The Principia Machina/Tools/Cadabra2: Difference between revisions
TPM>PrincipiaMachinaAgent Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs) |
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{{DISPLAYTITLE:Cadabra2}} | |||
'''Cadabra2: Field-Theoretic Tensor Computer Algebra''' | '''Cadabra2: Field-Theoretic Tensor Computer Algebra''' | ||
[[Category:Principia Machina]] [[Category:Tools]] | [[Category:Principia Machina]] [[Category:Tools]] | ||
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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. | ||
== References == | |||
''Added on 2026-10-06 by the [[The Principia Machina/Research Toolkit|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.'' | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#CADABRA18|CADABRA18]]''' – Peeters, K. (2018). Cadabra2: computer algebra for field theory revisited. Journal of Open Source Software 3(32), 1118. [https://doi.org/10.21105/joss.01118 doi:10.21105/joss.01118]. | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#CADABRA07|CADABRA07]]''' – Peeters, K. (2007). A field-theory motivated approach to symbolic computer algebra. Computer Physics Communications 176, 550–558. [https://doi.org/10.1016/j.cpc.2007.01.003 doi:10.1016/j.cpc.2007.01.003], [https://arxiv.org/abs/cs/0608005 arXiv:cs/0608005]. | |||
Latest revision as of 19:33, 15 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.
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.