Re: Symmetric polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg68994] Re: [mg68940] Symmetric polynomials
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Sat, 26 Aug 2006 02:04:33 -0400 (EDT)
• References: <200608250934.FAA09161@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```shubi at nusun.jinr.ru wrote:
> Dear All,
>
>    Is the possibility in "Mathematica" express symmetric functions, for
> example:
>
> P=y1^2 y2 y3 + y1 y2^2 y3 + y1 y2 y3^2 + y1^2 y2 y4 +
> y1 y2^2 y4 + y1^2 y3 y4 + y2^2 y3 y4 + y1 y3^2 y4 +
> y2 y3^2 y4 + y1 y2 y4^2 + y1 y3 y4^2 + y2 y3 y4^2;
>
> by the standard symmetric polynomials:
> S1=y1+y2+y3+y4;
> S2=y1^2+y2^2+y3^2+y4^2;
> S3=y1^3+y2^3+y3^3+y4^3;
>       . . .
>
> Best regards
>                       Nodar Shubitidze
>                       Joint Institute for Nuclear Research
>                       Dubna, Moscow region, Russia

Needs["Algebra`SymmetricPolynomials`"]

Then, use SymmetricReduction:

In[3]:=
SymmetricReduction[P,{y1,y2,y3,y4},{s1,s2,s3,s4}]

Out[3]=
{s1 s3-4 s4,0}

The second argument 0 indicates that P is symmetric, i.e., there is no
nonsymmetric piece left over.

Carl Woll
Wolfram Research

```

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