AugmentedSymmetricPolynomial
AugmentedSymmetricPolynomial[{r1,r2,…}]
represents a formal augmented symmetric polynomial with exponents r1, r2, ….
AugmentedSymmetricPolynomial[{{r11,…,r1n},{r21,…,r2n},…}]
represents a multivariate formal augmented symmetric polynomial with exponent vectors {r11, …, r1n}, {r21, …, r2n}, ….
AugmentedSymmetricPolynomial[rspec,data]
gives the augmented symmetric polynomial in data.
Details
- AugmentedSymmetricPolynomial[{r1,…,rk},{x1,…,xn}] is given by
, where the sum is taken over the index set 
and 
. - In the multivariate case, ri and xi are vectors and xiri is interpreted as xi1ri1xi2ri2⋯.
- AugmentedSymmetricPolynomial[rspec] can be used to represent formal augmented symmetric sums used in moment estimators.
- MomentConvert can be used to generate moment estimators in terms of AugmentedSymmetricPolynomial objects.
- MomentEvaluate can be used to evaluate polynomials of formal AugmentedSymmetricPolynomial objects on a dataset.
Examples
open allclose allBasic Examples (1)
Scope (2)
Use MomentEvaluate to evaluate formal augmented symmetric polynomials on data:
TraditionalForm formatting:
Applications (1)
Linearize polynomials in AugmentedSymmetricPolynomial:
Properties & Relations (1)
AugmentedSymmetricPolynomial with a single exponent is equivalent to PowerSymmetricPolynomial:
This relationship also holds for the multivariate generalization:
Text
Wolfram Research (2010), AugmentedSymmetricPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/AugmentedSymmetricPolynomial.html.
CMS
Wolfram Language. 2010. "AugmentedSymmetricPolynomial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AugmentedSymmetricPolynomial.html.
APA
Wolfram Language. (2010). AugmentedSymmetricPolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AugmentedSymmetricPolynomial.html