.get('label'))
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
#all data about this isogeny
data1=[str(c)+'='+str(data[c]) for c in data]
curves=data['label_of_curves_in_the_class']
#titles of all entries of curves
lab=curves[0]
titles_curves=[str(c) for c in C.ellcurves.curves.find_one({'label': lab})]
data1.append(titles_curves)
for lab in curves:
print lab
data_curves=C.ellcurves.curves.find_one({'label': lab})
data1.append([data_curves[t] for t in titles_curves])
response=make_response('\n'.join(str(an) for an in data1))
response.headers['Content-type'] = 'text/plain'
return response
def viewAll():
db = getDBConnection().upload
fs = GridFS(db)
approved = [
fs.get(x['_id'])
for x in db.fs.files.find({"metadata.status": "approved"})
]
unmoderated = [
fs.get(x['_id'])
for x in db.fs.files.find({"metadata.status": "unmoderated"})
]
return render_template("upload-view.html",
title="Uploaded data",
bread=get_bread(),
approved=approved,
unmoderated2=unmoderated)
def render_isogeny_class(label):
credit = ' '
label = "%s" % label
C = base.getDBConnection()
info = C.quadratic_twists.isogeny.files.find_one({'label': label})
data = C.quadratic_twists.isogeny.find_one({'label': label})
if data is None:
return "No such curves"
data['download_Rub_data_100'] = url_for('download_Rub_data', label=str(label), limit=100)
data['download_Rub_data'] = url_for('download_Rub_data', label=str(label))
if info and 'related_to' in info:
data['related_to'] = info['related_to']
else:
data['related_to'] = ''
if data['type'] == 'r':
type = 'real'
else:
type = 'imaginary'
t = "Quadratic Twist for isogeny class %s %s" % (data['iso_class'], type)
return render_template("quadratic_twists/iso_class.html", info=data, title=t)
def render_isogeny_class(label):
credit = ' '
label = "%s" % label
C = base.getDBConnection()
info = C.quadratic_twists.isogeny.files.find_one({'label': label})
data = C.quadratic_twists.isogeny.find_one({'label': label})
if data is None:
return "No such curves"
data['download_Rub_data_100'] = url_for('download_Rub_data', label=str(label), limit=100)
data['download_Rub_data'] = url_for('download_Rub_data', label=str(label))
if info and 'related_to' in info:
data['related_to'] = info['related_to']
else:
data['related_to'] = ''
if data['type'] == 'r':
type = 'real'
else:
type = 'imaginary'
t = "Quadratic Twist for isogeny class %s %s" % (data['iso_class'], type)
return render_template("quadratic_twists/iso_class.html", info=data, title=t)
def download_all():
label = (request.args.get('label'))
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
#all data about this isogeny
data1 = [str(c) + '=' + str(data[c]) for c in data]
curves = data['label_of_curves_in_the_class']
#titles of all entries of curves
lab = curves[0]
titles_curves = [
str(c) for c in C.ellcurves.curves.find_one({'label': lab})
]
data1.append(titles_curves)
for lab in curves:
print lab
data_curves = C.ellcurves.curves.find_one({'label': lab})
data1.append([data_curves[t] for t in titles_curves])
response = make_response('\n'.join(str(an) for an in data1))
response.headers['Content-type'] = 'text/plain'
return response
def updateMappingRule():
id = request.form['id']
print id
rules = filter(lambda x: x.strip() != "",
request.form['rule'].splitlines())
db = getDBConnection().upload
child_index = db.fs.files.find_one({"_id": ObjectId(id)
})['metadata']['child_index']
for child in child_index:
url = ""
for i in range(len(rules) / 2):
if re.search(rules[i + i], child[1]) is not None:
url = re.sub(rules[i + i], rules[i + i + 1], child[1])
break
db.fs.files.update({"_id": child[0]},
{"$set": {
"metadata.related_to": url
}})
print child[0], child[1], url
return "resp"
def download_hmf_sage(**args):
C = getDBConnection()
data = None
label = str(args['label'])
f = C.hmfs.forms.find_one({'label': label})
if f is None:
return "No such form"
F = WebNumberField(f['field_label'])
F_hmf = C.hmfs.fields.find_one({'label': f['field_label']})
outstr = 'P.<x> = PolynomialRing(QQ)\n'
outstr += 'g = P(' + str(F.coeffs()) + ')\n'
outstr += 'F.<w> = NumberField(g)\n'
outstr += 'ZF = F.ring_of_integers()\n\n'
outstr += 'NN = ZF.ideal(' + f["level_ideal"] + ')\n\n'
outstr += 'primes_array = [\n' + ','.join(
[st for st in F_hmf["primes"]]).replace('],[', '],\\\n[') + ']\n'
outstr += 'primes = [ZF.ideal(I) for I in primes_array]\n\n'
if f["hecke_polynomial"] != 'x':
outstr += 'hecke_pol = ' + f["hecke_polynomial"] + '\n'
outstr += 'K.<e> = NumberField(heckePol)\n'
else:
outstr += 'heckePol = x\nK = QQ\ne = 1\n'
outstr += '\nhecke_eigenvalues_array = [' + ', '.join(
[st for st in f["hecke_eigenvalues"]]) + ']'
outstr += '\nhecke_eigenvalues = {}\n'
outstr += 'for i in range(len(hecke_eigenvalues_array)):\n hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]\n\n'
outstr += 'AL_eigenvalues = {}\n'
for s in f["AL_eigenvalues"]:
outstr += 'ALEigenvalues[ZF.ideal(s[0])] = s[1]\n'
outstr += '\n# EXAMPLE:\n# pp = ZF.ideal(2).factor()[0][0]\n# hecke_eigenvalues[pp]\n'
return outstr
def download_hmf_sage(**args):
C = getDBConnection()
data = None
label = str(args['label'])
f = C.hmfs.forms.find_one({'label': label})
if f is None:
return "No such form"
F = WebNumberField(f['field_label'])
F_hmf = C.hmfs.fields.find_one({'label': f['field_label']})
outstr = 'P.<x> = PolynomialRing(QQ)\n'
outstr += 'g = P(' + str(F.coeffs()) + ')\n'
outstr += 'F.<w> = NumberField(g)\n'
outstr += 'ZF = F.ring_of_integers()\n\n'
outstr += 'NN = ZF.ideal(' + f["level_ideal"] + ')\n\n'
outstr += 'primes_array = [\n' + ','.join([st for st in F_hmf["primes"]]).replace('],[',
'],\\\n[') + ']\n'
outstr += 'primes = [ZF.ideal(I) for I in primes_array]\n\n'
if f["hecke_polynomial"] != 'x':
outstr += 'hecke_pol = ' + f["hecke_polynomial"] + '\n'
outstr += 'K.<e> = NumberField(heckePol)\n'
else:
outstr += 'heckePol = x\nK = QQ\ne = 1\n'
outstr += '\nhecke_eigenvalues_array = [' + ', '.join([st for st in f["hecke_eigenvalues"]]) + ']'
outstr += '\nhecke_eigenvalues = {}\n'
outstr += 'for i in range(len(hecke_eigenvalues_array)):\n hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]\n\n'
outstr += 'AL_eigenvalues = {}\n'
for s in f["AL_eigenvalues"]:
outstr += 'ALEigenvalues[ZF.ideal(s[0])] = s[1]\n'
outstr += '\n# EXAMPLE:\n# pp = ZF.ideal(2).factor()[0][0]\n# hecke_eigenvalues[pp]\n'
return outstr
def query(**kwargs):
C = getDBConnection()
degree = request.args.get("degree", 0, type=int)
level = request.args.get("level", 0, type=int)
first_zero_start = request.args.get("zerolowerbound", -1.0, type=float)
first_zero_end = request.args.get("zeroupperbound", -1.0, type=float)
sort = request.args.get("sort", "first_zero", type=str)
direction = request.args.get("direction", "up", type=str)
if sort not in ['degree', 'first_zero', 'level', 'coeffs']:
sort = "first_zero"
if direction not in ["up", "down"]:
direction = "up"
if direction == "up":
direction = pymongo.ASCENDING
else:
direction = pymongo.DESCENDING
filter = {}
if degree:
filter['degree'] = degree
if level:
filter['level'] = level
if first_zero_start != -1.0 or first_zero_end != -1.0:
filter['first_zero'] = {}
if first_zero_start != -1.0:
filter['first_zero']['$gte'] = float(first_zero_start)
if first_zero_end != -1.0:
filter['first_zero']['$lte'] = float(first_zero_end)
query = C.test.Lfunctions_test2.find(filter).sort(sort, direction)
pagination = LazyMongoDBPagination(query=query,
per_page=50,
page=request.args.get('page', 1),
endpoint=".query",
endpoint_params=dict(request.args))
return render_template('lf-list.html', pagination=pagination, title=title)
def padic_data():
info = {}
label = request.args['label']
p = int(request.args['p'])
info['p'] = p
N, iso, number = cremona_label_regex.match(label).groups()
#print N, iso, number
if request.args['rank'] == '0':
info['reg'] = 1
elif number == '1':
C = base.getDBConnection()
data = C.ellcurves.padic_db.find_one({'label': N + iso, 'p': p})
info['data'] = data
if data is None:
info['reg'] = 'no data'
else:
reg = sage.all.Qp(p, data['prec'])(int(data['unit'])) * sage.all.Integer(p)**int(data['val'])
reg = reg.add_bigoh(min(data['prec'], data['prec'] + data['val']))
info['reg'] = web_latex(reg)
else:
info['reg'] = "no data"
return render_template("elliptic_curve/elliptic_curve_padic.html", info = info)
def render_isogeny_class(iso_class):
info = {}
credit = 'John Cremona'
label=iso_class
C = base.getDBConnection()
data = C.ellcurves.isogeny.find_one({'label': label})
if data is None:
return "No such isogeny class"
ainvs = [int(a) for a in data['ainvs_for_optimal_curve']]
E = EllipticCurve(ainvs)
info = {'label': label}
info['optimal_ainvs'] = ainvs
if 'imag' in data:
info['imag']=data['imag']
if 'real' in data:
info['real']=data['real']
info['rank'] = data['rank']
info['isogeny_matrix']=latex(matrix(eval(data['isogeny_matrix'])))
info['modular_degree']=data['degree']
#info['f'] = ajax_more(E.q_eigenform, 10, 20, 50, 100, 250)
info['f'] = web_latex(E.q_eigenform(10))
G = E.isogeny_graph(); n = G.num_verts()
G.relabel(range(1,n+1)) # proper cremona labels...
info['graph_img'] = image_src(G.plot(edge_labels=True))
curves = data['label_of_curves_in_the_class']
info['curves'] = list(curves)
info['download_qexp_url'] = url_for('download_qexp', limit=100, ainvs=','.join([str(a) for a in ainvs]))
info['download_all_url'] = url_for('download_all', label=str(label))
friends=[('Elliptic Curve %s' % l , "/EllipticCurve/Q/%s" % l) for l in data['label_of_curves_in_the_class']]
friends.append(('Quadratic Twist', "/quadratic_twists/%s" % (label)))
friends.append(('Modular Form', url_for("emf.render_classical_modular_form_from_label",label="%s" %(label))))
info['friends'] = friends
t= "Elliptic Curve Isogeny Class %s" % info['label']
bread = [('Elliptic Curves ', url_for("rational_elliptic_curves")),('isogeny class %s' %info['label'],' ')]
return render_template("elliptic_curve/iso_class.html", info = info,bread=bread, credit=credit,title = t)
def admin():
db = getDBConnection().upload
fs = GridFS(db)
unmoderated = [
fs.get(x['_id'])
for x in db.fs.files.find({"metadata.status": "unmoderated"})
]
approved = [
fs.get(x['_id'])
for x in db.fs.files.find({"metadata.status": "approved"})
]
disapproved = [
fs.get(x['_id'])
for x in db.fs.files.find({"metadata.status": "disapproved"})
]
return render_template("upload-view.html",
title="Moderate uploaded data",
bread=get_bread(),
unmoderated=unmoderated
) #, approved=approved, disapproved=disapproved)
def main(argv):
file_name = argv[0]
database_collection = argv[1]
assert "." in database_collection
database_name, collection_name = database_collection.split(".")
# If you know what you are doing, remove the line below.
# In general you should just avoid using this with an existing collection as it might overwrite information
assert database_name == "limbo"
print "Importing file ", file_name, " to database ", database_name, " and collection ", collection_name
import json
import sys
sys.path.append("../")
import base
print "getting connection"
base._init(37010, "")
print "I have it"
C = base.getDBConnection()
collection = C[database_name][collection_name]
print "Got a collectiopn: ", collection
with open(file_name, "r") as f:
print "Loading data in memory"
data = json.load(f)
print "Done"
print "There are ", len(data), " items "
import sys
sys.path.append("../")
print "Uploading"
for x in data:
try:
collection.save(x)
except OverflowError:
print x
raise OverflowError
print "Done"
def main(argv):
file_name = argv[0]
database_collection = argv[1]
assert "." in database_collection
database_name, collection_name = database_collection.split(".")
# If you know what you are doing, remove the line below.
# In general you should just avoid using this with an existing collection as it might overwrite information
assert database_name == "limbo"
print("Importing file ", file_name, " to database ", database_name, " and collection ", collection_name)
import json
import sys
sys.path.append("../")
import base
print("getting connection")
base._init(37010, "")
print("I have it")
C = base.getDBConnection()
collection = C[database_name][collection_name]
print("Got a collectiopn: ", collection)
with open(file_name, "r") as f:
print("Loading data in memory")
data = json.load(f)
print("Done")
print("There are ", len(data), " items ")
import sys
sys.path.append("../")
print("Uploading")
for x in data:
try:
collection.save(x)
except OverflowError:
print(x)
raise OverflowError
print("Done")
def padic_data():
info = {}
label = request.args['label']
p = int(request.args['p'])
info['p'] = p
N, iso, number = cremona_label_regex.match(label).groups()
#print N, iso, number
if request.args['rank'] == '0':
info['reg'] = 1
elif number == '1':
C = base.getDBConnection()
data = C.ellcurves.padic_db.find_one({'label': N + iso, 'p': p})
info['data'] = data
if data is None:
info['reg'] = 'no data'
else:
reg = sage.all.Qp(p, data['prec'])(int(
data['unit'])) * sage.all.Integer(p)**int(data['val'])
reg = reg.add_bigoh(min(data['prec'], data['prec'] + data['val']))
info['reg'] = web_latex(reg)
else:
info['reg'] = "no data"
return render_template("elliptic_curve/elliptic_curve_padic.html",
info=info)
#
#
# Do not use this script -- it is out of date
#
#
import os.path
import gzip
import re
import sys
import time
import pymongo
import base
fields = base.getDBConnection().numberfields.fields
fields.ensure_index('degree')
fields.ensure_index('galois_group')
fields.ensure_index('signature')
fields.ensure_index('discriminant')
fields.ensure_index('class_number')
fields.ensure_index([('degree', pymongo.ASCENDING), ('discriminant', pymongo.DESCENDING)])
fields.ensure_index([('degree', pymongo.ASCENDING), ('discriminant', pymongo.ASCENDING)])
def coeffs(s):
return [a for a in s[1:-1].split(',')]
def base_label(d, r1, D, ind):
return str(d) + "." + str(r1) + "." + str(abs(D)) + "." + str(ind)
def number_field_search(**args):
info = to_dict(args)
if 'natural' in info:
field_id = info['natural']
field_id = parse_field_string(info['natural'])
return render_field_webpage({'label': field_id})
query = {}
for field in [
'degree', 'signature', 'discriminant', 'class_number',
'class_group', 'galois_group'
]:
if info.get(field):
if field in ['class_group', 'signature']:
query[field] = parse_list(info[field])
else:
if field == 'galois_group':
query[field] = complete_group_code(info[field])
else:
ran = info[field]
ran = ran.replace('..', '-')
query[field] = parse_range(ran)
if info.get('ur_primes'):
ur_primes = [int(a) for a in str(info['ur_primes']).split(',')]
else:
ur_primes = []
if info.get('count'):
try:
count = int(info['count'])
except:
count = 10
else:
info['count'] = 10
count = 10
if info.get('start'):
try:
start = int(info['start'])
if (start < 0): start += (1 - (start + 1) / count) * count
except:
start = 0
else:
start = 0
info['query'] = dict(query)
if 'lucky' in args:
import base
C = base.getDBConnection()
one = C.numberfields.fields.find_one(query)
if one:
label = one['label']
return render_field_webpage({'label': label})
if 'discriminant' in query:
import base
C = base.getDBConnection()
res = C.numberfields.fields.find(query).sort([
('degree', pymongo.ASCENDING), ('signature', pymongo.DESCENDING),
('discriminant', pymongo.ASCENDING)
]) # TODO: pages
nres = res.count()
else:
# find matches with negative discriminant:
neg_query = dict(query)
neg_query['discriminant'] = {'$lt': 0}
import base
C = base.getDBConnection()
res_neg = C.numberfields.fields.find(neg_query).sort([
('degree', pymongo.ASCENDING), ('discriminant', pymongo.DESCENDING)
])
nres_neg = res_neg.count()
# TODO: pages
# find matches with positive discriminant:
pos_query = dict(query)
pos_query['discriminant'] = {'$gt': 0}
import base
C = base.getDBConnection()
res_pos = C.numberfields.fields.find(pos_query).sort([
('degree', pymongo.ASCENDING), ('discriminant', pymongo.ASCENDING)
])
nres_pos = res_pos.count()
# TODO: pages
res = merge_sort(iter(res_neg), iter(res_pos))
nres = nres_pos + nres_neg
if ur_primes:
res = filter_ur_primes(res, ur_primes)
if (start >= nres): start -= (1 + (start - nres) / count) * count
if (start < 0): start = 0
res = iter_limit(res, count, start)
info['fields'] = res
info['number'] = nres
info['start'] = start
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
info['format_coeffs'] = format_coeffs
info['learnmore'] = [
('Number Field labels', url_for("render_labels_page")),
('Galois group labels', url_for("render_groups_page")),
('Discriminant ranges', url_for("render_discriminants_page"))
]
t = 'Number Field search results'
bread = [('Number Fields', url_for("number_field_render_webpage")),
('Search results', ' ')]
properties = []
return render_template("number_field/number_field_search.html",
info=info,
title=t,
properties=properties,
bread=bread)
def render_field_webpage(args):
data = None
if 'label' in args:
label = str(args['label'])
import base
C = base.getDBConnection()
data = C.numberfields.fields.find_one({'label': label})
if data is None:
return "No such field: " + label + " in the database"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
K = coeff_to_nf(data['coefficients'])
D = data['discriminant']
h = data['class_number']
data['galois_group'] = str(data['galois_group'][3])
data['class_group_invs'] = data['class_group']
if data['class_group_invs'] == []:
data['class_group_invs'] = 'Trivial'
data['class_group'] = str(AbelianGroup(data['class_group']))
sig = data['signature']
D = ZZ(data['discriminant'])
ram_primes = D.prime_factors()
npr = len(ram_primes)
ram_primes = str(ram_primes)[1:-1]
Gorder, Gsign, Gab = GG_data(data['galois_group'])
if Gab:
Gab = 'abelian'
else:
Gab = 'non-abelian'
unit_rank = sig[0] + sig[1] - 1
if unit_rank == 0:
reg = 1
else:
reg = K.regulator()
UK = K.unit_group()
info.update(data)
info.update({
'label':
field_pretty(label),
'polynomial':
web_latex(K.defining_polynomial()),
'ram_primes':
ram_primes,
'integral_basis':
web_latex(K.integral_basis()),
'regulator':
web_latex(reg),
'unit_rank':
unit_rank,
'root_of_unity':
web_latex(UK.torsion_generator()),
'fund_units':
', '.join([web_latex(u) for u in UK.fundamental_units()]),
'Gorder':
Gorder,
'Gsign':
Gsign,
'Gab':
Gab
})
info['downloads_visible'] = True
info['downloads'] = [('worksheet', '/')]
# info['friends'] = [('L-function', '/')]
info['friends'] = [('L-function', "/L/NumberField/%s" % label)]
info['learnmore'] = [
('Number Field labels', url_for("render_labels_page")),
('Galois group labels', url_for("render_groups_page")),
('Discriminant ranges', url_for("render_discriminants_page"))
]
bread = [('Number Fields', url_for("number_field_render_webpage")),
('%s' % info['label'], ' ')]
t = "Number Field %s" % info['label']
properties = ['<br>']
properties.extend('<table>')
properties.extend(
'<tr><td align=left><b>Degree:</b><td align=left> %s</td>' %
data['degree'])
properties.extend(
'<tr><td align=left><b>Signature:</b><td align=left>%s</td>' %
data['signature'])
properties.extend(
'<tr><td align=left><b>Discriminant:</b><td align=left>%s</td>' %
data['discriminant'])
if npr == 1:
properties.extend(
'<tr><td align=left><b>Ramified prime:</b><td align=left>%s</td>' %
ram_primes)
else:
if npr == 0:
properties.extend(
'<tr><td align=left><b>Ramified primes:</b><td align=left>%s</td>'
% "None")
else:
properties.extend(
'<tr><td align=left><b>Ramified primes:</b><td align=left>%s</td>'
% ram_primes)
properties.extend(
'<tr><td align=left><b>Class number:</b><td align=left>%s</td>' %
data['class_number'])
properties.extend(
'<tr><td align=left><b>Class group:</b><td align=left>%s</td>' %
data['class_group_invs'])
properties.extend(
'<tr><td align=left><b>Galois group:</b><td align=left>%s</td>' %
data['galois_group'])
properties.extend('</table>')
del info['_id']
return render_template("number_field/number_field.html",
properties=properties,
credit=NF_credit,
title=t,
bread=bread,
friends=info.pop('friends'),
info=info)