置换群python代码实现
时间: 2023-11-19 17:57:17 浏览: 68
以下是一个简单的置换群Python代码实现:
```python
class Permutation:
def __init__(self, perm):
self.perm = perm
def __mul__(self, other):
return Permutation([self.perm[i - 1] for i in other.perm])
def __pow__(self, power):
result = Permutation(range(1, len(self.perm) + 1))
for i in range(power):
result = result * self
return result
def order(self):
result = self
for i in range(2, len(self.perm) + 1):
if (self ** i).perm == result.perm:
return i
return 1
def to_cycles(self):
cycles = []
used = set()
for i in range(1, len(self.perm) + 1):
if i not in used:
cycle = [i]
used.add(i)
j = self.perm[i - 1]
while j != i:
cycle.append(j)
used.add(j)
j = self.perm[j - 1]
cycles.append(cycle)
return cycles
```
这个代码实现了置换群的基本操作,包括乘法、幂、阶和转换为循环表示。你可以根据自己的需要进行修改和扩展。