Looking for automated search engine for conjectures in algebraic

*To*: mathgroup at smc.vnet.net*Subject*: [mg97452] Looking for automated search engine for conjectures in algebraic*From*: dontdont at gmail.com*Date*: Fri, 13 Mar 2009 04:53:08 -0500 (EST)

There are search engines that look for symbolic generators for sequences. There are engines that look for symbolic forms that match real valued constants. There is a very successful engine that looks for conjectures in graph theory, unfortunately I cannot remember the name of that one at the moment. I think I remember, but I now cannot find, an engine that searches for conjectures in simple algebra or perhaps algebraic geometry. This does not need to produce a proof, just searching through the composition of an assortment of functions applied to a handful of test cases until it stumbles onto one or more likely conjectures that satisfies a conjunction of equalities will be enough. I'm almost certain I remember seeing this, but a day of google searches and asking a few people has turned up nothing. It might have been a Mathematica package, but I've searched Wolfram's site and not found anything. A tangible, but over-simplified example, might help. Imagine the cosine law for triangles was not known, but you suspect there is a relationship between the edges of any triangle. The engine would be handed an equality, with unknown functions on both sides, and a set of example triangles. The task is to search through a bounded set of functions applied to each triangle until it finds something that likely satisfies the equality as far as N[] is concerned. Can anyone recall where they saw something like this described? Or, as a last resort, how something like this might be coded up in Mathematica? Thank you