Distance invariant method for normalization of indexed differentials. (May 2021)

• Record Type: Journal Article
• Authors: Liu, Jiang; Ni, Feng
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 256
• Page End: 275
• Publication Date: 2021-05
• Subjects: nD symbolic computation -- Einstein summation convention -- Canonical form -- Mechanical theorem proving; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.05.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A distance from free to dummy indices is defined. The distance is invariant with respect to both monoterm symmetries and bottom antisymmetry. Using the distance invariant, we present an index-replacement algorithm. We then develop two normalization algorithms. One is with respect to monoterm symmetries and has complexity lower than known algorithms; the other allows one to determine the equivalence of indexed polynomials in the Einstein summation ring R 2 [ ∂̸ ] .