h.subst

强大的数学工具包

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        "substitution"
        SYNTAX: X = f(x1 = A1, ..., xn = An)

        f is a polynomial over Z, Q, Z/mZ, GF(p^t), a number field, 
        over R or C, a rational function or a matrix or a vector over 
        these structures, if possible.
        The variables x1, ..., xn must occur in f, n>0.
        A1, ..., An are expressions whose values are elements of Z, Q,
        Z/mZ, GF(p^t), algebraic numbers, floating point numbers or
        complex numbers, polynomials over these structures or rational 
        functions.

        The variables x1, ..., xn are substituted successively by 
        the values of A1, ..., An. The result of the substitution 
        is assigned to X.
        
        Recursive substituions and substitutions of the form
                X = f(x1 = x2 = ... = xm = A) or
                X = f(x1 = ... = A = ... = xm)
        (m <= n) are possible too.

        Warning: If for i<j Ai is a polynomial containing the
                 variable xj, then this xj is also substituted
                 by Aj.


        Example 1: (correct)

                f = x + y + z
                f(x = 3/2, y = a/b = z)


        Example 2: (correct)

                f = x*y + z + NF(A + 1/4)
                f(x = f(x = 9), y = NF(A-1))


        Example 3: (correct)

                a = {{x, y} {x^2 + y, y * x}}
                a(x = z/t, y = -3)


        Example 4: (incorrect)

                f = x + y
                f(x = 3 = 4)

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