.. _bibliography:

Bibliography
================================================================================

(In the PDF edition, this section is empty. See the bibliography listing at the end of the document.)

All referenced works: [BBK2014]_, [BF2020]_, [BFSS2006]_, [Boe2020]_, [Car2004]_, [Cho1999]_, [Coh1996]_, [Coh2000]_, [Fie2007]_, [GCL1992]_, [Har2010]_, [Har2015]_, [Har2018]_, [Joh2017]_, [JR1999]_, [Mos1971]_, [MP2006]_, [RF1994]_, [Ric1992]_, [Ric1995]_, [Ric1997]_, [Ric2007]_, [Ric2009]_, [Ste2002]_, [Ste2010]_, [Str1997]_, [Str2012]_, [vdH1995]_, [vdH2006]_, [vHP2012]_, [Zip1985]_.

.. [BBK2014] \D. H. Bailey, J. M. Borwein and A. D. Kaiser. "Automated simplification of large symbolic expressions". Journal of Symbolic Computation Volume 60, January 2014, Pages 120-136. https://doi.org/10.1016/j.jsc.2013.09.001

.. [BF2020] \F. Beukers and J. Forsgård. "Gamma-evaluations of hypergeometric series". Preprint, 2020. https://arxiv.org/abs/2004.08117

.. [BFSS2006] \A. Bostan, P. Flajolet, B. Salvy and É. Schost. "Fast computation of special resultants". Journal of Symbolic Computation, 41(1):1–29, January 2006. https://doi.org/10.1016/j.jsc.2005.07.001

.. [Boe2020] \H. Boehm. "Towards an API for the real numbers". PLDI 2020: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, June 2020, Pages 562-576. https://doi.org/10.1145/3385412.3386037

.. [Car2004] \J. Carette. "Understanding expression simplification." ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation, pp. 72-79. 2004. https://doi.org/10.1145/1005285.1005298

.. [Cho1999] \T. Chow. "What is a closed-form number?". The American Mathematical Monthly Volume 106, 1999 - Issue 5. https://doi.org/10.1080/00029890.1999.12005066

.. [Coh1996] \H. Cohen. *A course in computational algebraic number theory*. Third edition, Springer, 1996. https://doi.org/10.1007/978-3-662-02945-9

.. [Coh2000] \H. Cohen. *Advanced topics in computational number theory*. Springer, 2000. https://doi.org/10.1007/978-1-4419-8489-0

.. [Fie2007] \C. Fieker, "Sparse representation for cyclotomic fields". Experiment. Math. Volume 16, Issue 4 (2007), 493-500. https://doi.org/10.1080/10586458.2007.10129012

.. [GCL1992] \K. O. Geddes, S. R. Czapor and G. Labahn. *Algorithms for computer algebra*. Springer, 1992. https://doi.org/10.1007/b102438

.. [Har2010] \W. B. Hart. "Fast library for number theory: an introduction." International Congress on Mathematical Software. Springer, Berlin, Heidelberg, 2010. https://doi.org/10.1007/978-3-642-15582-6_18

.. [Har2015] \W. B. Hart. "ANTIC: Algebraic number theory in C". Computeralgebra-Rundbrief: Vol. 56, 2015

.. [Har2018] \W. B. Hart. "Algebraic number theory". Unpublished manuscript, 2018.

.. [Joh2017] \F. Johansson. "Arb: efficient arbitrary-precision midpoint-radius interval arithmetic". IEEE Transactions on Computers, vol 66, issue 8, 2017, pp. 1281-1292. https://doi.org/10.1109/TC.2017.2690633

.. [JR1999] \D. Jeffrey and A. D. Rich. "Simplifying square roots of square roots by denesting". Computer Algebra Systems: A Practical Guide, M.J. Wester, Ed., Wiley 1999.

.. [MP2006] \M. Monagan and R. Pearce. "Rational simplification modulo a polynomial ideal". Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06. https://doi.org/10.1145/1145768.1145809

.. [Mos1971] \J. Moses. "Algebraic simplification - a guide for the perplexed". Proceedings of the second ACM symposium on Symbolic and algebraic manipulation (1971), 282-304. https://doi.org/10.1145/362637.362648

.. [RF1994] \D. Richardson and J. Fitch. "The identity problem for elementary functions and constants". ISSAC '94: Proceedings of the international symposium on Symbolic and algebraic computation, August 1994, 285-290. https://doi.org/10.1145/190347.190429

.. [Ric1992] \D. Richardson. "The elementary constant problem". ISSAC '92: Papers from the international symposium on Symbolic and algebraic computation, August 1992, 108-116. https://doi.org/10.1145/143242.143284

.. [Ric1995] \D. Richardson. "A simplified method of recognizing zero among elementary constants". ISSAC '95: Proceedings of the 1995 international symposium on Symbolic and algebraic computation, April 1995, 104-109. https://doi.org/10.1145/220346.220360

.. [Ric1997] \D. Richardson. "How to recognize zero". Journal of Symbolic Computation 24.6 (1997): 627-645. https://doi.org/10.1006/jsco.1997.0157

.. [Ric2007] \D. Richardson. "Zero tests for constants in simple scientific computation". Mathematics in Computer Science volume 1, pages 21-37 (2007). https://doi.org/10.1007/s11786-007-0002-x

.. [Ric2009] \D. Richardson. "Recognising zero among implicitly defined elementary numbers". Preprint, 2009.

.. [Ste2002] \A. Steel. "A new scheme for computing with algebraically closed fields". In: Fieker C., Kohel D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_38

.. [Ste2010] \A. Steel. "Computing with algebraically closed fields". Journal of Symbolic Computation 45 (2010) 342-372. https://doi.org/10.1016/j.jsc.2009.09.005

.. [Str1997] \A. Strzebonski. "Computing in the field of complex algebraic numbers". Journal of Symbolic Computation (1997) 24, 647-656. https://doi.org/10.1006/jsco.1997.0158

.. [Str2012] \A. Strzebonski. "Real root isolation for exp-log-arctan functions". Journal of Symbolic Computation 47 (2012) 282–314. https://doi.org/10.1016/j.jsc.2011.11.004

.. [vHP2012] \M. van Hoeij and V. Pal. "Isomorphisms of algebraic number fields". Journal de Théorie des Nombres de Bordeaux, Vol. 24, No. 2 (2012), pp. 293-305. https://doi.org/10.2307/43973105

.. [vdH1995] \J. van der Hoeven, "Automatic numerical expansions". Proc. of the conference Real numbers and computers (1995), 261-274. https://www.texmacs.org/joris/ane/ane-abs.html

.. [vdH2006] \J. van der Hoeven, "Computations with effective real numbers". Theoretical Computer Science, Volume 351, Issue 1, 14 February 2006, Pages 52-60. https://doi.org/10.1016/j.tcs.2005.09.060

.. [Zip1985] \R. Zippel. "Simplification of expressions involving radicals". Journal of Symbolic Computation (1985) 1, 189-210. https://doi.org/10.1016/S0747-7171(85)80014-6

