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:

$$\frac{\delta S}{\delta \phi_i} = 0$$ 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 $\mathcal{L}$ invariant under global or local gauge transformations yields conserved Noether currents.