How to plot $\lbrace (x+y,x-y) \vert (x,y)\in (-1/2,1/2)^{2} \rbrace$

Question

I want to visualize the following set in Maple:

$\lbrace (x+y,x-y) \vert (x,y)\in (-\frac{1}{2},\frac{1}{2})^{2} \rbrace$

Which commands should I use? Is it even possible?

Answer 1

Try this:

with(plots):
for i from $0$ to $100$ do
$a_i$ := evalf($-\frac12+\frac{i}{100}$):
$b_i$ := evalf($-\frac12+\frac{i}{100}$):
od:
points := ${\text{seq}(\text{seq}([a_n+b_m, \ a_n-b_m, \ 1], n = 0 .. 100), m = 0 .. 100)}$:
pointplot3d(points, axes = normal, symbol = box);

Answer 2

The domain S can be visualized as a plot of the shaded interior of a polygon (square). This plot can be transformed by the given mapping.

f := plottools:-transform((x,y)->[x+y,x-y]):

S := plots:-polygonplot([[-1/2,-1/2], [-1/2,1/2],
                         [1/2,1/2], [1/2,-1/2]],
                        axes=box):

plots:-display(Array([S, f(S)]));