def bosonicConfigurations(L, N):
'''Input: 1D Lattice Size and Number of Bosons
Output: All possible configurations of bosons'''
#List that will store all configurations
configurations = []
#Store ordered partitions of N as a list
partitions = list(ordered_partitions(N))
for p in partitions:
#BH Lattice containing a partition of N followed by zeros
auxConfig = [0] * L
auxConfig[0:len(p)] = p
#Generate permutations based on current partition of N
partitionConfigs = list(multiset_permutations(auxConfig))
#Append permutations of current partition to list containing all configurations
configurations += partitionConfigs
#Promote configurations list to numpy array
configurations = np.array(configurations)
return configurations
def __init__(self, k):
self.k = k
Partitions = [p[::-1] for p in ordered_partitions(self.k)]
self.Dic = {}
M = [Memo(i).Data for i in range(self.k)]
for p in Partitions:
Deco = PartsStocker(p).Dic
for q in Partitions:
self.Dic[str(p)+str(q)] =sum(\
[x[1] * M[sum(x[0])][str(x[0])+str(q[1:])] for x in Deco[q[0]]])
def __init__(self, k):
self.k = k
# Generating partitions of k in the non-increasing order.
self.YoungDiagram = [p[::-1] for p in ordered_partitions(self.k)]
# Making n into a symbol.
n = Symbol('n')
# Maling a list of reciprocals of Schur polynomials for all Young Diagrams.
# [[permutation, Schur poly],[,],...]
self.ReciprocalList =\
{ str(p): self.SchurPolyReciprocal(p,n) for p in self.YoungDiagram}
def __init__(self, k):
self.k = k
# Generating all the partitions of k in the non-increasing order.
self.Partitions = [p[::-1] for p in ordered_partitions(self.k)]
# reading or making lists of characters and Schur's.
self.SGC = SGCTOganizer(self.k).Dic
self.SP = SchurPolyOganizer(self.k).List
# Making a list of Weingarten functions.
# [[partition type, the function],[],...]
self.List = [[p, self.Weingarten(p)] for p in self.Partitions]
def Partitions(n, outer, inner):
'''
bounded partitions
'''
for p in ordered_partitions(n):
p.reverse()
if len(p) >= len(inner) and len(p) <= len(outer):
bounded = True
for i in range(len(p)):
if p[i] > outer[i]:
bounded = False
if i < len(inner):
if p[i] < inner[i]:
bounded = False
if bounded:
yield p