Saif_Raad_pfd

A Unified Non-Recursive Framework for High-Order Partial Fraction Decomposition (PFD).

Author

Saif R. Lazim
Department of Mathematics, College of Science, University of Basrah

Overview

Saif_Raad_pfd is a Python library designed to compute exact, symbolic non-recursive partial fraction decompositions based on the mathematical research paper:

"A Unified Non-Recursive Framework for High-Order Partial Fraction Decomposition and Structural Challenges" (Saif R. Lazim, 2026).

It relies on exact rational representation via SymPy to prevent floating-point inaccuracies.

Features

• Non-recursive partial fraction expansion for high-order denominators.
• Decoupling of dual-binomial denominator structures without polynomial expansion.
• General multi-index summation expansions (r-th iterative expansions).
• Symbolic precision with exact fraction evaluation.
• Fully compatible with Python 3.8+.

Installation & Usage

Ensure SymPy is installed: pip install sympy

Import and use the library in Python:

from saif_raad_pfd import SaifPFD

pfd = SaifPFD()

# Example: Theorem 2.3 General Expansion
result = pfd.formula_2_3(coeffs=[2, 3], powers=[2, 4], a_last=5, n=3, r=2)
print(result)