h.eival

来自「强大的数学工具包」· EIVAL 代码 · 共 38 行

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                                *   eival   *
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        "eigenvalues"
        SYNTAX: X = eival(A, X1)

        A is a square matrix over Z, Q, Z/pZ or GF(p^n) 
        (where p is a prime).
        X1 is a variable.

        The roots of the characteristic polynomial of the matrix A 
        in Z, Q, Z/pZ or GF(p^n), respectively, i.e. the eigenvalues of 
        A are displayed on the screen.
        X is assigned the characteristic polynomial of the matrix A
        divided by its linear factors, i.e. the product of all 
        irreducible factors of degree >= 2.
        The factorization of X is displayed, too.

        At first the eigenvalues of A are stored in AV and then the
        irreducible factors with its exponents of the characteristic
        polynomial are stored in AV in the form factor - exponent
        (see "?avfunc").

        Warning: If p > 2^30, the primality of p is not tested.


        Example 1: (correct)

                eival({{1, 0} {0, 1}}, x)


        Example 2: (incorrect)

                eival({{7, 4711}}, y)

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