def elliptic_curve_search(**args): info = to_dict(args) query = {} bread = [('Elliptic Curves', url_for("ecnf.index")), ('$\Q$', url_for(".rational_elliptic_curves")), ('Search Results', '.')] if 'SearchAgain' in args: return rational_elliptic_curves() if 'jump' in args: label = info.get('label', '').replace(" ", "") m = match_lmfdb_label(label) if m: try: return by_ec_label(label) except ValueError: return elliptic_curve_jump_error(label, info, wellformed_label=True) elif label.startswith("Cremona:"): label = label[8:] m = match_cremona_label(label) if m: try: return by_ec_label(label) except ValueError: return elliptic_curve_jump_error(label, info, wellformed_label=True) elif match_cremona_label(label): return elliptic_curve_jump_error(label, info, cremona_label=True) elif label: # Try to parse a string like [1,0,3,2,4] as valid # Weistrass coefficients: lab = re.sub(r'\s','',label) lab = re.sub(r'^\[','',lab) lab = re.sub(r']$','',lab) try: labvec = lab.split(',') labvec = [QQ(str(z)) for z in labvec] # Rationals allowed E = EllipticCurve(labvec) # Now we do have a valid curve over Q, but it might # not be in the database. ainvs = [str(c) for c in E.minimal_model().ainvs()] data = db_ec().find_one({'ainvs': ainvs}) if data is None: info['conductor'] = E.conductor() return elliptic_curve_jump_error(label, info, missing_curve=True) return by_ec_label(data['lmfdb_label']) except (TypeError, ValueError, ArithmeticError): return elliptic_curve_jump_error(label, info) else: query['label'] = '' if info.get('jinv'): j = clean_input(info['jinv']) j = j.replace('+', '') if not QQ_RE.match(j): info['err'] = 'Error parsing input for the j-invariant. It needs to be a rational number.' return search_input_error(info, bread) query['jinv'] = str(QQ(j)) # to simplify e.g. 1728/1 for field in ['conductor', 'torsion', 'rank', 'sha']: if info.get(field): info[field] = clean_input(info[field]) ran = info[field] ran = ran.replace('..', '-').replace(' ', '') if not LIST_RE.match(ran): names = {'conductor': 'conductor', 'torsion': 'torsion order', 'rank': 'rank', 'sha': 'analytic order of Ш'} info['err'] = 'Error parsing input for the %s. It needs to be an integer (such as 25), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).' % names[field] return search_input_error(info, bread) # 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] if 'optimal' in info and info['optimal'] == 'on': # fails on 990h3 query['number'] = 1 if 'torsion_structure' in info and info['torsion_structure']: res = parse_torsion_structure(info['torsion_structure'],2) if 'Error' in res: info['err'] = res return search_input_error(info, bread) #update info for repeat searches info['torsion_structure'] = str(res).replace(' ','') query['torsion_structure'] = [str(r) for r in res] if info.get('surj_primes'): info['surj_primes'] = clean_input(info['surj_primes']) format_ok = LIST_POSINT_RE.match(info['surj_primes']) if format_ok: surj_primes = [int(p) for p in info['surj_primes'].split(',')] format_ok = all([ZZ(p).is_prime(proof=False) for p in surj_primes]) if format_ok: query['non-surjective_primes'] = {"$nin": surj_primes} else: info['err'] = 'Error parsing input for surjective primes. It needs to be a prime (such as 5), or a comma-separated list of primes (such as 2,3,11).' return search_input_error(info, bread) if info.get('nonsurj_primes'): info['nonsurj_primes'] = clean_input(info['nonsurj_primes']) format_ok = LIST_POSINT_RE.match(info['nonsurj_primes']) if format_ok: nonsurj_primes = [int(p) for p in info['nonsurj_primes'].split(',')] format_ok = all([ZZ(p).is_prime(proof=False) for p in nonsurj_primes]) if format_ok: if info['surj_quantifier'] == 'exactly': nonsurj_primes.sort() query['non-surjective_primes'] = nonsurj_primes else: if 'non-surjective_primes' in query: query['non-surjective_primes'] = { "$nin": surj_primes, "$all": nonsurj_primes } else: query['non-surjective_primes'] = { "$all": nonsurj_primes } else: info['err'] = 'Error parsing input for nonsurjective primes. It needs to be a prime (such as 5), or a comma-separated list of primes (such as 2,3,11).' return search_input_error(info, bread) if 'download' in info and info['download'] != '0': res = db_ec().find(query).sort([ ('conductor', ASCENDING), ('iso_nlabel', ASCENDING), ('lmfdb_number', ASCENDING) ]) return download_search(info, res) count_default = 100 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_ec().find(query) nres = cursor.count() if(start >= nres): start -= (1 + (start - nres) / count) * count if(start < 0): start = 0 res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING), ('lmfdb_number', ASCENDING) ]).skip(start).limit(count) info['curves'] = res info['format_ainvs'] = format_ainvs info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number']) info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1]) info['number'] = nres info['start'] = start info['count'] = count info['more'] = int(start + count < nres) if nres == 1: info['report'] = 'unique match' elif nres == 2: info['report'] = 'displaying both matches' 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 credit = 'John Cremona' if 'non-surjective_primes' in query: credit += 'and Andrew Sutherland' t = 'Elliptic Curves search results' return render_template("search_results.html", info=info, credit=credit, bread=bread, title=t)
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 elliptic_curve_search(**args): info = to_dict(args['data']) if 'jump' in info: label = info.get('label', '').replace(" ", "") # This label should be a full isogeny class label or a full # curve label (including the field_label component) try: nf, cond_label, iso_label, number = split_full_label(label.strip()) except IndexError: if not 'query' in info: info['query'] = {} bread = [("Elliptic Curves", url_for(".index"))] info['err'] = 'No elliptic curve in the database has label %s.' % label return search_input_error(info, bread) return show_ecnf(nf, cond_label, iso_label, number) query = {} bread = [('Elliptic Curves', url_for(".index")), ('Search Results', '.')] if 'conductor_norm' in info: Nnorm = clean_input(info['conductor_norm']) Nnorm = Nnorm.replace('..', '-').replace(' ', '') tmp = parse_range2(Nnorm, 'conductor_norm') 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 'conductor_label' in info: query['conductor_label'] = info['conductor_label'] deg = None if 'field' in info: field_label = parse_field_string(info['field']) #print("Field label was %s; after parsing, is %s" % (info['field'], field_label)) if FIELD_LABEL_RE.match(field_label): query['field_label'] = field_label deg = int(field_label.split(".")[0]) else: info['err'] = 'unrecognised field: %s' % info['field'] return search_input_error(info, bread) if 'jinv' in info: if deg == None: info['err'] = 'You must specify a field when searching by j-invariant' return search_input_error(info, bread) else: query['jinv'] = pol_string_to_j_list(info['jinv'], deg=deg) if info.get('torsion'): ran = info['torsion'] = clean_input(info['torsion']) ran = ran.replace('..', '-').replace(' ', '') if not LIST_RE.match(ran): info['err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).' return search_input_error(info, bread) # Past input check tmp = parse_range2(ran, 'torsion_order') # 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 'torsion_structure' in info and info['torsion_structure']: res = parse_torsion_structure(info['torsion_structure'],2) if 'Error' in res: info['err'] = res return search_input_error(info, bread) #update info for repeat searches info['torsion_structure'] = str(res).replace(' ','') query['torsion_structure'] = [int(r) for r in res] if 'include_isogenous' in info and info['include_isogenous'] == 'off': info['number'] = 1 query['number'] = 1 if 'include_base_change' in info and info['include_base_change'] == 'off': query['base_change'] = [] else: info['include_base_change'] = "on" info['query'] = query # process count and start if not default: count_default = 50 if info.get('count'): try: count = int(info['count']) except: count = count_default else: count = count_default 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 # make the query and trim results according to start/count: cursor = db_ecnf().find(query) nres = cursor.count() if(start >= nres): start -= (1 + (start - nres) / count) * count if(start < 0): start = 0 res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count) res = list(res) for e in res: e['numb'] = str(e['number']) e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label']) info['curves'] = res # [ECNF(e) for e in res] info['number'] = nres info['start'] = start info['count'] = count info['more'] = int(start + count < nres) info['field_pretty'] = field_pretty info['web_ainvs'] = web_ainvs 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 t = 'Elliptic Curve search results' return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args): info = to_dict(args['data']) if 'jump' in info: label = info.get('label', '').replace(" ", "") # This label should be a full isogeny class label or a full # curve label (including the field_label component) try: nf, cond_label, iso_label, number = split_full_label(label.strip()) except IndexError: if not 'query' in info: info['query'] = {} bread = [("Elliptic Curves", url_for(".index"))] info[ 'err'] = 'No elliptic curve in the database has label %s.' % label return search_input_error(info, bread) return show_ecnf(nf, cond_label, iso_label, number) query = {} bread = [('Elliptic Curves', url_for(".index")), ('Search Results', '.')] if 'conductor_norm' in info: Nnorm = clean_input(info['conductor_norm']) Nnorm = Nnorm.replace('..', '-').replace(' ', '') tmp = parse_range2(Nnorm, 'conductor_norm') 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 'conductor_label' in info: query['conductor_label'] = info['conductor_label'] if 'jinv' in info: query['jinv'] = info['jinv'] if info.get('torsion'): ran = info['torsion'] = clean_input(info['torsion']) ran = ran.replace('..', '-').replace(' ', '') if not LIST_RE.match(ran): info[ 'err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).' return search_input_error(info, bread) # Past input check tmp = parse_range2(ran, 'torsion_order') # 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 'torsion_structure' in info and info['torsion_structure']: res = parse_torsion_structure(info['torsion_structure'], 2) if 'Error' in res: info['err'] = res return search_input_error(info, bread) #update info for repeat searches info['torsion_structure'] = str(res).replace(' ', '') query['torsion_structure'] = [int(r) for r in res] if 'include_isogenous' in info and info['include_isogenous'] == 'off': query['number'] = 1 if 'include_base_change' in info and info['include_base_change'] == 'off': query['base_change'] = [] else: info['include_base_change'] = "on" if 'field' in info: query['field_label'] = parse_field_string(info['field']) info['query'] = query # process count and start if not default: count_default = 50 if info.get('count'): try: count = int(info['count']) except: count = count_default else: count = count_default 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 # make the query and trim results according to start/count: cursor = db_ecnf().find(query) nres = cursor.count() if (start >= nres): start -= (1 + (start - nres) / count) * count if (start < 0): start = 0 res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count) res = list(res) for e in res: e['numb'] = str(e['number']) e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label']) info['curves'] = res # [ECNF(e) for e in res] info['number'] = nres info['start'] = start info['count'] = count info['more'] = int(start + count < nres) info['field_pretty'] = field_pretty info['web_ainvs'] = web_ainvs 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 t = 'Elliptic Curve search results' return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args): info = to_dict(args["data"]) if "jump" in info: label = info.get("label", "").replace(" ", "") # This label should be a full isogeny class label or a full # curve label (including the field_label component) try: nf, cond_label, iso_label, number = split_full_label(label) except IndexError: if not "query" in info: info["query"] = {} bread = [("Elliptic Curves", url_for(".index"))] info["err"] = "No elliptic curve in the database has label %s." % label return search_input_error(info, bread) return show_ecnf(nf, cond_label, iso_label, number) query = {} bread = [("Elliptic Curves", url_for(".index")), ("Search Results", ".")] if "conductor_norm" in info: Nnorm = clean_input(info["conductor_norm"]) Nnorm = Nnorm.replace("..", "-").replace(" ", "") tmp = parse_range2(Nnorm, "conductor_norm") 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 "conductor_label" in info: query["conductor_label"] = info["conductor_label"] if "jinv" in info: query["jinv"] = info["jinv"] if info.get("torsion"): ran = info["torsion"] = clean_input(info["torsion"]) ran = ran.replace("..", "-").replace(" ", "") if not LIST_RE.match(ran): info[ "err" ] = "Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121)." return search_input_error(info, bread) # Past input check tmp = parse_range2(ran, "torsion_order") # 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 "torsion_structure" in info and info["torsion_structure"]: res = parse_torsion_structure(info["torsion_structure"], 2) if "Error" in res: info["err"] = res return search_input_error(info, bread) # update info for repeat searches info["torsion_structure"] = str(res).replace(" ", "") query["torsion_structure"] = [int(r) for r in res] if "include_isogenous" in info and info["include_isogenous"] == "off": query["number"] = 1 if "include_base_change" in info and info["include_base_change"] == "off": query["base_change"] = [] else: info["include_base_change"] = "on" if "field" in info: query["field_label"] = parse_field_string(info["field"]) info["query"] = query # process count and start if not default: count_default = 50 if info.get("count"): try: count = int(info["count"]) except: count = count_default else: count = count_default 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 # make the query and trim results according to start/count: cursor = db_ecnf().find(query) nres = cursor.count() if start >= nres: start -= (1 + (start - nres) / count) * count if start < 0: start = 0 res = ( cursor.sort( [ ("field_label", ASC), ("conductor_norm", ASC), ("conductor_label", ASC), ("iso_label", ASC), ("number", ASC), ] ) .skip(start) .limit(count) ) res = list(res) for e in res: e["numb"] = str(e["number"]) e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), e["field_label"]) info["curves"] = res # [ECNF(e) for e in res] info["number"] = nres info["start"] = start info["count"] = count info["more"] = int(start + count < nres) info["field_pretty"] = field_pretty info["web_ainvs"] = web_ainvs 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 t = "Elliptic Curve search results" return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)