def random_difference(n, k, p, q):
"""
Returns a difference that has the same sum as
the difference between p and q, but with a redistribution.
"""
diff = difference(n, k, p, q)
print 'the original difference :', diff
rootcount = 0
while(rootcount == 0):
S = sum(diff)
result = []
for i in range(k-1):
if(S > n-k):
r = randint(0, n-k)
else:
r = randint(0, S)
result.append(r)
S = S - r
result.append(S)
result.sort(reverse=True)
print 'original:', diff, 'redistributed:', result
ind = 0
while((ind < k-1) and (result[ind] > n-k)):
d = result[ind] - n + k
result[ind] = n-k
result[ind+1] = result[ind+1] + d
ind = ind + 1
result.sort(reverse=True)
q.sort(reverse=True)
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, result)
rootcount = resolve(n, k, [bp, bq, br], False)
return result
def random_difference(n, k, p, q):
"""
Returns a difference that has the same sum as
the difference between p and q, but with a redistribution.
"""
diff = difference(n, k, p, q)
print 'the original difference :', diff
rootcount = 0
while (rootcount == 0):
S = sum(diff)
result = []
for i in range(k - 1):
if (S > n - k):
r = randint(0, n - k)
else:
r = randint(0, S)
result.append(r)
S = S - r
result.append(S)
result.sort(reverse=True)
print 'original:', diff, 'redistributed:', result
ind = 0
while ((ind < k - 1) and (result[ind] > n - k)):
d = result[ind] - n + k
result[ind] = n - k
result[ind + 1] = result[ind + 1] + d
ind = ind + 1
result.sort(reverse=True)
q.sort(reverse=True)
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, result)
rootcount = resolve(n, k, [bp, bq, br], False)
return result
def write_triplet(n, k, p, q):
"""
Given a partition p and its complement q, computes the difference,
and checks the sum.
"""
r = difference(n, k, p, q)
q.sort(reverse=True)
r.sort(reverse=True)
# print 'the triplet :', p, q, r
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, r)
rc = resolve(n, k, [bp, bq, br], verbose=False)
print 'the brackets :', bp, bq, br, 'root count :', rc
def write_triplet(n, k, p, q):
"""
Given a partition p and its complement q, computes the difference,
and checks the sum.
"""
r = difference(n, k, p, q)
q.sort(reverse=True)
r.sort(reverse=True)
# print 'the triplet :', p, q, r
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, r)
rc = resolve(n, k, [bp, bq, br], verbose=False)
print 'the brackets :', bp, bq, br, 'root count :', rc
def main():
"""
Prompts the user for n, k, and m.
"""
n = input('Give the ambient dimension : ')
k = input('Give the dimension of the planes : ')
m = 3 # input('Give the number of conditions : ')
print '-> the parameters :', n, k, m
ans = raw_input('generate all partitions ? (y/n) ')
if(ans == 'y'):
generate_all_partitions(n, k, write)
else:
p, q, r = random_triplet(n, k)
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, r)
print 'the bracket representation :', bp, bq, br
rc = resolve(n,k, [bp, bq, br], verbose=False)
print 'the root count :', rc
def main():
"""
Prompts the user for n, k, and m.
"""
n = input('Give the ambient dimension : ')
k = input('Give the dimension of the planes : ')
m = 3 # input('Give the number of conditions : ')
print '-> the parameters :', n, k, m
ans = raw_input('generate all partitions ? (y/n) ')
if (ans == 'y'):
generate_all_partitions(n, k, write)
else:
p, q, r = random_triplet(n, k)
bp = partition2bracket(n, k, p)
bq = partition2bracket(n, k, q)
br = partition2bracket(n, k, r)
print 'the bracket representation :', bp, bq, br
rc = resolve(n, k, [bp, bq, br], verbose=False)
print 'the root count :', rc
def generate_all_differences2(n, k, p, q, val, r, fun=None):
"""
Recursive enumerator for all differences,
as called by generate_all_differences.
"""
if(len(r) == k):
br = partition2bracket(n, k, r)
rc = resolve(n, k, [p, q, br], False)
if(rc > 2):
if(fun != None):
fun(p,q,br,rc)
else:
print 'brackets :', [p, q, br], 'root count :', rc
elif(len(r) == k - 1):
if(val <= r[k-2]):
generate_all_differences2(n, k, p, q, 0, r+[val], fun)
else:
upper = min([val, n-k, r[len(r)-1]])
lower = val/(k - len(r))
for i in range(lower, upper+1):
generate_all_differences2(n, k, p, q, val-i, r+[i], fun)
def generate_all_differences2(n, k, p, q, val, r, fun=None):
"""
Recursive enumerator for all differences,
as called by generate_all_differences.
"""
if (len(r) == k):
br = partition2bracket(n, k, r)
rc = resolve(n, k, [p, q, br], False)
if (rc > 2):
if (fun != None):
fun(p, q, br, rc)
else:
print 'brackets :', [p, q, br], 'root count :', rc
elif (len(r) == k - 1):
if (val <= r[k - 2]):
generate_all_differences2(n, k, p, q, 0, r + [val], fun)
else:
upper = min([val, n - k, r[len(r) - 1]])
lower = val / (k - len(r))
for i in range(lower, upper + 1):
generate_all_differences2(n, k, p, q, val - i, r + [i], fun)
