The input and output of NCProcess

The input to the NCProcess commands is:

I1. A list of knowns.

I2. A list of unknowns (together with an order which gives you priorities for eliminating them, see §).

I3. Collections C and of equations in these knowns and unknowns.

The output of the NCProcess commands is a list of expressions which are mathematically equivalent to . When using NCProcess1, this equivalent list hopefully has solved for some unknowns. The output is presented to the user as

O1. Unknowns which have been solved for and equations which yield these unknowns.

O2. Equations involving no unknowns.

O3. Equations selected or created by the user. An example is given in the context of S1 and S2 below (§). There are also times during a strategy or prestrategy when one wants to introduce new variables and equations. This is illustrated in §.

O4. Equations involving only one unknown.

O5. Equations involving only 2 unknowns. etc.

We say that an equation which is in the output of an NCProcess command is digested if it occurs in items O1, O2 or O3 and is undigested otherwise. Often, in practice, the digested polynomial equations are those which are well understood.

We now turn to an example. In §, we compare the NCProcess commands to the Categorize operation which was described in §.