Timeline for answer to NSolve erroneously gives no solution to a polynomial system by Michael E2

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Jul 22, 2015 at 11:08	comment	added	Michael E2		@Andrei I recall checking something like that for this particular system. What happens if you fold in the plane and axis and solve each system? Something like `{y -> 0, x -> z t}` and `{y -> 0, x -> 0}`, and call `NSolve` on each. That's three calls total to `NSolve`, but each subsequent one is simpler. But if the way you suggest works, maybe it's simpler.
Jul 22, 2015 at 5:46	comment	added	Andrei		While this solution works for this particular instance of the problem, it is not general. E.g., `changevar = {y -> z s, x -> z s t}` does not solve the issue anymore, because it misses the hyperplane where `y = 0, x = 0, z > 0`. For the same reason, the extension of this approach to 4 or more equations can be challenging. Whereas removing simple factors from the Groebner Basis and then running NSolve should always do the trick, I guess.
Jul 21, 2015 at 17:35	comment	added	Andrei		This is also the fastest solution. Removing the factors from the Groebner Basis and then using NSolve takes about 3 sec (was the fastest solution so far). This solution takes about 0.6 sec.
Jul 21, 2015 at 17:31	vote	accept	Andrei
Jul 14, 2015 at 21:04	history	answered	Michael E2	CC BY-SA 3.0