def MOLS_table(start, stop=None, compare=False, width=None):
r"""
Prints the MOLS table that Sage can produce.
INPUT:
- ``start,stop`` (integers) -- print the table of MOLS for value of `n` such
that ``start<=n<stop``. If only one integer is given as input, it is
interpreted as the value of ``stop`` with ``start=0`` (same behaviour as
``range``).
- ``compare`` (boolean) -- if sets to ``True`` the MOLS displays
with `+` and `-` entries its difference with the table from the
Handbook of Combinatorial Designs (2ed).
- ``width`` (integer) -- the width of each column of the table. By default,
it is computed from range of values determined by the parameters ``start``
and ``stop``.
EXAMPLES::
sage: from sage.combinat.designs.latin_squares import MOLS_table
sage: MOLS_table(100)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
0| +oo +oo 1 2 3 4 1 6 7 8 2 10 5 12 4 4 15 16 5 18
20| 4 5 3 22 7 24 4 26 5 28 4 30 31 5 4 5 8 36 4 5
40| 7 40 5 42 5 6 4 46 8 48 6 5 5 52 5 6 7 7 5 58
60| 5 60 5 6 63 7 5 66 5 6 6 70 7 72 5 7 6 6 6 78
80| 9 80 8 82 6 6 6 6 7 88 6 7 6 6 6 6 7 96 6 8
sage: MOLS_table(100, width=4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
____________________________________________________________________________________________________
0| +oo +oo 1 2 3 4 1 6 7 8 2 10 5 12 4 4 15 16 5 18
20| 4 5 3 22 7 24 4 26 5 28 4 30 31 5 4 5 8 36 4 5
40| 7 40 5 42 5 6 4 46 8 48 6 5 5 52 5 6 7 7 5 58
60| 5 60 5 6 63 7 5 66 5 6 6 70 7 72 5 7 6 6 6 78
80| 9 80 8 82 6 6 6 6 7 88 6 7 6 6 6 6 7 96 6 8
sage: MOLS_table(100, compare=True)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
0| + +
20|
40|
60| +
80|
sage: MOLS_table(50, 100, compare=True)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
40|
60| +
80|
"""
from orthogonal_arrays import largest_available_k
if stop is None:
start, stop = 0, start
# make start and stop be congruent to 0 mod 20
start = start - (start % 20)
stop = stop - 1
stop = stop + (20 - (stop % 20))
assert start % 20 == 0 and stop % 20 == 0
if stop <= start:
return
if compare:
from sage.misc.misc import SAGE_SHARE
handbook_file = open(
SAGE_SHARE + "/combinatorial_designs/MOLS_table.txt", 'r')
hb = map(int, handbook_file.readlines()[9].split(','))
handbook_file.close()
# choose an appropriate width (needs to be >= 3 because "+oo" should fit)
if width is None:
from sage.rings.integer import Integer
width = max(3, Integer(stop - 1).ndigits(10))
from string import join
print " " * (width + 2) + join("{i:>{width}}".format(i=i, width=width)
for i in range(20))
print " " * (width + 1) + "_" * ((width + 1) * 20),
for i in range(start, stop):
if i % 20 == 0:
print "\n{:>{width}}|".format(i, width=width),
k = largest_available_k(i) - 2
if compare:
if i < 2 or hb[i] == k:
c = ""
elif hb[i] < k:
c = "+"
else:
c = "-"
else:
if i < 2:
c = "+oo"
else:
c = k
print '{:>{width}}'.format(c, width=width),
def MOLS_table(start,stop=None,compare=False,width=None):
r"""
Prints the MOLS table that Sage can produce.
INPUT:
- ``start,stop`` (integers) -- print the table of MOLS for value of `n` such
that ``start<=n<stop``. If only one integer is given as input, it is
interpreted as the value of ``stop`` with ``start=0`` (same behaviour as
``range``).
- ``compare`` (boolean) -- if sets to ``True`` the MOLS displays
with `+` and `-` entries its difference with the table from the
Handbook of Combinatorial Designs (2ed).
- ``width`` (integer) -- the width of each column of the table. By default,
it is computed from range of values determined by the parameters ``start``
and ``stop``.
EXAMPLES::
sage: from sage.combinat.designs.latin_squares import MOLS_table
sage: MOLS_table(100)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
0| +oo +oo 1 2 3 4 1 6 7 8 2 10 5 12 4 4 15 16 5 18
20| 4 5 3 22 7 24 4 26 5 28 4 30 31 5 4 5 8 36 4 5
40| 7 40 5 42 5 6 4 46 8 48 6 5 5 52 5 6 7 7 5 58
60| 5 60 5 6 63 7 5 66 5 6 6 70 7 72 5 7 6 6 6 78
80| 9 80 8 82 6 6 6 6 7 88 6 7 6 6 6 6 7 96 6 8
sage: MOLS_table(100, width=4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
____________________________________________________________________________________________________
0| +oo +oo 1 2 3 4 1 6 7 8 2 10 5 12 4 4 15 16 5 18
20| 4 5 3 22 7 24 4 26 5 28 4 30 31 5 4 5 8 36 4 5
40| 7 40 5 42 5 6 4 46 8 48 6 5 5 52 5 6 7 7 5 58
60| 5 60 5 6 63 7 5 66 5 6 6 70 7 72 5 7 6 6 6 78
80| 9 80 8 82 6 6 6 6 7 88 6 7 6 6 6 6 7 96 6 8
sage: MOLS_table(100, compare=True)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
0| + +
20|
40|
60| +
80|
sage: MOLS_table(50, 100, compare=True)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
________________________________________________________________________________
40|
60| +
80|
"""
from orthogonal_arrays import largest_available_k
if stop is None:
start,stop = 0,start
# make start and stop be congruent to 0 mod 20
start = start - (start%20)
stop = stop-1
stop = stop + (20-(stop%20))
assert start%20 == 0 and stop%20 == 0
if stop <= start:
return
if compare:
from sage.misc.misc import SAGE_SHARE
handbook_file = open(SAGE_SHARE+"/combinatorial_designs/MOLS_table.txt",'r')
hb = map(int,handbook_file.readlines()[9].split(','))
handbook_file.close()
# choose an appropriate width (needs to be >= 3 because "+oo" should fit)
if width is None:
from sage.rings.integer import Integer
width = max(3,Integer(stop-1).ndigits(10))
from string import join
print " "*(width+2) + join("{i:>{width}}".format(i=i,width=width) for i in range(20))
print " "*(width+1) + "_"*((width+1)*20),
for i in range(start,stop):
if i%20==0:
print "\n{:>{width}}|".format(i,width=width),
k = largest_available_k(i)-2
if compare:
if i < 2 or hb[i] == k:
c = ""
elif hb[i] < k:
c = "+"
else:
c = "-"
else:
if i < 2:
c = "+oo"
else:
c = k
print '{:>{width}}'.format(c,width=width),