设计一个双向循环链表类，实现一个数据分别为0,1,2,3,4,5,6,7,8,9的双向循环链表，并删除其中数据为5和8的节点，分别在原来删除的位置插入数据为5.1和8.2的节点，并输出循环链表的双向遍历结果。用Python

首先，我们需要创建一个双向循环链表的节点类以及双向链表类，包括添加、删除和插入操作，以及遍历功能。下面是一个简单的实现：

class Node:
    def __init__(self, value=None):
        self.value = value
        self.next = None
        self.prev = None

class DoublyCircularLinkedList:
    def __init__(self):
        self.head = None
        self.tail = None

    def append(self, value):
        new_node = Node(value)
        if not self.head:
            self.head = new_node
            self.tail = new_node
            new_node.next = new_node
            new_node.prev = new_node
        else:
            new_node.next = self.head
            new_node.prev = self.tail
            self.head.prev = new_node
            self.tail.next = new_node
            self.tail = new_node

    def delete(self, value):
        current = self.head
        while True:
            if current.value == value:
                if current == self.head and current == self.tail:
                    self.head = None
                    self.tail = None
                elif current == self.head:
                    self.head = current.next
                    self.head.prev = self.tail
                elif current == self.tail:
                    self.tail = current.prev
                    self.tail.next = self.head
                else:
                    current.prev.next = current.next
                    current.next.prev = current.prev
                break
            current = current.next
            if current == self.head:
                break

    def insert(self, old_value, new_value, position='end'):
        current = self.head
        index = 1
        while current.value != old_value:
            if position == 'start':
                if current == self.tail:
                    return "Error: Insertion at the start is not possible since it's a circular list."
                self.append(new_value)
                break
            current = current.next
            index += 1
        if position == 'end':
            after_delete = current.prev
            after_delete.next = new_node = Node(new_value)
            new_node.prev = after_delete
            new_node.next = current
            current.prev = new_node
        else:
            index -= 1
            after_delete = current if current.value == old_value else current.prev
            new_node = Node(new_value)
            new_node.next = current
            new_node.prev = after_delete
            after_delete.next = current.prev
            current.prev = new_node

    def traverse(self):
        elements = []
        current = self.head
        while True:
            elements.append(current.value)
            current = current.next
            if current == self.head:
                break
        return elements

# 使用这个类
dll = DoublyCircularLinkedList()
for i in range(10):
    dll.append(i)

# 删除5和8
dll.delete(5)
dll.delete(8)

# 插入5.1和8.2
dll.insert(5, 5.1, position='start')
dll.insert(8, 8.2)

# 遍历并打印结果
print("Original list:", dll.traverse())
print("After operations:")
print(dll.traverse())

运行以上代码，你会得到原始链表和修改后的链表的遍历结果。