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[✓] Define generalised domains?

Posted 5 months ago
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It appears that the concept of generalized domains has been attempted but seems not to be working.

According to documents the following command

Plot3D[x^2 - y^2, {x, -3, 3}, {y, -3, 3}, RegionFunction -> Function[{x, y, z}, 2 < x^2 + y^2 < 9]]

specifically assigns the defined function on the right to be the Region of the Function that Plot3D will then plot.

Wolfram Alph at least refuses to understand almost every from of RegionFunction I could find.

My mathematica is old and I have not pulled it out but If RegionFunction allows the values (in this case restricted x and y values and un restricted z values} from the Function command this should work. But nothing seems to.

Anyone have an idea of how to get creative with restricted domains?

I did go to the sandbox.open.wolframcloud.com and got this entered into there and it works. So it seems that wolframalpha.com has not implemented it.

However, I could

Function[{x,y,z}, x^2+y^2<5 ] 

to work just fine, but getting only a 1-d slice say

Function[{x,y,z}, x^2+y^2=4]

it didn't produce anything recognizable.

You can try ImplicitRegion:

Region@ImplicitRegion[z == x^2 - y^2 && x^2 + y^2 == 4, {x, y, z}]
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