h.ntpair

来自「强大的数学工具包」· NTPAIR 代码 · 共 34 行

                               * * * * * * *
                               *   ntpair  *
                               * * * * * * *

        "Neron-Tate pairing"
        SYNTAX: X = ntpair(P,Q)

        P and Q are expressions whose values are points on the 
        current elliptic curve. The current elliptic curve as well 
        as the points P and Q must be defined over Q or over a 
        quadratic number field.

        X is assigned the Neron-Tate pairing of P and Q,
              X = [h( P + Q ) - h(P) - h(Q)]/2
                = [h( P + Q ) - h( P - Q )]/4
        where h() is the Neron-Tate height.


        Example 1: (correct)

                ntpair(PT(0, 3, 1), PT(2, 4))


        Example 2: (correct)

                ntpair(PT(NF(A), NF(A+2), 3), PT(1, 0))


        Example 3: (incorrect)

                ntpair(PT(1,2))
                
_ERR_NR_232