Computer algebra | Algebraic geometry

Elimination theory

In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations. Classical elimination theory culminated with the work of Francis Macaulay on multivariate resultants, as described in the chapter on Elimination theory in the first editions (1930) of Bartel van der Waerden's Moderne Algebra. After that, elimination theory was ignored by most algebraic geometers for almost thirty years, until the introduction of new methods for solving polynomial equations, such as Gröbner bases, which were needed for computer algebra. (Wikipedia).

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Solving a system of equations with infinite many solutions

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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How to Use Elimination to Solve a System of Equations

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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How to Solve a System of Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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Using Elimination to Solve Systems

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

Video thumbnail

Solve a System of Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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How to Solve a System of Equation Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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Solve a system of equation when they are the same line

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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From playlist Solve a System of Equations Using Elimination | Hard

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From playlist Solve a System of Equations Using Elimination | Medium

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Tarski–Seidenberg theorem | Quantifier elimination | Bézout's theorem | Algebraically closed field | Israel Gelfand | Main theorem of elimination theory | Cramer's rule | Commutative algebra | Hilbert's Nullstellensatz | Polynomial | Smith normal form | David Hilbert | Francis Sowerby Macaulay | Invariant theory | Resultant | Gaussian elimination | Discriminant | Moderne Algebra | Cylindrical algebraic decomposition | Hermite normal form | Boolean satisfiability problem | Algebraic geometry | Buchberger's algorithm | Leopold Kronecker | Diophantine equation | Mathematical logic | Computer algebra | Triangular decomposition | Abelian group