**NOTE:** This section of the documentation is out of date!

In the Projection Phase, QEPCAD computes a set of polynomials
that implicitly defines the CAD that it will later explicitly
construct in the *Stack Construction Phase*. This set of
polynomials, the *projection factor set*, must satisfy
some special properties in order to define a CAD. So the goal
of this phase is to construct as small a set as we can while
ensuring that it defines a CAD and contains certain polynomials
we'll need to solve the quantifier elimination problem.
A *projection operator* is a function that's used to
define a projection factor set, and several are available in
QEPCAD.

**The Average User**

======================================================= Enter an informal description between '[' and ']': [ Using Hong's Projection at level 4 ] Enter a variable list: (a,b,d,c) Enter the number of free variables: 4 Enter a prenex formula: [ 54 c^3 - 27 a b c^2 + 6 a^3 c^2 - 144 b d c + 6 a^2 d c + 4 b^3 c - a^2 b^2 c + 96 a d^2 + 40 a b^2 d - 9 a^3 b d = 0 ]. ======================================================= Before Normalization > go Before Projection (c) > proj-op (m,m,h) Before Projection (c) > go Before Choice > go Before Solution >

`Error! Delineating polynomial should be added over cell(2,2)!`

"
during the stack construction phase. In this case it turns out
that McCallum's projection is not invalid, it's just that QEPCAD
can't `(x1,x2,...,xk)`

you should issue the command
`proj-op (m,m,h,h,h,...,h)`

where the list has
`h`

'.
**The Advanced User**

If you know some things about different projection operators you
can interact with QEPCAD to do better - specifically by removing
projection factors during the projection process. I'll add some
info on that in the future!

Christopher W Brown Last modified: Tue Mar 13 13:33:34 EDT 2007