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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 + tex2html) (b + tex2html ) + tex2html

where tex2html_wrap_inline5668 and tex2html_wrap_inline5670 are expressions involving tex2html_wrap_inline5496 , tex2html_wrap_inline5498 , tex2html_wrap_inline5484 , tex2html_wrap_inline5486 , A, tex2html_wrap_inline5482 , tex2html_wrap_inline5684 , tex2html_wrap_inline5686 and tex2html_wrap_inline5600 . Since there are many unknowns in the problem, there is probably excess freedom. Let us investigate what happens when we take tex2html_wrap_inline5690 . 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 tex2html_wrap_inline5694 . This defines c by the following equation


Since we have now solved for b and c, we can use these equations to solve for tex2html_wrap_inline5552 and tex2html_wrap_inline5704 .

Wed Jul 3 10:27:42 PDT 1996