region_plot and not equals

[Alex Jordan]

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.)