In this method, a node at the specified position in the circular doubly linked list is deleted. For example - if the given list is 10->20->30 and the 2nd node is deleted, the list becomes 10->20.

First, create two nodes temp and nodeToDelete to traverse through the list and track the node to delete respectively. After that count the number of elements in the list to check whether the specified position is valid or not (It must lie in the range of [1, n], where n is number of elements in the list). If the specified valid position is 1 and head is the only element in the list, then make the head as null. If the specified valid position is 1 and list contains more than one elements, then make next of head as new head and adjust links accordingly. If the specified valid position is greater than 1 then traverse to the node previous to the given position and delete the given node and adjust links accordingly. The function pop_at is created for this purpose. It is a 5-step process.

```void pop_at(int position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
Node* nodeToDelete = head;
Node* temp = head;
int NoOfElements = 0;

//2. Find the number of elements in the list
if(temp != NULL) {
NoOfElements++;
temp = temp->next;
}
while(temp != head) {
NoOfElements++;
temp = temp->next;
}

//3. check if the specified position is valid
if(position < 1 || position > NoOfElements) {
cout<<"\nInavalid position.";
} else if (position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if(head->next == head) {
head = NULL;
} else {
while(temp->next != head)
temp = temp->next;
head = head->next;
temp->next = head;
head->prev = temp;
free(nodeToDelete);
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp->next;
nodeToDelete = temp->next;
temp->next = temp->next->next;
temp->next->prev = temp;
free(nodeToDelete);
}
}
```
```void pop_at(struct Node** head_ref, int position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
struct Node *nodeToDelete = *head_ref;
struct Node *temp = *head_ref;
int NoOfElements = 0;

//2. Find the number of elements in the list
if(temp != NULL) {
NoOfElements++;
temp = temp->next;
}
while(temp != *head_ref) {
NoOfElements++;
temp = temp->next;
}

//3. check if the specified position is valid
if(position < 1 || position > NoOfElements) {
printf("\nInavalid position.");
} else if (position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if((*head_ref)->next == *head_ref) {
*head_ref = NULL;
} else {
while(temp->next != *head_ref)
temp = temp->next;
*head_ref = (*head_ref)->next;
temp->next = *head_ref;
(*head_ref)->prev = temp;
free(nodeToDelete);
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
temp = *head_ref;
for(int i = 1; i < position-1; i++)
temp = temp->next;
nodeToDelete = temp->next;
temp->next = temp->next->next;
temp->next->prev = temp;
free(nodeToDelete);
}
}
```
```def pop_at(self, position):

#1. create two nodes - temp and nodeToDelete
#   to traverse and track the node to delete
nodeToDelete = self.head
temp = self.head
NoOfElements = 0

#2. Find the number of elements in the list
if(temp != None):
NoOfElements += 1
temp = temp.next
while(temp != self.head):
NoOfElements += 1
temp = temp.next

#3. check if the specified position is valid
if(position < 1 or position > NoOfElements):
print("\nInavalid position.")
elif (position == 1):

#4. if the position is 1 and head is the only element
#   in the list, then make it null, else make next
#   of head as new head and adjust links accordingly
if(self.head.next == self.head):
self.head = None
else:
while(temp.next != self.head):
temp = temp.next
self.head = self.head.next
temp.next = self.head
self.head.prev = temp
nodeToDelete = None

else:

#5. Else, traverse to the node previous to
#   the given position and delete the given
#   node and adjust links accordingly
temp = self.head
for i in range(1, position-1):
temp = temp.next
nodeToDelete = temp.next
temp.next = temp.next.next
temp.next.prev = temp
nodeToDelete = None
```
```void pop_at(int position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

//2. Find the number of elements in the list
if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

//3. check if the specified position is valid
if(position < 1 || position > NoOfElements) {
System.out.print("\nInvalid position.");
} else if (position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}
```
```public void pop_at(int position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

//2. Find the number of elements in the list
if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

//3. check if the specified position is valid
if(position < 1 || position > NoOfElements) {
Console.Write("\nInvalid position.");
} else if (position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}
```
```public function pop_at(\$position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
\$nodeToDelete = \$this->head;
\$temp = \$this->head;
\$NoOfElements = 0;

//2. Find the number of elements in the list
if(\$temp != null) {
\$NoOfElements++;
\$temp = \$temp->next;
}
while(\$temp != \$this->head) {
\$NoOfElements++;
\$temp = \$temp->next;
}

//3. check if the specified position is valid
if(\$position < 1 || \$position > \$NoOfElements) {
echo "\nInvalid position.";
} else if (\$position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if(\$this->head->next == \$this->head) {
\$this->head = null;
} else {
while(\$temp->next != \$this->head)
\$temp = \$temp->next;
\$this->head = \$this->head->next;
\$temp->next = \$this->head;
\$this->head->prev = \$temp;
\$nodeToDelete = null;
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
\$temp = \$this->head;
for(\$i = 1; \$i < \$position-1; \$i++)
\$temp = \$temp->next;
\$nodeToDelete = \$temp->next;
\$temp->next = \$temp->next->next;
\$temp->next->prev = \$temp;
\$nodeToDelete = null;
}
}
```

The below is a complete program that uses above discussed concept to delete a node at a given position in the circular doubly linked list.

```#include <iostream>
using namespace std;

//node structure
struct Node {
int data;
Node* next;
Node* prev;
};

class LinkedList {
private:
Node* head;
public:
LinkedList(){
head = NULL;
}

//Add new element at the end of the list
void push_back(int newElement) {
Node* newNode = new Node();
newNode->data = newElement;
newNode->next = NULL;
newNode->prev = NULL;
if(head == NULL) {
head = newNode;
newNode->next = head;
newNode->prev = head;
} else {
Node* temp = head;
while(temp->next != head)
temp = temp->next;
temp->next = newNode;
newNode->next = head;
newNode->prev = temp;
head->prev = newNode;
}
}

//Delete an element at the given position
void pop_at(int position) {
Node* nodeToDelete = head;
Node* temp = head;
int NoOfElements = 0;

if(temp != NULL) {
NoOfElements++;
temp = temp->next;
}
while(temp != head) {
NoOfElements++;
temp = temp->next;
}

if(position < 1 || position > NoOfElements) {
cout<<"\nInavalid position.";
} else if (position == 1) {
if(head->next == head) {
head = NULL;
} else {
while(temp->next != head)
temp = temp->next;
head = head->next;
temp->next = head;
head->prev = temp;
free(nodeToDelete);
}
} else {
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp->next;
nodeToDelete = temp->next;
temp->next = temp->next->next;
temp->next->prev = temp;
free(nodeToDelete);
}
}

//display the content of the list
void PrintList() {
Node* temp = head;
if(temp != NULL) {
cout<<"\nThe list contains: ";
while(true) {
cout<<temp->data<<" ";
temp = temp->next;
if(temp == head)
break;
}
} else {
cout<<"\nThe list is empty.";
}
}
};

// test the code
int main() {
LinkedList MyList;

//Add three elements at the end of the list.
MyList.push_back(10);
MyList.push_back(20);
MyList.push_back(30);
MyList.PrintList();

//Delete an element at position 2
MyList.pop_at(2);
MyList.PrintList();

//Delete an element at position 1
MyList.pop_at(1);
MyList.PrintList();

return 0;
}
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```
```#include <stdio.h>
#include <stdlib.h>

//node structure
struct Node {
int data;
struct Node* next;
struct Node* prev;
};

//Add new element at the end of the list
void push_back(struct Node** head_ref, int newElement) {
struct Node *newNode, *temp;
newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = newElement;
newNode->next = NULL;
newNode->prev = NULL;
if(*head_ref == NULL) {
*head_ref = newNode;
newNode->next = *head_ref;
newNode->prev = *head_ref;
} else {
temp = *head_ref;
while(temp->next != *head_ref) {
temp = temp->next;
}
temp->next = newNode;
newNode->next = *head_ref;
newNode->prev = temp;
(*head_ref)->prev = newNode;
}
}

//Delete an element at the given position
void pop_at(struct Node** head_ref, int position) {
struct Node *nodeToDelete = *head_ref;
struct Node *temp = *head_ref;
int NoOfElements = 0;

if(temp != NULL) {
NoOfElements++;
temp = temp->next;
}
while(temp != *head_ref) {
NoOfElements++;
temp = temp->next;
}

if(position < 1 || position > NoOfElements) {
printf("\nInavalid position.");
} else if (position == 1) {

if((*head_ref)->next == *head_ref) {
*head_ref = NULL;
} else {
while(temp->next != *head_ref)
temp = temp->next;
*head_ref = (*head_ref)->next;
temp->next = *head_ref;
(*head_ref)->prev = temp;
free(nodeToDelete);
}
} else {
temp = *head_ref;
for(int i = 1; i < position-1; i++)
temp = temp->next;
nodeToDelete = temp->next;
temp->next = temp->next->next;
temp->next->prev = temp;
free(nodeToDelete);
}
}

//display the content of the list
void PrintList(struct Node* head_ref) {
struct Node* temp = head_ref;
if(head_ref != NULL) {
printf("\nThe list contains: ");
while (1) {
printf("%i ",temp->data);
temp = temp->next;
if(temp == head_ref)
break;
}
} else {
printf("\nThe list is empty.");
}
}

// test the code
int main() {
struct Node* MyList = NULL;

//Add three elements at the end of the list.
push_back(&MyList, 10);
push_back(&MyList, 20);
push_back(&MyList, 30);
PrintList(MyList);

//Delete an element at position 2
pop_at(&MyList, 2);
PrintList(MyList);

//Delete an element at position 1
pop_at(&MyList, 1);
PrintList(MyList);

return 0;
}
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```
```# node structure
class Node:
def __init__(self, data):
self.data = data
self.next = None
self.prev = None

#class Linked List
class LinkedList:
def __init__(self):
self.head = None

#Add new element at the end of the list
def push_back(self, newElement):
newNode = Node(newElement)
if(self.head == None):
self.head = newNode
newNode.next = self.head
newNode.prev = self.head
return
else:
temp = self.head
while(temp.next != self.head):
temp = temp.next
temp.next = newNode
newNode.next = self.head
newNode.prev = temp
self.head.prev = newNode

#Delete an element at the given position
def pop_at(self, position):
nodeToDelete = self.head
temp = self.head
NoOfElements = 0

if(temp != None):
NoOfElements += 1
temp = temp.next
while(temp != self.head):
NoOfElements += 1
temp = temp.next

if(position < 1 or position > NoOfElements):
print("\nInavalid position.")
elif (position == 1):
if(self.head.next == self.head):
self.head = None
else:
while(temp.next != self.head):
temp = temp.next
self.head = self.head.next
temp.next = self.head
self.head.prev = temp
nodeToDelete = None

else:
temp = self.head
for i in range(1, position-1):
temp = temp.next
nodeToDelete = temp.next
temp.next = temp.next.next
temp.next.prev = temp
nodeToDelete = None

#display the content of the list
def PrintList(self):
temp = self.head
if(temp != None):
print("\nThe list contains:", end=" ")
while (True):
print(temp.data, end=" ")
temp = temp.next
if(temp == self.head):
break
else:
print("\nThe list is empty.")

# test the code
MyList = LinkedList()

#Add three elements at the end of the list.
MyList.push_back(10)
MyList.push_back(20)
MyList.push_back(30)
MyList.PrintList()

#Delete an element at position 2
MyList.pop_at(2)
MyList.PrintList()

#Delete an element at position 1
MyList.pop_at(1)
MyList.PrintList()
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```
```//node structure
class Node {
int data;
Node next;
Node prev;
};

class LinkedList {
Node head;

LinkedList(){
head = null;
}

//Add new element at the end of the list
void push_back(int newElement) {
Node newNode = new Node();
newNode.data = newElement;
newNode.next = null;
newNode.next = null;
if(head == null) {
head = newNode;
newNode.next = head;
newNode.prev = head;
} else {
Node temp = new Node();
temp = head;
while(temp.next != head)
temp = temp.next;
temp.next = newNode;
newNode.next = head;
newNode.prev = temp;
head.prev = newNode;
}
}

//Delete an element at the given position
void pop_at(int position) {
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

if(position < 1 || position > NoOfElements) {
System.out.print("\nInvalid position.");
} else if (position == 1) {
if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}

//display the content of the list
void PrintList() {
Node temp = new Node();
temp = this.head;
if(temp != null) {
System.out.print("\nThe list contains: ");
while(true) {
System.out.print(temp.data + " ");
temp = temp.next;
if(temp == this.head)
break;
}
} else {
System.out.print("\nThe list is empty.");
}
}
};

// test the code
public class Implementation {
public static void main(String[] args) {
LinkedList MyList = new LinkedList();

//Add three elements at the end of the list.
MyList.push_back(10);
MyList.push_back(20);
MyList.push_back(30);
MyList.PrintList();

//Delete an element at position 2
MyList.pop_at(2);
MyList.PrintList();

//Delete an element at position 1
MyList.pop_at(1);
MyList.PrintList();
}
}
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```
```using System;

//node structure
class Node {
public int data;
public Node next;
public Node prev;
};

class LinkedList {
Node head;

public LinkedList(){
head = null;
}

//Add new element at the end of the list
public void push_back(int newElement) {
Node newNode = new Node();
newNode.data = newElement;
newNode.next = null;
newNode.prev = null;
if(head == null) {
head = newNode;
newNode.next = head;
newNode.prev = head;
} else {
Node temp = new Node();
temp = head;
while(temp.next != head)
temp = temp.next;
temp.next = newNode;
newNode.next = head;
newNode.prev = temp;
head.prev = newNode;
}
}

//Delete an element at the given position
public void pop_at(int position) {
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

if(position < 1 || position > NoOfElements) {
Console.Write("\nInvalid position.");
} else if (position == 1) {

if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}

//display the content of the list
public void PrintList() {
Node temp = new Node();
temp = this.head;
if(temp != null) {
Console.Write("\nThe list contains: ");
while(true) {
Console.Write(temp.data + " ");
temp = temp.next;
if(temp == this.head)
break;
}
} else {
Console.Write("\nThe list is empty.");
}
}
};

// test the code
class Implementation {
static void Main(string[] args) {
LinkedList MyList = new LinkedList();

//Add three elements at the end of the list.
MyList.push_back(10);
MyList.push_back(20);
MyList.push_back(30);
MyList.PrintList();

//Delete an element at position 2
MyList.pop_at(2);
MyList.PrintList();

//Delete an element at position 1
MyList.pop_at(1);
MyList.PrintList();
}
}
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```
```<?php
//node structure
class Node {
public \$data;
public \$next;
public \$prev;
}

class LinkedList {
public \$head;

public function __construct(){
\$this->head = null;
}

//Add new element at the end of the list
public function push_back(\$newElement) {
\$newNode = new Node();
\$newNode->data = \$newElement;
\$newNode->next = null;
\$newNode->prev = null;
if(\$this->head == null) {
\$this->head = \$newNode;
\$newNode->next = \$this->head;
} else {
\$temp = new Node();
\$temp = \$this->head;
while(\$temp->next !== \$this->head) {
\$temp = \$temp->next;
}
\$temp->next = \$newNode;
\$newNode->next = \$this->head;
\$newNode->prev = \$temp;
\$this->head->prev = \$newNode;
}
}

//Delete an element at the given position
public function pop_at(\$position) {
\$nodeToDelete = \$this->head;
\$temp = \$this->head;
\$NoOfElements = 0;

if(\$temp != null) {
\$NoOfElements++;
\$temp = \$temp->next;
}
while(\$temp != \$this->head) {
\$NoOfElements++;
\$temp = \$temp->next;
}

if(\$position < 1 || \$position > \$NoOfElements) {
echo "\nInvalid position.";
} else if (\$position == 1) {
if(\$this->head->next == \$this->head) {
\$this->head = null;
} else {
while(\$temp->next != \$this->head)
\$temp = \$temp->next;
\$this->head = \$this->head->next;
\$temp->next = \$this->head;
\$this->head->prev = \$temp;
\$nodeToDelete = null;
}
} else {
\$temp = \$this->head;
for(\$i = 1; \$i < \$position-1; \$i++)
\$temp = \$temp->next;
\$nodeToDelete = \$temp->next;
\$temp->next = \$temp->next->next;
\$temp->next->prev = \$temp;
\$nodeToDelete = null;
}
}

//display the content of the list
public function PrintList() {
\$temp = new Node();
\$temp = \$this->head;
if(\$temp != null) {
echo "\nThe list contains: ";
while(true) {
echo \$temp->data." ";
\$temp = \$temp->next;
if(\$temp == \$this->head)
break;
}
} else {
echo "\nThe list is empty.";
}
}
};

// test the code
\$MyList = new LinkedList();

//Add three elements at the end of the list.
\$MyList->push_back(10);
\$MyList->push_back(20);
\$MyList->push_back(30);
\$MyList->PrintList();

//Delete an element at position 2
\$MyList->pop_at(2);
\$MyList->PrintList();

//Delete an element at position 1
\$MyList->pop_at(1);
\$MyList->PrintList();
?>
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```