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The idea of a strategy is the similar to that of a prestrategy, except that it incorporates motivated unknowns. The idea of a strategy is :

The input to a strategy is a set of equations C.

S0 tex2html_wrap_inline5406 . Set tex2html_wrap_inline4764 .
S1 tex2html_wrap_inline5406 . Run NCProcess1 which creates a display of the output (see O1-O5 in §) which contains collected forms of the polynomial equations. Look at the list of polynomials involving only one unknown or one motivated unknown (say a particular equation tex2html_wrap_inline4766 only depends upon the motivated unknown tex2html_wrap_inline5414 ).
S2 tex2html_wrap_inline5406 . The user must now make a decision about equations in tex2html_wrap_inline5414 (e.g., tex2html_wrap_inline4766 is a Ricatti equation so I shall not try to simplify it, but leave it for Matlab). Now the user declares a new unknown y and adds the relation tex2html_wrap_inline5424 as a user creation. The user would also select the equation tex2html_wrap_inline4766 as important. User selecting an equation corresponds to adding it to the set tex2html_wrap_inline4190 . See § for variants on this step.
S3 tex2html_wrap_inline5406 . Either do the ``End game'' (see §) or Go to S1 tex2html_wrap_inline5406.

The above listing is, in fact, a statement of a 1-strategy. Sometimes one needs a 2-strategy in that the key is equations in 1 or 2 unknowns (motivated or not). Typically, if a problem is solved with a 1-strategy, then the computer has done a lot for you, while if the problem requires a 2-strategy, then it has done less, and with a 3-strategy much less.

As with a prestrategy, the point is to isolate and to minimize what the user must do. This is the crux of a strategy.

Wed Jul 3 10:27:42 PDT 1996