I'm not sure what I would expect to see, but the following produces something I would not expect:
region_plot([x <> 1], (x,-2,2), (y,-2,2))
The output has the region left of x=1 shaded, but not the region right of x=1. Similar "one-sided" results with
region_plot([x <> y], (x,-2,2), (y,-2,2))
region_plot([x^2+y^2-1 <> 0], (x,-2,2), (y,-2,2))
region_plot([x^2 <> 1], (x,-2,2), (y,-2,2))
Based on the documentation for region_plot, this seems like a bug. Is that right?
I'm looking at this as part of trying to understand how Sage might compare a set expressed as
x^2 != y
with, say, a set expressed as
|x| < sqrt(y) or |x| > sqrt(y)
and determine they are equal. What syntax would be appropriate for making such a comparison?
(Sorry for two questions in one post.)