M = list(M)
T = [[-1 for x in range(n)] for x in xrange(n)]
for i, a in enumerate(M):
for j, b in enumerate(M):
T[i][j] = M.index(funcs.compose(a, b))
return T
def isAbelian(M):
for a, b in itertools.combinations(M, 2):
if funcs.compose(a, b) != funcs.compose(b, a):
return False
return True
ops = ladr_python.opsInFile(sys.stdin)
i = 1
for (down_table, up_table) in ops:
up_grp = generate(map(tuple, zip(*up_table)))
dn_grp = generate(map(tuple, zip(*down_table)))
print "Up:"
print ladr_python.matrixToLadr(table(up_grp), i)
print "Abelian=" + str(isAbelian(up_grp)) + ", cycle=" + str(
max([len(generate([x])) for x in up_grp]))
print "Dn:"
print ladr_python.matrixToLadr(table(dn_grp), i)
print "Abelian=" + str(isAbelian(dn_grp)) + ", cycle=" + str(
max([len(generate([x])) for x in dn_grp]))
print "Wh:"
whole_grp = generate(up_grp.union(dn_grp))
print ladr_python.matrixToLadr(table(whole_grp), i)
#!/usr/bin/python import ladr_python import sys import funcs (down_table, up_table) = ladr_python.opsInFile(sys.stdin).next() down_cols = [funcs.cycles(p) for p in zip(*down_table)] up_cols = [funcs.cycles(p) for p in zip(*up_table)] print "------ up ------" for c in up_cols: print " ".join(map(lambda(s): str(list(s)), c)) print "------ down ------" for c in down_cols: print " ".join(map(lambda(s): str(list(s)), c))
#!/usr/bin/python
import ladr_python
import funcs
import sys
if len(sys.argv) < 3:
sys.exit('Usage: %s smalls bigs small_prefix big_prefix' % sys.argv[0])
(pref1, pref2) = (sys.argv[3], sys.argv[4])
smalls = ladr_python.opsInFile(open(sys.argv[1]))
i = 0
for (sd, su) in smalls:
j = 0
i += 1
bigs = ladr_python.opsInFile(open(sys.argv[2]))
for (bd, bu) in bigs:
j += 1
if funcs.embeds([(sd, bd), (su, bu)]):
print "\t\"%s_%i\" -> \"%s_%i\";" % (pref1, i, pref2, j)
#!/usr/bin/python
import ladr_python
import sys
import congruences
ops = ladr_python.opsInFile(open(sys.argv[1]))
i = 1
for (d, u) in ops:
print "%i\t%i" % (i, len(list(congruences.congruences(u, d))))
i += 1
def table(M):
n = len(M)
M = list(M)
T = [[-1 for x in range(n)] for x in xrange(n)]
for i, a in enumerate(M):
for j, b in enumerate(M):
T[i][j] = M.index( funcs.compose(a,b) )
return T
def isAbelian(M):
for a, b in itertools.combinations(M, 2):
if funcs.compose(a,b) != funcs.compose(b,a):
return False
return True
ops = ladr_python.opsInFile(sys.stdin)
i = 1
for (down_table, up_table) in ops:
up_grp = generate(map(tuple, zip(*up_table)))
dn_grp = generate(map(tuple, zip(*down_table)))
print "Up:"
print ladr_python.matrixToLadr(table(up_grp), i)
print "Abelian=" + str(isAbelian(up_grp)) + ", cycle=" + str(max([len(generate([x])) for x in up_grp]))
print "Dn:"
print ladr_python.matrixToLadr(table(dn_grp), i)
print "Abelian=" + str(isAbelian(dn_grp)) + ", cycle=" + str(max([len(generate([x])) for x in dn_grp]))
print "Wh:"
whole_grp = generate(up_grp.union(dn_grp))
print ladr_python.matrixToLadr(table(whole_grp), i)
print "Abelian=" + str(isAbelian(whole_grp)) + ", cycle=" + str(max([len(generate([x])) for x in whole_grp]))
#!/usr/bin/python
import ladr_python
import funcs
import sys
if len(sys.argv) < 3:
sys.exit('Usage: %s bigs smalls big_prefix small_prefix' % sys.argv[0])
(pref1, pref2) = (sys.argv[3], sys.argv[4])
bigs = ladr_python.opsInFile(open(sys.argv[1]))
i = 0
for (bd, bu) in bigs:
j = 0
i += 1
smalls = ladr_python.opsInFile(open(sys.argv[2]))
for (sd, su) in smalls:
j += 1
if funcs.mapsonto([ (bd, sd), (bu, su) ]):
print "\t\"%s_%i\" -> \"%s_%i\";" % (pref1, i, pref2, j)
#!/usr/bin/python import ladr_python import sys import congruences ops = ladr_python.opsInFile(open(sys.argv[1])) i = 1 for (d, u) in ops: print "%i\t%i" % (i, len(list(congruences.congruences(u, d)))) i += 1