PyStein Documentation

The pystein package contains utilities for computing symbolic quantities that arise in general relativity. Presently, this package is essentially a sympy extension that computes components of tensors directly.

Contents:

Installation

The pystein package is available on PyPI, and can be installed via pip, see Installation.

Symbolic Utilities

The symbolic utilities within pystein extend those of sympy.diffgeom and are capable of:

  • constructing metric tensors in arbitrary coordinates

  • computing coefficients of curvature tensors

  • computing coefficients of matter tensors

  • computing the Einstein equations

For more see the tutorial on the symbolic tools (Tutorial: Symbolic Tools).

Numeric Utilities

The pystein package contains some limited numerical utilities, including:

  • ability to numerically integrate the geodesic equations geodesic.numerical_geodesic

  • convenience functions to compute multiple geodesics from a variety of initial conditions (2D)

These utilities are compatible with the symbolic tools thanks to sympy.lambdify, which is used to convert symbolic equations into numeric equations.

For more, see the tutorial on the numeric tools (Tutorial: Numerical Geodesics).

Note

The numeric tools in pystein are still in beta. For “bad” initial conditions you may encounter warnings and errors from numpy and scipy.

Quick Start

The below code snippet gives a concise example of computing curvature coefficients. For a more explanation on this snippet see Quick Start with pystein.

# Imports
import sympy
from sympy.diffgeom import Manifold, Patch
from pystein import coords, metric, curvature
from pystein.utilities import tensor_pow as tpow

# Create metric
M = Manifold('M', dim=2)
P = Patch('origin', M)
theta, phi, a = sympy.symbols('theta phi a', nonnegative=True)
cs = coords.CoordSystem('spherical', P, [theta, phi])
dtheta, dphi = cs.base_oneforms()
ds2 = a ** 2 * (tpow(dtheta, 2) + sympy.sin(theta) ** 2 * tpow(dphi, 2))
g = metric.Metric(twoform=ds2)

# Compute Christoffel Component
curvature.christoffel_symbol_component(0, 1, 0, g)

For more detail on the symbolic utilities, see Tutorial: Symbolic Tools.

API Reference

Indices and tables