Hypergeometric polynomials and integer programming
TL;DR: In this paper, a hypergeometric sensitivity analysis for small variations of constraint constants with creation operators and -functions is presented. But the sensitivity analysis is restricted to the case of -hypergeometric differential equations.
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Abstract: We examine connections between -hypergeometric differential equations and the theory of integer programming. In the first part, we develop a 'hypergeometric sensitivity analysis' for small variations of constraint constants with creation operators and -functions. In the second part, we study the indicial polynomial ( -function) along the hyperplane 0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gr ¨ bases are used to prove theorems and give counter examples.
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HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4.
Vladimir V. Bytev,Vladimir V. Bytev,Mikhail Yu. Kalmykov,Mikhail Yu. Kalmykov,Bernd A. Kniehl +4 more
TL;DR: The current version ofHYPERDIRE includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulation with Appell hypergeometry functions F_1, F_2,F_3,F-4 of two variables.
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Isomorphism Classes of A-Hypergeometric Systems
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The A-hypergeometric System Associated with a Monomial Curve
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Macaulay matrix for Feynman integrals: linear relations and intersection numbers
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References
Ideals, Varieties, and Algorithms
TL;DR: In the Groebner package, the most commonly used commands are NormalForm, for doing the division algorithm, and Basis, for computing a Groebners basis as mentioned in this paper. But these commands require a large number of variables.
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Discriminants, Resultants, and Multidimensional Determinants
Izrailʹ Moiseevich Gelʹfand,Mikhail Kapranov,Andrei Zelevinsky +2 more
- 10 May 2013
TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.
3.1K
•Book
Gröbner bases and convex polytopes
Bernd Sturmfels
- 14 Dec 1995
TL;DR: Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The second hypersimplex $\mathcal A$-graded algebras Canonical subalgebra bases Generators, Betti numbers and localizations Toric varieties in algebraic geometry as mentioned in this paper.
1.9K
•Book
Using Algebraic Geometry
David A. Cox,John Little,Donal O'Shea +2 more
- 01 Jan 1998
TL;DR: The Berlekamp-Massey-Sakata Decoding Algorithm is used for solving Polynomial Equations and for computations in Local Rings.