##  [Dehomogenization](/dehomogenization) 

  ##  [Dehomogenization](https://puremath.quantumdictionary.io/dehomogenization-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The operation of setting the homogenizing variable to a nonzero scalar (commonly 1) or otherwise restricting to an affine chart to recover an affine polynomial or affine variety from a homogeneous polynomial.

 

 

 

 

 





 

 



 ##  [Dehomogenization](https://algebra.quantumdictionary.io/dehomogenization-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The algebraic operation that recovers an affine polynomial or system from a homogeneous (projective) polynomial by specializing the homogenizing variable to a nonzero constant (commonly 1) or by choosing an affine patch; it converts homogeneous equations in projective coordinates into ordinary polynomial equations in affine coordinates.