The Principia Machina/Tools/Cadabra2: Difference between revisions
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== Mathematical Evaluation for TPM & SVD == | == Mathematical Evaluation for TPM & SVD == | ||
* '''Action Functional Variation (9.5/10):''' Natively evaluates functional action derivatives: | * '''Action Functional Variation (9.5/10):''' Natively evaluates functional action derivatives: | ||
<math display="block">\frac{\delta S}{\delta \phi_i} = 0</math> | |||
for multi-field Lagrangians containing continuous scalar, vector, and tensor quantities. | 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. | * '''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 | * '''Noether Symmetry Evaluation:''' Automatically verifies whether a continuous candidate Lagrangian density <math>\mathcal{L}</math> invariant under global or local gauge transformations yields conserved Noether currents. | ||
Revision as of 00:59, 6 October 2026
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:
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 invariant under global or local gauge transformations yields conserved Noether currents.