Abstract
AbstractMany problems in mathematics and computer science involve summations. We present a procedure that automatically proves equations involving finite summations, inspired by the theory of holonomic sequences. The procedure is designed to be interleaved with the activities of a higher-order automatic theorem prover. It performs an induction and automatically solves the induction step, leaving the base cases to the theorem prover.
Publisher
Springer Nature Switzerland
Reference20 articles.
1. Abramov, S.A., Bronstein, M., Petkovsek, M., Schneider, C.: On rational and hypergeometric solutions of linear ordinary difference equations in $${\Pi }$$$${\Sigma }$$*-field extensions. J. Symb. Comput. 107, 23–66 (2021)
2. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence);H Barbosa,2019
3. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence);A Bhayat,2020
4. Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED. J. Formaliz. Reason. 9(1), 101–148 (2016)
5. Bueso, J., Gómez-Torrecillas, J., Verschoren, A.: Gröbner bases for modules. In: Bueso, J., Gómez-Torrecillas, J., Verschoren, A. (eds.) Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups, pp. 169–202. Springer, Dordrecht (2003). https://doi.org/10.1007/978-94-017-0285-0_5