Message Boards Message Boards

0
|
7706 Views
|
8 Replies
|
2 Total Likes
View groups...
Share
Share this post:

Power[ ] is not working inside of Sum [ ]?

Yuri Pitushkevich
Posted 3 years ago

Morning! I'm trying to solve expression, using palette comands only. I want to get all roots of expression, than get sum of squared roots. But ^2 is not working at all. What am I doing wrong? My code be like:

a = Solve[x^7-1==0,x];

res = \!\(UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(7\)]\(Power[\((x /. a[\([n]\)])\), 2]\)\)

Also is there any way to simplify result? FullSimplify returns 0 and Simplify is not working at all. Res is:

1-(-1)^(1/7)+(-1)^(2/7)-(-1)^(3/7)+(-1)^(4/7)-(-1)^(5/7)+(-1)^(6/7)
POSTED BY: Yuri Pitushkevich
8 Replies
Sort By:

Does anyone can explain, whyn am I getting 0 as a result of FullSimplify? enter image description here
POSTED BY: Yuri Pitushkevich

The result is zero and FullSimplify manages to make that determination. This is a good outcome. If FullSimplify gave, say,Pi^2+EulerGamma`, that would indicate it was having a very bad day.
POSTED BY: Daniel Lichtblau

But as I can see, the result should be equal to 1. Or not?
POSTED BY: Yuri Pitushkevich

I'd go with the "or not" option on that.
POSTED BY: Daniel Lichtblau

If you check e.g. the Wikipedia page for resultants you find that this sum-of-squared-roots can be found using the computation below.

In[810]:= Coefficient[Resultant[x^2 - y, x^7 - 1, x], y^6]

(* Out[810]= 0 *)

Also there is a more direct method using RootSum (which may well use the above approach under the hood).

In[815]:= RootSum[#^7 - 1 &, #^2 &]

(* Out[815]= 0 *)
POSTED BY: Daniel Lichtblau

There are 7 solutions for x they are enter image description here . .Using N[a] you get

{{x -> 1.},

{x -> -0.9009688679024191 - 0.4338837391175581 I},

{x -> 0.6234898018587336 + 0.7818314824680298 I},

{x -> -0.22252093395631445 - 0.9749279121818236 I},

{x -> -0.22252093395631434 + 0.9749279121818236 I},

{x -> 0.6234898018587335 - 0.7818314824680299 I},

{x -> -0.900968867902419 + 0.43388373911755823 I}}

-
POSTED BY: Marvin Ray Burns

Yes, and I'm trying to get Sum of all roots^2 enter image description here

But as you can see on my screenshot, each root is not powered. And even after FullSimplity, roots are not 1 or -1, but (-1)^(1/7)
POSTED BY: Yuri Pitushkevich 
a = Solve[x^7 - 1 == 0, x]

Out[42]= {{x -> 1}, {x -> -(-1)^(1/7)}, {x -> (-1)^( 2/7)}, {x -> -(-1)^(3/7)}, {x -> (-1)^( 4/7)}, {x -> -(-1)^(5/7)}, {x -> (-1)^(6/7)}}

  t = N[Total[x^2 /. a]]

Out[53]= 1.1102230246251565*10^-16 + 0. I

Chop[t]

Out[54]= 0
POSTED BY: Marvin Ray Burns
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract