def print_query(query, families=False, pad=1):
if type(query) in (sqlite3.Cursor, list):
longest = ""
results = []
for q in query:
results.append(q)
longest = max((q[1], longest), key=len) # to ensure proper padding
for r in results:
print_query(r, families=families, pad=len(longest))
return
n, p_str, sol = query
family = ""
if families:
_p = Partition(*map(int, p_str.split(",")))
if _p.is_one_dimensional():
family = "[1D]"
if _p.is_hook():
family = "[HOOK]"
elif _p.is_self_conjugate():
family = "[SELF-CONJ]"
print u"{:{pad}} \u22a2 {:2}: solution {} {}".format("(" + p_str + ")",
n,
sol,
family,
pad=pad +
2).encode("utf-8")
def find_solution(shape,
verbose=False,
skip_known_families=True,
return_matrix=False):
if type(shape) is Partition:
shape = shape.vals
if skip_known_families:
p = Partition(*shape)
if p.is_one_dimensional():
if verbose:
print "Skipping 1D partition"
return 1
elif p.is_self_conjugate():
if verbose:
print "Skipping self-conjugate partition"
return 0
elif p.is_hook():
if verbose:
print "Skipping hook partition"
i = sum(p.vals)
r = p.vals[1:].count(1)
choose = factorial(i - 1) / (factorial(r) * factorial(i - 1 - r))
if (i % 2, r % 2, choose % 2) == (1, 0, 1):
return 1
else:
return 0
if shape == (1, ):
# isolate this case to avoid numpy exception when building matrix
return 1
if verbose:
print "Generating all standard {}-tableaux...\n".format(shape)
polys = []
if verbose:
print "-" * 20
for t in [t for t in total_order(shape)][::-1]:
standards = [t]
#if verbose:
# print "Next tableaux:\n{}\n".format(t)
poly = set([tab for tab in t.polytabloid() if tab != t])
if len(poly) > 1:
for s in poly:
if s.vals != t.vals:
print "{} --> {}".format(t.vals, s.vals)
standards.append(s)
polys.append(standards)
columns = []
if verbose:
print "Creating matrix from polytabloids."
for i, poly in enumerate(polys):
vec = [0] * len(polys)
vec[i] = 1
if len(poly) > 1:
for s in poly:
#find the index of the standard tableaux
x = [l[0] for l in polys].index(s)
vec[x] = 1
columns.append(vec)
matrix = column_stack(columns)
if return_matrix:
print matrix
return matrix
if verbose:
print matrix
solution = map(int, linalg.solve(matrix, [1] * len(polys)))
if verbose:
print "Solution vector: {}".format(solution)
print "Sum of standard coefficients is congruent to {} (mod 2).".format(
sum(solution) % 2)
return sum(solution)