PMA Publisher: Published from the Principia Machina source

2026-10-15T19:34:17Z

Published from the Principia Machina source

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	'''xAct: Abstract-Index Tensor Computer Algebra for Gravity'''		'''xAct: Abstract-Index Tensor Computer Algebra for Gravity'''
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	* '''[[The Principia Machina/Research Toolkit/Bibliography#XPERM2008\|XPERM2008]]''' – Martín-García J.M. (2008). xPerm: fast index canonicalization for tensor computer algebra. Comput. Phys. Commun. 179(8), 597–603. [https://doi.org/10.1016/j.cpc.2008.05.009 doi:10.1016/j.cpc.2008.05.009].		* '''[[The Principia Machina/Research Toolkit/Bibliography#XPERM2008\|XPERM2008]]''' – Martín-García J.M. (2008). xPerm: fast index canonicalization for tensor computer algebra. Comput. Phys. Commun. 179(8), 597–603. [https://doi.org/10.1016/j.cpc.2008.05.009 doi:10.1016/j.cpc.2008.05.009].
	* '''[[The Principia Machina/Research Toolkit/Bibliography#XACT\|XACT]]''' – Martín-García J.M. et al. (2025). xAct: Efficient tensor computer algebra for the Wolfram Language, v1.3.0. [http://www.xact.es www.xact.es].		* '''[[The Principia Machina/Research Toolkit/Bibliography#XACT\|XACT]]''' – Martín-García J.M. et al. (2025). xAct: Efficient tensor computer algebra for the Wolfram Language, v1.3.0. [http://www.xact.es www.xact.es].

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2026-10-06T03:41:02Z

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DeltaS Zero: Physics tool added 2026-10-06: xAct; scores by the research pass, with references (tpm_toolkit 0.1.0)

2026-10-06T03:40:47Z

Physics tool added 2026-10-06: xAct; scores by the research pass, with references (tpm_toolkit 0.1.0)

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'''xAct: Abstract-Index Tensor Computer Algebra for Gravity'''
[[Category:Principia Machina]] [[Category:Tools]]

''Added to the survey on 2026-10-06 by the [[The Principia Machina/Research Toolkit|Research Toolkit]]'s research pass. The scores below are that pass's assessment from the evidence cited under References, on the survey's four axes and scale; they are not the original survey's (2026-09-26), and no rule of the Principia Machina reads them. See [[The Principia Machina/Tools#The additions of 2026-10-06|the additions]] on the front page.''

== Overview & Architectural Fit ==
'''xAct''' is a suite of packages for tensor computer algebra in the Wolfram Language. Its core (xCore, xPerm, xTensor, xCoba) canonicalizes tensor expressions with their symmetries; around it some 27 packages add perturbation theory (xPert), curvature invariants (Invar), spinors, differential forms (xTerior) and utilities (xTras). It is the reference tensor system of general relativity, and complements Cadabra2.

== Mathematical Evaluation for TPM ==
* '''Lagrangian / Action (7.5/10):''' The standard tool for the step <math>\delta S / \delta g^{\mu\nu}</math>: varying a covariant action, such as <math>S = \frac{1}{16\pi G}\int R\,\sqrt{-g}\,d^4x</math> plus matter, with respect to the metric or the fields; xPert takes the same action to second order. The variational-derivative function names were not re-checked in this pass.
* '''Field / PDE (6/10):''' Derives covariant field and perturbation equations; does no numerics.
* '''Relativity (9.5/10):''' Canonicalization, curvature invariants, perturbation theory and spinors: the reference system for relativity.
* '''Quantum / Data (2.5/10):''' No quantum or data focus.

== Integration Pipeline ==
# '''Declare''' the manifold, the metric and the fields with their index symmetries.
# '''Vary''' the action to get the field equations.
# '''Check identities off shell''': the contracted Bianchi identity <math>\nabla^\mu G_{\mu\nu} = 0</math> and the identities that diffeomorphism invariance implies.
# '''Perturb''' with xPert to second order, <math>S^{(2)}[h]</math>, for stability and the propagating degrees of freedom.
# '''Cross-check''' components against [[The Principia Machina/Tools/SageMath|SageManifolds]], which is free.

== Status, Licence and Limits ==
* '''Status:''' Active. Version 1.3.0, released 29 December 2025.
* '''Licence:''' GPL; the Mathematica host is commercial.
* '''Home:''' http://www.xact.es
* '''Limits:''' Needs a Mathematica licence, which limits who can reproduce a result. High-order perturbations need care with performance and memory. Results depend on declaring index symmetries correctly. xAct's site asks users to cite each package's own paper as well.

== On the Principia Machina ==
A tool runs only where the sponsor installed and bound it, and what it returns is untrusted input, vetted before use; its numbers are never values of the site's calculator, TPC. An equation it derives is transcribed into the kernel's form grammar before anything checks it, and lands as a RESULT of regime L with EQUATION and ROLE. See [[The Principia Machina/Agent/Tools|Agent/Tools]] and [[The Principia Machina/Tools/Operator's guide|the operator's guide]].

== References ==
* '''[[The Principia Machina/Research Toolkit/Bibliography#XPERM2008|XPERM2008]]''' – Martín-García J.M. (2008). xPerm: fast index canonicalization for tensor computer algebra. Comput. Phys. Commun. 179(8), 597–603. [https://doi.org/10.1016/j.cpc.2008.05.009 doi:10.1016/j.cpc.2008.05.009].
* '''[[The Principia Machina/Research Toolkit/Bibliography#XACT|XACT]]''' – Martín-García J.M. et al. (2025). xAct: Efficient tensor computer algebra for the Wolfram Language, v1.3.0. [http://www.xact.es www.xact.es].

The Principia Machina/Tools/xAct - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: Physics tool added 2026-10-06: xAct; scores by the research pass, with references (tpm_toolkit 0.1.0)