References

1. S.A. Abramov. [Indefinite sums of rational functions.](https://dl.acm.org/doi/10.1145/220346.220386) *Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 1995: 303-308.

2. A. Bostan, S. Chen,  F. Chyzak and Z. Li. [Complexity of creative telescoping for bivariate rational functions.](https://dl.acm.org/doi/10.1145/1837934.1837975) *Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 2010: 203-210.

3. A. Bostan, S. Chen, F. Chyzak,  Z. Li and G. Xin. [Hermite reduction and creative telescoping for hyperexponential functions.](https://arxiv.org/abs/1301.5038) *Proceedings of the 2013 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 2013: 77-84.

4. A. Bostan, F. Chyzak, P. Lairez and B.Salvy. [Generalized Hermite reduction, creative telescoping and
definite integration of D-finite functions.](https://doi.org/10.1145/3208976.3208992) *Proceedings of the 2018 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 2018: 95-102.

5. M. Bronstein. [*Symbolic Integration I: transcendental functions.*](https://www.springer.com/gp/book/9783662033869) Berlin: Springer-Verlag, 2005.

6. S. Chen, H. Du and Z. Li. [Additive decompositions in primitive extensions.](https://arxiv.org/abs/1802.02329) *Proceedings of the 2018 International Symposium on Symbolic and Algebraic Computation.* New York, USA: ACM, 135-142.

7. S. Chen, M. van Hoeij, M. Kauers and C. Koutschan. [Reduction-based creative telescoping for Fuchsian D-finite functions.](https://dl.acm.org/doi/10.1145/2930889.2930901) *Journal of Symbolic Computation,* 2018, 85:108-127.

8. S. Chen, H. Huang, M. Kauers and Z. Li. [A modified Abramov-Petkovšek reduction and creative telescoping for hypergeometric terms.](https://dl.acm.org/doi/10.1145/2755996.2756648) *Proceedings of the 2015 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 2015: 117-124.

9. S. Chen, M. Kauers and C. Koutschan. [Reduction-based creative telescoping for algebraic functions.](https://dl.acm.org/doi/10.1145/2930889.2930901) *Proceedings of the 2016 International Symposium on Symbolic and Algebraic Computation.* New York, NY, USA: ACM, 2016: 175-182.

10. D. Cox, J. Little, and D. O'Shea. [*Ideals, Varieties and Algorithms.*](https://www.springer.com/gp/book/9783319167206) Fourth Edition, Springer, 2015.

11. H. Du, H. Huang and Z. Li. [A q-analogue of the modified Abramov-Petkovšek reduction.](https://link.springer.com/chapter/10.1007/978-3-319-73232-9_5) *Advances in Computer Algebra.* S. Schneider and C. Zima (eds.) Springer International Publishing, 2018: 105-129.

12. C. Hermite. [Sur l'intégration des fractions rationnelles.](http://www.numdam.org/item/NAM_1872_2_11__145_0/) *Ann. Sci. École Norm. Sup.(2),* 1872(1): 215-218.

13. M. V. Ostrogradsky. De l'intégration des fractions rationnelles. *Bull. de la classe physico-mathématique de l'Acad. Impériale des Sciences de Saint-Pétersbourg,* 1845, 4: 145-167, 286-300.

14. C. Raab. [Definite Integration in Differential Fields.](http://www3.risc.jku.at/publications/download/risc_4583/PhD_CGR.pdf) PhD thesis, RISC, Johannes Kepler University, Linz, Austria, 2012.

15. M. Singer, S. David and B. Caviness. [An extension of Liouville’s theorem on integration in finite terms.](https://dl.acm.org/doi/10.1145/800206.806366) *SIAM J. Comput.* 1985, 14: 966-990.

16. J. van der Hoeven. [Constructing reductions for creative telescoping.](https://link.springer.com/article/10.1007%2Fs00200-020-00413-3) *AAECC.* 2020.

17. O. Zariski and P. Samuel. [*Commutative Algebra I.*](https://www.springer.com/gp/book/9780387900896) Graduate Texts in Mathematics, Springer, 1975.