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We describe algorithm Hyper which can be used to find all hypergeometric solutions of linear recurrences with polynomial coefficients. 1. Introduction Let K be a field of characteristic zero. We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations. Let K(More)
Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling(More)
We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. On the basis of this form we propose an algorithm which, given a rational function R, extracts a rational part F from the product of consecutive values of R: n−1 k=n 0 R(k) = F (n) n−1 k=n 0 V (k) where the(More)
1 Introduction Let K be a field of characteristic O and L : K[Z]-+ K[Z] an endomorphism of the K-linear space of univariate poly-nomials over K. We consider the following computational tasks concerning L: Tl, T2< T3. Homogeneous equation Ly = O: Compute a basis of Ker L in K[z]. Inhomogeneous equation Ly = f: Given ~ 6 K[z], compute a basis of the affine(More)
While in the univariate case solutions of linear recurrences with constant coeecients have rational generating functions, we show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-nite but not(More)
We present an algorithm which, given a hypergeometric term <i>T</i>(<i>n</i>), constructs hypergeometric terms <i>T</i><subscrpt>1</subscrpt>(<i>n</i>) and <i>T</i><subscrpt>2</subscrpt>(<i>n</i>) such that <i>T</i>(<i>n</i>) = <i>T</i><subscrpt>1</subscrpt>(<i>n</i> + 1) -<i>T</i><subscrpt>1</subscrpt>(<i>n</i>) + <i>T</i><subscrpt>2</subscrpt>(<i>n</i>),(More)
D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals (resp. sums) of hyperexponential functions. They are a subclass of Liouvillian solutions, and can be constructed by recursively finding hyperexponential solutions and reducing the order. Knowing d'Alembertian solutions of <italic>Ly =(More)
We consider planar lattice walks that start from a prescribed position, take their steps in a given finite subset of Z 2 , and always stay in the quadrant x ≥ 0, y ≥ 0. We first give a criterion which guarantees that the length generating function of these walks is D-finite, that is, satisfies a linear differential equation with polynomial coefficients.(More)
Electropermeabilization is a phenomenon that transiently increases permeability of the cell plasma membrane. In the state of high permeability, the plasma membrane allows ions, small and large molecules to be introduced into the cytoplasm, although the cell plasma membrane represents a considerable barrier for them in its normal state. Besides introduction(More)