       Re: Usage of #1

• To: mathgroup at smc.vnet.net
• Subject: [mg96322] Re: Usage of #1
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 11 Feb 2009 05:23:53 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <gmrmdk\$9uk\$1@smc.vnet.net>

```In article <gmrmdk\$9uk\$1 at smc.vnet.net>,
Nandhini <nandhini.gopalan at gmail.com> wrote:

> Im very new to mathematica. I have got a result where im getting
> something like "Root[1+a #1+a^2 #1^5 &,1]. i wud like to know how else
> i can write it. i dont want the #1 to b displayed. is tehre any
> alternative. Plz help me out of this.

A Root[poly, n] object is an exact representation of the nth root of the
polynomial poly (written as an pure function, that is why you see the #
character or Slot[]). Note that the polynomial expressed as a pure
function in the Root[] object is the same as the original polynomial fed
to the Solve[] function.

To get the corresponding numerical values, one can use the N[] function,
and, in some cases, one can try to get a representation with radicals by
applying the ToRadicals[] function. For instance,

In:= Solve[x^5 + 2 x + 1 == 0, x]

Out=
5                                  5
{{x -> Root[1 + 2 #1 + #1  & , 1]}, {x -> Root[1 + 2 #1 + #1  & , 2]},

5                                  5
{x -> Root[1 + 2 #1 + #1  & , 3]}, {x -> Root[1 + 2 #1 + #1  & , 4]},

5
{x -> Root[1 + 2 #1 + #1  & , 5]}}

In:= % // N

Out= {{x -> -0.486389}, {x -> -0.701874 - 0.879697 I}, {x ->
-0.701874 +
0.879697 I}, {x -> 0.945068- 0.854518 I}, {x -> 0.945068+ 0.854518
I}}

In:= ToRadicals[Root[#^3 + # + 11 &, 1] + Root[#^5 - 2 &, 3]]

Out=
1                    1/3
(- (-99 + Sqrt))
4/5  1/5             2           1/3    2
(-1)    2    - (--------------------)    + -------------------------
3 (-99 + Sqrt)                  2/3
3

Regards,
--Jean-Marc

```

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