def make_class(self):
curves_data = db_g2c().curves.find({"class" : self.label}).sort([("disc_key", pymongo.ASCENDING), ("label", pymongo.ASCENDING)])
self.curves = [ {"label" : c['label'], "equation_formatted" : list_to_min_eqn(c['min_eqn']), "url": url_for_label(c['label'])} for c in curves_data ]
self.ncurves = curves_data.count()
self.bad_lfactors = [ [c[0], list_to_factored_poly_otherorder(c[1])] for c in self.bad_lfactors]
for endalgtype in ['end_alg', 'rat_end_alg', 'real_end_alg', 'geom_end_alg', 'rat_geom_end_alg', 'real_geom_end_alg']:
if hasattr(self, endalgtype):
setattr(self,endalgtype + '_name',end_alg_name(getattr(self,endalgtype)))
else:
setattr(self,endalgtype + '_name','')
self.st_group_name = st_group_name(self.st_group)
if hasattr(self, 'geom_end_field') and self.geom_end_field <> '':
self.geom_end_field_name = field_pretty(self.geom_end_field)
else:
self.geom_end_field_name = ''
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
if hasattr(self, 'is_simple'):
if self.is_simple:
self.is_simple_name = 'yes'
else:
self.is_simple_name = 'no'
else:
self.is_simple_name = '?'
if hasattr(self, 'is_geom_simple'):
if self.is_geom_simple:
self.is_geom_simple_name = 'yes'
else:
self.is_geom_simple_name = 'no'
else:
self.is_geom_simple_name = '?'
x = self.label.split('.')[1]
self.friends = [
('L-function', url_for("l_functions.l_function_genus2_page", cond=self.cond,x=x)),
('Siegel modular form someday', '.')]
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) <> 1:
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecproduct_wurl.append({'label' : curve_label, 'url' : crv_url})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass", nf = crv_spl[0], conductor_label = crv_spl[1], class_label = crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({'label' : curve_label, 'url' : crv_url, 'nf' : crv_spl[0]})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms", level=mf_spl[0], weight=mf_spl[1], character=mf_spl[2], label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage", field_label=mf_spl[0], label=mf_label)
self.friends.append(('Hilbert modular form ' + mf_label, mf_url))
self.properties = [('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor','%s' % self.cond),
('Sato-Tate group', '\(%s\)' % self.st_group_name),
('\(\mathrm{End}(J_{\overline{\Q}}) \otimes \R\)','\(%s\)' % self.real_geom_end_alg_name),
('\(\mathrm{GL}_2\)-type','%s' % self.is_gl2_type_name)]
self.title = "Genus 2 Isogeny Class %s" % (self.label)
self.downloads = [
('Download Euler factors', ".")] # url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves', url_for(".download_g2c_all", label=self.label))]
self.bread = [
('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond, url_for(".by_conductor", conductor=self.cond)),
('%s' % self.label, ' ')
]
data_description = 'defining the hyperelliptic curve y^2+h(x)y=f(x).'
function_body = {'magma':['R<x>:=PolynomialRing(Rationals());',
'return [HyperellipticCurve(R!r[1],R!r[2]):r in data];'],
'sage':['R.<x>=PolynomialRing(QQ)',
'return [HyperellipticCurve(R(r[0]),R(r[1])) for r in data]'],
'gp':['[apply(Polrev,c)|c<-data];']}
@search_wrap(template="g2c_search_results.html",
table=db.g2c_curves,
title='Genus 2 Curve Search Results',
err_title='Genus 2 Curves Search Input Error',
shortcuts={'jump':genus2_jump,
'download':G2C_download()},
projection=['label','eqn','st_group','is_gl2_type','is_simple_geom','analytic_rank'],
cleaners={"class": lambda v: class_from_curve_label(v["label"]),
"equation_formatted": lambda v: list_to_min_eqn(literal_eval(v.pop("eqn"))),
"st_group_link": lambda v: st_link_by_name(1,4,v.pop('st_group'))},
bread=lambda:[('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')],
learnmore=learnmore_list,
credit=lambda:credit_string)
def genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
data_description = 'defining the hyperelliptic curve y^2+h(x)y=f(x).'
function_body = {'magma':['R<x>:=PolynomialRing(Rationals());',
'return [HyperellipticCurve(R![c:c in r[1]],R![c:c in r[2]]):r in data];'],
'sage':['R.<x>=PolynomialRing(QQ)',
'return [HyperellipticCurve(R(r[0]),R(r[1])) for r in data]'],
'gp':['[apply(Polrev,c)|c<-data];']}
@search_wrap(template="g2c_search_results.html",
table=db.g2c_curves,
title='Genus 2 Curve Search Results',
err_title='Genus 2 Curves Search Input Error',
shortcuts={'jump':genus2_jump,
'download':G2C_download()},
projection=['label','eqn','st_group','is_gl2_type','is_simple_geom','analytic_rank'],
cleaners={"class": lambda v: class_from_curve_label(v["label"]),
"equation_formatted": lambda v: list_to_min_eqn(literal_eval(v.pop("eqn"))),
"st_group_link": lambda v: st_link_by_name(1,4,v.pop('st_group'))},
bread=lambda:[('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')],
learnmore=learnmore_list,
credit=lambda:credit_string)
def genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
def genus2_curve_search(**args):
info = to_dict(args)
if 'download' in info and info['download'] == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(info["jump"].strip()):
data = render_isogeny_class(info["jump"].strip())
else:
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(info["jump"].strip()) and ZZ(info["jump"][1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one({'hash':int(info["jump"][1:])})
if c:
data = render_isogeny_class(c["label"])
else:
data = "Hash not found"
else:
data = "Invalid label"
if isinstance(data,str):
flash(Markup(data + " <span style='color:black'>%s</span>"%(info["jump"])),"error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'torsion_order')
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if info.get('g20') and info.get('g21') and info.get('g22'):
query['g2inv'] = [ info['g20'], info['g21'], info['g22'] ]
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id', 'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
count = parse_count(info, 50)
start = parse_start(info)
cursor = g2cdb().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING), ("class", pymongo.ASCENDING), ("disc_key", pymongo.ASCENDING), ("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = g2cdb().isogeny_classes.find_one({'label' :
isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["st_group_href"] = st_group_href(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def genus2_curve_search(info):
if 'jump' in info:
jump = info["jump"].strip()
if re.match(r'^\d+\.[a-z]+\.\d+\.\d+$',jump):
return redirect(url_for_curve_label(jump), 301)
else:
if re.match(r'^\d+\.[a-z]+$', jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
if re.match(r'^\#\d+$',jump) and ZZ(jump[1:]) < 2**61:
c = g2c_db_curves().find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(url_for_isogeny_class_label(c["class"]), 301)
else:
errmsg = "hash %s not found"
else:
errmsg = "%s is not a valid genus 2 curve or isogeny class label"
flash_error (errmsg, jump)
return redirect(url_for(".index"))
if info.get('download','').strip() == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',(('Genus 2 Curves', url_for(".index")), ('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type','is of GL2-type')
parse_bool(info,query,'has_square_sha','has square Sha')
parse_bool(info,query,'locally_solvable','is locally solvable')
parse_bool(info,query,'is_simple_geom','is geometrically simple')
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_wpts','rational Weierstrass points')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'torsion_order','torsion order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,[int(n) for n in query['torsion']],1)
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ","")
query.pop('torsion') # search using string key, not array of ints
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']"%(info['g20'], info['g21'], info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id', 'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("g2c_search_results.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
# Database query happens here
info["query"] = query # save query for reuse in download_search
cursor = g2c_db_curves().find(query, {'_id':False, 'label':True, 'eqn':True, 'st_group':True, 'is_gl2_type':True, 'is_simple_geom':True, 'analytic_rank':True})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING), ("disc_key", ASCENDING), ("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_simple_geom"] = v["is_simple_geom"]
v_clean["equation_formatted"] = list_to_min_eqn(literal_eval(v["eqn"]))
v_clean["st_group_link"] = st_link_by_name(1,4,v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
title = info.get('title','Genus 2 Curve search results')
credit = credit_string
return render_template("g2c_search_results.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def genus2_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
jump = info["jump"].strip()
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(jump):
return redirect(url_for_curve_label(jump), 301)
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(jump) and ZZ(jump[1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(url_for_isogeny_class_label(c["label"]), 301)
else:
errmsg = "Hash not found"
else:
errmsg = "Invalid label"
flash(Markup(errmsg + " <span style='color:black'>%s</span>"%(jump)),"error")
return redirect(url_for(".index"))
if 'download' in info and info['download'] == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',(('Genus 2 Curves', url_for(".index")), ('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
parse_bool(info,query,'is_simple_geom')
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'torsion_order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,[int(n) for n in query['torsion']],1)
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2inv'] = [ info['g20'], info['g21'], info['g22'] ]
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id', 'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
# Database query happens here
cursor = g2cdb().curves.find(query,{'_id':int(0),'label':int(1),'min_eqn':int(1),'st_group':int(1),'is_gl2_type':int(1),'analytic_rank':int(1)})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING), ("disc_key", ASCENDING), ("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_gl2_type_display"] = '✔' if v["is_gl2_type"] else '' # display checkmark if true, blank otherwise
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(v['st_group'])
v_clean["st_group_href"] = st_group_href(v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
title = info.get('title','Genus 2 Curve search results')
credit = credit_string
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(), bread=bread, title=title)
def genus2_curve_search(**args):
info = to_dict(args)
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
return render_curve_webpage_by_label(info["jump"])
if info.get("disc"):
field = "abs_disc"
ran = info["disc"]
ran = ran.replace('..', '-').replace(' ','')
# Past input check
dlist = parse_discs(ran)
tmp = g2_list_to_query(dlist)
if len(tmp) == 1:
tmp = tmp[0]
else:
query[tmp[0][0]] = tmp[0][1]
tmp = tmp[1]
print tmp
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("is_gl2_type"):
query['is_gl2_type']=bool(info['is_gl2_type'])
for fld in ['aut_grp', 'geom_aut_grp','st_group','real_geom_end_alg']:
if info.get(fld):
query[fld] = info[fld]
for fld in ['aut_grp', 'geom_aut_grp']:
if info.get(fld):
query[fld] = eval(info[fld])
if info.get("cond"):
field = "cond"
ran = str(info[field])
ran = ran.replace('..', '-').replace(' ','')
# Past input check
tmp = parse_range2(ran, field)
print tmp
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("count"):
try:
count = int(info["count"])
except:
count = 100
else:
count = 100
info["query"] = dict(query)
#res = db_g2c().curves.find(query).sort([("cond", pymongo.ASCENDING),
#("label", pymongo.ASCENDING)]).limit(count)
res = db_g2c().curves.find(query).sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)])
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' : isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
credit = 'Genus 2 Team'
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit, bread=bread, title=title)
def genus2_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
jump = info["jump"].strip()
curve_label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+$')
if curve_label_regex.match(jump):
return redirect(url_for_curve_label(jump), 301)
else:
class_label_regex = re.compile(r'\d+\.[a-z]+$')
if class_label_regex.match(jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
class_label_regex = re.compile(r'#\d+$')
if class_label_regex.match(jump) and ZZ(jump[1:]) < 2**61:
c = g2cdb().isogeny_classes.find_one(
{'Lhash': jump[1:].strip()})
if c:
return redirect(
url_for_isogeny_class_label(c["label"]), 301)
else:
errmsg = "Hash not found"
else:
errmsg = "Invalid label"
flash(Markup(errmsg + " <span style='color:black'>%s</span>" % (jump)),
"error")
return redirect(url_for(".index"))
if 'download' in info and info['download'] == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',
(('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type')
parse_bool(info, query, 'has_square_sha')
parse_bool(info, query, 'locally_solvable')
parse_bool(info, query, 'is_simple_geom')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'cond')
parse_ints(info, query, 'num_rat_wpts', 'Weierstrass points')
parse_ints(info, query, 'torsion_order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,
[int(n) for n in query['torsion']],
1)
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2inv'] = [info['g20'], info['g21'], info['g22']]
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id',
'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
info["query"] = dict(query)
# Database query happens here
cursor = g2cdb().curves.find(
query, {
'_id': int(0),
'label': int(1),
'min_eqn': int(1),
'st_group': int(1),
'is_gl2_type': int(1),
'analytic_rank': int(1)
})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING),
("disc_key", ASCENDING),
("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_gl2_type_display"] = '✔' if v[
"is_gl2_type"] else '' # display checkmark if true, blank otherwise
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(v['st_group'])
v_clean["st_group_href"] = st_group_href(v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
title = info.get('title', 'Genus 2 Curve search results')
credit = credit_string
return render_template("search_results_g2.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)
def genus2_curve_search(**args):
info = to_dict(args)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_dict"] = real_geom_end_alg_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
return render_curve_webpage_by_label(info["jump"])
if info.get("disc"):
field = "abs_disc"
ran = info["disc"]
ran = ran.replace('..', '-').replace(' ','')
# Past input check
dlist = parse_discs(ran)
tmp = g2_list_to_query(dlist)
if len(tmp) == 1:
tmp = tmp[0]
else:
query[tmp[0][0]] = tmp[0][1]
tmp = tmp[1]
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("is_gl2_type"):
if info['is_gl2_type'] == "True":
query['is_gl2_type']= True
elif info['is_gl2_type'] == "False":
query['is_gl2_type']= False
for fld in ['st_group', 'real_geom_end_alg']:
if info.get(fld):
query[fld] = info[fld]
for fld in ['aut_grp', 'geom_aut_grp','igusa_clebsch']:
if info.get(fld):
query[fld] = map(int,info[fld].strip()[1:-1].split(","))
if info.get('torsion'):
res = parse_torsion_structure(info['torsion'],4)
if 'Error' in res:
# no error handling of malformed input yet!
info['torsion'] = ''
#info['err'] = res
#return search_input_error(info, bread)
else:
#update info for repeat searches
info['torsion'] = str(res).replace(' ','')
query['torsion'] = [int(r) for r in res]
if info.get('ic0'):
query['igusa_clebsch']=[info['ic0'], info['ic1'], info['ic2'], info['ic3'] ]
for fld in ["cond", "num_rat_wpts", "torsion_order", "two_selmer_rank"]:
if info.get(fld):
field = fld
ran = str(info[field])
ran = ran.replace('..', '-').replace(' ','')
# Past input check
tmp = parse_range2(ran, field)
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
info["query"] = dict(query)
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
info['count'] = count
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' : isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit, bread=bread, title=title)
def genus2_curve_search(**args):
info = to_dict(args)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_dict"] = real_geom_end_alg_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
return render_curve_webpage_by_label(info["jump"])
if info.get("disc"):
field = "abs_disc"
ran = info["disc"]
ran = ran.replace('..', '-').replace(' ','')
# Past input check
dlist = parse_discs(ran)
tmp = g2_list_to_query(dlist)
if len(tmp) == 1:
tmp = tmp[0]
else:
query[tmp[0][0]] = tmp[0][1]
tmp = tmp[1]
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("is_gl2_type"):
if info['is_gl2_type'] == "True":
query['is_gl2_type']= True
elif info['is_gl2_type'] == "False":
query['is_gl2_type']= False
for fld in ['st_group', 'real_geom_end_alg']:
if info.get(fld):
query[fld] = info[fld]
for fld in ['aut_grp', 'geom_aut_grp','torsion','igusa_clebsch']:
if info.get(fld):
query[fld] = map(int,info[fld].strip()[1:-1].split(","))
if info.get('ic0'):
query['igusa_clebsch']=[info['ic0'], info['ic1'], info['ic2'], info['ic3'] ]
for fld in ["cond", "num_rat_wpts", "torsion_order", "two_selmer_rank"]:
if info.get(fld):
field = fld
ran = str(info[field])
ran = ran.replace('..', '-').replace(' ','')
# Past input check
tmp = parse_range2(ran, field)
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
info["query"] = dict(query)
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
info['count'] = count
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' : isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit, bread=bread, title=title)
def genus2_curve_search(**args):
info = to_dict(args)
print "info", info
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+')
if label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
data = "Invalid label"
print data
if data == "Invalid label":
flash(Markup("The label <span style='color:black'>%s</span> is invalid."%(info["jump"])),"error")
return redirect(url_for(".index"))
if data == "Data for curve not found":
flash(Markup("No genus 2 curve with label <span style='color:black'>%s</span> was found in the database."%(info["jump"])),"error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info,query,'abs_disc','absolute discriminant')
parse_bool(info,query,'is_gl2_type')
parse_bool(info,query,'has_square_sha')
parse_bool(info,query,'locally_solvable')
for fld in ('st_group', 'real_geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
for fld in ('aut_grp', 'geom_aut_grp'):
#Encoded into a GAP ID.
parse_bracketed_posints(info,query,fld,exactlength=2)
# igusa and igusa_clebsch invariants not currently searchable
parse_bracketed_posints(info, query, 'torsion', 'torsion structure', maxlength=4,check_divisibility="increasing")
parse_ints(info,query,'cond','conductor')
parse_ints(info,query,'num_rat_wpts','Weierstrass points')
parse_ints(info,query,'torsion_order')
parse_ints(info,query,'two_selmer_rank','2-Selmer rank')
parse_ints(info,query,'analytic_rank','analytic rank')
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html", info=info, title='Genus 2 Curves Search Input Error', bread=bread, credit=credit_string)
info["query"] = dict(query)
print "query", info["query"]
print "info", info
count = parse_count(info, 50)
start = parse_start(info)
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one({'label' :
isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start+count<nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html", info=info, credit=credit,learnmore=learnmore_list(),
bread=bread, title=title)
credit = credit_string
title = 'Genus 2 curves over $\Q$'
bread = [('Genus 2 Curves', url_for(".index")), ('$\Q$', ' ')]
table=db.g2c_curves,
title='Genus 2 Curve Search Results',
err_title='Genus 2 Curves Search Input Error',
shortcuts={
'jump': genus2_jump,
'download': download_search
},
projection=[
'label', 'eqn', 'st_group', 'is_gl2_type', 'is_simple_geom',
'analytic_rank'
],
cleaners={
"class":
lambda v: class_from_curve_label(v["label"]),
"equation_formatted":
lambda v: list_to_min_eqn(literal_eval(v.pop("eqn"))),
"st_group_link":
lambda v: st_link_by_name(1, 4, v.pop('st_group'))
},
bread=lambda: [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('Search Results', '.')],
learnmore=learnmore_list,
credit=lambda: credit_string)
def genus2_curve_search(info, query):
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
def genus2_curve_search(**args):
info = to_dict(args)
if 'download' in info and info['download'] == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
label_regex = re.compile(r'\d+\.[a-z]+.\d+.\d+')
if label_regex.match(info["jump"].strip()):
data = render_curve_webpage_by_label(info["jump"].strip())
else:
data = "Invalid label"
if data == "Invalid label":
flash(
Markup(
"The label <span style='color:black'>%s</span> is invalid."
% (info["jump"])), "error")
return redirect(url_for(".index"))
if data == "Data for curve not found":
flash(
Markup(
"No genus 2 curve with label <span style='color:black'>%s</span> was found in the database."
% (info["jump"])), "error")
return redirect(url_for(".index"))
return data
try:
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type')
parse_bool(info, query, 'has_square_sha')
parse_bool(info, query, 'locally_solvable')
for fld in ('st_group', 'real_geom_end_alg'):
if info.get(fld): query[fld] = info[fld]
for fld in ('aut_grp', 'geom_aut_grp'):
parse_bracketed_posints(info, query, fld,
exactlength=2) #Encoded into a GAP ID.
# igusa and igusa_clebsch invariants not currently searchable
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'cond', 'conductor')
parse_ints(info, query, 'num_rat_wpts', 'Weierstrass points')
parse_ints(info, query, 'torsion_order')
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
except ValueError as err:
info['err'] = str(err)
return render_template("search_results_g2.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
info["query"] = dict(query)
count = parse_count(info, 50)
start = parse_start(info)
cursor = db_g2c().curves.find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one(
{'label': isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
if isogeny_class["is_gl2_type"] == True:
v_clean["is_gl2_type_display"] = '✔' #checkmark
else:
v_clean["is_gl2_type_display"] = ''
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
v_clean["st_group_name"] = st_group_name(isogeny_class['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)
def genus2_curve_search(info):
if 'jump' in info:
jump = info["jump"].strip()
if re.match(r'^\d+\.[a-z]+\.\d+\.\d+$', jump):
return redirect(url_for_curve_label(jump), 301)
else:
if re.match(r'^\d+\.[a-z]+$', jump):
return redirect(url_for_isogeny_class_label(jump), 301)
else:
# Handle direct Lhash input
if re.match(r'^\#\d+$', jump) and ZZ(jump[1:]) < 2**61:
c = g2c_db_curves().find_one({'Lhash': jump[1:].strip()})
if c:
return redirect(
url_for_isogeny_class_label(c["class"]), 301)
else:
errmsg = "hash %s not found"
else:
errmsg = "%s is not a valid genus 2 curve or isogeny class label"
flash_error(errmsg, jump)
return redirect(url_for(".index"))
if info.get('download', '').strip() == '1':
return download_search(info)
info["st_group_list"] = st_group_list
info["st_group_dict"] = st_group_dict
info["real_geom_end_alg_list"] = real_geom_end_alg_list
info["real_geom_end_alg_to_ST0_dict"] = real_geom_end_alg_to_ST0_dict
info["aut_grp_list"] = aut_grp_list
info["aut_grp_dict"] = aut_grp_dict
info["geom_aut_grp_list"] = geom_aut_grp_list
info["geom_aut_grp_dict"] = geom_aut_grp_dict
bread = info.get('bread',
(('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')))
query = {}
try:
parse_ints(info, query, 'abs_disc', 'absolute discriminant')
parse_bool(info, query, 'is_gl2_type', 'is of GL2-type')
parse_bool(info, query, 'has_square_sha', 'has square Sha')
parse_bool(info, query, 'locally_solvable', 'is locally solvable')
parse_bool(info, query, 'is_simple_geom', 'is geometrically simple')
parse_ints(info, query, 'cond', 'conductor')
parse_ints(info, query, 'num_rat_wpts', 'rational Weierstrass points')
parse_bracketed_posints(info,
query,
'torsion',
'torsion structure',
maxlength=4,
check_divisibility="increasing")
parse_ints(info, query, 'torsion_order', 'torsion order')
if 'torsion' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,
[int(n) for n in query['torsion']],
1)
if 'torsion' in query:
query['torsion_subgroup'] = str(query['torsion']).replace(" ", "")
query.pop('torsion') # search using string key, not array of ints
parse_ints(info, query, 'two_selmer_rank', '2-Selmer rank')
parse_ints(info, query, 'analytic_rank', 'analytic rank')
# G2 invariants and drop-list items don't require parsing -- they are all strings (supplied by us, not the user)
if 'g20' in info and 'g21' in info and 'g22' in info:
query['g2_inv'] = "['%s','%s','%s']" % (info['g20'], info['g21'],
info['g22'])
if 'class' in info:
query['class'] = info['class']
for fld in ('st_group', 'real_geom_end_alg', 'aut_grp_id',
'geom_aut_grp_id'):
if info.get(fld): query[fld] = info[fld]
except ValueError as err:
info['err'] = str(err)
return render_template("g2c_search_results.html",
info=info,
title='Genus 2 Curves Search Input Error',
bread=bread,
credit=credit_string)
# Database query happens here
info["query"] = query # save query for reuse in download_search
cursor = g2c_db_curves().find(
query, {
'_id': False,
'label': True,
'eqn': True,
'st_group': True,
'is_gl2_type': True,
'is_simple_geom': True,
'analytic_rank': True
})
count = parse_count(info, 50)
start = parse_start(info)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([("cond", ASCENDING), ("class", ASCENDING),
("disc_key", ASCENDING),
("label", ASCENDING)]).skip(start).limit(count)
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["class"] = class_from_curve_label(v["label"])
v_clean["is_gl2_type"] = v["is_gl2_type"]
v_clean["is_simple_geom"] = v["is_simple_geom"]
v_clean["equation_formatted"] = list_to_min_eqn(literal_eval(v["eqn"]))
v_clean["st_group_link"] = st_link_by_name(1, 4, v['st_group'])
v_clean["analytic_rank"] = v["analytic_rank"]
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda label: url_for_curve_label(label)
info["class_url"] = lambda label: url_for_isogeny_class_label(label)
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
title = info.get('title', 'Genus 2 Curve search results')
credit = credit_string
return render_template("g2c_search_results.html",
info=info,
credit=credit,
learnmore=learnmore_list(),
bread=bread,
title=title)
def make_class(self):
from lmfdb.genus2_curves.genus2_curve import url_for_curve_label
# Data
curves_data = g2cdb().curves.find({"class" : self.label},{'_id':int(0),'label':int(1),'min_eqn':int(1),'disc_key':int(1)}).sort([("disc_key", ASCENDING), ("label", ASCENDING)])
assert curves_data
self.curves = [ {"label" : c['label'], "equation_formatted" : list_to_min_eqn(c['min_eqn']),
"url": url_for_curve_label(c['label'])} for c in curves_data ]
self.ncurves = curves_data.count()
self.bad_lfactors = [ [c[0], list_to_factored_poly_otherorder(c[1])]
for c in self.bad_lfactors]
# Data derived from Sato-Tate group
self.st_group_name = st_group_name(self.st_group)
self.st_group_href = st_group_href(self.st_group)
self.st0_group_name = st0_group_name(self.real_geom_end_alg)
# Later used in Lady Gaga box:
self.real_geom_end_alg_disp = [r'\End(J_{\overline{\Q}}) \otimes \R',
end_alg_name(self.real_geom_end_alg)]
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
# Endomorphism data
endodata = g2cdb().endomorphisms.find_one({"label" :
self.curves[0]['label']})
self.gl2_statement_base = \
gl2_statement_base(endodata['factorsRR_base'], r'\(\Q\)')
self.endo_statement_base = \
"""Endomorphism algebra over \(\Q\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_base'],
endodata['factorsRR_base'], r'')
endodata['fod_poly'] = intlist_to_poly(endodata['fod_coeffs'])
self.fod_statement = fod_statement(endodata['fod_label'],
endodata['fod_poly'])
if endodata['fod_label'] != '1.1.1.1':
self.endo_statement_geom = \
"""Endomorphism algebra over \(\overline{\Q}\):<br>""" + \
endo_statement_isog(endodata['factorsQQ_geom'],
endodata['factorsRR_geom'], r'\overline{\Q}')
else:
self.endo_statement_geom = ''
# Title
self.title = "Genus 2 Isogeny Class %s" % (self.label)
# Lady Gaga box
self.properties = (
('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor','%s' % self.cond),
('Sato-Tate group', self.st_group_href),
('\(%s\)' % self.real_geom_end_alg_disp[0],
'\(%s\)' % self.real_geom_end_alg_disp[1]),
('\(\mathrm{GL}_2\)-type','%s' % self.is_gl2_type_name)
)
x = self.label.split('.')[1]
self.friends = [('L-function', url_for("l_functions.l_function_genus2_page", cond=self.cond,x=x))]
#self.downloads = [('Download Euler factors', ".")]
#self.downloads = [
# ('Download Euler factors', "."),
# url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves',
# url_for(".download_g2c_all", label=self.label))
# ]
# Breadcrumbs
self.bread = (
('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond, url_for(".by_conductor", cond=self.cond)),
('%s' % self.label, ' ')
)
# More friends (NOTE: to be improved)
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) != 1:
self.friends.append(('Elliptic curve ' + curve_label,
crv_url))
self.ecproduct_wurl.append({'label' : curve_label, 'url' :
crv_url})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass", nf = crv_spl[0],
conductor_label = crv_spl[1], class_label = crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({'label' : curve_label, 'url' :
crv_url, 'nf' : crv_spl[0]})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms",
level=mf_spl[0], weight=mf_spl[1], character=mf_spl[2],
label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage",
field_label=mf_spl[0], label=mf_label)
self.friends.append(('Hilbert modular form ' + mf_label, mf_url))
def make_class(self):
curves_data = db_g2c().curves.find({
"class": self.label
}).sort([("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)])
self.curves = [{
"label": c['label'],
"equation_formatted": list_to_min_eqn(c['min_eqn']),
"url": url_for_label(c['label'])
} for c in curves_data]
self.ncurves = curves_data.count()
self.bad_lfactors = [[c[0],
list_to_factored_poly_otherorder(c[1])]
for c in self.bad_lfactors]
for endalgtype in [
'end_alg', 'rat_end_alg', 'real_end_alg', 'geom_end_alg',
'rat_geom_end_alg', 'real_geom_end_alg'
]:
if hasattr(self, endalgtype):
setattr(self, endalgtype + '_name',
end_alg_name(getattr(self, endalgtype)))
else:
setattr(self, endalgtype + '_name', '')
self.st_group_name = st_group_name(self.st_group)
if hasattr(self, 'geom_end_field') and self.geom_end_field <> '':
self.geom_end_field_name = field_pretty(self.geom_end_field)
else:
self.geom_end_field_name = ''
if self.is_gl2_type:
self.is_gl2_type_name = 'yes'
else:
self.is_gl2_type_name = 'no'
if hasattr(self, 'is_simple'):
if self.is_simple:
self.is_simple_name = 'yes'
else:
self.is_simple_name = 'no'
else:
self.is_simple_name = '?'
if hasattr(self, 'is_geom_simple'):
if self.is_geom_simple:
self.is_geom_simple_name = 'yes'
else:
self.is_geom_simple_name = 'no'
else:
self.is_geom_simple_name = '?'
x = self.label.split('.')[1]
self.friends = [('L-function',
url_for("l_functions.l_function_genus2_page",
cond=self.cond,
x=x)), ('Siegel modular form someday', '.')]
self.ecproduct_wurl = []
if hasattr(self, 'ecproduct'):
for i in range(2):
curve_label = self.ecproduct[i]
crv_url = url_for("ec.by_ec_label", label=curve_label)
if i == 1 or len(set(self.ecproduct)) <> 1:
self.friends.append(
('Elliptic curve ' + curve_label, crv_url))
self.ecproduct_wurl.append({
'label': curve_label,
'url': crv_url
})
self.ecquadratic_wurl = []
if hasattr(self, 'ecquadratic'):
for i in range(len(self.ecquadratic)):
curve_label = self.ecquadratic[i]
crv_spl = curve_label.split('-')
crv_url = url_for("ecnf.show_ecnf_isoclass",
nf=crv_spl[0],
conductor_label=crv_spl[1],
class_label=crv_spl[2])
self.friends.append(('Elliptic curve ' + curve_label, crv_url))
self.ecquadratic_wurl.append({
'label': curve_label,
'url': crv_url,
'nf': crv_spl[0]
})
if hasattr(self, 'mfproduct'):
for i in range(len(self.mfproduct)):
mf_label = self.mfproduct[i]
mf_spl = mf_label.split('.')
mf_spl.append(mf_spl[2][-1])
mf_spl[2] = mf_spl[2][:-1] # Need a splitting function
mf_url = url_for("emf.render_elliptic_modular_forms",
level=mf_spl[0],
weight=mf_spl[1],
character=mf_spl[2],
label=mf_spl[3])
self.friends.append(('Modular form ' + mf_label, mf_url))
if hasattr(self, 'mfhilbert'):
for i in range(len(self.mfhilbert)):
mf_label = self.mfhilbert[i]
mf_spl = mf_label.split('-')
mf_url = url_for("hmf.render_hmf_webpage",
field_label=mf_spl[0],
label=mf_label)
self.friends.append(
('Hilbert modular form ' + mf_label, mf_url))
self.properties = [('Label', self.label),
('Number of curves', str(self.ncurves)),
('Conductor', '%s' % self.cond),
('Sato-Tate group', '\(%s\)' % self.st_group_name),
('\(\mathrm{End}(J_{\overline{\Q}}) \otimes \R\)',
'\(%s\)' % self.real_geom_end_alg_name),
('\(\mathrm{GL}_2\)-type',
'%s' % self.is_gl2_type_name)]
self.title = "Genus 2 Isogeny Class %s" % (self.label)
self.downloads = [
('Download Euler factors', ".")
] # url_for(".download_g2c_eulerfactors", label=self.label)),
# ('Download stored data for all curves', url_for(".download_g2c_all", label=self.label))]
self.bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")),
('%s' % self.cond,
url_for(".by_conductor", conductor=self.cond)),
('%s' % self.label, ' ')]
def genus2_curve_search(**args):
info = to_dict(args)
query = {} # database callable
bread = [('Genus 2 Curves', url_for(".index")),
('$\Q$', url_for(".index_Q")), ('Search Results', '.')]
#if 'SearchAgain' in args:
# return rational_genus2_curves()
if 'jump' in args:
return render_curve_webpage_by_label(info["jump"])
if info.get("disc"):
field = "abs_disc"
ran = info["disc"]
ran = ran.replace('..', '-').replace(' ', '')
# Past input check
dlist = parse_discs(ran)
tmp = g2_list_to_query(dlist)
if len(tmp) == 1:
tmp = tmp[0]
else:
query[tmp[0][0]] = tmp[0][1]
tmp = tmp[1]
print tmp
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("is_gl2_type"):
query['is_gl2_type'] = bool(info['is_gl2_type'])
for fld in ['aut_grp', 'geom_aut_grp', 'st_group', 'real_geom_end_alg']:
if info.get(fld):
query[fld] = info[fld]
for fld in ['aut_grp', 'geom_aut_grp']:
if info.get(fld):
query[fld] = eval(info[fld])
if info.get("cond"):
field = "cond"
ran = str(info[field])
ran = ran.replace('..', '-').replace(' ', '')
# Past input check
tmp = parse_range2(ran, field)
print tmp
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if info.get("count"):
try:
count = int(info["count"])
except:
count = 100
else:
count = 100
info["query"] = dict(query)
#res = db_g2c().curves.find(query).sort([("cond", pymongo.ASCENDING),
#("label", pymongo.ASCENDING)]).limit(count)
res = db_g2c().curves.find(query).sort([("cond", pymongo.ASCENDING),
("class", pymongo.ASCENDING),
("disc_key", pymongo.ASCENDING),
("label", pymongo.ASCENDING)])
nres = res.count()
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
res_clean = []
for v in res:
v_clean = {}
v_clean["label"] = v["label"]
v_clean["isog_label"] = v["class"]
isogeny_class = db_g2c().isogeny_classes.find_one(
{'label': isog_label(v["label"])})
v_clean["is_gl2_type"] = isogeny_class["is_gl2_type"]
v_clean["equation_formatted"] = list_to_min_eqn(v["min_eqn"])
res_clean.append(v_clean)
info["curves"] = res_clean
info["curve_url"] = lambda dbc: url_for_label(dbc['label'])
info["isog_url"] = lambda dbc: isog_url_for_label(dbc['label'])
credit = credit_string
title = 'Genus 2 Curves search results'
return render_template("search_results_g2.html",
info=info,
credit=credit,
bread=bread,
title=title)
