symmetric function
[/sɪˈmetrɪk ˈfʌŋkʃən/]
nounfemininepl: symmetric functions / funções simétricas
função simétrica
1. A mathematical function of multiple variables that remains unchanged when any two variables are interchanged or permuted in any way
The function f(x, y) = x + y is a symmetric function because f(x, y) = f(y, x).
A função f(x, y) = x + y é uma função simétrica porque f(x, y) = f(y, x).
2. In algebra, a polynomial in n variables that is invariant under all permutations of the variables
Elementary symmetric functions are building blocks for all symmetric polynomials.
As funções simétricas elementares são blocos de construção para todos os polinômios simétricos.
3. A function used extensively in combinatorics, number theory, and algebraic geometry
Symmetric functions appear naturally in the study of polynomial rings and invariant theory.
Funções simétricas aparecem naturalmente no estudo de anéis polinomiais e teoria dos invariantes.
This is a specialized mathematical term used primarily in academic and professional contexts within both Brazilian Portuguese and English-speaking mathematical communities. The terminology is standardized internationally, particularly in higher mathematics education and research. It appears frequently in advanced mathematics curricula, especially in courses on algebra, combinatorics, and number theory at universities in Brazil and the United States.
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