Cadabra

Cadabra handles tensor algebra using TeX-like expressions and Python-directed transformations. Its quick start declares index sets before a substitution that needs fresh dummy indices, then uses declared antisymmetry to canonicalise an expression. Properties are needed when a manipulation depends on them; entering every tensor does not require a full manifold setup. The underscore refers to the last-used expression. Derivative symbols and implicit dependencies also need the appropriate properties so the system can distinguish derivative behavior. This explicit control suits field-theory calculations involving symmetry or non-commuting objects. The GPLv3 project offers native notebooks, command-line and Jupyter routes. The homepage's cloud service requires contacting the project for access, and its dated notebook release notes include Jupyter export rather than establishing universal hosted availability.