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General comments

The advantages of the proposed algorithm is that it is easy to use and implement for a fast check. For sharp system it may provide quickly solutions with a reasonable accuracy. The drawback is that it may provide solutions intervals which does not contain roots or, worse, miss some roots if Dist is not set to 0 (see section

This algorithm may be used also for analysis: if we have to solve numerous systems we may use this algorithm with a low M in order to fast check if the current system may have some real roots, in which case we may consider using a more sophisticated algorithm.

This solving algorithm may be tested on-line on the web page ALIAS-on-line that can be found on the COPRIN web page.

Jean-Pierre Merlet 2012-12-20