[Maxima-bugs] [ maxima-Bugs-3054399 ] Sum incorrectly calculated

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Bugs item #3054399, was opened at 2010-08-27 17:30
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Simplification
Group: None
>Status: Pending
>Resolution: Works For Me
Priority: 5
Private: No
Submitted By: Dženan Zukić (dzenanz)
Assigned to: Nobody/Anonymous (nobody)
Summary: Sum incorrectly calculated

Initial Comment:
The commands below are steps to reproduce. The correct sum for n=5 is 0.25.

(%i2) declare (n, constant);
(%o2) done
(%i6) sum((0.25+cos(2*i*%pi)+0.5*cos(4*i*%pi))/n,i,0,n-1);
(%o6) 1.75

GUI: wxMaxima on Win7 x64
-------------------------------------------------------------
Maxima version: 5.22.1
Maxima build date: 11:48 8/13/2010
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
-------------------------------------------------------------

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>Comment By: Dieter Kaiser (crategus)
Date: 2010-08-29 03:38

Message:
I do not see a problem and I get the expected results:

(%i2) sum((1/4+cos(2*i*%pi)+1/2*cos(4*i*%pi))/n,i,0,n-1);
(%o2) 7/4

This is the same as 

(%i26) 7/4*sum(1/n,i,0,n-1);
(%o26) 7/4

When a division by n is missing in the cos functions we have to use the
function simplify_sum to get a simplified result:

(%i20)
simplify_sum(sum((1/4+cos(2*i*%pi/n)+1/2*cos(4*i*%pi/n))/n,i,0,n-1));
(%o20) 1/4

This again is a correct result. The result does not depend on n.

Setting the status to pending and the resolution to "works for me".
Dieter Kaiser


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Comment By: Dženan Zukić (dzenanz)
Date: 2010-08-27 21:08

Message:
You missed division by n (at the end). And I missed division by n within
cosines. I will have to check this again on Monday - I guess I have found a
bug in my code now :D

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Comment By: Raymond Toy (rtoy)
Date: 2010-08-27 19:55

Message:
Why is the correct answer 0.25?  

0.25+cos(2*i*%pi)+0.5*cos(4*i*%pi) = 0.25 + 1 + 0.5 = 1.75 for all integer
i.

So it looks like the sum should always be 1.75 to me.  Did I miss
something?

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