A multidimensional polynomial is a mathematical expression involving multiple variables raised to various powers. These polynomials can be defined in two or more dimensions, unlike univariate polynomials, which only have one variable. They are commonly used in multiple fields such as algebra, calculus, and applied mathematics, notably in areas such as statistics, physics, and engineering.
Frequency of Use: This term is primarily used in written contexts, especially in academic papers, textbooks, and technical documents related to mathematics and engineering. It is less commonly used in everyday spoken language, as it is more specialized.
A multidimensional polynomial can describe complex relationships in data.
Translation: Полином многомерных переменных может описывать сложные взаимоотношения в данных.
Solving a multidimensional polynomial often requires advanced techniques.
Translation: Решение многомерного полинома часто требует использования продвинутых техник.
In computer graphics, a multidimensional polynomial is used for surface modeling.
Translation: В компьютерной графике многомерный полином используется для моделирования поверхности.
While "multidimensional polynomial" itself is not a common idiomatic expression, it can appear in various mathematical phrases and contexts. Below are some idioms and expressions related specifically to polynomials:
Polynomial time refers to an algorithm's efficiency in relation to the size of the input.
Translation: Полиномиальное время относится к эффективности алгоритма в зависимости от размера входных данных.
Root of a polynomial means a value for which the polynomial equals zero. Translation: Корень полинома означает значение, при котором полином равен нулю.
Polynomial regression is a form of regression analysis that models the relationship between a dependent variable and one or more independent variables as an nth degree polynomial. Translation: Полиномиальная регрессия — это форма анализа регрессии, моделирующая взаимосвязь между зависимой переменной и одной или несколькими независимыми переменными как полиномом n-й степени.
Polynomial expression generally suggests that the algebraic expression consists of multiple terms. Translation: Полиномное выражение обычно подразумевает, что алгебраическое выражение состоит из нескольких членов.
The term "multidimensional" derives from the prefix "multi-", meaning 'many' or 'multiple', and "dimensional," which pertains to dimensions or aspects of an object or a space. The word "polynomial" comes from the Latin "poly," meaning 'many,' and "nomios," from Greek meaning 'terms,’ thus representing an expression with multiple terms.
Synonyms:
- Multi-variable polynomial
- Multivariate polynomial
- Higher-order polynomial
Antonyms:
- Univariate polynomial
- Linear polynomial
- Monomial
This structured breakdown provides comprehensive insights into the term "multidimensional polynomial," covering its meanings, uses, and related aspects in mathematics.