h.ecfunc

强大的数学工具包

                                * * * * * * *
                                *  ecfunc   *
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        The variable HEIGHTBOUND determines the upper bound of the
        height of points for the search in the algorithm of finding
        basis points of an elliptic curve (i.e. basismwg and faintp). 
        By default, HEIGHTBOUND = 11. In order to adjust this bound
        to s, please type "HEIGHTBOUND = s", where s is an integer,
        a rational or a floating point number with 0 <= s <= 2^999.
        If HEIGHTBOUND is zero, then the height of points is 
        unlimited.

        If you need help in dealing with elliptic curves, please type 
        "? EC", "? PT" or "? curec".

        The following functions are available for elliptic curves:

        *           aftopr      ecnpsnf     ntpair      sgnfeq 
        +           areptsli    elog        ordtsg      swnf    
        -           basismwg    faintp      prtoaf      taalg    
        ==          bitrans     fp          ptcoef      tavb2 
        !=          cond        intcoef     puto        tavb4  
                    cper        isptec      red         tavb6    
                    curec       jinv        reg         tavb8 
                    derivL      minim       rk          tavc4
                    discec      mtoi        rk2d        tavc6
                    eccoef      np          rkbsd       tors      
                    ecgnp       npfe        rkg2d       whei
                    ecinf       nthei       rper

                
        '+'             means   addition;

        '-'                     subtraction;

        '*'                     multiplication;

        '=='                    equal;
   
        '!='                    not equal;

        'aftopr'                conversion from affine to projective 
                                representation;

        'areptsli'              are points linearly independent? ;

        'basismwg'              basis of Mordell-Weil-group;

        'bitrans'               birational transformation of an elliptic
                                curve or a point;

        'cond'                  conductor;      

        'cper'                  complex period;
        
        'curec'                 current elliptic curve; 

        'derivL'                derivation L-series;
        
        'discec'                discriminant of an elliptic curve;      

        'eccoef'                elliptic curve coefficient;

        'ecgnp'                 elliptic curve with given number of points;
                                (only in SIEMENS-version)
        
        'ecinf'                 elliptic curve information;

        'ecnpscf'               elliptic curve with point order with small cofactor;

        'elog'                  elliptic logarithm;

        'faintp'                finding all integral points;

        'fp'                    finding point;
        
        'intcoef'               elliptic curve with integer coefficients;

        'isptec'                is point on an elliptic curve? ;
        
        'jinv'                  j-invariant;                            
        
        'minim'                 global minimal model;

        'mtoi'                  modular to integer;                     
        
        'np'                    number of points;

        'npfe'                  number of points after field extension;

        'nthei'                 Neron-Tate height;

        'ntpair'                Neron-Tate pairing;

        'ordtsg'                order of Tate-Shafarevic-group;

        'prtoaf'                conversion from projective to affine 
                                representation;         

        'ptcoef'                point on elliptic curve coefficient;
        
        'puto'                  display internal object;
        
        'red'                   reduction of an elliptic curve;

        'reg'                   regulator;

        'rk'                    rank;

        'rk2d'                  rank via 2-descent;

        'rkbsd'                 rank via Birch and Swinnerton-Dyer conjecture;

        'rkg2d'                 rank via general 2-descent;

        'rper'                  real period;

        'sgnfeq'                sign of functional equation;
        
        'swnf'                  short Weierstrass normal form;

        'taalg'                 Tate's algorithm;
        
        'tavb2'                 Tate's value b2;

        'tavb4'                 Tate's value b4;
        
        'tavb6'                 Tate's value b6;
        
        'tavb8'                 Tate's value b8;
        
        'tavc4'                 Tate's value c4;
        
        'tavc6'                 Tate's value c6;
        
        'tors'                  torsion group; 

        'whei'                  Weil height;