anvaya 1.0.4

Anvaya (अन्वय) - A comprehensive Python mathematics library inspired by ancient Indian mathematical traditions

Anvaya (अन्वय)

A Comprehensive Python Mathematics Library

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Anvaya (Sanskrit: अन्वय) means "logical connection" or "coherent reasoning." It represents the systematic thread that links mathematical premises to universal truths.

Anvaya is a production-ready, high-performance mathematics library for Python. It bridges the gap between symbolic reasoning and numerical computation, providing a unified interface for 14 different mathematical domains.

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📑 Table of Contents

• 📚 Detailed Documentation
• 📦 Installation
• 🚀 Quick Start
• 🧮 Domain Guides
  • 1. Algebra
  • 2. Linear Algebra
  • 3. Calculus
  • 4. Probability
  • 5. Statistics
  • 6. Number Theory
  • 7. Numerical Methods
  • 8. Complex Analysis
  • 9. Differential Equations
  • 10. Graph Theory
  • 11. Optimization
  • 12. Discrete Math
  • 13. Vector Calculus
  • 14. Symbolic Engine
• 🛠 Advanced Features
• 🧬 Symbolic Engine
• 🤝 Contributing

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� Detailed Documentation

Since Anvaya covers 14+ mathematical domains, we have detailed guides for each. You can access them directly on GitHub by clicking the links below:

Category	Detailed Guide	API Reference
Getting Started	Installation | Quick Start	-
Core domains	Algebra | Linear Algebra | Calculus	API
Probability & Stats	Probability | Statistics	API
Advanced Math	Complex Analysis | Number Theory | Differential Eqs	API
Applied Math	Graph Theory | Numerical Methods | Optimization	API
Discrete & Others	Discrete Math | Vector Calculus | Symbolic Engine	API

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�📦 Installation

Anvaya requires Python 3.8 or higher. Use pip to install:

pip install anvaya

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🚀 Quick Start

Solving a complex problem with Anvaya is intuitive. Here is a 30-second example of symbolic variables, algebra, and calculus working together:

from anvaya import algebra, calculus
from anvaya.symbolic import var

# 1. Define variables
x = var('x')

# 2. Expand a polynomial
polynomial = (x + 3)**2
expanded = algebra.expand_poly(polynomial)
print(f"Expanded: {expanded}")  # x**2 + 6*x + 9

# 3. Find the derivative
derivative = calculus.diff(expanded, x)
print(f"Derivative: {derivative}")  # 2*x + 6

# 4. Solve for roots
roots = algebra.solve_linear(derivative, x)
print(f"Roots: {roots}")  # [-3]

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🧮 Domain Guides

1. Algebra

Handle equations, polynomials, and simplifications with ease.

from anvaya import algebra
from anvaya.symbolic import var

x = var('x')

# Solve quadratic equation x^2 - 5x + 6 = 0
roots = algebra.solve_quadratic(x**2 - 5*x + 6, x)
print(roots)  # [2, 3]

# Factorize expression
expr = x**2 + 2*x + 1
print(algebra.factor_poly(expr))  # (x + 1)**2

2. Linear Algebra

Perform matrix operations with high precision and safe error handling.

from anvaya import linear_algebra as la
import numpy as np

# Create a matrix
A = la.matrix([[1, 2], [3, 4]])

# Calculate Determinant
print(la.determinant(A))  # -2.0

# Compute Eigenvalues and Eigenvectors (Structured Result)
result = la.eigenvalues(A)
print(f"Values: {result.values}")
print(f"Vectors:\n{result.vectors}")

# Solve System Ax = b
b = [5, 11]
x = la.solve_linear_system(A, b)
print(f"Solution: {x}") # [1.0, 2.0]

3. Calculus

Perform symbolic differentiation, integration, and limit calculations.

from anvaya import calculus
from anvaya.symbolic import var

x = var('x')

# Differentiation
print(calculus.diff(x**3, x))  # 3*x**2

# Definite Integration (from 0 to 1)
integral = calculus.integrate(x**2, x, 0, 1)
print(integral)  # 1/3

# Limits
print(calculus.limit(1/x, x, 0, direction='+'))  # oo (Infinity)

4. Probability

Modern API for probability distributions and Bayesian inference.

from anvaya import probability as prob

# Probability Distributions
normal = prob.Normal(mean=0, std=1)
print(normal.pdf(0))  # 0.3989 (Bell curve peak)
print(normal.cdf(0))  # 0.5 (Area to the left)

# Bayes Theorem
# P(A|B) = P(B|A)*P(A) / P(B)
prob_a_given_b = prob.bayes_theorem(p_b_given_a=0.9, p_a=0.01, p_b=0.05)
print(f"Probability: {prob_a_given_b}") # 0.18

5. Statistics

Descriptive statistics and data analysis tools.

from anvaya import statistics as stats

# Descriptive Statistics
data = [10, 20, 20, 30, 40, 50]
print(stats.mean(data))    # 28.33
print(stats.median(data))  # 25.0
print(stats.mode(data))    # 20
print(stats.std(data))     # Standard deviation

6. Number Theory

Prime numbers, modular arithmetic, and ancient algorithms.

from anvaya import number_theory as nt

# Prime factorization
print(nt.prime_factors(360))  # {2: 3, 3: 2, 5: 1}

# Euler's Totient
print(nt.totient(10))  # 4 (Numbers 1, 3, 7, 9 are coprime to 10)

# Modular Inverse
print(nt.mod_inverse(3, 11))  # 4 (3*4 = 12 ≡ 1 mod 11)

# Greatest Common Divisor
print(nt.gcd(48, 18))  # 6

7. Numerical Methods

Root finding and numerical integration when symbolic math isn't enough.

from anvaya import numerical

# Find root of f(x) = x^2 - 2 near x=1.5
def f(x): return x**2 - 2
root = numerical.root_find(f, 1.5)
print(f"Square root of 2 is approx: {root:.6f}") # 1.414214

8. Complex Analysis

Work with complex numbers and their operations.

from anvaya import complex_analysis as ca

# Create complex numbers
z1 = ca.complex_num(3, 4)  # 3 + 4i
z2 = ca.complex_num(1, 2)  # 1 + 2i

# Operations
print(ca.add(z1, z2))       # (4+6j)
print(ca.magnitude(z1))     # 5.0
print(ca.phase(z1))         # 0.9273 radians

9. Differential Equations

Solve ordinary differential equations numerically.

from anvaya import differential_equations as de

# Solve dy/dx = y with y(0) = 1
def dydt(t, y): return y
solution = de.solve_ode(dydt, y0=1, t_span=(0, 2))
print(solution)  # Exponential growth solution

10. Graph Theory

Create and analyze graphs and networks.

from anvaya import graph_theory as gt

# Create a graph
g = gt.Graph()
g.add_edge('A', 'B', weight=4)
g.add_edge('B', 'C', weight=3)
g.add_edge('A', 'C', weight=10)

# Shortest path
path = gt.shortest_path(g, 'A', 'C')
print(path)  # ['A', 'B', 'C'] with cost 7

11. Optimization

Find minimum and maximum values of functions.

from anvaya import optimization as opt

# Minimize f(x) = (x-3)^2
def f(x): return (x - 3)**2
result = opt.minimize(f, x0=0)
print(f"Minimum at x = {result:.2f}")  # 3.0

12. Discrete Math

Combinatorics, permutations, and set operations.

from anvaya import discrete

# Combinations and Permutations
print(discrete.combinations(5, 2))   # 10
print(discrete.permutations(5, 2))   # 20
print(discrete.factorial(5))         # 120

13. Vector Calculus

Operations on vector fields and multivariable functions.

from anvaya import vector_calculus as vc

# Vector operations
v1 = [1, 2, 3]
v2 = [4, 5, 6]

print(vc.dot_product(v1, v2))    # 32
print(vc.cross_product(v1, v2))  # [-3, 6, -3]
print(vc.magnitude(v1))          # 3.74

14. Symbolic Engine

Create and manipulate symbolic mathematical expressions.

from anvaya.symbolic import var, simplify

x, y = var('x'), var('y')

# Build expressions
expr = (x + y)**2
expanded = expr.expand()
print(expanded)  # x**2 + 2*x*y + y**2

# Simplify
expr2 = (x**2 - 1)/(x - 1)
print(simplify(expr2))  # x + 1

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🛠 Advanced Features

Safe Error Handling

Anvaya doesn't just crash; it tells you why a calculation failed using custom exceptions.

from anvaya import linear_algebra as la
from anvaya import SingularMatrixError

A = [[1, 1], [1, 1]] # Singular matrix (no inverse)

try:
    inv = la.inverse(A)
except SingularMatrixError as e:
    print(f"Math Error: {e}") # Matrix is singular or nearly singular

Type Safety

Full support for Python type hints and PEP 561 compliance, making it perfect for large-scale applications with VS Code or PyCharm.

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🧬 Symbolic Engine

The core of Anvaya is its SymbolicEngine. You can use it to parse strings into math or manipulate variables.

from anvaya.symbolic import engine

# Parse from string
my_math = engine.expr("x**2 + 2*x + 1")
print(engine.factor(my_math)) # (x + 1)**2

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🤝 Contributing

We welcome contributions to Anvaya! Whether it's adding new modules (like Tensor Calculus or Financial Math) or improving performance.

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
3. Commit your Changes (git commit -m 'Add some AmazingFeature')
4. Push to the Branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

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👨‍💻 Author

Akash Rahut

• GitHub: @Akashrahut100
• AI & Data Science Engineer
• Building intelligent, scalable, and data-driven systems at the intersection of mathematics, software architecture, and artificial intelligence.

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📜 License

Distributed under the MIT License. See LICENSE for more information.

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“स्थानात् स्थानं दशगुणं स्यात्” — Āryabhaṭīya (499 CE)

(The logic of numbers shapes the universe)