Skip to main content

calculus and analysis - Why the Kernel crashes on these integrals in V12?


Reported to WRI, [CASE:4331819]




This is using V12, on windows 10, 64 bit. Note: these integrals work OK on 11.3 on same PC.


enter image description here




Any idea why the Kernel now crashes on these types of integrals?


ClearAll[x,a,b,c,e,d,f,g,n];

(*these from file #40,41*)

Integrate[(1 + x^2)^3/(1 + x^2 + x^4)^(3/2), x];
Integrate[(1 + x^2)^2/(1 + x^2 + x^4)^(3/2), x];
Integrate[(1 + x^2)/(1 + x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)^3/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)^2/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(7 + 5*x^2)/(2 + 3*x^2 + x^4)^(3/2), x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2)^3, x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2)^2, x];
Integrate[(2 + 3*x^2 + x^4)^(3/2)*(7 + 5*x^2), x];
Integrate[(7+5*x^2)^4/(2+3*x^2+x^4)^(3/2),x];

Integrate[(7+5*x^2)^2/(2+3*x^2+x^4)^(3/2),x];
Integrate[(4+3*x^2+x^4)^(3/2)*(7+5*x^2),x];
Integrate[(d+e*x^2)*(a+b*x^2+c*x^4)^(3/2)/(f*x)^(1/2),x];

(*these from file #42*)
Integrate[(a*g - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2), x];
Integrate[(a*g+e*x-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(a*g+f*x^3-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(a*g+e*x+f*x^3-c*g*x^4)/(a+b*x^2+c*x^4)^(3/2),x];


(*these from file #44*)
Integrate[(A+B*x^2)*(d+e*x^2)/(a+b*x^2+c*x^4)^(3/2),x];
Integrate[(A+B*x^2)/(a+b*x^2+c*x^4)^(3/2),x]

(*these from file #49*)
Integrate[(-a*h*x^(n/2 - 1) + c*f*x^(n - 1) + c*g*x^(2*n - 1) +c*h*x^((5*n)/2 - 1))/(a + b*x^n + c*x^(2*n))^(3/2), x];
Integrate[(x^(n/2 - 1)*(-a*h + c*f*x^(n/2) + c*g*x^((3*n)/2)+c*h*x^(2*n)))/(a + b*x^n + c*x^(2*n))^(3/2), x];
Integrate[((d*x)^(n/2-1)*(-a*h+c*f*x^(n/2)+c*g*x^((3*n)/2)+c*h*x^(2*n)))/(a+b*x^n+c*x^(2*n))^(3/2),x];
(*etc..*)


Mathematica graphics


Mathematica graphics


Mathematica graphics


No problem with V 11.3


Mathematica graphics


Mathematica graphics


Mathematica graphics


Does this happen to others and on other systems or just on windows 10?


It looks like it is the same bug that is causing all these crashes, but I can't be sure.


I am finding that V12 kernel crashes more than V 11.3 kernel and also in strange ways. This makes it very hard to run a long script, when kernel keeps crashing.



ps. I think WRI should have been able to detect these before making a release by running regression tests. I am using Rubi integration test files to find these problems.


pps. I hope I do not get downvoted again for asking about a possible problem in Mathematica like in the last post on that bizarre kernel crash.




Comments

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.