Universal coextensions within a variety.
Classically, in order to resolve an equation over a free monoid , we reduce it by a suitable family of substitutions to a family of equations , , each involving less variables than , and then combine solutions of into solutions of . The problem is to get in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to . We carry out such a parametrization in the case the prime equations in the graph...
Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family of substitutions to a family of equations ≈ , , each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at most three...
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