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Continuous timevarying linear systems
, 1998
"... We discuss implicit systems of ordinary linear differential equations with (time) variable coefficients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called timevarying linear systems or behaviours, from the system theoretic point of view. The ..."
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We discuss implicit systems of ordinary linear differential equations with (time) variable coefficients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called timevarying linear systems or behaviours, from the system theoretic point of view. The basic result, inspired by an analogous one for multidimensional constant linear systems, is a duality theorem which establishes a categorical one–one correspondence between timevarying linear systems or behaviours and finitely generated modules over a suitable skewpolynomial ring of differential operators. This theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic (hyper)functions or of distributions on R. It is used to obtain various results on key notions of linear system theory. Several new algorithms for modules over rings of differential operators and, in particular, new Gröbner basis algorithms due to Insa and Pauer make the system
R.: Noetherian Quotient of the Algebra of Partial Difference Polynomials and Gröbner Bases of Symmetric Ideals
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IOS Press Computing Properties of Numerical Imperative Programs by Symbolic Computation
"... Abstract. We show how properties of an interesting class of imperative programs can be calculated by means of relational modeling and symbolic computation. The ideas of [5, 26] are implemented using symbolic computations based on Maple [30]. ..."
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Abstract. We show how properties of an interesting class of imperative programs can be calculated by means of relational modeling and symbolic computation. The ideas of [5, 26] are implemented using symbolic computations based on Maple [30].
5.2. Library OreModules of Mgfun 5 5.3. Library libaldor 6 5.4. Library Algebra 6
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1 Reverse engineering of holonomic functions and sequences from imperative scientific computation code
, 2006
"... www.cas.mcmaster.ca/˜carette Given some imperative code which either computes terms from a holonomic sequence, or an approximation to a holonomic function via truncated Taylor series, we would like to know exactly which sequence or function we are dealing with. We present a method to solve this prob ..."
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www.cas.mcmaster.ca/˜carette Given some imperative code which either computes terms from a holonomic sequence, or an approximation to a holonomic function via truncated Taylor series, we would like to know exactly which sequence or function we are dealing with. We present a method to solve this problem. Leveraging a lot of work in finding closedforms solutions to recurrence equations, we have a prototype which will find a closedform (whenever possible) for such code. Many examples are provided which to show the variety of situations where our method is applicable.