Re: Root function

• To: mathgroup at smc.vnet.net
• Subject: [mg51031] Re: [mg51009] Root function
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 2 Oct 2004 03:18:01 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Mathematica is giving you exact answers as the various roots of cubic
equations. To obtain approximate roots you can add N.

Eigensystem[{{-1, 1, 0, 0}, {1, -2, 1, 0}, {0, 1, -2, 0}, {0, 0, 1, 0}}] //
N
{{-3.24698, -1.55496, -0.198062,
0.}, {{-1.80194, 4.04892, -3.24698, 1.}, {1.24698, -0.692021, -1.55496,
1.}, {-0.445042, -0.356896, -0.198062, 1.}, {0., 0., 0., 1.}}}

Or, in this case, if you want an exact answer you could use

Eigensystem[{{-1, 1, 0, 0}, {1, -2, 1, 0}, {0, 1, -2, 0}, {0, 0, 1,
0}}] // ToRadicals

(output omitted)

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Ben [mailto:bmauer at wisc.edu]
To: mathgroup at smc.vnet.net

When I try to diagonalize this matrix in mathematica 5:
Eigensystem[{{-1, 1, 0, 0}, {1, -2, 1, 0}, {0, 1, -2, 0}, {0, 0, 1, 0}}]
I get this ugly mess

\!\({{Root[1 + 6\ #1 + 5\ #1\^2 + #1\^3 &, 1], Root[1 + 6\ #1 +
5\ #1\^2 + #1\^3 &, 2], Root[
1 + 6\ #1 + 5\ #1\^2 + #1\^3 &, 3], 0}, {{\(-1\) - 3\
Root[1 + 6\ #1 + 5\ #1\^2 + #1\^3 &, 1] - Root[1 + 6\ #1 +
etc etc etc

Mathematica 4 gives me the right answer.
How do I get v5 to not spit this out and what does it mean?

```

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