h.curgf2bit

来自「强大的数学工具包」· CURGF2BIT 代码 · 共 46 行

                               * * * * * * *
                               * curgf2bit *
                               * * * * * * *

        "current Galois-field over characteristic 2, special bit
         representation"
        SYNTAX: X = curgf2bit(A,S)

        A is a variable.
        S is a sequence of 0 and 1.
        S is interpreted as the coefficients of a polynomial Q over
        Z/2Z in the variable A. (For example the sequence 100101 stands
        for the polynomial A^5 + A^2 + 1.)
        Q must be an irreducible polynomial of degree greater than 1.

        X is assigned the value of Q.
        X is stored in the variable curGaloisField.

        curgf2bit specifies the current Galois-field GF(2^n) = Z/2Z(al)
        where al is a root of X.
        If it is possible, the user is asked if he wants to embed the
        variables over the old Galois-field in the new one. Then all
        structures over the old Galois-field are isomorphically 
        embedded in the new one. Otherwise those elements are 
        considered such as they are as elements of the recently 
        specified Galois-field GF(2^n).
        They are entered and displayed by the symbol 'GF' as 
        polynomials in the variable A. They can also be entered by the
        symbol 'GF2bit'.

        If p = 2 and the user is embedding elliptic curves, of which he 
        knows the number of points, over the old Galois-field into the
        new one, he can get the number of points over the new one.


        Example 1: (correct)

                X = curgf2bit(A, 1110101 )

        
        Example 2: (incorrect)

                curgf2bit(A, A^5+A^2+1 )

_ERR_NR_015