h.linequ

来自「强大的数学工具包」· LINEQU 代码 · 共 53 行

                                * * * * * * *
                                *   linequ  *
                                * * * * * * *

        "linear equations"
        SYNTAX: X = linequ(A, b)

        A is a nonzero (m x n) - matrix.
        b is a vector of length m.

        A and b are defined over Z or Q, over polynomials over Z or 
        Q, over rational functions over Q, over Z/pZ, over GF(p^n) 
        (where p is a single precision prime number) or over a number 
        field.

        linequ solves the system 
                      (*)   A * X = b
        of linear equations over Q, rational functions, Z/pZ, GF(p^n) 
        or a number field, respectively:
        If (*) is uniquely solvable, the solution is assigned to X.
        If (*) is unsolvable, a message is displayed.
        If (*) is not uniquely solvable, a basis of the null space
        is displayed and a special solution of (*) is assigned to X.

        In the third case the vectors of the null space are stored in
        AV (see "?avfunc").


        Example 1: (correct)

                linequ({{1 ,2} {3, 4}}, {2 ,1})


        Example 2: (correct)

                linequ({{1, 0} {3, 0}}, {1, 1})

                The system is unsolvable over Q!


        Example 3: (incorrect)

                linequ({{1, 2} {3, 4}}, {1, 2, 3})

_ERR_NR_072


        Example 4: (incorrect)

                linequ({{0, 0} {0, 0}}, {0, 1})

_ERR_NR_092