main.py

import sys, subprocess
from tqdm import tqdm

N_semigroups = [1, 1, 4, 18, 126, 1160, 15973, 836021, 1843120128]
N_semilattices = [1, 1, 1, 2, 5, 15, 53, 222, 1078]

template = """
LoadPackage("smallsemi");;

n := {n};;

for k in [{a}..{b}] do
m := RecoverMultiplicationTable(n, k);;
l := List(m, row -> JoinStringsWithSeparator(row, ""));;
Print(JoinStringsWithSeparator(l, ""));
Print("\\n");
od;

quit;;
"""

def is_semilattice(n, line):
    for x in range(n):
        if int(line[n*x + x]) != (x + 1):
            return False
    for x in range(n):
        for y in range(n):
            if line[n*x + y] != line[n*y + x]:
                return False
    return True

def make_iter_of_semigroups(n, a, b):
    print("-"*50)
    script_fn = "script_of_main_py.txt"
    gap_code = template.format(n=n, a=a, b=b)
    with open(script_fn, "w") as f:
        f.write(gap_code)
    print(script_fn + ":")
    print(gap_code)
    cmd = "cat {script_fn} | ./gap.sh -q".format(script_fn=script_fn)
    print("cmd:", cmd)
    process = subprocess.Popen(cmd, stdout=subprocess.PIPE, shell=True)
    print("-"*50)
    return iter(process.stdout.readline, b'')

def go(n, only_semilattices=False, start_a=None, progbar=True, islog=False):
    print("-"*50)
    only_semilattices = bool(only_semilattices)
    print("only_semilattices:", only_semilattices)
    l = N_semigroups[n]
    a, b = 1, l
    if start_a is not None:
        a = start_a
    print("a, b, l:", a, b, l)
    i, j = a-1, 0 # i -- количество найденых полугрупп, j -- количество найденых полурешеток
    t = ""
    if only_semilattices:
        t = "_semilattices"
    output_fn = "{}_{:010}_{:010}{}.txt".format(n, a, b, t)
    output_file = open(output_fn, "w")
    print("output_fn:", output_fn)
    print("-"*50)
    if progbar:
        pbar = tqdm(total=l)
    pbar.update(i)
    while True:
        a = i+1
        for line in make_iter_of_semigroups(n, a, b):
            line = line.strip().decode()
            if not line.isdigit():
                continue
            if progbar:
                pbar.update(1)
            i += 1
            if only_semilattices:
                flag = is_semilattice(n, line)
                if islog:
                    print(line, flag)
                if not flag:
                    continue
                j += 1
            output_file.write(line)
        if i == l:
            break
    if progbar:
        pbar.close()
    output_file.close()
    print("-"*50)
    print("The End:", (n, a, b), (l, i, j))
    print("-"*50)

args = sys.argv[1:]
go(*map(int, args))