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MathGroup Archive 1997

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Re: errors in 3.0(beta) and 2.2

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5623] Re: [mg5604] errors in 3.0(beta) and 2.2
  • From: Sherman Reed <Sherman.Reed at worldnet.att.net>
  • Date: Wed, 1 Jan 1997 21:04:53 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 06:59 AM 12/27/96 +0000, you wrote:
>(* It is very easy to get completely wrong results
>in both 2.2 and 3.0(beta) using one line examples.=20
>The following example concerns LegendreP[10,10,x]=20
>in 2.2 on a Mac, but I got similar results with
>3.0(beta). I noticed the errors when using Plot[]
>with LegendreP[10,10,Cos[t*Degree]]
>	I would appreciate comments, workarounds etc.=20
>Does the released version of 3.0 have these errors?
>
>$Version
>Macintosh 2.2 (May 4, 1993)
>
>(* Notice LegendreP[10,10,x] is a simple polynomial=20
>of degree 10 *)
>
>LegendreP[10,10,x]
>                  2       4       6      8    10
>654729075 (1 - 5 x  + 10 x  - 10 x  + 5 x  - x  )
>
>(*The following two results look reasonable *)
>LegendreP[10,10,Cos[179*Degree]]//N
>          -9
>2.27155 10
>LegendreP[10,10,Cos[t*Degree]]/.t->179.0//N
>          -9
>2.27155 10
>
>(* The next result is wrong *)
>LegendreP[10,10,Cos[179.0*Degree]]//N
>          8
>1.02775 10
>
>(* All the following results are wrong *)
>LegendreP[10,10,Cos[179.9999*Degree]]//N
>           48
>-2.68317 10
>LegendreP[10,10,Cos[179.99999*Degree]]//N
>          51
>4.88061 10
>LegendreP[10,10,Cos[179.999999*Degree]]//N
>          57
>4.87838 10
>LegendreP[10,10,Cos[t*Degree]]/.t->179.999999//N
>0
>
>
Jonathan

I got different but clearly erroneous answers
using 3.0 on Win 95.

I have included a workaround that I put together
after looking at the form of LegendreP[10,10,x].
It appears that my answers are consistent.

I also plotted the function around Pi and found
that the granularity is similar to the answers
I got with my approximation.

Looks like someone did the coding that did not
appreciate how errors can propagate and/or a
serious error exists in the coding.

LegendreP[10,10,x](* 3.0 view *)
\!\(\(-654729075\)\=20
    \((\(-1\) + 5\ x\^2 - 10\ x\^4 + 10\ x\^6 - 5\ x\^8 + x\^10)\)\)
reed[x_]:=3D-654729075*(-1+x^2*(5+x^2*(-10+x^2*
		(10+x^2*(-5+x^2)))))(* s.c.reed view *)
LegendreP[10,10,Cos[179*Degree]]//N
\!\(\(-2.18068588186959289`*^-7\)\)
reed[Cos[179*Degree]]//N
\!\(\(-2.90758117582612385`*^-7\)\)
LegendreP[10,10,Cos[t*Degree]]/.t->179.0//N
-2.18069=D710\^-7
reed[Cos[t*Degree]]/.t->179.0//N
-2.90758=D710\^-7
LegendreP[10,10,Cos[179.0*Degree]]//N
1.31519=D710\^11
reed[Cos[179.0*Degree]]//N
-2.90758=D710\^-7
LegendreP[10,10,Cos[179.9999*Degree]]//N
7.8638=D710\^50
reed[Cos[179.9999*Degree]]//N
4.36137=D710\^-7
LegendreP[10,10,Cos[179.99999*Degree]]//N
-7.91843=D710\^60
reed[Cos[179.99999*Degree]]//N
1.45379=D710\^-7
LegendreP[10,10,Cos[179.999999*Degree]]//N
1.91079=D710\^72
reed[Cos[179.999999*Degree]]//N
1.45379=D710\^-7

Hope this helps.

Sherman C. Reed



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