Land Surveyor Forum

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  • Party Chief
    Jaybird July 17, 2015 at 5:48pm

    A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n,

    f(x_1,...,x_n)=(g_1(x_1,...,x_n),...,g_m(x_1,...,x_n)),

    for suitable polynomials g_1,...,g_m in K[X_1,...,X_n]. The zero set of f is the set of all solutions of the simultaneous equations g_1=...=g_m=0, and is an algebraic variety in K^n.

    An example of polynomial map is the ith coordinate map delta_i:K^n->K, defined by delta_i(x_1,...,x_n)=x_i for all i=1,...,n. In the language of set theory, it is the projection of the Cartesian product K^n onto the ith factor.

    Polynomial maps can be defined on any nonempty subset S of K^n. If S is an affine variety, then the set of all polynomial maps from S to K is the coordinate ring K[S] of S. If T is an affine variety of K^m, then every polynomial map f:S->T induces a ring homomorphism F:K[T]->K[S], defined by F(phi)=phi degreesf. Conversely, every ring homomorphism G:K[T]->K[S] determines a polynomial map g:S->T, where g=(G(delta_1),...,G(delta_m)).

    A polynomial map f:R->R is a real-valued polynomial function. Its graph is the plane algebraic curve with Cartesian equation y=f(x).

    and

    This looks interesting to check out  and this  hope this helps

    Field
    A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic…
    • Party Chief
      Jaybird > Jaybird October 6, 2015 at 10:24pm
      All I could find at the time til someone came along...cheers!
    • Student Surveyor
      Mat Win > Jaybird October 6, 2015 at 10:19pm

      Thanks Justin

      But hmmmm i really dont understand what you have said

      thanks for the download

      cheers

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