Knowra Polynomial degree Polynomial degree The degree of a nonzero polynomial is the greatest degree among its nonzero terms. In one variable it is the largest exponent with a nonzero coefficient; in several variables, it is usually the largest sum of exponents in a term.
Polynomial : An expression formed from variables, coefficients, and nonnegative integer powers, combined by addition and multiplication. Degree is a property assigned to polynomials and their terms.
Total degree : The largest sum of variable exponents among a polynomial's nonzero terms. This is the standard multivariable interpretation of polynomial degree.
Fundamental theorem of algebra : The theorem that every nonconstant complex polynomial has a complex root and factors into linear factors over the complex numbers. A degree-n polynomial has exactly n complex roots when multiplicities are counted.
Polynomial degree in several variables : The study of degree conventions for polynomials with two or more variables, including total, partial, and separate degrees. Multivariable polynomials admit several useful notions that need not agree.
Monomial : A product of a coefficient and variables raised to nonnegative integer powers. Each nonzero term is a monomial whose degree contributes to the polynomial's degree.
Leading term : The greatest term of a polynomial under a specified monomial ordering, including its coefficient. In one variable, its exponent is the polynomial's degree.
Polynomial interpolation : The construction of a polynomial matching prescribed values at specified points. With distinct nodes, n data values determine an interpolating polynomial of degree at most n−1.
Partial degree : The greatest exponent of a specified variable among a polynomial's nonzero terms. It measures degree in one variable while treating the others as coefficients.
Coefficient : A numerical or symbolic factor multiplying a variable or product of variables. A term with a zero coefficient is absent and cannot determine the degree.
Degree of a product : The degree relation governing the product of nonzero polynomials, typically additive under standard conventions. Multiplying leading terms explains why degrees add for nonzero univariate polynomials.
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