Download e-book for iPad: Algebraic and Algorithmic Aspects of Differential and by Moulay Barkatou, Thomas Cluzeau, Georg Regensburger, Markus

By Moulay Barkatou, Thomas Cluzeau, Georg Regensburger, Markus Rosenkranz (eds.)

ISBN-10: 3642544789

ISBN-13: 9783642544781

ISBN-10: 3642544797

ISBN-13: 9783642544798

This ebook constitutes the court cases of the fifth overseas assembly on Algebraic and Algorithmic features of Differential and fundamental Operators, AADIOS 2012, held on the purposes of machine Algebra convention in Sofia, Bulgaria, on June 25-28, 2012. the complete of nine papers offered during this quantity comprises 2 invited papers and seven ordinary papers that have been conscientiously reviewed and chosen from thirteen submissions. the subjects of curiosity are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary difficulties and green's operators, preliminary worth difficulties for differential equations, symbolic integration and differential galois concept, symbolic operator calculi, algorithmic D-module idea, rota-baxter algebra, differential algebra, in addition to discrete analogs and software program elements of the above.

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Additional info for Algebraic and Algorithmic Aspects of Differential and Integral Operators: 5th International Meeting, AADIOS 2012, Held at the Applications of Computer Algebra Conference, ACA 2012, Sofia, Bulgaria, June 25-28, 2012, Selected and Invited Papers

Example text

4 Matrices and Structure of Modules . . . . . . . . . . . . . 5 The Structure of a Finitely Generated Module . . . . . . . . Diagonalization. . . . . . . . . . . . . . . . . . . . . . Krull-Schmidt Theorem and Elementary Divisors. . . . . . . Jacobson Normal Form and Invariant Factors. . . . . . . . . 3 Left PBW Rings . . . . . . . . . . . . . . . . . . . . . . . . 1 (Left) PBW Rings . . . . . . .

Diagonalization. . . . . . . . . . . . . . . . . . . . . . Krull-Schmidt Theorem and Elementary Divisors. . . . . . . Jacobson Normal Form and Invariant Factors. . . . . . . . . 3 Left PBW Rings . . . . . . . . . . . . . . . . . . . . . . . . 1 (Left) PBW Rings . . . . . . . . . . . . . . . . . . . . . 2 Differential and Difference Operator Rings . . . . . . . . . . 4 Algorithms for Modules over a Left PBW Ring .

Conversely, an abelian group M with a map R × M → M that sends each (r, m) ∈ R × M to some element of M , denoted by rm, and satisfying the properties above, gives a homomorphism of rings λ : R → End(M ), by means of the rule λ(r)(m) := rm, which makes M a left R-module. Definition 1 stresses the fact that elements of a ring R are interpreted as linear operators on any left R-module. We sometimes write R M to emphasize the left action of R on M . A right R-module is, by definition, a left module over Rop .

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Algebraic and Algorithmic Aspects of Differential and Integral Operators: 5th International Meeting, AADIOS 2012, Held at the Applications of Computer Algebra Conference, ACA 2012, Sofia, Bulgaria, June 25-28, 2012, Selected and Invited Papers by Moulay Barkatou, Thomas Cluzeau, Georg Regensburger, Markus Rosenkranz (eds.)


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