箱玉系その3

ベーテ仮説と組合せ論1.3の例で見てみると、確かに等速直線運動をしている。

python soliton_config.py
path [ 20 ]: [1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1]
type: 20
4 *** 0
6 ** 5
6 ** 4
12 * 7

path [ 21 ]: [1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2]
type: 21
5 *** 3
7 ** 7
7 ** 6
13 * 8

path [ 23 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2]
type: 23
7 *** 6
9 ** 9
9 ** 8
15 * 9

path [ 25 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2]
type: 25
9 *** 9
11 ** 11
11 ** 10
17 * 10

path [ 28 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2]
type: 28
12 *** 12
14 ** 13
14 ** 12
20 * 11

path [ 31 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2]
type: 31
15 *** 15
17 ** 15
17 ** 14
23 * 12

path [ 34 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2]
type: 34
18 *** 18
20 ** 17
20 ** 16
26 * 13

path [ 37 ]: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2]
type: 37
21 *** 21
23 ** 19
23 ** 18
29 * 14

#!/usr/bin/python

class YoungDiagram:
    def __init__(self):
        self.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):
        self.type = 0
        self.u1 = YoungDiagram()
        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 sort_rigging(self):
        i = 0
        while i < len(self.u1.shape):
            l = len(filter(lambda x: x == self.u1.shape[i], self.u1.shape))
            self.rigging[i:i+l] = sorted(self.rigging[i:i+l], reverse=True)
            i += l
    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
            m = map(lambda x: x < self.u1.shape[i] , self.u1.shape)
            try:
                j = m.index(True)
                if j < i:
                    self.u1.shape[i],self.u1.shape[j] =self.u1.shape[j],self.u1.shape[i]
                    self.rigging[i],self.rigging[j] = self.rigging[j],self.rigging[i]
                    i = j
            except ValueError:
                0 #nothing to do
            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])
        self.sort_rigging()
    def add(self, list):
        c = 0
        self.path = list
        for v in list:
            if v == 1:
                self.add_1()
            else:
                self.add_2()
            c+= 1
    def __str__(self):
        print "path [", len(self.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 ""
def move(l, ball):
    while True: 
        try:
            n = l.index(ball)
            l[n] = 'done'
            m = l[n+1:]
            try:
                n2 = m.index(1)
                m[n2] = 'new'
            except ValueError:
                m.append('new')
            l[n+1:] = m
        except ValueError:
            break
    for i in range(len(l)):
        if l[i] == 'new':
            l[i] = ball
        elif l[i] == 'done':
            l[i] = 1        

##test
l=[1,1,1,2,2,2,1,1,1,1,2,1,2,2,1,1,1,2,2,1]

for i in range(8):
    c = Configuration()
    c.add(l)
    print c
    move(l, 2)