pchjlib 1.7.2

A Python toolkit for mathematical operations and string processing, including prime numbers, Fibonacci sequences, and Caesar ciphers.

PCHJLIB - Joesifer

📚 Requirements

• Python: >= 3.7
• gmpy2: Optional for big integer support in features like checking large primes. Install via pip install gmpy2.

🛠️ Installation

🚀 Install the core library without optional dependencies.

💡 Note: To download the icon (logo) to your site-packages folder, run pchj-icon. Warning: This modifies folder attributes (sets system/hidden) on Windows only.

🔧 Option 1: Install from GitHub (development version)

python -m pip install git+https://github.com/Joesifer/pchjlib.git

📦 Option 2: Install from PyPI (stable release)

python -m pip install pchjlib

🔄 Then run:

pchj-icon

🌟 Optional: Enable additional features

To activate big integer support (e.g., for large primes in is_prime), install gmpy2:

python -m pip install gmpy2

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❓ Basic Usage

💡 Note: {function} can be is_prime, generate_prime_list, etc. {___} can be primes, fibonacci, sequence_generation, etc.

✅ Option 1: Import a single function

from pchjlib.{___} import {function}
result = {function}(value_1, value_2, ...)

✅ Option 2: Call via the module

import pchjlib.{___}
result = pchjlib.{___}.{function}(value_1, value_2, ...)

---

🌟 Key Features

• 🔍 Special Number Checking and Generation: Supports prime, emirp, Fibonacci, perfect, narcissistic, amicable, square, strong, twin prime, abundant, and happy numbers.
• 🔗 Divisor and Multiple Operations: Generate divisor lists, compute GCD, LCM, and perform prime factorization.
• 🧹 List and String Processing: Remove duplicates, extract digits/numbers/characters, and compress/decompress strings.
• 🔐 Encryption and Decryption: Implements Caesar cipher (for educational use only).
• ✨ Special Calculations: Includes electricity bill calculation, largest number with a given digit sum, sequence generation, and inversion counting.

📚 Table of Contents

• 🔢 Prime and Related Number Functions
• 🌀 Fibonacci Functions
• 🧠 Perfect, Narcissistic, Amicable, and Happy Number Functions
• 📐 Square, Strong, and Friendly Number Functions
• 📊 Divisor and Multiple Functions
• 👯 Twin Prime and Abundant Number Functions
• 🔍 Prime Factorization Functions
• 🧵 List and String Processing Functions
• 🏛️ Caesar Cipher Functions
• 💥 Special Calculation Functions
• 🔁 Sequence Generation Functions
• 🔢 Inversion Counting Functions
• 📋 Sample Command List for the pchjlib Library
• 🧪 Running Tests
• 🛠️ Update History

---

🔢 Prime and Related Number Functions (primes.py)

Note: Miller-Rabin primality test is now deterministic using fixed witnesses for accuracy.

is_prime(input_number) Checks if a number is prime.

• Parameter: input_number (int)
• Returns: True if prime, False otherwise.
• Raises: InvalidInputError if not an integer.

Notes:

• Negative numbers, 0, and 1 always return False.
• Uses quick trial division by small primes and perfect square elimination.
• Falls back on a deterministic Miller–Rabin test with bases chosen according to the number’s bit length.
• If gmpy2 is installed, powmod and isqrt are accelerated.

Example:

>>> is_prime(7)
True
>>> is_prime(4)
False
>>> is_prime(-5)
False

generate_prime_list(limit) Generates primes from 0 to limit using the Sieve algorithm.

• Parameter: limit (int)
• Returns: List of primes.
• Raises: InvalidInputError if limit < 2 or not an integer.
• Example: generate_prime_list(10) → [2, 3, 5, 7]

is_emirp(input_number) Checks if a number is an emirp (prime with prime reverse).

• Parameter: input_number (int)
• Returns: True if emirp, False otherwise.
• Raises: InvalidInputError if not a positive integer >= 2.
• Example: is_emirp(13) → True

generate_emirp_list(limit) Generates emirp numbers from 2 to limit.

• Parameter: limit (int)
• Returns: List of emirp numbers.
• Raises: InvalidInputError if limit < 2 or not an integer.
• Example: generate_emirp_list(20) → [13, 17]

---

🌀 Fibonacci Functions (fibonacci.py)

fibonacci_at_index(index) Calculates the Fibonacci number at a given index with caching.

• Parameter: index (int)
• Returns: Fibonacci number.
• Raises: InvalidInputError if not a non-negative integer.
• Example: fibonacci_at_index(5) → 5

generate_fibonacci_list(count) Generates the first count Fibonacci numbers.

• Parameter: count (int)
• Returns: List of Fibonacci numbers.
• Raises: InvalidInputError if not a non-negative integer.
• Example: generate_fibonacci_list(5) → [0, 1, 1, 2, 3]

---

🧠 Perfect, Narcissistic, Amicable, and Happy Number Functions (special_numbers1.py)

sum_of_divisors(input_number) Computes the sum of positive divisors (excluding itself).

• Parameter: input_number (int)
• Returns: Sum of divisors.
• Raises: InvalidInputError if not a positive integer.
• Example: sum_of_divisors(6) → 6

sum_of_digits(input_number) Calculates the sum of a number's digits.

• Parameter: input_number (int)
• Returns: Sum of digits.
• Raises: InvalidInputError if not an integer.
• Example: sum_of_digits(123) → 6

is_perfect_number(input_number) Checks if a number is perfect.

• Parameter: input_number (int)
• Returns: True if perfect, False otherwise.
• Raises: InvalidInputError if not a positive integer.
• Example: is_perfect_number(6) → True

generate_perfect_number_list(limit) Generates perfect numbers from 1 to limit.

• Parameter: limit (int)
• Returns: List of perfect numbers.
• Raises: InvalidInputError if not a positive integer.
• Example: generate_perfect_number_list(10) → [6]

is_narcissistic_number(input_number) Checks if a number is narcissistic.

• Parameter: input_number (int)
• Returns: True if narcissistic, False otherwise.
• Raises: InvalidInputError if not a non-negative integer.
• Example: is_narcissistic_number(153) → True

generate_narcissistic_number_list(limit) Generates narcissistic numbers from 0 to limit.

• Parameter: limit (int)
• Returns: List of narcissistic numbers.
• Raises: InvalidInputError if not a non-negative integer.
• Example: generate_narcissistic_number_list(10000) → [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474]

are_amicable_numbers(number1, number2) Checks if two numbers are amicable.

• Parameters: number1, number2 (int)
• Returns: True if amicable, False otherwise.
• Raises: InvalidInputError if not positive integers.
• Example: are_amicable_numbers(220, 284) → True

is_happy_number(input_number) Checks if a number is happy.

• Parameter: input_number (int)
• Returns: True if happy, False otherwise.
• Raises: InvalidInputError if not a positive integer.
• Example: is_happy_number(19) → True

generate_happy_number_list(limit) Generates happy numbers from 1 to limit.

• Parameter: limit (int)
• Returns: List of happy numbers.
• Raises: InvalidInputError if not a positive integer.
• Example: generate_happy_number_list(10) → [1, 7, 10]

---

📐 Square, Strong, and Friendly Number Functions (special_numbers2.py)

is_square_number(input_number) Checks if a number is a perfect square.

• Parameter: input_number (int)
• Returns: True if square, False otherwise.
• Raises: InvalidInputError if not a non-negative integer.
• Example: is_square_number(16) → True

generate_square_number_list(limit) Generates square numbers from 0 to limit.

• Parameter: limit (int)
• Returns: List of square numbers.
• Raises: InvalidInputError if not a non-negative integer.
• Example: generate_square_number_list(10) → [0, 1, 4, 9]

are_friendly_numbers(number1, number2) Checks if two numbers are friendly.

• Parameters: number1, number2 (int)
• Returns: True if friendly, False otherwise.
• Raises: InvalidInputError if not positive integers.
• Example: are_friendly_numbers(30, 140) → True

is_strong_number(input_number) Checks if a number is strong (sum of factorial of digits equals number).

• Parameter: input_number (int)
• Returns: True if strong, False otherwise.
• Raises: InvalidInputError if not a non-negative integer.
• Example: is_strong_number(145) → True

---

📊 Divisor and Multiple Functions (divisors_multiples.py)

sum_of_divisors(input_number) Computes the sum of positive divisors (excluding itself).

• Parameter: input_number (int)
• Returns: Sum of divisors.
• Raises: InvalidInputError if not a positive integer.
• Example: sum_of_divisors(6) → 6

generate_divisor_list(input_number, positive_only=True) Generates divisors of a number.

• Parameters: input_number (int), positive_only (bool)
• Returns: List of divisors.
• Raises: InvalidInputError if not an integer or zero.
• Example: generate_divisor_list(6) → [1, 2, 3, 6]

generate_multiple_list(base_number, limit, positive_only=True) Generates multiples of a number up to limit times.

• Parameters: base_number (int), limit (int), positive_only (bool)
• Returns: List of multiples.
• Raises: InvalidInputError if not integers, number is zero, or limit < 1.
• Example: generate_multiple_list(3, 5) → [3, 6, 9, 12, 15]

common_divisors(numbers) Generates common divisors for a list of numbers.

• Parameter: numbers (list)
• Returns: List of common divisors.
• Raises: InvalidInputError if not a list or contains non-integers; MathError if fewer than 2 non-zero elements.
• Example: common_divisors([12, 18]) → [1, 2, 3, 6]

greatest_common_divisor(numbers) Computes the GCD of a list of numbers.

• Parameter: numbers (list)
• Returns: GCD value.
• Raises: InvalidInputError if not a list or contains non-integers; MathError if fewer than 2 non-zero elements.
• Example: greatest_common_divisor([12, 18]) → 6

least_common_multiple(numbers) Computes the LCM of a list of numbers.

• Parameter: numbers (list)
• Returns: LCM value.
• Raises: InvalidInputError if not a list, contains non-integers, or zeros; MathError if fewer than 2 elements.
• Example: least_common_multiple([4, 6]) → 12

---

👯 Twin Prime and Abundant Number Functions (twin_abundant.py)

is_twin_prime(input_number) Checks if a number is a twin prime.

• Parameter: input_number (int)
• Returns: True if twin prime, False otherwise.
• Raises: InvalidInputError if not an integer.
• Example: is_twin_prime(5) → True

generate_twin_prime_list(limit) Generates twin primes from 2 to limit.

• Parameter: limit (int)
• Returns: List of twin primes.
• Raises: InvalidInputError if not an integer >= 2.
• Example: generate_twin_prime_list(20) → [3, 5, 7, 11, 13, 17, 19]

is_abundant_number(input_number) Checks if a number is abundant.

• Parameter: input_number (int)
• Returns: True if abundant, False otherwise.
• Raises: InvalidInputError if not a positive integer.
• Example: is_abundant_number(12) → True

generate_abundant_number_list(limit) Generates abundant numbers from 1 to limit.

• Parameter: limit (int)
• Returns: List of abundant numbers.
• Raises: InvalidInputError if not a positive integer.
• Example: generate_abundant_number_list(20) → [12, 18, 20]

---

🔍 Prime Factorization Functions (prime_factorization.py)

prime_factors(input_number) Factorizes a number into prime factors.

• Parameter: input_number (int)
• Returns: List of prime factors.
• Raises: InvalidInputError if not a positive integer > 1.
• Example: prime_factors(12) → [2, 2, 3]

greatest_common_prime_divisor(number1, number2) Finds the greatest common prime divisor of two numbers.

• Parameters: number1, number2 (int)
• Returns: Greatest common prime divisor.
• Raises: InvalidInputError if not positive integers > 1; MathError if no common prime divisor.
• Example: greatest_common_prime_divisor(12, 18) → 3

---

🧵 List and String Processing Functions (string_processing.py)

remove_duplicates(items) Removes duplicates from a list and sorts in descending order.

• Parameter: items (list)
• Returns: Sorted list without duplicates.
• Raises: InvalidInputError if not a list/tuple.
• Example: remove_duplicates([1, 2, 2, 3]) → [3, 2, 1]

extract_digits_from_string(text) Extracts individual digits from a string.

• Parameter: text (str)
• Returns: List of digits.
• Example: extract_digits_from_string("abc123") → [1, 2, 3]

extract_numbers_from_string(text) Extracts full numbers from a string.

• Parameter: text (str)
• Returns: List of numbers.
• Example: extract_numbers_from_string("abc123def456") → [123, 456]

extract_characters(text) Extracts non-digit characters from a string.

• Parameter: text (str)
• Returns: List of characters.
• Example: extract_characters("a1b2c3") → ['a', 'b', 'c']

compress_string(text, compress_type) Compresses a string using two methods.

• Parameters: text (str), compress_type (int)
• Returns: Compressed string.
• Example (type 1): compress_string("google", 1) → 'e2gl2o'
• Example (type 2): compress_string("google", 2) → 'g2ogle'

compress_string_without_numbers(input_text) Compresses a string by removing consecutive duplicates.

• Parameter: input_text (str)
• Returns: Compressed string.
• Example: compress_string_without_numbers("hhhoocssssiiinnnhhhhh") → 'hocsinh'

decompress_string(text) Decompresses a string with numeric counts.

• Parameter: text (str)
• Returns: Decompressed string.
• Example: decompress_string("g2ogle") → "google"

unique_characters_string(text) Creates a string with unique characters in order of appearance.

• Parameter: text (str)
• Returns: String with no duplicates.
• Example: unique_characters_string("google") → "gole"

---

🏛️ Caesar Cipher Functions (caesar_cipher.py)

caesar_cipher_to_numbers(text, shift) Converts a string to a list of Caesar cipher numbers.

• Parameters: text (str), shift (int)
• Returns: List of shifted numbers.
• Example: caesar_cipher_to_numbers("ABC", 3) → [3, 4, 5]

caesar_cipher_from_numbers(numbers, shift) Decodes a list of Caesar cipher numbers into a string.

• Parameters: numbers (list), shift (int)
• Returns: Decoded string.
• Example: caesar_cipher_from_numbers([3, 4, 5], 3) → "ABC"

---

💥 Special Calculation Functions (special_calculations.py)

calculate_electricity_bill_vietnam(old_reading, new_reading) Calculates an electricity bill based on Vietnamese pricing tiers.

• Parameters: old_reading, new_reading (float)
• Returns: String with consumption and cost.
• Example: calculate_electricity_bill_vietnam(100, 150) → "- Electricity consumed this month: 50.0 Kwh\n- Electricity bill this month: 83900.0 VND"

largest_number_with_digit_sum(digit_count, target_sum) Finds the largest number with digit_count digits summing to target_sum.

• Parameters: digit_count (int), target_sum (int)
• Returns: Largest number as a string.
• Example: largest_number_with_digit_sum(3, 15) → '960'

---

🔁 Sequence Generation Functions (sequence_generation.py)

generate_sequence_rule_1(count) Generate a sequence according to the rule: 1 divisible by 1, 2 by 2, etc.

• Parameter: count (int)
• Returns: List of sequence numbers.
• Example: generate_sequence_rule_1(10) → [1, 4, 6, 9, 12, 15, 16, 20, 24, 28]

generate_sequence_rule_2(base, count) Generates count multiples of base.

• Parameters: base (int), count (int)
• Returns: List of multiples.
• Example: generate_sequence_rule_2(2, 5) → [2, 4, 6, 8, 10]

generate_sequence_rule_3(count, base) Generates powers of base from 1 to count.

• Parameters: count (int), base (int)
• Returns: List of powers.
• Example: generate_sequence_rule_3(5, 2) → [2, 4, 8, 16, 32]

---

🔢 Inversion Counting Functions (inversion_counting.py)

count_inversions(numbers) Counts the number of inversions in a list.

• Parameter: numbers (list)
• Returns: Number of inversions.
• Example: count_inversions([1, 3, 2]) → 1

---

📋 Sample Command List for the pchjlib Library

1. Primes and Emirps

• Check if a number is prime: python pchjmain.py primes_and_emirps --is_prime <number> Example: python pchjmain.py primes_and_emirps --is_prime 17

• Generate a list of primes: python pchjmain.py primes_and_emirps --generate_prime_list <limit> Example: python pchjmain.py primes_and_emirps --generate_prime_list 50

• Check if a number is an emirp: python pchjmain.py primes_and_emirps --is_emirp <number> Example: python pchjmain.py primes_and_emirps --is_emirp 13

• Generate a list of emirps: python pchjmain.py primes_and_emirps --generate_emirp_list <limit> Example: python pchjmain.py primes_and_emirps --generate_emirp_list 100

2. Twin Primes and Abundant Numbers

• Check if a number is a twin prime: python pchjmain.py twin_primes_and_abundant --is_twin_prime <number> Example: python pchjmain.py twin_primes_and_abundant --is_twin_prime 5

• Generate a list of twin primes: python pchjmain.py twin_primes_and_abundant --generate_twin_prime_list <limit> Example: python pchjmain.py twin_primes_and_abundant --generate_twin_prime_list 50

• Check if a number is abundant: python pchjmain.py twin_primes_and_abundant --is_abundant <number> Example: python pchjmain.py twin_primes_and_abundant --is_abundant 12

• Generate a list of abundant numbers: python pchjmain.py twin_primes_and_abundant --generate_abundant_list <limit> Example: python pchjmain.py twin_primes_and_abundant --generate_abundant_list 100

3. Fibonacci Sequence

• Compute the Fibonacci number at a given index: python pchjmain.py fibonacci --at_index <index> Example: python pchjmain.py fibonacci --at_index 10

• Generate a list of Fibonacci numbers: python pchjmain.py fibonacci --generate_list <count> Example: python pchjmain.py fibonacci --generate_list 5

4. Special Numbers 1 (Perfect, Narcissistic, Amicable, Happy)

• Check if a number is perfect: python pchjmain.py special_numbers_1 --is_perfect <number> Example: python pchjmain.py special_numbers_1 --is_perfect 28

• Generate a list of perfect numbers: python pchjmain.py special_numbers_1 --generate_perfect_list <limit> Example: python pchjmain.py special_numbers_1 --generate_perfect_list 1000

• Check if a number is narcissistic: python pchjmain.py special_numbers_1 --is_narcissistic <number> Example: python pchjmain.py special_numbers_1 --is_narcissistic 153

• Generate a list of narcissistic numbers: python pchjmain.py special_numbers_1 --generate_narcissistic_list <limit> Example: python pchjmain.py special_numbers_1 --generate_narcissistic_list 1000

• Check if two numbers are amicable: python pchjmain.py special_numbers_1 --are_amicable <number1> <number2> Example: python pchjmain.py special_numbers_1 --are_amicable 220 284

• Check if a number is happy: python pchjmain.py special_numbers_1 --is_happy <number> Example: python pchjmain.py special_numbers_1 --is_happy 19

• Generate a list of happy numbers: python pchjmain.py special_numbers_1 --generate_happy_list <limit> Example: python pchjmain.py special_numbers_1 --generate_happy_list 100

5. Special Numbers 2 (Square, Strong, Friendly)

• Check if a number is a perfect square: python pchjmain.py special_numbers_2 --is_square <number> Example: python pchjmain.py special_numbers_2 --is_square 16

• Generate a list of perfect squares: python pchjmain.py special_numbers_2 --generate_square_list <limit> Example: python pchjmain.py special_numbers_2 --generate_square_list 100

• Check if a number is strong: python pchjmain.py special_numbers_2 --is_strong <number> Example: python pchjmain.py special_numbers_2 --is_strong 145

• Check if two numbers are friendly: python pchjmain.py special_numbers_2 --are_friendly <number1> <number2> Example: python pchjmain.py special_numbers_2 --are_friendly 30 140

6. Divisors and Multiples

• Generate a list of divisors: python pchjmain.py divisors_and_multiples --generate_divisor_list <number> Example: python pchjmain.py divisors_and_multiples --generate_divisor_list 28

• Generate a list of multiples: python pchjmain.py divisors_and_multiples --generate_multiple_list <number> <limit> Example: python pchjmain.py divisors_and_multiples --generate_multiple_list 3 20

• Find common divisors: python pchjmain.py divisors_and_multiples --common_divisors <number1> <number2> [<number3> ...] Example: python pchjmain.py divisors_and_multiples --common_divisors 12 18 24

• Compute GCD (Greatest Common Divisor): python pchjmain.py divisors_and_multiples --gcd <number1> <number2> [<number3> ...] Example: python pchjmain.py divisors_and_multiples --gcd 12 18 24

• Compute LCM (Least Common Multiple): python pchjmain.py divisors_and_multiples --lcm <number1> <number2> [<number3> ...] Example: python pchjmain.py divisors_and_multiples --lcm 4 5 6

7. Prime Factorization

• Prime factorization: python pchjmain.py prime_factorization --prime_factors <number> Example: python pchjmain.py prime_factorization --prime_factors 100

• Greatest common prime divisor: python pchjmain.py prime_factorization --greatest_common_prime_divisor <number1> <number2> Example: python pchjmain.py prime_factorization --greatest_common_prime_divisor 12 18

8. String Processing

• Remove duplicate elements: python pchjmain.py string_processing --remove_duplicates <elem1> <elem2> ... Example: python pchjmain.py string_processing --remove_duplicates 1 2 2 3 4 4

• Extract digits: python pchjmain.py string_processing --extract_digits "<string>" Example: python pchjmain.py string_processing --extract_digits "a1b2c3"

• Extract numbers: python pchjmain.py string_processing --extract_numbers "<string>" Example: python pchjmain.py string_processing --extract_numbers "a12b34c56"

• Extract non-digit characters: python pchjmain.py string_processing --extract_characters "<string>" Example: python pchjmain.py string_processing --extract_characters "a1b2c3"

• Compress a string (type 1 or 2): python pchjmain.py string_processing --compress "<string>" <compress_type> Example: python pchjmain.py string_processing --compress "aaabbbcc" 1

• Compress a string without counts: python pchjmain.py string_processing --compress_without_numbers "<string>" Example: python pchjmain.py string_processing --compress_without_numbers "aaabbbcc"

• Decompress a string: python pchjmain.py string_processing --decompress "<compressed_string>" Example: python pchjmain.py string_processing --decompress "a3b2c1"

• Get unique characters in a string: python pchjmain.py string_processing --unique_characters "<string>" Example: python pchjmain.py string_processing --unique_characters "aaabbbcc"

9. Caesar Cipher

• Convert text to Caesar numbers: python pchjmain.py caesar_cipher --to_numbers "<text>" <shift> Example: python pchjmain.py caesar_cipher --to_numbers "abc" 3

• Convert Caesar numbers back to text: python pchjmain.py caesar_cipher --from_numbers <shift> <num1> <num2> ... Example: python pchjmain.py caesar_cipher --from_numbers 3 4 5 6

10. Special Calculations

• Calculate an electricity bill: python pchjmain.py special_calculations --electricity_bill <old_reading> <new_reading> Example: python pchjmain.py special_calculations --electricity_bill 100 200

• Find the largest number with given digits sum: python pchjmain.py special_calculations --largest_number <digit_count> <digit_sum> Example: python pchjmain.py special_calculations --largest_number 3 15

11. Sequence Generation

• Generate sequence by rule 1: python pchjmain.py sequence_generation --rule1 <count> Example: python pchjmain.py sequence_generation --rule1 5

• Generate sequence by rule 2: python pchjmain.py sequence_generation --rule2 <base> <count> Example: python pchjmain.py sequence_generation --rule2 2 5

• Generate sequence by rule 3: python pchjmain.py sequence_generation --rule3 <count> <base> Example: python pchjmain.py sequence_generation --rule3 5 2

12. Inversion Counting

• Count inversions in a list: python pchjmain.py inversion_counting --count <elem1> <elem2> ... Example: python pchjmain.py inversion_counting --count 2 3 1 4

---

Note

• Replace <...> with actual values when running the command.
• Ensure commands are executed in the directory containing pchjmain.py.
• For detailed help on any category, run python pchjmain.py <category> -h (e.g., python pchjmain.py primes_and_emirps -h).

---

🧪 Running Tests

To run the unit tests for the library, navigate to the project root and execute:

python -m unittest discover tests

This will discover and run all tests in the tests/ directory. Ensure the library is installed in editable mode (pip install -e .) for proper import resolution.

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🛠️ Update History

📅 Latest Update: August 15, 2025 📦 Total Releases: 99

📌 2025

1.7.2 → 1.7.1 (August 15, 2025)

• Optimize the is_prime function.

1.7.0 (August 12, 2025)

• Performance Improvements: Implemented merge sort for O(n log n) inversion counting; added Pollard's Rho for faster prime factorization on large numbers; made sequence generation dynamic to handle larger counts; integrated optional gmpy2 for accelerated GCD/LCM.
• Code Quality Enhancements: Standardized function names (e.g., calculate_electricity_bill_Vietnamese to calculate_electricity_bill_vietnam); replaced wildcard imports with explicit ones in __init__.py; fixed bug in largest_number_with_digit_sum for correct largest output (e.g., '960' for 3 digits sum 15); improved CLI error handling with detailed tracebacks; added user warning for side-effects in pchjicon.py; made Miller-Rabin primality test deterministic using fixed witnesses.
• Documentation Updates: Fixed incorrect examples in README (e.g., largest number); summarized update history for brevity; removed redundant sections and added warnings for probabilistic methods (now deterministic) and side-effects.

1.6.5 → 1.5.0 (August 11-12, 2025)

• Fixed minor bugs and optimized generate_sequence_rule_3/generate_sequence_rule_2.
• Updated is_strong_number to standard factorion definition.
• Removed solve_equation and its CLI category.
• Eliminated numpy dependency; added optional gmpy2 integration.
• Added type hints, examples, and performance optimizations (e.g., iterative Fibonacci).

1.4.5 → 1.3.0 (August 7-8, 2025)

• Fixed minor bugs.

1.2.3 → 1.0.1 (August 4–5, 2025)

• Removed unused functions; added logo support via pchj-icon.
• Added Sample Command List; enhanced CLI.

1.0.0 → 0.1.5.1 (August 3-4, 2025)

• Major overhaul: Optimizations, error handling, documentation, and tests.
• Removed legacy dependencies and functions; switched README to English.

0.1.5 → 0.1.4 (August 2, 2025)

• Removed Roman numeral conversion; fixed matrix program.
• Added negative divisors/multiples; merged string compression.

0.1.3.2 → 0.1.2 (August 1, 2025)

• Minor fixes; consolidated strong-number logic; optimized Fibonacci/primes.

0.1.1.3 → 0.1.0.7 (July 31, 2025)

• README updates; dependency fixes.

0.1.0.6 → 0.1.0.3 (July 28–30, 2025)

• Bug fixes.

0.1.0.2 → 0.1.0 (July 28, 2025)

• Minor fixes; removed legacy functions; code overhaul.

0.0.5.2.1 → 0.0.5.0 (July 26-27, 2025)

• README tweaks; updated teen code.

📌 2024

• 0.0.4.1 (October 17, 2024): Added sequence creation; updated one-two-three.
• 0.0.4.0 → 0.0.3.5 (May 3–5, 2024): README fixes; updated Christmas tree variants; testing.
• 0.0.3.4 (February 26, 2024): Added common divisors list.
• 0.0.3.3 → 0.0.3 (February 20–21, 2024): README enhancements; added abundant check and unique string; removed duplicates check.
• 0.0.2.10 → 0.0.2.6 (February 18–19, 2024): README updates; testing; switched to MIT License.
• 0.0.2.5 → 0.0.2.1 (February 14–18, 2024): README and tests.
• 0.0.2 → 0.0.0.1 (February 14, 2024): Dependency fixes; testing; initial release.