thesis_draw(client_x, client_y, do_guides){
    synthesis = document.getElementById("synthesis");
    var synthesis_context = synthesis.getContext("2d");
    synthesis_context.font = "16px sans-serif";
    // background
    synthesis_context.fillStyle="#eeeeee";
    synthesis_context.fillRect(0, 0, w, h);

    // synthesis
    var A = [];
    var B = [];

    A[0] = [];
    for(var j = 0; j < synthesis_n-1; ++j)
        A[0][j+1] = Math.pow(synthesis_xs[1], j) * (j+1);
    A[0][0] = 0.0;
    B[0] = (synthes