# PowerSymmetricPolynomial

PowerSymmetricPolynomial[r]

represents a formal power symmetric polynomial with exponent r.

PowerSymmetricPolynomial[{r1,r2,}]

represents a multivariate formal power symmetric polynomial with exponents r1, r2, .

PowerSymmetricPolynomial[rspec,data]

gives the power symmetric polynomial in data.

# Details

• PowerSymmetricPolynomial[r,{x1,x2,,xn}] is given by .
• PowerSymmetricPolynomial[{r1,r2,},{{x11,x12,},,{xn 1,xn 2,}}] is given by .
• PowerSymmetricPolynomial[rspec] can be used to represent formal power sums used in moment estimators.
• MomentConvert can be used to generate moment estimators in terms of PowerSymmetricPolynomial objects.
• MomentEvaluate can be used to evaluate polynomials of formal PowerSymmetricPolynomial objects on a dataset.

# Examples

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## Scope(3)

PowerSymmetricPolynomial of order 0 is effectively the number of data points:

Use MomentEvaluate to evaluate formal power symmetric polynomials on data:

## Applications(1)

Linearize power symmetric polynomials using AugmentedSymmetricPolynomial:

Check equality for 5 variables:

## Properties & Relations(1)

PowerSymmetricPolynomial is equivalent to AugmentedSymmetricPolynomial with a single exponent:

This relationship also holds for the multivariate generalization:

Wolfram Research (2010), PowerSymmetricPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html.

#### Text

Wolfram Research (2010), PowerSymmetricPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html.

#### CMS

Wolfram Language. 2010. "PowerSymmetricPolynomial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html.

#### APA

Wolfram Language. (2010). PowerSymmetricPolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html

#### BibTeX

@misc{reference.wolfram_2024_powersymmetricpolynomial, author="Wolfram Research", title="{PowerSymmetricPolynomial}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html}", note=[Accessed: 19-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_powersymmetricpolynomial, organization={Wolfram Research}, title={PowerSymmetricPolynomial}, year={2010}, url={https://reference.wolfram.com/language/ref/PowerSymmetricPolynomial.html}, note=[Accessed: 19-July-2024 ]}