ShowRegion Package

ShowRegion[{x,xmin,xmax}, {y,ymin,ymax}] produces a graphic of the region in the plane consisting of all points {x,y} with xmin < x < xmax and ymin < y < ymax. If the four bounds are numeric, this is simply a rectangle; but either or both of the bounds on y may be given as expressions in x, leading to a more complicated region. Red line segments and an error message will appear if the bounds supplied do not yield a well-defined region. The bounds on the first variable must be numeric. ShowRegion[{y,ymin,ymax},{x,xmin,xmax}] will also work; here the bounds on x may be expressions in y. One may also work in polar coordinates: ShowRegion[{\[Theta],\[Theta]min,\[Theta]max}, {r,rmin,rmax}] produces a graphic of the appropriate polar region, where rmin and rmax may be expressions in \[Theta]; and ShowRegion[{r,rmin,rmax},{ \[Theta],\[Theta]min,\[Theta]max}] produces a graphic of the appropriate polar region, where \[Theta]min and \[Theta]max may be expressions in r. ShowRegion will accept any options accepted by ParametricPlot; Note that the option setting AspectRatio->Automatic is usually needed to produce the same scaling on both coordinate axes. Note that ShowRegion is sensitive to the names of the variables; do not deviate from the names x, y, r, and \[Theta], and only call the command from the Global` context. You can type \[Theta] from the keyboard with the key sequence Escape-th-Escape.