Re: Bug in math4
- To: mathgroup at smc.vnet.net
- Subject: [mg20701] Re: [mg20633] Bug in math4
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Mon, 8 Nov 1999 02:48:45 -0500
- References: <80384p$aeq@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Further "insight": exact = Integrate[Sqrt[2 - Sin[x]], x] -2*EllipticE[1/2*(Pi/2 - x), -2] (exact/.x->4)-(exact/.x->1) 3.73785 where did the extra EllipticF come from in the original Integrate? Kevin Ersek, Ted R <ErsekTR at navair.navy.mil> wrote in message news:80384p$aeq at smc.vnet.net... > Lennart Bengtsson wrote: > ------------------------------ > I just want to point out that there seems to be a serious bug > in the new mathematica version 4.0 for Solaris. See the following > example: > > In[25]:= NIntegrate[Sqrt[2-Sin[x]],{x,1,4}] > > Out[25]= 3.73785 (correct) > > In[26]:= N[Integrate[Sqrt[2-Sin[x]],{x,1,4}]] > > Out[26]= 3.73785 + 4.00431 I (incorrect, the integrand is real) > > The bug is not observed with version 3 of mathematica. > > ---------------------------- > > Consider the following: > > In[1]:= > int = Integrate[Sqrt[2 - Sin[x]], {x, 157/100, 158/100}] > > Out[1]= > -2*EllipticE[(-79/50 + Pi/2)/2, -2] + > 2*EllipticE[(-157/100 + Pi/2)/2, -2] + > 4*EllipticF[I*ArcSinh[1/Sqrt[2]], -2] > > > In[2]:= > N[int] > > Out[2]= > 0.01 + 4.00431*I (*** Wrong answer ***) > > > In[3]:= > a = Take[int, 2] > > Out[3]= > -2*EllipticE[(-79/50 + Pi/2)/2, -2] + 2*EllipticE[(-157/100 + Pi/2)/2, -2] > > > In[4]:= > N[a] > > Out[4]= > 0.01 > > > In[5]:= > NIntegrate[Sqrt[2 - Sin[x]], {x, 157/100, 158/100}] > > Out[5]= > 0.01 > > Above we get the right answer if we throw away the last term of (int). I > suspect Mathematica thought it had to throw in the extra term to get around > what it thought was a singularity in the anti-derivative. > > Why does it come out right in Version 3, but not in Version 4 ? I suspect > Version 4 tries harder to locate singularities between the limits of > integration to avoid wrong answers given with Version 3. However, it seems > the new method thinks there is a singularity in this problem when there is > none. > > -------------------- > Regards, > Ted Ersek > > For Mathematica tips, tricks see > http://www.dot.net.au/~elisha/ersek/Tricks.html >