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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