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3594 bytes, as of the version from 2021-05-06 16:25. Recorded here, not run.
#The abc data is taken from the ABC@HOME project of Bart de Smit:
#
# https://www.math.leidenuniv.nl/~desmit/abc/
#
import yaml
import os
import mpmath
from utils.utils import numbers_to_yaml
from utils.utils import real_interval_to_sage_string
path = 'data/Number_theory/Abc-triples_of_high_merit'
prec10 = 100 #relative precision in base 10
num_digits_m = 14
RIFprec = RealIntervalField(prec10 * 3.4 * 2)
#First we parse the html files for abc-triples:
abcms = []
#abc_filename = "abc-quality.html"
#abc_filename = "abc-unbeaten.html"
abc_filename = "abc-merit.html"
#abc_filename = "abc-size.html"
with open(os.path.join(path,abc_filename),"r") as fp:
for line_index, line in enumerate(fp):
print("line:",line)
print("line_index:",line_index)
if line.startswith("<tr>"):
entries = line.strip().split('<td class="abcnum">')
entries = entries[-3:]
#print(len(entries))
#print(entries)
abc = []
ps = []
BIG_exponent = 1
for s in entries:
s = s.replace("<sup>","**")
s = s.replace("</sup>"," ")
s = s.replace("​"," ")
s = s.replace("·"," ")
s = s.replace("BIG **","BIG**")
factors = s.split(" ")
x = 1
for f in factors:
print(f)
if f == "":
continue
if f.startswith("BIG"):
#We omit the abc-triples where one of the
#factors is "BIG".
#This BIG factor can be computed
#from a+b=c and the other numbers.
#However it is not necessarily a prime.
#Thus computing rad(a*b*c) would require
#a factorization of BIG, which seems
#computationally difficult.
#So for simplicity we omit them from our
#heuristic.
#break
ipower = f.find('**')
if ipower != -1:
BIG_exponent = ZZ(f[ipower+2:])
f = '0'
else:
ipower = f.find('**')
if ipower == -1:
prime = f
else:
prime = f[:ipower]
ps.append(ZZ(prime))
x *= eval(f)
#print(x)
#if f == "BIG":
# break
abc.append(x)
print("abc:",abc)
if len(abc) == 3:
a,b,c = abc
if a+b==c:
pass
elif c == 0:
c = a+b
elif a == 0:
a = c-b
elif b == 0:
b = c-a
else:
print("error in abc:",abc)
raise
#compute quality:
BIG = a*b*c
for p in ps:
BIG = BIG.prime_to_m_part(p)
if BIG > 1:
print("BIG:",BIG)
BIG = ZZ(BIG^(1/BIG_exponent))
if BIG > 1:
print("BIG:",BIG)
#if BIG.is_square():
# BIG = ZZ(sqrt(BIG))
#assert(BIG.is_perfect_power())
reliable_m = False
try:
alarm(1)
BIG = BIG.radical()
reliable_m = True
except AlarmInterrupt:
pass
cancel_alarm()
#BIG = BIG.squarefree_part()
rad_abc = RIF(BIG * prod(ps))
q = RIF(log(c)/log(rad_abc))
m = (q-1)^2*log(rad_abc)*log(log(rad_abc))
abcms.append((a,b,c,m,reliable_m))
#break
#print("abcms:",abcms)
print("len(abcms):",len(abcms))
#Convert data to numberdb-format:
numbers = {}
m_strs = set()
for a,b,c,m,reliable_m in abcms:
m_str = real_interval_to_sage_string(
RIFprec(m),
max_digits = num_digits_m,
).replace('?','')
if not reliable_m:
m_str += "*"
m_strs.add(m_str)
numbers_m = {}
numbers_m['a'] = {
'param-latex': '$a$',
'number': str(a),
}
numbers_m['b'] = {
'param-latex': '$b$',
'number': str(b),
}
numbers_m['c'] = {
'param-latex': '$c$',
'number': str(c),
}
numbers[m_str] = numbers_m
print('len(m_sts):',len(m_strs))
filename = os.path.join(path, 'numbers.yaml')
yaml.dump(numbers, stream = open(filename, 'w'), sort_keys = False)