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The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference inDuluth, 1983, where one of the a...
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We pres...
J.Ritt [1] has investigated the structure of complex polynomials with respect to superposition. The polynomial P(x) is said to be indecomposable iff the representation P = P1 ◦ P2 means that e...
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F be the corresponding free...
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger’s framework of (differential) creative telescoping. Our c...
INTRODUCTION.Itisthepurposeofthispapertopresentsomeresults,ontheproblemofinterpolationandapproximationtoafunctiouf(z),analyticonaclosedlimitedpointsetEinthecomplexz-planewhosecomplementKisconnectedand...
We show that the uniqueness of the Gosper-Petkov·sek representation of rational func- tions can be utilized to give a simpler version of Gosper's algorithm. This approach also applies to Petkov·sek's ...

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