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Desingularization explains order-degree curves for ore operators
TLDR
Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. Expand
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Ore Polynomials in Sage
We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; GCRD and LCLM; D-finite closure properties; naturalExpand
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Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences
TLDR
We extend the class of P-solvable loops with non-trivial arithmetic to include sums and products of hypergeometric and C- nite sequences. Expand
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Invariant Generation for Multi-Path Loops with Polynomial Assignments
TLDR
In this paper we study a class of multi-path program loops with numeric variables, in particular nested loops with conditionals, where assignments to program variables are polynomial expressions over program variables. Expand
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Desingularization of First Order Linear Difference Systems with Rational Function Coefficients
TLDR
We describe two algorithms to (partially) desingularize first order linear difference systems with rational function coefficients. Expand
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Improved polynomial remainder sequences for ore polynomials
TLDR
Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. Expand
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Aligator.jl - A Julia Package for Loop Invariant Generation
TLDR
We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Expand
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Adapting Real Quantifier Elimination Methods for Conflict Set Computation
TLDR
We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice. Expand
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Improved polynomial remainder sequences for Ore polynomials☆
TLDR
Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. Expand
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Formal solutions of completely integrable Pfaffian systems with normal crossings
TLDR
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables using a combination of several reduction techniques. Expand