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 b  
    1212Algorithm
    1313---------
    1414
    15 We use Hunter's algorithm ([C]_, Section 9.3) with modifications
    16 due to Takeuchi [T]_ and the author [V]_.
     15We use Hunter's algorithm ([Cohen2000]_, Section 9.3) with modifications
     16due to Takeuchi [Takeuchi1999]_ and the author [Voight2008]_.
    1717
    1818We enumerate polynomials `f(x) = x^n + a_{n-1} x^{n-1} + \dots + a_0`.   
    1919Hunter's theorem gives bounds on `a_{n-1}` and `a_{n-2}`; then given
    2020`a_{n-1}` and `a_{n-2}`, one can recursively compute bounds on `a_{n-3},
    2121\dots, a_0`, using the fact that the polynomial is totally real by
    2222looking at the zeros of successive derivatives and applying
    23 Rolle's theorem. See [T]_ for more details.
     23Rolle's theorem. See [Takeuchi1999]_ for more details.
    2424
    2525Examples
    2626--------
     
    6868References
    6969----------
    7070   
    71 .. [C] Henri Cohen, Advanced topics in computational number
     71.. [Cohen2000] Henri Cohen, Advanced topics in computational number
    7272   theory, Graduate Texts in Mathematics, vol. 193,
    7373   Springer-Verlag, New York, 2000.
    7474
    75 .. [M] Jacques Martinet, Petits discriminants des corps de nombres, Journ. Arithm. 1980,
     75.. [Martinet1980] Jacques Martinet, Petits discriminants des corps de nombres, Journ. Arithm. 1980,
    7676   Cambridge Univ. Press, 1982, 151--193.       
    7777
    78 .. [T] Kisao Takeuchi, Totally real algebraic number fields of
     78.. [Takeuchi1999] Kisao Takeuchi, Totally real algebraic number fields of
    7979   degree 9 with small discriminant, Saitama Math. J.
    8080   17 (1999), 63--85 (2000).
    8181       
    82 .. [V] John Voight, Enumeration of totally real number fields
    83    of bounded root discriminant, to appear in
    84    Lect. Notes in Comp. Sci.
     82.. [Voight2008] John Voight, Enumeration of totally real number fields of bounded root
     83   discriminant, Lect. Notes in Comp. Sci. 5011 (2008).
    8584
    8685Authors
    8786-------
     
    165164    - John Voight (2007-09-03)
    166165
    167166    NOTES:
    168     The values are calculated by Martinet [M]_.
     167    The values are calculated by Martinet [Martinet1980]_.
    169168    """
    170169
    171170    if n <= 10: