# algebraic equation

The equation

$$f({x}_{1},{x}_{2},\mathrm{\dots},{x}_{m})=0,$$ |

where the left hand is a polynomial^{} in ${x}_{1}$, ${x}_{2}$, …, ${x}_{m}$ with coefficients in a certain field, is called an algebraic equation over that field. Often the field in question is $\mathbb{Q}$; then the coefficients may be assumed to be integers.

By the degree of an algebraic equation is meant the degree of the polynomial.

E.g. $3{x}^{2}-1=0$ and ${x}^{3}+{x}^{2}y+x{y}^{2}+{y}^{3}=0$ are algebraic equations over the field $\mathbb{Q}$, the degrees of which are 2 and 3.

Title | algebraic equation |

Canonical name | AlgebraicEquation |

Date of creation | 2013-03-22 15:14:07 |

Last modified on | 2013-03-22 15:14:07 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 7 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 13P05 |

Classification | msc 11C08 |

Classification | msc 12E05 |

Related topic | Equation |

Related topic | PolynomialEquationOfOddDegree |

Related topic | SymmetricQuarticEquation |

Defines | degree of equation |