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Re: Integration bugs in Mathematica 3.0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg9276] Re: [mg9213] Integration bugs in Mathematica 3.0
*From*: Elias Saab <mathes at math.missouri.edu>
*Date*: Mon, 27 Oct 1997 02:46:47 -0500
*Sender*: owner-wri-mathgroup at wolfram.com
Did you try this one?
In[5]:= 2 Integrate[Sqrt[R^2-x^2-y^2],{x,-R,R},
{y,-Sqrt[R^2-x^2],Sqrt[R^2-x^2]}] //Timing
3
4 Pi R
Out[5]= {1.98 Second, -------}
3
The above example was executed in 2.2 on an SGI 133 MHZ. I tried it on a
Pentium II 300MHZ with Mathematica 3.01 and nothing happen in about 1
minute. I told Wolfram about this problem even before the release of
3.0. It did not seem that they did anything about it. Elias Saab
On Fri, 24 Oct 1997, Carlos A. Felippa wrote:
> In a recent FEM project assigned as HW, about one third of the Integrate
> results (216 out of roughly 600) were wrong. Extracted sample:
>
> fu=(2+Cos[phiQ])/Sqrt[6-2*Cos[phiQ]*(-2+Cos[theta])-4*Cos[theta]];
> BQ=Integrate[fu,{theta,0,Pi}];
> Print["BQ=",BQ//InputForm];
> fu=fu/.{phiQ->0};
> BQ=Integrate[fu,{theta,0,Pi}];
> Print["BQ=",BQ//InputForm];
>
> Results:
>
> BQ=0 (* wrong *)
> BQ=3*EllipticK[-3] (* demonstrates bug *)
>
> The students were not amused. 2.2 does it right, but most of them did
> not have access to it on campus machines.
>
> Further, Integrate takes 2-5 times longer than in 2.2.
>
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