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
Load the package:
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
- References:
- Symmetric polynomials
- From: shubi@nusun.jinr.ru
- Symmetric polynomials