# Ticket #9359: trac_9359-docfix.patch

File trac_9359-docfix.patch, 2.4 KB (added by David Loeffler, 12 years ago)

fix duplicate citation

• ## sage/rings/number_field/totallyreal.pyx

# HG changeset patch
# User David Loeffler <d.loeffler.01@cantab.net>
# Date 1285673392 -3600
# Node ID 62945bccdb3bbeb4531b7d7ac63668491a4e2e76
# Parent  ae11a4bd7bec1c4f77bd1e7cf64fde8745d9ba36
#9359: fix duplicate citations in reference manual

diff -r ae11a4bd7bec -r 62945bccdb3b sage/rings/number_field/totallyreal.pyx
 a Algorithm --------- We use Hunter's algorithm ([C]_, Section 9.3) with modifications due to Takeuchi [T]_ and the author [V]_. We use Hunter's algorithm ([Cohen2000]_, Section 9.3) with modifications due to Takeuchi [Takeuchi1999]_ and the author [Voight2008]_. We enumerate polynomials `f(x) = x^n + a_{n-1} x^{n-1} + \dots + a_0`. Hunter's theorem gives bounds on `a_{n-1}` and `a_{n-2}`; then given `a_{n-1}` and `a_{n-2}`, one can recursively compute bounds on `a_{n-3}, \dots, a_0`, using the fact that the polynomial is totally real by looking at the zeros of successive derivatives and applying Rolle's theorem. See [T]_ for more details. Rolle's theorem. See [Takeuchi1999]_ for more details. Examples -------- References ---------- .. [C] Henri Cohen, Advanced topics in computational number .. [Cohen2000] Henri Cohen, Advanced topics in computational number theory, Graduate Texts in Mathematics, vol. 193, Springer-Verlag, New York, 2000. .. [M] Jacques Martinet, Petits discriminants des corps de nombres, Journ. Arithm. 1980, .. [Martinet1980] Jacques Martinet, Petits discriminants des corps de nombres, Journ. Arithm. 1980, Cambridge Univ. Press, 1982, 151--193. .. [T] Kisao Takeuchi, Totally real algebraic number fields of .. [Takeuchi1999] Kisao Takeuchi, Totally real algebraic number fields of degree 9 with small discriminant, Saitama Math. J. 17 (1999), 63--85 (2000). .. [V] John Voight, Enumeration of totally real number fields of bounded root discriminant, to appear in Lect. Notes in Comp. Sci. .. [Voight2008] John Voight, Enumeration of totally real number fields of bounded root discriminant, Lect. Notes in Comp. Sci. 5011 (2008). Authors ------- - John Voight (2007-09-03) NOTES: The values are calculated by Martinet [M]_. The values are calculated by Martinet [Martinet1980]_. """ if n <= 10: