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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents Koutschan, Christoph 4 results

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Algorithmic methods for enumerative combinatorics - lecture 1 - Koutschan, Christoph (Author of the conference) | CIRM H

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We showcase several algorithmic methods that can assist in solving combinatorial problems. Such algorithms include recurrence guessing, closure properties for D-finite functions, creative telescoping, or cylindrical algebraic decomposition, which are implemented in many today's computer algebra systems. We demonstrate with numerous examples how these can be applied beneficially in the context of enumerative combinatorics.

05A19 ; 05A20 ; 47L20 ; 68W30

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Algorithmic methods for enumerative combinatorics - lecture 2 - Koutschan, Christoph (Author of the conference) | CIRM H

Multi angle

We showcase several algorithmic methods that can assist in solving combinatorial problems. Such algorithms include recurrence guessing, closure properties for D-finite functions, creative telescoping, or cylindrical algebraic decomposition, which are implemented in many today's computer algebra systems. We demonstrate with numerous examples how these can be applied beneficially in the context of enumerative combinatorics.

05A19 ; 05A20 ; 47L20 ; 68W30

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Creative telescoping for D-finite functions - Lecture 1 - Koutschan, Christoph (Author of the conference) | CIRM H

Multi angle

D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions from combinatorics, etc. Whenever one wishes to study the integral or the sum of a D-finite function, the method of creative telescoping may be applied. This method has been systematically introduced by Zeilberger in the 1990s, and since then has found applications in various different domains. In this lecture, we explain the underlying theory, review some of the history and talk about some recent developments in this area.[-]
D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions from combinatorics, etc. Whenever one wishes to study the integral or the sum of a D-finite function, the method of creative telescoping may be applied. This method has been s...[+]

68W30 ; 47L20

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Creative telescoping for D-finite functions - Lecture 2 - Koutschan, Christoph (Author of the conference) | CIRM H

Multi angle

D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions from combinatorics, etc. Whenever one wishes to study the integral or the sum of a D-finite function, the method of creative telescoping may be applied. This method has been systematically introduced by Zeilberger in the 1990s, and since then has found applications in various different domains. In this lecture, we explain the underlying theory, review some of the history and talk about some recent developments in this area.[-]
D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions from combinatorics, etc. Whenever one wishes to study the integral or the sum of a D-finite function, the method of creative telescoping may be applied. This method has been s...[+]

68W30 ; 47L20

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