numcore 0.1.10

A comprehensive mathematics library... Growing daily with new functions

🧮 numcore

A comprehensive mathematics library built from scratch by a first-year student. Growing daily with new functions across statistics, number theory, linear algebra, and more.

🚀 Installation

pip install numcore

📖 Usage

Statistical Analysis

from numcore import (mean, median, std, analyze_list, covariance, 
                     z_score, coefficient_of_variation)

data = [23, 45, 67, 45, 89, 34, 78, 98, 54, 55]
print(mean(data))      # 58.8
print(std(data))       # 23.82

# Advanced stats
print(z_score(75, data))                    # Standard score
print(coefficient_of_variation(data))       # Relative variability
print(covariance([1,2,3], [2,4,6]))        # Covariance

Means (Arithmetic, Geometric, Harmonic)

from numcore import mean, geometric_mean, harmonic_mean

data = [2, 4, 8]
print(mean(data))             # 4.67 (arithmetic)
print(geometric_mean(data))   # 4.0 (geometric)
print(harmonic_mean(data))    # 3.43 (harmonic)

Number Theory

from numcore import (is_prime, gcd, euler_totient, mobius,
                     legendre_symbol, is_coprime, catalan_number)

print(is_prime(17))          # True
print(euler_totient(9))      # 6
print(mobius(30))            # -1
print(is_coprime(8, 15))     # True
print(catalan_number(5))     # 42

Sequences

from numcore import (fibonacci, arithmetic_seq, geometric_seq,
                     lucas, collatz, harmonic_series)

print(fibonacci(10))            # [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
print(arithmetic_seq(2, 3, 5))  # [2, 5, 8, 11, 14]
print(geometric_seq(2, 3, 4))   # [2, 6, 18, 54]
print(harmonic_series(5))       # 2.283... (1 + 1/2 + 1/3 + 1/4 + 1/5)

Combinatorics & Probability

from numcore import npr, ncr, binomial_coeff

print(npr(5, 3))           # 60 (permutations)
print(ncr(5, 3))           # 10 (combinations)
print(binomial_coeff(5, 2)) # 10 (same as ncr)

Financial Mathematics

from numcore import rate_of_return

print(rate_of_return(110, 100))  # 10.0% gain
print(rate_of_return(90, 100))   # -10.0% loss

✨ Features

Input Functions (2)

• n_input(n) - Get n integers with validation
• input_matrix() - Interactive matrix input

Basic Statistics (6)

• mean(lst) - Arithmetic mean
• median(lst) - Middle value
• mode(lst) - Most common value(s)
• variance(lst, sample) - Variance
• std(lst, sample) - Standard deviation
• analyze_list(lst) - Comprehensive analysis

Advanced Statistics (7)

• geometric_mean(lst) - Geometric mean
• harmonic_mean(lst) - Harmonic mean
• covariance(lst1, lst2) - Covariance
• z_score(x, lst) - Standard score
• percentile(lst, p) - pth percentile value
• coefficient_of_variation(lst) - Relative variability (CV)
• mean_absolute_deviation(lst) - MAD

Number Theory (22)

• factorial(n), nth_root(num, n)
• divisors(num), proper_divisors(num), common_divisors(a,b)
• gcd(a, b), lcm(a, b)
• is_prime(num), primes(num)
• prime_divisors(num), prime_factorization(num), prime_factors(num)
• is_perfect(num), is_armstrong(num), is_amicable(a,b)
• euler_totient(num) - Euler's φ function
• mobius(num) - Möbius μ function
• quadratic_residue(num), quadratic_non_residue(num)
• legendre_symbol(a, p) - Legendre symbol
• is_coprime(a, b) - Check if coprime
• catalan_number(n) - nth Catalan number

Sequences (15)

• Fibonacci: fibonacci(n), nth_fibonacci(n)
• Lucas: lucas(n), nth_lucas(n)
• Arithmetic: arithmetic_seq(a,d,n), nth_arithmetic(a,d,n), arithmetic_sum(a,d,n)
• Geometric: geometric_seq(a,r,n), nth_geometric(a,r,n), geometric_sum(a,r,n)
• Harmonic: harmonic_seq(a,d,n), nth_harmonic(a,d,n), harmonic_sum(a,d,n)
• Special: collatz(n), farey(num), harmonic_series(n)

Combinatorics (3)

• npr(n, r) - Permutations
• ncr(n, r) - Combinations
• binomial_coeff(n, k) - Binomial coefficient

Digit Operations (3)

• digits(num) - Extract digits as list
• reverse_number(num) - Reverse digits
• sum_of_digits(num) - Sum all digits

List Utilities (4)

• counter(lst) - Count occurrences
• product(lst) - Multiply all elements
• power_list(lst, power) - Apply power to each
• reciprocal_list(lst) - Calculate reciprocals

Basic Matrix Operations (8)

• create_matrix(rows, cols, fill) - Create matrix
• matrix_shape(matrix) - Get dimensions
• matrix_add(mat1, mat2) - Addition
• matrix_sub(mat1, mat2) - Subtraction
• scalar_multiply(matrix, scalar) - Scalar multiplication
• matrix_multiply(mat1, mat2) - Matrix multiplication
• print_matrix(matrix) - Pretty print

Advanced Matrix Operations (9)

• matrix_identity(n) - Identity matrix
• matrix_transpose(matrix) - Transpose
• matrix_trace(matrix) - Trace
• determinant(matrix) - Determinant (recursive)
• matrix_minor(matrix) - Matrix of minors
• matrix_cofactor(matrix) - Cofactor matrix
• matrix_power(matrix, n) - Matrix exponentiation
• is_square(matrix) - Check if square
• is_orthogonal(matrix) - Check orthogonality

Utility Functions (2)

• signum(x) - Sign function
• rate_of_return(current, original) - Financial return %

🎯 Roadmap

• Statistical analysis (basic & advanced)
• Number theory suite
• Sequence generation
• Matrix operations (basic & advanced)
• Combinatorics
• Trigonometry (sin, cos, tan with degrees)
• Linear algebra (eigenvalues, decomposition)
• Calculus (derivatives, integrals)
• Probability distributions
• Graph theory
• Optimization algorithms
• And more... continuously growing!

📊 Current Library

Total Functions: 84

Growing daily with new mathematical capabilities!

💡 Example Use Cases

Portfolio Analysis

from numcore import rate_of_return, mean, std

returns = [5.2, -2.1, 8.3, 3.4, -1.5]
avg_return = mean(returns)
volatility = std(returns)
print(f"Average: {avg_return}%, Volatility: {volatility}%")

Data Science: Z-Scores

from numcore import z_score

exam_scores = [72, 85, 90, 65, 88, 92, 78]
your_score = 88

z = z_score(your_score, exam_scores)
print(f"Your z-score: {z:.2f}")  # How many std devs above/below mean

Catalan Numbers (Binary Trees)

from numcore import catalan_number

# How many different binary trees with n nodes?
for n in range(6):
    print(f"{n} nodes: {catalan_number(n)} trees")
# 0: 1, 1: 1, 2: 2, 3: 5, 4: 14, 5: 42

Covariance (Relationship Between Variables)

from numcore import covariance

hours_studied = [2, 4, 6, 8, 10]
exam_scores = [55, 65, 75, 85, 95]

cov = covariance(hours_studied, exam_scores)
print(f"Covariance: {cov}")  # Positive = both increase together

🛠️ Development

Requirements

• Python 3.7+
• No external dependencies!

Organization

Functions are organized by category for easy navigation and use.

📝 License

MIT License - see LICENSE file for details

👨‍💻 Author

Ujwal Mantri

• PyPI: numcore
• GitHub: ujwalmantri
• Email: [e-mail]

🌟 Support

If you find this helpful:

• ⭐ Star on GitHub
• 📦 pip install numcore
• 📢 Share with others

🎓 Learning Journey

Milestones

• ✅ Published to PyPI
• ✅ 84+ functions implemented
• ✅ Advanced statistics suite
• ✅ Complete sequence generation
• ✅ Graduate-level number theory
• 🎯 Next: Organizing into modules
• 🔄 Continuously adding new functions

What Makes This Special

• Built from scratch by first-year student
• Pure Python (zero dependencies)
• Comprehensive documentation
• Real mathematical algorithms
• Open source learning resource
• Growing daily!

📚 Function Categories

Category	Count	Status
Statistics	13	✅ Comprehensive
Number Theory	22	🔄 Growing
Sequences	15	✅ Complete
Combinatorics	3	🔄 Growing
Matrix Operations	17	✅ Complete
List Utilities	4	✅ Complete
Digit Operations	3	✅ Complete
Financial Math	1	🔄 Starting
Utilities	2	🔄 Starting
Input/Output	2	✅ Complete
Total	84+	🔄 Active Development

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Crafted with Python. Powered by curiosity. Open-sourced for learning. ⚡