APU has been written (using the operator overloading facility in C++) to produce user code which looks like the routines written for a computer algebra system like Maple. Syntax is therefore simple in APU : to add two polynomials one simply writes
p3 = p1 + p2;
Though knowledge of C++ would be nice, one is not required to know a whole lot about C++ to write a program in APU. In fact, one could use one of the example programs included in with the code as a starting point for writing their own application. If you feel you do not have a good enough knowledge of C++ the best way to get started would be to examine the two example programs provided with the toolkit. The first one counts the number of real intersections of (the algebraic sets defined by) two polynomials in two variables. The common roots are projected on to one axis by computing the Sylvester resultant of the two polynomials. A straightforward Sturm sequence computation gives the number of common real roots in the generic case. The second example program deals with implicit point location in semi-algebraic varieties.