The Principia Machina/Tools/Cadabra2

Cadabra2: Field-Theoretic Tensor Computer Algebra

Overview & Architectural Fit

Cadabra2 is a field-theoretic computer algebra system specifically designed for tensor calculus, field theory, differential geometry, and variational action principles.

Mathematical Evaluation for TPM & SVD

• Action Functional Variation (9.5/10): Natively evaluates functional action derivatives:

$$\frac{\delta S}{\delta {\varphi }_i}=0$$ for multi-field Lagrangians containing continuous scalar, vector, and tensor quantities.

• Covariant & Contravariant Tensor Algebra: Handles implicit index contractions, Riemann curvature tensors, Ricci scalars, Gamma matrices, and non-commuting Grassmann algebras.
• Noether Symmetry Evaluation: Automatically verifies whether a continuous candidate Lagrangian density $ℒ$ invariant under global or local gauge transformations yields conserved Noether currents.

References

Added on 2026-10-06 by the Research Toolkit: the tool's citations, each checked against the registry or the project's own page that day. The text above is the survey's own.

• CADABRA18 – Peeters, K. (2018). Cadabra2: computer algebra for field theory revisited. Journal of Open Source Software 3(32), 1118. doi:10.21105/joss.01118.
• CADABRA07 – Peeters, K. (2007). A field-theory motivated approach to symbolic computer algebra. Computer Physics Communications 176, 550–558. doi:10.1016/j.cpc.2007.01.003, arXiv:cs/0608005.