  We introduce a new, open-source computational general relativity framework
for the Wolfram Language called Gravitas, which boasts a number of novel and
distinctive features as compared to the many pre-existing computational and
numerical relativity frameworks currently available within the open-source
community. These include, but are not limited to: seamless integration of its
powerful symbolic and numerical subsystems, and, by extension, seamless
transition between analytic/continuous representations and numerical/discrete
representations of arbitrary spacetime geometries; highly modular, general and
extensible representations of spacetime geometries, spacetime topologies, gauge
conditions, coordinate systems, matter fields, evolution equations and initial
data; ability to set up and run complex numerical relativity simulations, and
to perform 2D and 3D visualizations, symbolic computations and numerical
analysis (including the extraction of gravitational wave signals) on the
resulting data, all from within a single notebook environment; and a
totally-unstructured adaptive refinement scheme based on hypergraph rewriting,
allowing for exceedingly efficient discretization and numerical evolution of
Cauchy initial data for a wide range of challenging computational problems
involving strong relativistic field dynamics. In this first in a series of two
articles covering the framework, we focus on the design and capabilities of
Gravitas's symbolic subsystem, including its general and flexible handling of
arbitrary geometries parametrized by arbitrary curvilinear coordinate systems
(along with an in-built library of standard metrics and coordinate conditions),
as well as its various high-level tensor calculus and differential geometry
features. We proceed to show how this subsystem can be used to solve the
Einstein field equations both analytically and numerically.
