# Interesting Progression of ParametricRegion: Bug?

Bug introduced In 10.1 or earlier and fixed 11.1

Consider the following ParametricRegion from an answer to this question:

region = ParametricRegion[{{(1 + r - 12 r^2 + 4 r^3)/(2 r - 2),
z Sqrt[(4 r^2)/(r - 1)^2 (r - r^2 (r - 3)^2)]},
2 < r < 4 && -1 < z < 1}, {r, z}];


Now let's discretize this region using various versions of Mathematica starting from 10.1:

DiscretizeRegion[region]    Something is seriously wrong here, seems like a progression from 10.1 to 10.2, then a serious (let's call it a bug) regression from 10.2 to 10.3. 10.4 just gets the region wrong. The problem seems to be with ParametricRegion and how Mathematica handles them because I get similar wrong results with RegionPlot too. Can anyone confirm these?

• Did your laptop installed all the Mathematica version like $10.1,10.2,10.3$ and $10.4$? – xyz Mar 23 '16 at 7:33
• I found the same result (for v.10.4) on Windows and Linux x86 – physicien Mar 23 '16 at 17:10
• Same with v 10.3 on Linux. – Öskå Mar 23 '16 at 19:41
• @RunnyKine Shouldn't the B-word now be used without a question mark? – gwr Mar 24 '16 at 10:00
• @gwr. You're probably right, but I can't think of a better way to rephrase it. – RunnyKine Mar 24 '16 at 10:15

## 1 Answer

This bug is fixed in 11.1:

region = ParametricRegion[{{(1 + r - 12 r^2 + 4 r^3)/(2 r - 2),
z Sqrt[(4 r^2)/(r - 1)^2 (r - r^2 (r - 3)^2)]},
2 < r < 4 && -1 < z < 1}, {r, z}];

DiscretizeRegion[region] 