The Structure of Polynomial Invariants of Linear Loops

Autor:	M. S. Lvov
Rok vydání:	2015
Předmět:	Algebra Linear map Polynomial General Computer Science Invariant polynomial Operator (physics) Diagonalizable matrix Invariants of tensors Bracket polynomial Mathematics Characteristic polynomial
Zdroj:	Cybernetics and Systems Analysis. 51:448-460
ISSN:	1573-8337 1060-0396
DOI:	10.1007/s10559-015-9736-7
Popis:	This article considers the problem of generating polynomial invariants for iterative loops with loop initialization statements and nonsingular linear operators in loop bodies. The set of such invariants forms an ideal in the ring of polynomials in the loop variables. Two algorithms are presented one of which calculates basic invariants for a linear operator in the form of a Jordan cell and the other calculates basic invariants for a diagonalizable linear operator with an irreducible minimal characteristic polynomial. The following theorem on the structure of the basis of the ideal of invariants for such an operator is proved: this basis consists of basic invariants of Jordan cells and basic invariants of the diagonalizable part of the linear operator being considered.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9b30ba8a72113b803cc3c094c00ba79f https://doi.org/10.1007/s10559-015-9736-7 Zobrazit plný text záznamu Full text from SpringerLink