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Any efficient way to make complete homogeneous symmetric functions in Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126819] Any efficient way to make complete homogeneous symmetric functions in Mathematica?
  • From: Rex <aoirex at gmail.com>
  • Date: Sun, 10 Jun 2012 02:14:38 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

We do have elementary symmetric functions, SymmetricPolynomial[k,{x_1..x_n}]
http://reference.wolfram.com/mathematica/ref/SymmetricPolynomial.html

But I didn't found complete homogeneous symmetric functions.

The induction method to compute h_n from e_i and h_j (j<=n-1) is not that efficient. 
https://en.wikipedia.org/wiki/Complete_homogeneous_symmetric_polynomial

Is there any easier way to do this?



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