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MathGroup Archive 1997

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Re: Integrate got slower in Version 3.0/Example

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8990] Re: Integrate got slower in Version 3.0/Example
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Tue, 7 Oct 1997 03:35:36 -0400
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Elias Saab wrote:
> 
> In version 2.2
> 
> In[1]:= Integrate[Sqrt[R^2-x^2-y^2],{x,-R,R},
>         {y,-Sqrt[R^2-x^2],Sqrt[R^2-x^2]}]//Timing
> 
>                             3
>                       2 Pi R
> Out[1]= {5.17 Second, -------}
>                          3
> 
> In Version 3.0
> Integrate[Sqrt[R^2-x^2-y^2],{x,-R,R},
>         {y,-Sqrt[R^2-x^2],Sqrt[R^2-x^2]}]//Timing
> Integrate::"gener": "Unable to check convergence"
> 
>                            3
>                       2 Pi R
> Out[1]= {32.8 Second, -------}
>                          3

For

  In[1]:= Integrate[Sqrt[R^2 - x^2 - y^2], {x, -R, R}, 
     {y, -Sqrt[R^2 - x^2], Sqrt[R^2 - x^2]}]//Timing

  Integrate::"gener": "Unable to check convergence"

  Out[1]=
	                     3
	               2 Pi R
	{13.92 Second, -------}
	                  3

you can turn off GenerateConditions:

  In[2]:= SetOptions[Integrate,GenerateConditions->False]
  Out[2]= {Assumptions->{},GenerateConditions->False,
	PrincipalValue->False}

but this is not faster for this case:

  In[3]:= Integrate[Sqrt[R^2 - x^2 - y^2], {x, -R, R}, 
     {y, -Sqrt[R^2 - x^2], Sqrt[R^2 - x^2]}]//Timing

  Integrate::"gener": "Unable to check convergence"

  Out[3]=
	                     3
	               2 Pi R
	{13.41 Second, -------}
	                  3

However, why not use polar coordinates anyway?

  In[4]:= PowerExpand[Integrate[r*Sqrt[R^2 - r^2], 
    {theta, 0, 2*Pi}, {r, 0, R}]]//Timing

  Out[4]=
                     3
               2 Pi R
 {0.41 Second, -------}
                  3

Cheers,
	Paul 
s
____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia           
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au 
AUSTRALIA                             http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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