A generic cylindrical algebraic decomposition describes a semialgebraic set 
away from an exceptional set
of lower dimension, using a union 
of full-dimensional cylindrical cells. The symmetric
difference of 
and 
has measure zero in 
. Generic decompositions can be faster to compute because
they do not resolve all lower-dimensional cells.
For example, a generic decomposition of the closed disk 
can give its open disk 
, omitting the boundary circle. For the unit circle
alone, the full-dimensional part in 
is empty.
A generic description can also ignore a lower-dimensional exclusion. For 
with 
, it can give the entire open triangle,
leaving the excluded line to the exceptional set.
The command GenericCylindricalDecomposition[ineqs, vars] implements generic cylindrical algebraic decomposition in the Wolfram
Language. It returns a pair whose first element describes 
and whose second describes an exceptional algebraic
set 
containing the symmetric
difference of 
and 
. The returned 
may be the empty set, and it
need not consist only of points where the two descriptions
differ (Wolfram Research 2007).
