Ticket #8184: trac_8184-indentation.patch

File trac_8184-indentation.patch, 6.8 KB (added by Robert Miller, 13 years ago)

Apply on top of trac_8184-eclib.patch

  • sage/libs/mwrank/interface.py

    Fix indentation in some docstrings
    
    
    diff -r da1d714ce6c6 -r d35e82645fb5 sage/libs/mwrank/interface.py
    a b  
    244244        """
    245245        Returns the rank of this curve, computed using 2-descent.
    246246
    247         In general this may only be a lower bound for the rank; an
    248         upper bound may be obtained using the function rank_bound().
    249         To test whether the value has been proved to be correct, use
    250         the method \method{certain}.
     247        In general this may only be a lower bound for the rank; an
     248        upper bound may be obtained using the function rank_bound().
     249        To test whether the value has been proved to be correct, use
     250        the method \method{certain}.
    251251
    252         EXAMPLES::
     252        EXAMPLES::
    253253
    254             sage: E = mwrank_EllipticCurve([0, -1, 0, -900, -10098])
    255             sage: E.rank()
    256             0
    257             sage: E.certain()
    258             True
     254            sage: E = mwrank_EllipticCurve([0, -1, 0, -900, -10098])
     255            sage: E.rank()
     256            0
     257            sage: E.certain()
     258            True
    259259
    260         ::
     260        ::
    261261
    262             sage: E = mwrank_EllipticCurve([0, -1, 1, -929, -10595])
    263             sage: E.rank()                                         
    264             0
    265             sage: E.certain()                                       
    266             False
     262            sage: E = mwrank_EllipticCurve([0, -1, 1, -929, -10595])
     263            sage: E.rank()                                         
     264            0
     265            sage: E.certain()                                       
     266            False
    267267
    268268        """
    269269        return self.__two_descent_data().getrank()
     
    273273        Returns an upper bound for the rank of this curve, computed
    274274        using 2-descent.
    275275
    276         If the curve has no 2-torsion, this is equal to the 2-Selmer
    277         rank.  If the curve has 2-torsion, the upper bound may be
    278         smaller than the bound obtained from the 2-Selmer rank minus
    279         the 2-rank of the torsion, since more information is gained
    280         from the 2-isogenous curve or curves.
     276        If the curve has no 2-torsion, this is equal to the 2-Selmer
     277        rank.  If the curve has 2-torsion, the upper bound may be
     278        smaller than the bound obtained from the 2-Selmer rank minus
     279        the 2-rank of the torsion, since more information is gained
     280        from the 2-isogenous curve or curves.
    281281
    282282        EXAMPLES:
    283283
     
    307307            sage: E.rank_bound()
    308308            2
    309309
    310         In this case the value returned by \method{rank} is only a
    311         lower bound in general (though in this is correct)::
     310        In this case the value returned by \method{rank} is only a
     311        lower bound in general (though in this is correct)::
    312312
    313313            sage: E.rank()
    314314            0
    315             sage: E.certain()
    316             False
     315            sage: E.certain()
     316            False
     317
    317318        """
    318319        return self.__two_descent_data().getrankbound()
    319320
    320321    def selmer_rank(self):
    321322        r"""
    322         Returns the rank of the 2-Selmer group of the curve.
    323        
     323        Returns the rank of the 2-Selmer group of the curve.
     324   
    324325        EXAMPLES:
    325326
    326         The following is the curve 960D1, which has rank 0, but Sha of
     327        The following is the curve 960D1, which has rank 0, but Sha of
    327328        order 4.  The 2-torsion has rank 2, and the Selmer rank is 3::
    328329       
    329330            sage: E = mwrank_EllipticCurve([0, -1, 0, -900, -10098])
    330331            sage: E.selmer_rank()
    331332            3
    332333
    333         Nevertheless, we can obtain a tight upper bound on the rank
    334         since a second descent is performed which establishes the
    335         2-rank of Sha::
     334        Nevertheless, we can obtain a tight upper bound on the rank
     335        since a second descent is performed which establishes the
     336        2-rank of Sha::
    336337
    337338            sage: E.rank_bound()
    338339            0
     
    355356            sage: E.rank_bound()
    356357            2
    357358
    358         In cases like this with no 2-torsion, the rank upper bound is
    359         always equal to the 2-Selmer rank.  If we ask for the rank,
    360         all we get is a lower bound::
    361            
     359        In cases like this with no 2-torsion, the rank upper bound is
     360        always equal to the 2-Selmer rank.  If we ask for the rank,
     361        all we get is a lower bound::
     362       
    362363            sage: E.rank()
    363364            0
    364             sage: E.certain()
    365             False
     365            sage: E.certain()
     366            False
    366367
    367368        """
    368369        return self.__two_descent_data().getselmer()
     
    411412        called, then it is first called by \method{certain}
    412413        using the default parameters.
    413414
    414         The result is true if and only if the results of the methods
    415         \method{rank} and \method{rank_bound} are equal.
     415        The result is true if and only if the results of the methods
     416        \method{rank} and \method{rank_bound} are equal.
    416417       
    417418        EXAMPLES:
    418        
     419   
    419420        A $2$-descent does not determine $E(\Q)$ with certainty
    420421        for the curve $y^2 + y = x^3 - x^2 - 120x - 2183$.
    421422       
     
    427428            sage: E.rank()   
    428429            0
    429430
    430         The previous value is only a lower bound; the upper bound is greater::
     431        The previous value is only a lower bound; the upper bound is greater::
    431432
    432433            sage: E.rank_bound()   
    433434            2
  • sage/schemes/elliptic_curves/ell_rational_field.py

    diff -r da1d714ce6c6 -r d35e82645fb5 sage/schemes/elliptic_curves/ell_rational_field.py
    a b  
    24592459            sage: E.selmer_rank()
    24602460            3
    24612461       
    2462         Here the Selmer rank is equal to the 2-torsion rank (=1) plus
    2463         the 2-rank of Sha (=2), and the rank itself is zero::
    2464 
    2465             sage: E.rank()
    2466             0
    2467        
     2462        Here the Selmer rank is equal to the 2-torsion rank (=1) plus
     2463        the 2-rank of Sha (=2), and the rank itself is zero::
     2464
     2465            sage: E.rank()
     2466            0
     2467   
    24682468        In contrast, for the curve 571A, also with rank 0 and Sha of
    24692469        order 4, we get a worse bound::
    24702470       
     
    24742474            sage: E.rank_bound()
    24752475            2
    24762476
    2477         To establish that the rank is in fact 0 in this case, we would
    2478         need to carry out a higher descent::
    2479 
    2480             sage: E.three_selmer_rank() # optional: magma
    2481             0
    2482 
    2483         Or use the L-function to compute the analytic rank::   
    2484            
     2477        To establish that the rank is in fact 0 in this case, we would
     2478        need to carry out a higher descent::
     2479
     2480            sage: E.three_selmer_rank() # optional: magma
     2481            0
     2482
     2483        Or use the L-function to compute the analytic rank::   
     2484           
    24852485            sage: E.rank(only_use_mwrank=False)
    24862486            0
     2487
    24872488        """
    24882489        try:
    24892490            return self.__selmer_rank
     
    25182519            2
    25192520            sage: E.rank(only_use_mwrank=False)   # uses L-function
    25202521            0
     2522
    25212523        """
    25222524        try:
    25232525            return self.__rank_bound