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Bronstein's lazy Hermite reduction is a symbolic integration technique thatreduces algebraic functions to integrands with only simple poles without theprior computation of an integral basis. We sharpen the lazy Hermite reductionby combining it with the polynomial reduction to solve the decompositionproblem of algebraic functions. The sharpened reduction is then used to designa reduction-based telescoping algorithm for algebraic functions in twovariables.

Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions