165844 20260115140311.0 doi 10.1016/j.cpc.2008.04.018 sideral 143322 ART-2008-143322 eng Martín-García, J.M. The Invar tensor package: Differential invariants of Riemann 2008 The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple). Access copy available to the general public Unrestricted info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.12 2008 PHYSICS, MATHEMATICAL 11 / 46 = 0.239 2008 Q1 T1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS 18 / 94 = 0.191 2008 Q1 T1 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion Yllanes, D. (orcid)0000-0001-7276-2942 Portugal, R. 179, 8 (2008), 586-590 Comput. phys. commun. COMPUTER PHYSICS COMMUNICATIONS 0010-4655 147449 http://zaguan.unizar.es/record/165844/files/texto_completo.pdf Preprint 1420022 http://zaguan.unizar.es/record/165844/files/texto_completo.jpg?subformat=icon icon Preprint oai:zaguan.unizar.es:165844 articulos driver 2026-01-15-12:36:31 ARTICLE