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