1

Is there an official taxonomy of equations that defines all the different types of equations that can be constructed using simple algebraic methods. For example, if I have an equation like the following:

enter image description here

how can I find what this type of equation is called?

Tyler Durden
  • 954
  • Maybe it's worth pointing out that that equation would usually be written as $x^3y + xy^2 - x - y =0$, and so is a 4th-degree polynomial equation in two variables. I think there is a complete taxonomy of such equations. The first such taxonomy for third-degree polynomials was by Newton. – MJD Nov 28 '17 at 21:03

1 Answers1

1

Such an equation (that can be written $P(x,y)=0$, where $P$ is a polynomial) is called an algebraic equation. The field devoted to understanding the solutions of such equations is called algebraic geometry. (In the case of just one equation and two variables like your example, the set of solutions is called an algebraic curve).

It is not the case that every such equation has a specific name (since there are infinitely many of them), but there is a partial classification of such equations (though it would be hard to formulate in simple terms if you're not familiar with differential geometry or algebraic geometry).

Albert
  • 9,170