Dehomogenization

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.

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.