1. The implement of the induction method: km-sys.mpl

    Function KernelMethod solve the equation system

    The basic input is
    where K is an n by n matrice, A is an n by l matrice and B is an n by 1 matrix. The output is a set of solutions. Each solution is an array of length l, indicating G1,G2,...Gl.

    For example, the command

    {[x, -2*x]}

    We may get extra equations by setting y to be some special values. This can be done by input the list [[y=y1, M1],[y=y2, M2], ...], where Mi is the transfer matrix of F(x,yi) and G(x). For example, if G(x)=F(x,0), then we can input KernelMethod(K,A,B,x,y,[[y=0,Id(n)]]), where Id(n) is the identity matrix of order n.

    For example, the command

    {[1-2*x, x-1, 3*x-1]}

    For examples, see examples.mws

  2. The implement of the elimination method: km-sys.mpl

    You need first read the maple program for wu's method: wsolve.mpl

    The usage is exactly the same as above. The output will be the algebraic equations that $g_1, \ldots, g_l$ satisfy. See the examples KM-wu-examples.mws

  3. The examples in the paper: PaperEx.mws