x

y

f(x, y) = (x * y)
dt = 1
g(x, y) = x - y
x0actual = 0.4 (slider from -5 to 5, step 0.1)
y0actual = 0.3
x1actual: x0actual + (f(x0actual, y0actual) * dt)
y1actual: y0actual + (g(x0actual, y0actual) * dt)
x2actual: x1actual + (f(x1actual, y1actual) * dt)
y2actual: y1actual + (g(x1actual, y1actual) * dt)
x3actual: x2actual + (f(x2actual, y2actual) * dt)
y3actual: y2actual + (g(x2actual, y2actual) * dt)
x4actual: x3actual + (f(x3actual, y3actual) * dt)
y4actual: y3actual + (g(x3actual, y3actual) * dt)
x5actual: x4actual + (f(x4actual, y4actual) * dt)
y5actual: y4actual + (g(x4actual, y4actual) * dt)
ymax = 2
ymin = -0.5
ny = 10
dyfe: (ymax - ymin) / ny
xmin = -0.5
xmax = 2
nx = 10
dxfe: (xmax - xmin) / nx
X5possibilities = Sequence(Sequence[(x5actual + i, y5actual + j), i, (ceil((xmin - x5actual) / dxfe) * dxfe), xmax - x5actual, dxfe], j, (ceil((ymin - y5actual) / dyfe) * dyfe), ymax - y5actual, dyfe)
X4possibilities = Sequence(Sequence[(x4actual + i, y4actual + j), i, (ceil((xmin - x4actual) / dxfe) * dxfe), xmax - x4actual, dxfe], j, (ceil((ymin - y4actual) / dyfe) * dyfe), ymax - y4actual, dyfe)
X3possibilities = Sequence(Sequence[(x3actual + i, y3actual + j), i, (ceil((xmin - x3actual) / dxfe) * dxfe), xmax - x3actual, dxfe], j, (ceil((ymin - y3actual) / dyfe) * dyfe), ymax - y3actual, dyfe)
X2possibilities = Sequence(Sequence[(x2actual + i, y2actual + j), i, (ceil((xmin - x2actual) / dxfe) * dxfe), xmax - x2actual, dxfe], j, (ceil((ymin - y2actual) / dyfe) * dyfe), ymax - y2actual, dyfe)
X1possibilities = Sequence(Sequence[(x1actual + i, y1actual + j), i, (ceil((xmin - x1actual) / dxfe) * dxfe), xmax - x1actual, dxfe], j, (ceil((ymin - y1actual) / dyfe) * dyfe), ymax - y1actual, dyfe)
X0possibilities = Sequence(Sequence[(x0actual + i, y0actual + j), i, (ceil((xmin - x0actual) / dxfe) * dxfe), xmax - x0actual, dxfe], j, (ceil((ymin - y0actual) / dyfe) * dyfe), ymax - y0actual, dyfe)
tmax = 5.5
tmin: ((-0.1) * tmax)
nsteps = 0 (slider from 0 to 5, step 1)
xlabeldisplayed: "" + (LaTeX[xlabel]) + ""
ylabeldisplayed: "" + (LaTeX[ylabel]) + ""
X0 = Point(X0possibilities)
X1 = Point(X1possibilities)
h = Segment(X0, X1)
X2 = Point(X2possibilities)
i = Segment(X1, X2)
X3 = Point(X3possibilities)
j = Segment(X2, X3)
X4 = Point(X4possibilities)
k = Segment(X3, X4)
X5 = Point(X5possibilities)
l = Segment(X4, X5)
x0: x(X0)
x1: x(X1)
x2: x(X2)
x3: x(X3)
x4: x(X4)
x5: x(X5)
y0: y(X0)
y1: y(X1)
y2: y(X2)
y3: y(X3)
y4: y(X4)
y5: y(X5)
Asub = (0.5307743216412972, 0.5024906600249066)
Bsub = (0.1981519507186858, 0.5721757322175731)
Csub = (1.0080645161290323, 0.8050660792951542)
Dsub = (1.1451612903225807, 1.3061674008810573)
Esub = (0.467741935483871, 1.5209251101321586)
dx = 0.1
dy = 0.1
A = DynamicCoordinates(Asub, If[x(Asub) > xmax, xmax, If[x(Asub)  <  xmin, xmin, (round(x(Asub) / dx) * dx)]], If[y(Asub) > ymax, ymax, If[y(Asub)  <  ymin, ymin, (round(y(Asub) / dy) * dy)]])
B = DynamicCoordinates(Bsub, If[x(Bsub) > xmax, xmax, If[x(Bsub)  <  xmin, xmin, (round(x(Bsub) / dx) * dx)]], If[y(Bsub) > ymax, ymax, If[y(Bsub)  <  ymin, ymin, (round(y(Bsub) / dy) * dy)]])
C = DynamicCoordinates(Csub, If[x(Csub) > xmax, xmax, If[x(Csub)  <  xmin, xmin, (round(x(Csub) / dx) * dx)]], If[y(Csub) > ymax, ymax, If[y(Csub)  <  ymin, ymin, (round(y(Csub) / dy) * dy)]])
D = DynamicCoordinates(Dsub, If[x(Dsub) > xmax, xmax, If[x(Dsub)  <  xmin, xmin, (round(x(Dsub) / dx) * dx)]], If[y(Dsub) > ymax, ymax, If[y(Dsub)  <  ymin, ymin, (round(y(Dsub) / dy) * dy)]])
E = DynamicCoordinates(Esub, If[x(Esub) > xmax, xmax, If[x(Esub)  <  xmin, xmin, (round(x(Esub) / dx) * dx)]], If[y(Esub) > ymax, ymax, If[y(Esub)  <  ymin, ymin, (round(y(Esub) / dy) * dy)]])
dvec = 0.1
Adir = Vector(((f(A), g(A)) / Length[(f(A), g(A))] * dvec))
Adirs: {Adir, Rotate[Adir, 0.7854], Rotate[Adir, 1.5708], Rotate[Adir, 2.35619], Rotate[Adir, 3.141592653589793], Rotate[Adir, 3.92699], Rotate[Adir, 4.71239], Rotate[Adir, 5.49779]}
Bdir = Vector(((f(B), g(B)) / Length[(f(B), g(B))] * dvec))
Avecpossibilities: A + Adirs
Avechead = Point(Avecpossibilities)
Avec = Vector(A, Avechead)
Cdir = Vector(((f(C), g(C)) / Length[(f(C), g(C))] * dvec))
Ddir = Vector(((f(D), g(D)) / Length[(f(D), g(D))] * dvec))
Edir = Vector(((f(E), g(E)) / Length[(f(E), g(E))] * dvec))
Bdirs: {Bdir, Rotate[Bdir, 0.7854], Rotate[Bdir, 1.5708], Rotate[Bdir, 2.35619], Rotate[Bdir, 3.141592653589793], Rotate[Bdir, 3.92699], Rotate[Bdir, 4.71239], Rotate[Bdir, 5.49779]}
Edirs: {Edir, Rotate[Edir, 0.7854], Rotate[Edir, 1.5708], Rotate[Edir, 2.35619], Rotate[Edir, 3.141592653589793], Rotate[Edir, 3.92699], Rotate[Edir, 4.71239], Rotate[Edir, 5.49779]}
Ddirs: {Ddir, Rotate[Ddir, 0.7854], Rotate[Ddir, 1.5708], Rotate[Ddir, 2.35619], Rotate[Ddir, 3.141592653589793], Rotate[Ddir, 3.92699], Rotate[Ddir, 4.71239], Rotate[Ddir, 5.49779]}
Cdirs: {Cdir, Rotate[Cdir, 0.7854], Rotate[Cdir, 1.5708], Rotate[Cdir, 2.35619], Rotate[Cdir, 3.141592653589793], Rotate[Cdir, 3.92699], Rotate[Cdir, 4.71239], Rotate[Cdir, 5.49779]}
Bvecpossibilities: B + Bdirs
Cvecpossibilities: C + Cdirs
Dvecpossibilities: D + Ddirs
Evecpossibilities: E + Edirs
Bvechead = Point(Bvecpossibilities)
Cvechead = Point(Cvecpossibilities)
Dvechead = Point(Dvecpossibilities)
Evechead = Point(Evecpossibilities)
Bvec = Vector(B, Bvechead)
Cvec = Vector(C, Cvechead)
Dvec = Vector(D, Dvechead)
Evec = Vector(E, Evechead)
npoints = 0 (slider from 0 to 5, step 1)
Bveccorrect: Bvechead ≟ B + Bdir ∨ Length[(f(B), g(B))] ≟ 0
Aveccorrect: Avechead ≟ A + Adir ∨ Length[(f(A), g(A))] ≟ 0
Cveccorrect: Cvechead ≟ C + Cdir ∨ Length[(f(C), g(C))] ≟ 0
Dveccorrect: Dvechead ≟ D + Ddir ∨ Length[(f(D), g(D))] ≟ 0
Eveccorrect: Evechead ≟ E + Edir ∨ Length[(f(E), g(E))] ≟ 0