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the multiplicative order, that is, the number of times the polynomial is divisible by some value; the order of the polynomial considered as a power series, that is, the degree of its non-zero term of lowest degree; or; the order of a spline, either the degree+1 of the polynomials defining the spline or the number of knot points used to ...
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
The commutative law of addition can be used to rearrange terms into any preferred order. In polynomials with one indeterminate, the terms are usually ordered according to degree, either in "descending powers of x", with the term of largest degree first, or in "ascending powers of x". The polynomial 3x 2 − 5x + 4 is written in descending ...
The order polynomial is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts the number of order-preserving maps from a poset to a chain of length n {\displaystyle n} .
is an N-th order even order modified Chebyshev polynomial C e i {\displaystyle Ce_{i}} is the i -th even order modified Chebyshev node For example, the 4th order Chebyshev polynomial from the example above is X 4 − X 2 + .125 {\displaystyle X^{4}-X^{2}+.125} , which by inspection contains no roots of zero.
Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define this more precisely, the maximum number of inflection points possible in a polynomial curve is n-2 , where n is the order of the polynomial equation.
Order (differential equation) or order of highest derivative, of a differential equation Leading-order terms; NURBS order, a number one greater than the degree of the polynomial representation of a non-uniform rational B-spline
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
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