Titlebook: Symbolic Integration I; Transcendental Funct Manuel Bronstein Book 19971st edition Springer-Verlag Berlin Heidelberg 1997 Subresultanten.Sy

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The Coupled Differential System,., .. in ., to decide whether the system of equations . has a solution in . × ., and to find one if there are some. It turns out that (8.1) is not really a second order equation, but the coupled system for the real and imaginary parts of a Risch differential equation. Indeed, suppose that (.., ..) ∈

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Differential Fields,ction can be seen as a univariate rational function over a field with an arbitrary derivation, we first need to study the general properties of derivations over rings and fields. This will allow us to generalize the rational function integration algorithms to large classes of transcendental functions (Chap. 5).

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