箱玉系その2

ベーテ仮説と組合せ論 例5.5(p107)のパスとrigged configuration
の対応をチェックするためのpythonスクリプト

前回のスクリプトと合わせると、
ソリトン->rigged configuration
による時間発展の線形化が確認できるはず。(後日に記載予定)

python soliton_config.py
path [1, 2, 1, 2, 1, 1, 2, 2]
type: 8
0 ** 0
2 * 0
2 * 0

path [1, 2, 1, 1, 2, 1, 2, 2]
type: 8
0 ** 0
2 * 1
2 * 0

path [1, 2, 1, 1, 2, 2, 1, 2]
type: 8
0 ** 0
2 * 2
2 * 0

path [1, 1, 2, 1, 2, 1, 2, 2]
type: 8
0 ** 0
2 * 1
2 * 1

path [1, 1, 2, 1, 2, 2, 1, 2]
type: 8
0 ** 0
2 * 2
2 * 1

path [1, 1, 2, 2, 1, 2, 1, 2]
type: 8
0 ** 0
2 * 2
2 * 2

#!/usr/bin/python

class YoungDiagram:
    def __init__(self):
        self.shape = []
    def __init__(self, shape):
        self.shape = shape
    def depth(self):
        return len(self.shape)
    def total(self):
        return sum(self.shape)
    def transpose_shape(self):
        list = []
        for i in range(self.shape[0]):
            list.append(len(filter(lambda x: x>i, self.shape)))
        return list
    def first(self):
        if len(self.shape) == 0:
            return 0
        return self.shape[0]
    def m(self,j):
        return len(filter(lambda x: x == j, self.shape))
    def q(self, j):
        if len(self.shape) == 0:
            return 0
        s = 0
        for k in range(self.shape[0]+1):
            s += min(j, k)*self.m(k)
        return s
    def __str__(self):
        for i in self.shape:
            print "\t","*"*i
        return ""

# n=1 type(1^L) only
class Configuration:
    def __init__(self, type, shape):
        self.type = type
        self.u1 = YoungDiagram(shape)
        self.update_vacancy()
        self.rigging = []
    def p(self, j):
        return self.type - 2 * self.u1.q(j)
    def update_vacancy(self):
        self.vacancy = []
        list = []
        for j in range(self.u1.first()+1):
            list.append(self.p(j))
        for j in self.u1.shape:
            self.vacancy.append(list[j])
    def singular_test(self):
        list = []
        for i in range(len(self.vacancy)):
            list.append(self.vacancy[i] == self.rigging[i])
        return list
    def add_1(self):
        self.type += 1
        self.update_vacancy()
    def add_2(self):
        list = self.singular_test()
        try:
            i = list.index(True) # index of a singular string
            self.type += 1
            self.u1.shape[i] += 1 # extend the singular string
            self.update_vacancy()
            self.rigging[i] = self.vacancy[i]
        except ValueError: # no singular string, add 1-string
            self.type += 1
            self.u1.shape.append(1)
            self.update_vacancy()
            try:
                i = self.u1.shape.index(1)
                self.rigging.insert(i, self.vacancy[-1])
            except ValueError:
                self.rigging.append(self.vacancy[-1])
    def add(self, list):
        self.path = list
        for v in list:
            if v == 1:
                self.add_1()
            else:
                self.add_2()
    def __str__(self):
        print "path", self.path
        print "type:",self.type
        for i in range(len(self.vacancy)):
            print "\t",self.vacancy[i], "*"*self.u1.shape[i], self.rigging[i]
        return ""
##test
c = Configuration(0, [])
c.add([1,2,1,2,1,1,2,2])
print c
c = Configuration(0, [])
c.add([1,2,1,1,2,1,2,2])
print c
c = Configuration(0, [])
c.add([1,2,1,1,2,2,1,2])
print c
c = Configuration(0, [])
c.add([1,1,2,1,2,1,2,2])
print c
c = Configuration(0, [])
c.add([1,1,2,1,2,2,1,2])
print c
c = Configuration(0, [])
c.add([1,1,2,2,1,2,1,2])
print c