The kernel shouldn't crash. I've let the appropriate developers know and they will be looking into it. Not sure what the input is intended to do, perhaps something like Reap[NIntegrate[ 1, {x, y} \[Element] Triangle[{{0, 0}, {1, 2}, {2, 1}}], Method -> "MonteCarlo", EvaluationMonitor :> Sow[{x, y}]]] may work?

@ilian Nice to meet you-WRI engineer.Reap-Sow works normally. But I only want the first random point in this region.

@ilian I can't translate the Chinese sentence in the window into English.

I can't translate it either, but I think it is the standard Windows "memory could not be written" crash dialog, e.g. i.stack.imgur.com/U4QK1.jpg The first point sown would be Reap[NIntegrate[...]][[2, 1, 1]]. In other threads, there are also several nice ways to generate random points in a region.

@ilian Yes,your guess is true,since I find that the meaning of sentences of two windows matches.

@ilian I need a function to generate random points in arbitary region (ranged from 0 dimension to 3 dimension) .

This functionality is coming soon, but for the time being perhaps try NIntegrate`RandomRegion[reg, n] to generate n random points.

@ilian I wonder why mathematica don't have a function to calculate the differential-Grobner basis,since I find it useful for a large number of problem.And I notice that DSolve in mathematica for PDE is relatively weaker than maple.I suggest that WRI should strength the functionality in this field in next editions.

@ilian That's a surprising exciting information for me.Thank you.

@ilian It failed when the region is Triangle[{{0, 0}, {1, 2}, {2, 1}}].In other words, NIntegrateRandomRegionTriangle[{{0, 0}, {1, 2}, {2, 1}}], 1] doesn't work

The exact input I used was

NIntegrate`RandomRegion[Triangle[{{0, 0}, {1, 2}, {2, 1}}], 1]

so the function is NIntegrate`RandomRegion, the first argument is Triangle[{{0, 0}, {1, 2}, {2, 1}}] and the second argument is 1

and I got {{0.976003, 1.2532}} as a result, which is indeed a point inside the triangle

This code doesn't work.

yes, I can see it doesn't work in the released version

(already fixed in the development version)

as a workaround, I would suggest

(sorry about the poor formatting, the only change in the input was to discretize the region first, that is use DiscretizeRegion[Triangle[{{0, 0, 0}, {1, 0, 0}, {0, 1, 1}}]])

I find it work in several regions that previously didn't work without DiscretizeRegion!

Would mathematica have a further development in symbolic solving the systems of PDEs?

Mathematica is useful in diverse fields but in symbolic solving the systems of PDEs , it often behaves weaker strangely.

yes, DSolve is under active development

by the way, please feel free to send any functionality wishes or examples that could be improved to [email protected]

feedback is always appreciated, and support can file suggestions to our development team

I can send email to [email protected]?Right?

yes, absolutely

I'm moved by your enthusiasm.

Since I am a Chinese student with about one-year learning experience in mathematica,I feel WRI is remote to me.I am not skilled in computer algorithm,so I tend to need good internal functions.