Date: 12 September 2013

step=%v

x_0=%x

(x_0,x_1)=%v

(x_1,x_2)=%v

(x_2,x_3)=%v

(x_3,x_4)=%v

(x_4,x_5)=%v

x

n

(x_5,x_6)=%v

ymax = 5
ymin = -1
A0_sub = (3.1913499344692, 1.2386117136659431)
f(x) = (((0.7 * (x - 1)) * (x - 2)) * (x - 4)) + x
xmax = 5
xmin = -1
X0point_sub = Point(Segment[(xmin, 0), (xmax, 0)])
threshold = 0.1697056274847714
step = 0 (slider from 0 to 12, step 1)
x0 = 3
x0found: (abs(x(X0point_sub) - x0)  <  threshold) ∧ (step > 0)
X0point = DynamicCoordinates(X0point_sub, If[x(X0point_sub) > xmax, xmax, If[x(X0point_sub)  <  xmin, xmin, If[x0found, x0, x(X0point_sub)]]], 0)
A0match: (x(X0point), f(x(X0point)))
A0found: (Distance[A0_sub, A0match]  <  threshold) ∧ (step > 1)
A5_sub = (2.554390563564875, 3.581560283687943)
A4_sub = (1.0681520314547834, 2.8439716312056738)
A3_sub = (1.8859764089121884, 4)
A2_sub = (1.7758846657929224, 0.3333333333333333)
A1_sub = (3.3643512450851896, 0.36659436008676743)
A0 = DynamicCoordinates(A0_sub, If[x(A0_sub) > xmax, xmax, If[x(A0_sub)  <  xmin, xmin, If[A0found, x(A0match), x(A0_sub)]]], If[y(A0_sub) > ymax, ymax, If[y(A0_sub)  <  ymin, ymin, If[A0found, y(A0match), y(A0_sub)]]])
x1: y(A0)
B1match: (x1, x1)
B1_sub = (1.7916120576671033, 0.691973969631236)
B1found: (Distance[B1_sub, B1match]  <  threshold) ∧ (step > 2)
B1 = DynamicCoordinates(B1_sub, If[x(B1_sub) > xmax, xmax, If[x(B1_sub)  <  xmin, xmin, If[B1found, x(B1match), x(B1_sub)]]], If[y(B1_sub) > ymax, ymax, If[y(B1_sub)  <  ymin, ymin, If[B1found, y(B1match), y(B1_sub)]]])
A1match: (x(B1), f(x(B1)))
A1found: (Distance[A1_sub, A1match]  <  threshold) ∧ (step > 3)
A1 = DynamicCoordinates(A1_sub, If[x(A1_sub) > xmax, xmax, If[x(A1_sub)  <  xmin, xmin, If[A1found, x(A1match), x(A1_sub)]]], If[y(A1_sub) > ymax, ymax, If[y(A1_sub)  <  ymin, ymin, If[A1found, y(A1match), y(A1_sub)]]])
x2: y(A1)
B2match: (x2, x2)
B2_sub = (1.9646133682830926, 2.0455531453362252)
B2found: (Distance[B2_sub, B2match]  <  threshold) ∧ (step > 4)
B2 = DynamicCoordinates(B2_sub, If[x(B2_sub) > xmax, xmax, If[x(B2_sub)  <  xmin, xmin, If[B2found, x(B2match), x(B2_sub)]]], If[y(B2_sub) > ymax, ymax, If[y(B2_sub)  <  ymin, ymin, If[B2found, y(B2match), y(B2_sub)]]])
A2match: (x(B2), f(x(B2)))
A2found: (Distance[A2_sub, A2match]  <  threshold) ∧ (step > 5)
A2 = DynamicCoordinates(A2_sub, If[x(A2_sub) > xmax, xmax, If[x(A2_sub)  <  xmin, xmin, If[A2found, x(A2match), x(A2_sub)]]], If[y(A2_sub) > ymax, ymax, If[y(A2_sub)  <  ymin, ymin, If[A2found, y(A2match), y(A2_sub)]]])
x3: y(A2)
B3match: (x3, x3)
B3_sub = (1.0524246395806027, 0.6879432624113475)
B3found: (Distance[B3_sub, B3match]  <  threshold) ∧ (step > 6)
B3 = DynamicCoordinates(B3_sub, If[x(B3_sub) > xmax, xmax, If[x(B3_sub)  <  xmin, xmin, If[B3found, x(B3match), x(B3_sub)]]], If[y(B3_sub) > ymax, ymax, If[y(B3_sub)  <  ymin, ymin, If[B3found, y(B3match), y(B3_sub)]]])
A3match: (x(B3), f(x(B3)))
A3found: (Distance[A3_sub, A3match]  <  threshold) ∧ (step > 7)
A3 = DynamicCoordinates(A3_sub, If[x(A3_sub) > xmax, xmax, If[x(A3_sub)  <  xmin, xmin, If[A3found, x(A3match), x(A3_sub)]]], If[y(A3_sub) > ymax, ymax, If[y(A3_sub)  <  ymin, ymin, If[A3found, y(A3match), y(A3_sub)]]])
x4: y(A3)
B4match: (x4, x4)
B4_sub = (3.4665792922673653, 4)
B4found: (Distance[B4_sub, B4match]  <  threshold) ∧ (step > 8)
B4 = DynamicCoordinates(B4_sub, If[x(B4_sub) > xmax, xmax, If[x(B4_sub)  <  xmin, xmin, If[B4found, x(B4match), x(B4_sub)]]], If[y(B4_sub) > ymax, ymax, If[y(B4_sub)  <  ymin, ymin, If[B4found, y(B4match), y(B4_sub)]]])
A4match: (x(B4), f(x(B4)))
A4found: (Distance[A4_sub, A4match]  <  threshold) ∧ (step > 9)
A4 = DynamicCoordinates(A4_sub, If[x(A4_sub) > xmax, xmax, If[x(A4_sub)  <  xmin, xmin, If[A4found, x(A4match), x(A4_sub)]]], If[y(A4_sub) > ymax, ymax, If[y(A4_sub)  <  ymin, ymin, If[A4found, y(A4match), y(A4_sub)]]])
x5: y(A4)
B5match: (x5, x5)
B5_sub = (1.3433813892529487, 3.382978723404255)
B5found: (Distance[B5_sub, B5match]  <  threshold) ∧ (step > 10)
B5 = DynamicCoordinates(B5_sub, If[x(B5_sub) > xmax, xmax, If[x(B5_sub)  <  xmin, xmin, If[B5found, x(B5match), x(B5_sub)]]], If[y(B5_sub) > ymax, ymax, If[y(B5_sub)  <  ymin, ymin, If[B5found, y(B5match), y(B5_sub)]]])
A5match: (x(B5), f(x(B5)))
A5found: (Distance[A5_sub, A5match]  <  threshold) ∧ (step > 11)
fxmax = 1.0E100
fxmin = -1.0E100
g = Function(f, fxmin, fxmax)
diagonal = Segment((Max[xmin, ymin], Max[xmin, ymin]), (Min[xmax, ymax], Min[xmax, ymax]))
threshold_manual = false
c = Segment(A0, X0point)
d = Segment(A0, B1)
e = Segment(A1, B1)
h = Segment(A1, B2)
i = Segment(A2, B2)
j = Segment(A2, B3)
A0shadow: A0
A1shadow: A1
A2shadow: A2
X0pointshadow: X0point
B1shadow: B1
B2shadow: B2
B3shadow: B3
a = Segment(A3, B3)
b = Segment(A3, B4)
k = Segment(A4, B4)
A3shadow: A3
B4shadow: B4
A4shadow: A4
l = Segment(A4, B5)
A5 = DynamicCoordinates(A5_sub, If[x(A5_sub) > xmax, xmax, If[x(A5_sub)  <  xmin, xmin, If[A5found, x(A5match), x(A5_sub)]]], If[y(A5_sub) > ymax, ymax, If[y(A5_sub)  <  ymin, ymin, If[A5found, y(A5match), y(A5_sub)]]])
m = Segment(A5, B5)
xlabeldisplayed: "" + (LaTeX[statevariable]) + "_{" + (LaTeX[timevariable]) + "}"
ylabeldisplayed: "" + (LaTeX[statevariable]) + "_{" + (LaTeX[timevariable]) + "+1}"
xX0a: x(X0point)
text1: "" + statevariable + "_0=" + xX0a + ""
text2: "(" + statevariable + "_0," + statevariable + "_1)=" + A0 + ""
text3: "(" + statevariable + "_1," + statevariable + "_2)=" + A1 + ""
text4: "(" + statevariable + "_2," + statevariable + "_3)=" + A2 + ""
text5: "(" + statevariable + "_3," + statevariable + "_4)=" + A3 + ""
text6: "(" + statevariable + "_4," + statevariable + "_5)=" + A4 + ""
text7: "(" + statevariable + "_5," + statevariable + "_6)=" + A5 + ""
B5shadow: B5