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

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

How to remap graph properties?

Graph objects support both custom properties, which do not have special meanings, and standard properties, which may be used by some functions. When importing from formats such as GraphML, we usually get a result with custom properties. What is the simplest way to remap one property to another, e.g. to remap a custom property to a standard one so it can be used with various functions? Example: Let's get Zachary's karate club network with edge weights and vertex names from here: http://nexus.igraph.org/api/dataset_info?id=1&format=html g = Import[ "http://nexus.igraph.org/api/dataset?id=1&format=GraphML", {"ZIP", "karate.GraphML"}] I can remap "name" to VertexLabels and "weights" to EdgeWeight like this: sp[prop_][g_] := SetProperty[g, prop] g2 = g // sp[EdgeWeight -> (PropertyValue[{g, #}, "weight"] & /@ EdgeList[g])] // sp[VertexLabels -> (# -> PropertyValue[{g, #}, "name"]...
Post a Comment
Read more