ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 26 Jul 2018 15:40:47 -0500Symmetric polynomial as a polynomial on elementary symmetric polynomialshttp://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/ `SymmetricFunctions`, together with the various provided bases, is very good at writing a symmetric polynomial as the *linear combination* of what is called *elementary functions* here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a *polynomial* on what is called *elementary symmetric polynomials* in the same paper. Can that be computed with Sage?Tue, 16 Feb 2016 10:07:18 -0600http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/Comment by slelievre for <p><code>SymmetricFunctions</code>, together with the various provided bases, is very good at writing a symmetric polynomial as the <em>linear combination</em> of what is called <em>elementary functions</em> here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a <em>polynomial</em> on what is called <em>elementary symmetric polynomials</em> in the same paper. Can that be computed with Sage?</p>
http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?comment=43173#post-id-43173Documentation and tutorials:
- [SageMath documentation on symmetric functions](http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/sf/sf.html)
- [Demo on symmetric functions](https://more-sagemath-tutorials.readthedocs.io/en/latest/demo-symmetric-functions.html)
- [Tutorial on symmetric functions](https://more-sagemath-tutorials.readthedocs.io/en/latest/tutorial-symmetric-functions.html)Thu, 26 Jul 2018 15:40:47 -0500http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?comment=43173#post-id-43173Comment by slelievre for <p><code>SymmetricFunctions</code>, together with the various provided bases, is very good at writing a symmetric polynomial as the <em>linear combination</em> of what is called <em>elementary functions</em> here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a <em>polynomial</em> on what is called <em>elementary symmetric polynomials</em> in the same paper. Can that be computed with Sage?</p>
http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?comment=43170#post-id-43170Possibly related questions (including the present one):
- [Ask Sage 9737 (2013-01): Symmetric polynomials of squares of variables](https://ask.sagemath.org/question/9737)
- [Ask Sage 32569 (2016-02): Symmetric polynomial as polynomial on elementary symmetric polynomials](https://ask.sagemath.org/question/32569)
- [Ask Sage 33378 (2016-05): Symmetric function as polynomial on elementary symmetric functions](https://ask.sagemath.org/question/33378)
- [Ask Sage 42872 (2018-07): Symmetric polynomial in terms of elementary symmetric polynomials](https://ask.sagemath.org/question/42872)Thu, 26 Jul 2018 15:40:16 -0500http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?comment=43170#post-id-43170Answer by tmonteil for <p><code>SymmetricFunctions</code>, together with the various provided bases, is very good at writing a symmetric polynomial as the <em>linear combination</em> of what is called <em>elementary functions</em> here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a <em>polynomial</em> on what is called <em>elementary symmetric polynomials</em> in the same paper. Can that be computed with Sage?</p>
http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?answer=33382#post-id-33382See also the following answer to close question (and answer): http://ask.sagemath.org/question/33378/convert-a-symmetric-function-into-a-polynomial-on-elementary-symmetric-functions/?answer=33381#post-id-33381
Thu, 12 May 2016 03:08:53 -0500http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?answer=33382#post-id-33382Answer by giomasce for <p><code>SymmetricFunctions</code>, together with the various provided bases, is very good at writing a symmetric polynomial as the <em>linear combination</em> of what is called <em>elementary functions</em> here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a <em>polynomial</em> on what is called <em>elementary symmetric polynomials</em> in the same paper. Can that be computed with Sage?</p>
http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?answer=32588#post-id-32588 The answer is actually implicit in the linked page: elementary functions have the property that (with Sage's notation) `e[i, j, ...] = e[i]*e[j]*...`. So there you have your polynomial.Wed, 17 Feb 2016 11:45:17 -0600http://ask.sagemath.org/question/32569/symmetric-polynomial-as-a-polynomial-on-elementary-symmetric-polynomials/?answer=32588#post-id-32588