标签：
剧情提要：正剧开始：
星历2016年04月28日 10:41:37, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[对称与群]。
<span style="font-size:18px;">>>>
乘法表：首行顺序
I --- r1 --- r2 --- r3 --- ρ1 --- ρ2 --- 结果：
I --- ,r1 --- ,r2 --- ,r3 --- ,ρ1 --- ,ρ2 --- ,
r1 --- ,I --- ,ρ1 --- ,ρ2 --- ,r2 --- ,r3 --- ,
r2 --- ,ρ2 --- ,I --- ,ρ1 --- ,r3 --- ,r1 --- ,
r3 --- ,ρ1 --- ,ρ2 --- ,I --- ,r1 --- ,r2 --- ,
ρ1 --- ,r3 --- ,r1 --- ,r2 --- ,ρ2 --- ,I --- ,
ρ2 --- ,r2 --- ,r3 --- ,r1 --- ,I --- ,ρ1 --- ,
#三角形所有变换
def tmp():
a0 = [1, 2, 3];
allTransfer = [# = C(3, 2)
[1, 2, 3],#I
[1, 3, 2], #r1
[3, 2, 1], #r2
[2, 1, 3], #r3
[2, 3, 1], #rou1
[3, 1, 2], #rou2
];
sTable = ['I', 'r1', 'r2', 'r3', 'ρ1', 'ρ2'];
#总变化数
N = 6;
print('乘法表：首行顺序');
for i in range(N):
print(sTable[i], ' --- ', end = '');
print('结果：');
#乘法表
for n in range(N):
print('');
for m in range(N):
a1 = allTransfer[n];
a2 = allTransfer[m];
b0 = [0]*len(a0);
for i in range(len(b0)):
b0[i] = a0[a1[i]-1];
b1 = [0]*len(a0);
for i in range(len(b1)):
b1[i] = b0[a2[i]-1];
for i in range(N):
if (b1 == allTransfer[i]):
print(sTable[i], ' --- ', end = ',');
break;</span>
<span style="font-size:18px;">乘法表：首行顺序
I --- r1 --- r2 --- r3 --- r4 --- ρ1 --- ρ2 --- ρ3 --- 结果：
I --- ,r1 --- ,r2 --- ,r3 --- ,r4 --- ,ρ1 --- ,ρ2 --- ,ρ3 --- ,
r1 --- ,I --- ,ρ3 --- ,ρ2 --- ,ρ1 --- ,r4 --- ,r3 --- ,r2 --- ,
r2 --- ,ρ1 --- ,I --- ,ρ3 --- ,ρ2 --- ,r1 --- ,r4 --- ,r3 --- ,
r3 --- ,ρ2 --- ,ρ1 --- ,I --- ,ρ3 --- ,r2 --- ,r1 --- ,r4 --- ,
r4 --- ,ρ3 --- ,ρ2 --- ,ρ1 --- ,I --- ,r3 --- ,r2 --- ,r1 --- ,
ρ1 --- ,r2 --- ,r3 --- ,r4 --- ,r1 --- ,ρ2 --- ,ρ3 --- ,I --- ,
ρ2 --- ,r3 --- ,r4 --- ,r1 --- ,r2 --- ,ρ3 --- ,I --- ,ρ1 --- ,
ρ3 --- ,r4 --- ,r1 --- ,r2 --- ,r3 --- ,I --- ,ρ1 --- ,ρ2 --- ,
#正方形所有变换
def tmp2():
a0 = [1, 2, 3, 4];
allTransfer = [
[1, 2, 3, 4],#I
[3,2,1,4], #r1
[4,3,2,1], #r2
[1,4,3,2], #r3
[2,1,4,3], #r4
[2,3,4,1], #rou1
[3,4,1,2], #rou2
[4,1,2,3], #rou3
];
sTable = ['I', 'r1', 'r2', 'r3','r4','ρ1', 'ρ2', 'ρ3'];
#总变化数
N = 8;
print('乘法表：首行顺序');
for i in range(N):
print(sTable[i], ' --- ', end = '');
print('结果：');
#乘法表
for n in range(N):
print('');
for m in range(N):
a1 = allTransfer[n];
a2 = allTransfer[m];
b0 = [0]*len(a0);
for i in range(len(b0)):
b0[i] = a0[a1[i]-1];
b1 = [0]*len(a0);
for i in range(len(b1)):
b1[i] = b0[a2[i]-1];
for i in range(N):
if (b1 == allTransfer[i]):
print(sTable[i], ' --- ', end = ',');
break;</span>
<span style="font-size:18px;">def tmp():
N = 4;
originArray = [0]*N;
for i in range(N):
originArray[i] = i+1;
result = flip(originArray, 2);
print('原：',originArray);
print('变：', result);
for i in range(1, 4):
result = rotate(originArray, i);
print('原：',originArray);
print('变：', result);
#翻转（反射）
#array 和 不动的顶点序号，从1计数
#如三角形是1, 2, 3
def flip(array, vertex):
if (vertex <= 0):
return array;
vertex -= 1;
size = len(array);
newArray = [0]*size;
if (size == 3):
for i in range(size):
newArray[(vertex-i)%size] = array[(vertex+i)%size];
elif (size == 4):
#正方形，实在看不出映射规律，只能穷举
if (vertex == 1):
return [array[2], array[1], array[0], array[3]];
elif (vertex == 2):
return [array[3], array[2], array[1], array[0]];
elif (vertex == 3):
return [array[0], array[3], array[2], array[1]];
elif (vertex == 4):
return [array[1], array[0], array[3], array[2]];
else:
return array;
return newArray;
#旋转
#顶点数指从原位置逆时针旋转过几个顶点
#取值范围是从1 ~ 顶点数-1
def rotate(array, vertex):
if (vertex <= 0):
return array;
size = len(array);
newArray = [0]*size;
for i in range(size):
newArray[i] = array[(vertex+i)%size];
return newArray;
if __name__ == '__main__':
tmp();</span>
<span style="font-size:18px;">>>>
[3, 1, 2]
#例
def tmp():
a0 = [1, 2, 3];
a1 = [1, 3, 2];
a2 = [2, 1, 3];
b0 = [0]*len(a0);
for i in range(len(b0)):
b0[i] = a0[a1[i]-1];
b1 = [0]*len(a0);
for i in range(len(b1)):
b1[i] = b0[a2[i]-1];
print(b1);
#######
>>>
[2, 3, 1]
a0 = [1, 2, 3];
a1 = [2, 1,3];
a2 = [1, 3, 2];
</span>
<span style="font-size:18px;">>>>
首行是： 0 ---- 1 ---- 2 ---- 3 结果：
0 ---- 1 ---- 2 ---- 3 ----
1 ---- 2 ---- 3 ---- 0 ----
2 ---- 3 ---- 0 ---- 1 ----
3 ---- 0 ---- 1 ---- 2 ----
def tmp3():
a = [0, 1, 2, 3];
b = a;
print('首行是：', ' 0 ---- 1 ---- 2 ---- 3', '结果：');
for i in range(4):
print('');
for j in range(4):
print((a[i]+b[j])%4, ' ---- ', end = '');
if __name__ == '__main__':
tmp3();</span>
<span style="font-size:18px;">>>>
[0, 0] --- [0, 1] --- [0, 2] --- [1, 0] --- [1, 1] --- [1, 2] ---
[0, 1] --- [0, 2] --- [0, 0] --- [1, 1] --- [1, 2] --- [1, 0] ---
[0, 2] --- [0, 0] --- [0, 1] --- [1, 2] --- [1, 0] --- [1, 1] ---
[1, 0] --- [1, 1] --- [1, 2] --- [0, 0] --- [0, 1] --- [0, 2] ---
[1, 1] --- [1, 2] --- [1, 0] --- [0, 1] --- [0, 2] --- [0, 0] ---
[1, 2] --- [1, 0] --- [1, 1] --- [0, 2] --- [0, 0] --- [0, 1] ---
def tmp4():
a = [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2]];
b = a;
for i in range(6):
print('');
for j in range(6):
x = (a[i][0]+b[j][0])%2;
y = (a[i][1]+b[j][1])%3;
print([x, y], ' --- ', end='');
</span>
[人叫板老师]是很让小伟无语的，就这功法的难度，要是结丹期修士不被弄晕，
那绝对是个天才。
本节到此结束，欲知后事如何，请看下回分解。
标签：
原文地址：http://blog.csdn.net/mwsister/article/details/51272401
