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12
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Jan
26
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Jul
13
revised Colorize and the Four-Color Theorem
added phrase that it is unsolved whether 4-coloring a planar graph is polynomial time or not.
Jul
12
comment Colorize and the Four-Color Theorem
Note sure how to post art on this site. Here is a pdf with some diagrams illustrating my points. <<stanwagon.com/public/StackExchangeNotes.pdf >>
Jul
11
answered Colorize and the Four-Color Theorem
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26
awarded  Yearling
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awarded  Nice Answer
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Jan
27
comment Updating Wagon's FindAllCrossings2D[] function
Not on hand. But this function is used many many times in the VisualDSolve project to find equilibrium points for two autonomous DEs and I must have found some difficult examples there. Now, it is possible as Mathematica changes internally that some of the problems disappear. Let me mention that this function was able to solve one of the "100 Digit Challenge" problems in optimizing a complicated function of 2 vbles by finding all of the critical points in the region, and there were well over 2000 of them.
Jan
26
comment Updating Wagon's FindAllCrossings2D[] function
I'm afraid I cannot remember exactly why I chose 97 and 103, but the reason is related to the effect that when things are too symmetric then there can be problems at the centers of symmetry. So it is best to add in a little asymmetry. Also I note that someone commented that some new Mathematica functions do some of these sorts of things.. but only for nice functions. If one had the Zeta function involved, say, then I do not believe their new algebraic ideas would work. Of course, since typical usages might be in DEs, finding equil. pts., it might be worth adding some cases to detect niceness.
Jan
26
answered Updating Wagon's FindAllCrossings2D[] function