Re: Strange timing behavior of Integrate[]
- To: mathgroup at smc.vnet.net
- Subject: [mg8457] Re: [mg8341] Strange timing behavior of Integrate[]
- From: "C. Woll" <carlw at u.washington.edu>
- Date: Sat, 30 Aug 1997 00:43:11 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Hi Carlos,
I don't have any additional comments on timing behavior, but as far as
your integral is concerned, have you considered that for n,m even:
Integrate[Sin[phi]^n Cos[phi]^m,{phi,0,2 pi}] is 2 Beta[(n+1)/2,(m+1)/2]
and for n or m odd, the above integral vanishes?
Carl Woll
Dept of Physics
U of Washington
On Tue, 26 Aug 1997, Carlos A. Felippa wrote:
> I am doing an acoustic radiation study with Mma 3.0 in which I have to
> evaluate thousands of trigonometric integrals of the form sin[phi]^m*cos[phi]^n
> over 0->2 Pi for a wide range of integers m and n. I noticed that some
> combinations took enormous times to evaluate forcing aborts.
>
> I traced it to the phenomenon exemplified by the equivalent commands
>
> Print [Integrate[(a+b)^12*Cos[phi]^8*Sin[phi]^8,{phi,0,2*Pi}]//Timing];
> Print [(a+b)^12*Integrate[Cos[phi]^8*Sin[phi]^8,{phi,0,2*Pi}]//Timing];
>
> The result is obviously the same. However, On a Mac 8500/120,
> the first form takes 4.85 seconds while the second completes in 0.53 Seconds.
> For more complex factors the time ratio may reach into the thousands.
>
> What is going on? It seems as if Integrate[] cannot identify invariant
> expressions.
>
>
>
>