Determinants | Polynomials | Computer algebra

Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant. The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation. The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usual resultant) is a generalization, introduced by Macaulay, of the usual resultant. It is, with Gröbner bases, one of the main tools of elimination theory. (Wikipedia).

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From playlist Vector Math Lessons

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From playlist Vectors

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From playlist SpoonFeedMe: Engineering Mechanics (Statics & Dynamics)

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From playlist Vectors

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From playlist Differential Equations

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Rational function | Empty sum | Vector space | Indeterminate (variable) | Codomain | Minimal polynomial (field theory) | Francis Sowerby Macaulay | Rational number | Symbolic integration | E (mathematical constant) | Quasi-homogeneous polynomial | Discriminant | Field extension | Projective line | Sylvester matrix | Square matrix | Partial fraction decomposition | Generic property | Prime number | Irreducible polynomial | Complex number | Polynomial greatest common divisor | Nonlinear algebra | Computer algebra system | Chinese remainder theorem | Subring | Ideal (ring theory) | Antiderivative | Symmetric polynomial | Reciprocal polynomial | Degree of a polynomial | Algebraic set | System of polynomial equations | Free module | Elementary symmetric polynomial | Linear map | Monic polynomial | Arithmetic mean | Monomial basis | Bézout's theorem | Dimension of an algebraic variety | Integral domain | Algebraic closure | Elimination theory | Homogeneous polynomial | Algebraic number | Radical of an ideal | Hilbert's Nullstellensatz | Polynomial | Point at infinity | Curve | Determinant | Minor (linear algebra) | Parametric equation | Hypersurface | Bézout matrix | Mathematics | Time complexity | Computer algebra | Gröbner basis | Modular arithmetic | Principal ideal | Commutative ring | Bézout's identity | Algebraically closed field | Monomial | Greatest common divisor | Gaussian elimination | Homogeneous coordinates | Cylindrical algebraic decomposition | Field (mathematics) | Ring homomorphism | Root of a function | Square-free polynomial | Number theory | Linear form | Algorithm | Generic polynomial