Next: Step 3 Up: Solving (HGRAIL) using NCProcess Previous: Step 1 : Process

### Step 2: The user attacks

Now the reader must apply his expertise to the nontrivial polynomial equations left undigested by the NCProcess1 command. A key observation is that the first key polynomial equation contains b but not c and the second key polynomial equation contains c but not b. In other words, b and c appear in decoupled equations.

Observe that the first key polynomial from the above spreadsheet is quadratic in b. We could complete the square and put the polynomial in the form

(6.10)                               (b + ) (b + ) +

where and are expressions involving , , , , A, , , and . Since there are many unknowns in the problem, there is probably excess freedom. Let us investigate what happens when we take . This yields the polynomial equation

which we could add to the starting polynomial equations and proceed. We can also complete the square for the expression in c and put that expression in the form

We also assume that . This defines c by the following equation

Since we have now solved for b and c, we can use these equations to solve for and .

Helton
Wed Jul 3 10:27:42 PDT 1996