Subject: Numerical evaluation of sequence looks suspicious
From: Henry Lenzi
Date: Wed, 31 May 2006 18:03:55 -0300
Hi folks --
Don't you think the following numerical evaluation of a list smells fishy?
First we make a normal sequence:
(%i88) symbolic_list:makelist(x*sin(%pi/x),x,1,15);
3 sqrt(3) %pi
%pi %pi
(%o88) [0, 2, --------- , 2 sqrt(2), 5 sin(---), 3, 7 sin(---), 8 sin(---),
2 5
7 8
%pi %pi %pi %pi %pi
%pi
9 sin(---), 10 sin(---), 11 sin(---), 12 sin(---), 13 sin(---), 14 sin(---),
9 10 11 12
13 14
%pi
15 sin(---)]
15
(I hope you can see the correct fractions above - if not, I apologize
for misformatting):
Then we ask for the numerical evaluation of the previous list:
(%i89) floating_list:ev(symbolic_list,float);
(%o89) [0, 2, 2.598076211353316, 2.82842712474619, 5 sin(0.2 %pi), 3,
7 sin(.1428571428571428 %pi), 8 sin(0.125 %pi), 9 sin(.1111111111111111 %pi),
10 sin(0.1 %pi), 11 sin(.09090909090909091 %pi),
12 sin(.08333333333333333 %pi), 13 sin(.07692307692307693 %pi),
14 sin(.07142857142857142 %pi), 15 sin(.06666666666666667 %pi)]
So, what's with these sines?
TIA,
Henry Lenzi