h.swnf

强大的数学工具包

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                               *   swnf    *
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        "short Weierstrass normal form"
        SYNTAX: X = swnf(E, s)

        E is an expression whose value is an elliptic curve over Q,
        Z/pZ (where p is a prime) or over a number field.
        s is equal to 0 or 1.
        
        X is assigned an elliptic curve in short Weierstrass normal 
        form which is birational isomorphic to E.
 
        If s=1 and E is given in general Weierstrass normal form, 
        the parameters r, s, t and u of the birational transformation 
           x  ->  u^2*x + r,
           y  ->  u^3*y + u^2*s*x + t 
        are displayed.

        In this case the parameters r,s,t,u are stored in AV 
        (see "?avfunc").


        Example 1: (correct)

                swnf(EC(4, 2, 0, 1, 3), 1)


        Example 2: (incorrect)

                swnf(EC(4, 2, 0, 1, 3), x)
                
_ERR_NR_121


        Example 3: (incorrect)

                swnf(EC(4, 2, 0, 1, 3))
                
_ERR_NR_232


        Example 4: (incorrect)

                swnf(O, 0)
                
_ERR_NR_120