Polymath Physics

A world-class, heavily optimized, polymorphic physics and calculus engine backed by Triton GPU parallelization and SymPy's Exact Computer Algebra System (CAS).

Key Features

1. True Polymorphism: Pass raw floats for blistering bare-metal speed, pass Vector3D objects for spatial mechanics, or pass sympy.Symbol variables to generate exact algebraic equations.
2. Deep Calculus Integration: The engine doesn't just calculate numbers—it calculates equations. You can pass abstract algebraic positions and natively derive exact velocity and acceleration formulas.
3. Strict Domain Gatekeeping: polymath-physics intercepts invalid physics requests (like passing negative masses or 3D vectors into scalar fields) with strict, polymorphic type-checking before the math ever crashes.
4. GPU Acceleration (Opt-in): For massive N-Body simulations and fluid dynamics, the library falls back onto highly parallelized Triton GPU kernels.

Installation

Install the core library (Zero external dependencies outside of sympy):

pip install polymath-physics

Install with massive parallel GPU acceleration enabled (Requires CUDA):

pip install polymath-physics[gpu]

Quick Start: The Power of Polymorphism

1. Bare-Metal Speed

When you need raw performance, just pass standard floats. The engine evaluates it instantly.

from physics.astrophysics.cosmology import schwarzschild_radius

# Calculate the Event Horizon of a black hole with mass 1.989e30 kg
r = schwarzschild_radius(mass=1.989e30)
print(r) # Returns: 2953.25 meters

2. Exact Calculus & Algebra

By combining polymath-physics with SymPy, you can derive exact mathematical formulas instead of just numeric answers.

from physics.solver import AlgebraicSolver
from physics.mechanics.calculus_kinematics import derive_velocity

# Create a variable 't' for time
t = AlgebraicSolver.create_symbol('t')

# Define an abstract position equation: p(t) = 5t^3 + 2t
position_eq = 5*(t**3) + 2*t

# Natively derive the exact algebraic velocity curve!
velocity_eq = derive_velocity(position_eq, time_symbol=t)
print(velocity_eq) # Returns: 15*t**2 + 2

3. Strict Physics Guardrails

Our built-in PhysicsDomainError strictly prevents invalid concepts (like negative mass) from polluting your calculations.

from physics.astrophysics.cosmology import schwarzschild_radius

# This will immediately raise a PhysicsDomainError!
schwarzschild_radius(mass=-500) 

Architecture

polymath-physics spans across dozens of graduate-level domains, including:

• Classical Mechanics & Calculus Kinematics
• Quantum Mechanics & Plasma Physics
• General Relativity & Cosmology
• Advanced Fluid Dynamics & Thermodynamics

Complete API Reference

For an exhaustive list of all 100+ functions available in this library, please refer to the API Reference (or see the included API_REFERENCE.md file).