Libraries

### KYky Standard Library

KYky's Standard Library is a collection of common mathematical functions implemented in Python. It contains functions to perform various mathematical operations, including calculating factorials, determining if a number is prime, converting degrees to radians, and more. This library is intended to provide developers with a set of tools that they can use to perform common mathematical operations efficiently and accurately in their Python programs. The library also includes functions to convert numbers between different bases and to perform various trigonometric and logarithmic functions. KYky's Standard Library is designed to be easy to use and can help save time and effort when developing Python applications that require mathematical computations.

```

# Function to find the factorial of a number
def factorial(n):
    return math.factorial(n)

# Function to check if a number is prime
def is_prime(n):
    return n > 1 and all(n % i != 0 for i in range(2, int(math.sqrt(n)) + 1))

# Function to convert degrees to radians
def degrees_to_radians(degrees):
    return math.radians(degrees)

# Function to convert radians to degrees
def radians_to_degrees(radians):
    return math.degrees(radians)

# Function to calculate the distance between two points
def distance(x1, y1, x2, y2):
    return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

# Function to calculate the area of a circle
def circle_area(radius):
    return math.pi * radius ** 2

# Function to calculate the area of a rectangle
def rectangle_area(width, height):
    return width * height

# Function to calculate the area of a triangle
def triangle_area(base, height):
    return 0.5 * base * height

# Function to calculate the slope of a line
def slope(x1, y1, x2, y2):
    return (y2 - y1) / (x2 - x1)

# Function to calculate the midpoint of a line
def midpoint(x1, y1, x2, y2):
    return ((x1 + x2) / 2, (y1 + y2) / 2)

# Function to calculate the average of a list of numbers
def average(numbers):
    return sum(numbers) / len(numbers)

# Function to calculate the standard deviation of a list of numbers
def standard_deviation(numbers):
    mean = sum(numbers) / len(numbers)
    variance = sum([(x - mean) ** 2 for x in numbers]) / len(numbers)
    return math.sqrt(variance)

# Function to find the greatest common divisor (GCD) of two numbers
def gcd(a, b):
    return math.gcd(a, b)

# Function to find the least common multiple (LCM) of two numbers
def lcm(a, b):
    return abs(a * b) // math.gcd(a, b)

# Function to check if a number is even
def is_even(n):
    return n % 2 == 0

# Function to check if a number is odd
def is_odd(n):
    return n % 2 != 0

# Function to calculate the absolute value of a number
def absolute_value(n):
    return abs(n)

# Function to round a number to a given number of decimal places
def round_number(n, decimal_places):
    return round(n, decimal_places)

# Function to calculate the square root of a number
def square_root(n):
    return math.sqrt(n)

# Function to calculate the cube root of a number
def cube_root(n):
    return n ** (1 / 3)

# Function to calculate the nth root of a number
def nth_root(n, root):
    return n ** (1 / root)

# Function to calculate the logarithm of a number with a given base
def logarithm(n, base):
    return math.log(n, base)

# Function to calculate the natural logarithm of a number
def natural_logarithm(n):
    return math.log(n)

# Function to calculate the sine of an angle
def sine(angle):
    return math.sin(angle)

# Function to calculate the cosine of an angle
def cosine(angle):
    return math.cos(angle)

# Function to calculate the tangent of an angle
def tangent(angle):
    return math.tan(angle)

# Function to calculate the arctangent of a number
def arctangent(n):
    return math.atan(n)

# Function to calculate the hyperbolic sine of an angle
def hyperbolic_sine(angle):
    return math.sinh(angle)

# Function to calculate the hyperbolic cosine of an angle
def hyperbolic_cosine(angle):
    return math.cosh(angle)

# Function to calculate the hyperbolic tangent of an angle
def hyperbolic_tangent(angle):
    return math.tanh(angle)

# Function to convert a number from decimal to binary
def decimal_to_binary(n):
    return bin(n)[2:]

# Function to convert a number from binary to decimal
def binary_to_decimal(n):
    return int(n, 2)

# Function to convert a number from decimal to hexadecimal
def decimal_to_hexadecimal(n):
    return hex(n)[2:]

# Function to convert a number from hexadecimal to decimal
def hexadecimal_to_decimal(n):
    return int(n, 16)

# Function to calculate the exponential function
def exponential(x):
    return math.exp(x)

# Function to calculate the power of a number
def power(x, y):
    return math.pow(x, y)

# Function to calculate the absolute difference between two numbers
def absolute_difference(x, y):
    return abs(x - y)

# Function to calculate the maximum of two numbers
def maximum(x, y):
    return max(x, y)

# Function to calculate the minimum of two numbers
def minimum(x, y):
    return min(x, y)

# Function to calculate the floor division of two numbers
def floor_division(x, y):
    return x // y

# Function to calculate the modulus of two numbers
def modulus(x, y):
    return x % y

# Function to calculate the sum of a list of numbers
def sum(numbers):
    return math.fsum(numbers)

# Function to calculate the median of a list of numbers
def median(numbers):
sorted_numbers = sorted(numbers)
length = len(numbers)
if length % 2 == 0:
    return (sorted_numbers[length // 2 - 1] + sorted_numbers[length // 2]) / 2
else:
    return sorted_numbers[length // 2]

# Function to calculate the mode of a list of numbers
def mode(numbers):
from collections import Counter
counter = Counter(numbers)
mode_count = max(counter.values())
    return [k for k, v in counter.items() if v == mode_count]

# Function to sort a list of numbers
def sort(numbers):
    return sorted(numbers)

# Function to reverse a list of numbers
def reverse(numbers):
    return numbers[::-1]

# Function to check if a string is a palindrome
def is_palindrome(s):
    return s == s[::-1]

# Function to split a string into a list of words
def split_words(s):
    return s.split()

# Function to join a list of words into a string
def join_words(words):
    return " ".join(words)

# Function to calculate the sum of a list of numbers
def sum(numbers):
    return sum(numbers)

# Function to calculate the dot product of two vectors
def dot_product(vector1, vector2):
    return sum([vector1[i] * vector2[i] for i in range(len(vector1))])

# Function to calculate the cross product of two vectors
def cross_product(vector1, vector2):
    if len(vector1) != 3 or len(vector2) != 3:
        raise ValueError("Vectors must have length 3")
    x1, y1, z1 = vector1
    x2, y2, z2 = vector2
    return [y1 * z2 - z1 * y2, z1 * x2 - x1 * z2, x1 * y2 - y1 * x2]

# Function to calculate the mean of a list of numbers
def mean(numbers):
    return sum(numbers) / len(numbers)

# Function to calculate the median of a list of numbers
def median(numbers):
    n = len(numbers)
    numbers_sorted = sorted(numbers)
    if n % 2 == 0:
        return (numbers_sorted[n // 2 - 1] + numbers_sorted[n // 2]) / 2
    else:
        return numbers_sorted[n // 2]

# Function to calculate the variance of a list of numbers
def variance(numbers):
    mean = sum(numbers) / len(numbers)
    return sum([(x - mean) ** 2 for x in numbers]) / len(numbers)

# Function to calculate the covariance of two lists of numbers
def covariance(x, y):
    mean_x = sum(x) / len(x)
    mean_y = sum(y) / len(y)
    return sum([(x[i] - mean_x) * (y[i] - mean_y) for i in range(len(x))]) / len(x)

# Function to calculate the correlation coefficient of two lists of numbers
def correlation_coefficient(x, y):
    cov = covariance(x, y)
    std_x = standard_deviation(x)
    std_y = standard_deviation(y)
    return cov / (std_x * std_y)

# Function to calculate the sum of a list of numbers
def sum_list(numbers):
    return sum(numbers)

# Function to calculate the product of a list of numbers
def product_list(numbers):
    result = 1
    for number in numbers:
        result *= number
    return result

# Function to calculate the greatest common divisor (GCD) of multiple numbers
def gcd_multiple(numbers):
    result = numbers[0]
    for number in numbers[1:]:
        result = math.gcd(result, number)
    return result

# Function to calculate the least common multiple (LCM) of multiple numbers
def lcm_multiple(numbers):
    result = numbers[0]
    for number in numbers[1:]:
        result = abs(result * number) // math.gcd(result, number)
    return result

# Function to calculate the factorial of a number using recursion
        return 1
    else:
        return n * factorial_recursive(n-1)

# Function to calculate the Fibonacci sequence up to a certain number of terms
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    else:
        fib_sequence = [0, 1]
        while len(fib_sequence) < n:
            fib_sequence.append(fib_sequence[-1] + fib_sequence[-2])
        return fib_sequence

# Function to check if a string is a palindrome
def is_palindrome(string):
    return string == string[::-1]

# Function to convert a string to a list of characters
def string_to_list(string):
    return list(string)

# Function to convert a list of characters to a string
def list_to_string(characters):
    return "".join(characters)

# Function to check if a list is sorted in ascending order
def is_sorted_ascending(numbers):
    return all(numbers[i] <= numbers[i+1] for i in range(len(numbers)-1))

# Function to check if a list is sorted in descending order
def is_sorted_descending(numbers):
    return all(numbers[i] >= numbers[i+1] for i in range(len(numbers)-1))

# Function to sort a list of numbers in ascending order
def sort_ascending(numbers):
    return sorted(numbers)

# Function to sort a list of numbers in descending order
def sort_descending(numbers):
    return sorted(numbers, reverse=True)

# Function to remove duplicates from a list
def remove_duplicates(numbers):
    return list(set(numbers))

# Function to reverse the order of a list
def reverse_list(numbers):
    return numbers[::-1]

# Function to shuffle the order of a list
def shuffle_list(numbers):
    random.shuffle(numbers)
    return numbers

# Function to generate a list of random integers within a specified range
def generate_random_integers(start, stop, count):
    return [random.randint(start, stop) for _ in range(count)]

# Function to generate a list of random floats within a specified range
def generate_random_floats(start, stop, count):
    return [random.uniform(start, stop) for _ in range(count)]

# Function to generate a list of random strings of a specified length
def generate_random_strings(length, count):
    return ["".join(random.choices(string.ascii_letters + string.digits, k=length)) for _ in range(count)]

# Function to calculate the sum of a list of numbers
def sum(numbers):
    return sum(numbers)

# Function to calculate the product of a list of numbers
def product(numbers):
result = 1
for n in numbers:
result *= n
    return result

# Function to check if a string is a palindrome
def is_palindrome(s):
    return s == s[::-1]

# Function to generate a random integer between two numbers
def random_integer(start, end):
    return random.randint(start, end)

# Function to generate a random string of a given length
def random_string(length):
    return ''.join(random.choice(string.ascii_letters) for i in range(length))

# Function to check if a string contains only alphanumeric characters
def is_alphanumeric(s):
    return s.isalnum()

# Function to check if a string contains only alphabetical characters
def is_alpha(s):
    return s.isalpha()

# Function to check if a string contains only digit characters
def is_digit(s):
    return s.isdigit()

# Function to check if a string contains only lowercase characters
def is_lowercase(s):
    return s.islower()

# Function to check if a string contains only uppercase characters
def is_uppercase(s):
    return s.isupper()

# Function to capitalize the first letter of a string
def capitalize(s):
    return s.capitalize()

# Function to convert a string to lowercase
def to_lowercase(s):
    return s.lower()

# Function to convert a string to uppercase
def to_uppercase(s):
    return s.upper()

# Function to remove whitespace from the beginning and end of a string
def strip(s):
    return s.strip()

# Function to split a string into a list of words
def split(s):
    return s.split()

# Function to join a list of words into a single string
def join(words):
    return ' '.join(words)

# Function to count the occurrences of a substring in a string
def count_substring(s, sub):
    return s.count(sub)

# Function to replace all occurrences of a substring in a string with another string
def replace_substring(s, old, new):
    return s.replace(old, new)

# Function to reverse a string
def reverse_string(s):
    return s[::-1]

# Function to sort a list of numbers in ascending order
def sort_ascending(numbers):
    return sorted(numbers)

# Function to sort a list of numbers in descending order
def sort_descending(numbers):
    return sorted(numbers, reverse=True)

# Function to shuffle a list
def shuffle_list(lst):
random.shuffle(lst)
    return lst

# Function to zip two lists into a list of tuples
def zip_lists(lst1, lst2):
    return list(zip(lst1, lst2))

# Function to unzip a list of tuples into two lists
def unzip_list(lst):
    return zip(*lst)

# Function to calculate the factorial of a number using recursion
    return 1
else:
    return n * recursive_factorial(n - 1)

# Function to check if a string is a palindrome
def is_palindrome(s):
s = s.lower()
s = ''.join(c for c in s if c.isalnum())
    return s == s[::-1]

# Function to generate a random integer within a given range
def random_integer(min_val, max_val):
    return random.randint(min_val, max_val)

# Function to generate a random string of a given length
def random_string(length):
    return ''.join(random.choices(string.ascii_letters + string.digits, k=length))

# Function to calculate the greatest common divisor (GCD) of more than two numbers
def multi_gcd(numbers):
    return math.gcd(*numbers)

# Function to calculate the least common multiple (LCM) of more than two numbers
def multi_lcm(numbers):
    return abs(reduce(lambda a, b: a*b // math.gcd(a, b), numbers))

# Function to convert a number from decimal to octal
def decimal_to_octal(n):
    return oct(n)[2:]

# Function to convert a number from octal to decimal
def octal_to_decimal(n):
    return int(n, 8)

# Function to calculate the standard deviation of a sample
def sample_standard_deviation(numbers):
mean = sum(numbers) / len(numbers)
variance = sum([(x - mean) ** 2 for x in numbers]) / (len(numbers) - 1)
    return math.sqrt(variance)

# Function to calculate the binomial coefficient of n and k
def binomial_coefficient(n, k):
    return math.comb(n, k)

# Function to check if a number is a power of two
def is_power_of_two(n):
    return n > 0 and not (n & (n - 1))

# Function to convert a string to title case
def to_title_case(s):
    return s.title()

# Function to reverse a string
def reverse_string(s):
    return s[::-1]

# Function to sort a list in ascending order
def sort_ascending(lst):
    return sorted(lst)

# Function to sort a list in descending order
def sort_descending(lst):
    return sorted(lst, reverse=True)

# Function to shuffle a list
def shuffle_list(lst):
random.shuffle(lst)
    return lst

# Function to count the occurrences of an element in a list
def count_occurrences(lst, element):
    return lst.count(element)

# Function to remove all occurrences of an element from a list
lst.remove(element)
    return lst

# Function to insert an element at a given index in a list
def insert_element(lst, element, index):
lst.insert(index, element)
    return lst

# Function to remove the first occurrence of an element from a list
def remove_first_occurrence(lst, element):
lst.remove(element)
    return lst

# Function to remove the last occurrence of an element from a list
def remove_last_occurrence(lst, element):
index = len(lst) - 1 - lst[::-1].index(element)
del lst[index]
    return lst

# Function to calculate the sum of a list of numbers
def sum_numbers(numbers):
    return sum(numbers)

# Function to calculate the product of a list of numbers
def product_numbers(numbers):
    return reduce(lambda x, y: x * y, numbers)
```

### KYky's Future Libraries

The success and widespread adoption of a programming language often depends on the availability of robust and versatile libraries that expand its capabilities. KYky1.0, being a new programming language, has the opportunity to build a wide range of libraries to meet the needs of its users. In this context, we present a list of 30 libraries that could be built for KYky1.0, each with a brief explanation of its purpose. While some of these libraries, such as GUI, networking, and database, are commonly found in most programming languages, others, such as virtual reality, augmented reality, and robotics, represent emerging fields with significant potential for growth. The possibilities are endless, and the development of these libraries can help make KYky1.0 a more powerful and versatile language that can meet the diverse needs of its users.

Here are 30 libraries that you might consider building:

1. GUI library: a library to create graphical user interfaces for desktop and mobile applications.
2. Networking library: a library to perform network operations, such as sending and receiving data over the internet.
3. Database library: a library to connect and query various databases.
4. Cryptography library: a library to encrypt and decrypt data using various cryptographic algorithms.
5. Image processing library: a library to process and manipulate images.
6. Math library: a library to perform advanced mathematical calculations.
7. Data science library: a library to perform data analysis and statistical modeling.
8. Machine learning library: a library to build and train machine learning models.
9. Natural language processing library: a library to process and analyze human language.
10. Audio library: a library to process and manipulate audio data.
11. Video library: a library to process and manipulate video data.
12. Virtual reality library: a library to create virtual reality applications and experiences.
13. Augmented reality library: a library to create augmented reality applications and experiences.
14. Game development library: a library to create 2D and 3D games.
15. Physics library: a library to perform physics simulations.
16. Robotics library: a library to control robots and perform robotics-related tasks.
17. IoT library: a library to build and connect Internet of Things devices.
18. Computer vision library: a library to perform computer vision tasks, such as object detection and recognition.
19. Blockchain library: a library to interact with blockchain networks and smart contracts.
20. Security library: a library to perform security-related tasks, such as secure communication and authentication.
21. Audio processing library: a library to process and analyze audio signals.
22. Image recognition library: a library to recognize and classify images using machine learning.
23. Text-to-speech library: a library to convert text to speech.
24. Speech-to-text library: a library to convert speech to text.
25. Geospatial library: a library to process and analyze geospatial data, such as maps and satellite images.
26. Time series library: a library to analyze and model time series data.
27. Financial library: a library to perform financial calculations, such as portfolio optimization and risk management.
28. Optimization library: a library to perform optimization tasks, such as linear and non-linear programming.
29. Neural network library: a library to build and train neural networks.
30. Distributed computing library: a library to perform distributed computing tasks, such as parallel processing and cluster computing.

These are just a few examples of the types of libraries that can be built for KYky1.0. Depending on the needs of the user base, many other libraries can be developed to expand the capabilities of the language.