The cylindrical parts of a system of real algebraic equations and inequalities in variables 
, ..., 
are regions described by conditions of the form
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where '
'
is one of 
,
,
or 
,
and 
and 
are 
or algebraic expressions in variables 
, ..., 
that are real-valued whenever real
numbers 
,
..., 
satisfy
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
A disjunction of descriptions of cylindrical parts describes their union. To form a cylindrical algebraic decomposition, the parts must be cells whose coordinate projections are identical or disjoint at every level.
