Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions

Shaoshi Chen (KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
*Lixin Du (School of Mathematical Sciences University of Chinese Academy of Sciences)
Manuel Kauers (Institute for Algebra, Johannes Kepler University)

Bronstein's lazy Hermite reduction is a symbolic integration technique that reduces algebraic functions to integrands with only simple poles without the prior computation of an integral basis. We sharpen the lazy Hermite reduction by combining it with the polynomial reduction to solve the decomposition problem of algebraic functions. The sharpened reduction is then used to design a reduction-based telescoping algorithm for algebraic functions in two variables.