000165844 001__ 165844 000165844 005__ 20260115140311.0 000165844 0247_ $$2doi$$a10.1016/j.cpc.2008.04.018 000165844 0248_ $$2sideral$$a143322 000165844 037__ $$aART-2008-143322 000165844 041__ $$aeng 000165844 100__ $$aMartín-García, J.M. 000165844 245__ $$aThe Invar tensor package: Differential invariants of Riemann 000165844 260__ $$c2008 000165844 5060_ $$aAccess copy available to the general public$$fUnrestricted 000165844 5203_ $$aThe 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). 000165844 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000165844 590__ $$a2.12$$b2008 000165844 591__ $$aPHYSICS, MATHEMATICAL$$b11 / 46 = 0.239$$c2008$$dQ1$$eT1 000165844 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b18 / 94 = 0.191$$c2008$$dQ1$$eT1 000165844 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000165844 700__ $$0(orcid)0000-0001-7276-2942$$aYllanes, D. 000165844 700__ $$aPortugal, R. 000165844 773__ $$g179, 8 (2008), 586-590$$pComput. phys. commun.$$tCOMPUTER PHYSICS COMMUNICATIONS$$x0010-4655 000165844 8564_ $$s147449$$uhttps://zaguan.unizar.es/record/165844/files/texto_completo.pdf$$yPreprint 000165844 8564_ $$s1420022$$uhttps://zaguan.unizar.es/record/165844/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000165844 909CO $$ooai:zaguan.unizar.es:165844$$particulos$$pdriver 000165844 951__ $$a2026-01-15-12:36:31 000165844 980__ $$aARTICLE