Week 9: 7/23/01-7/27/01

Day 1:

-copied article from the Proceedings of the Annual Symposium on Foundations of Computer Science

-found at UMASS but can't be requested:
Carl Lee, "The associahedron and triangulations of the n-gon"
Danzig, Hoffman and Hu, Triangulations (tilings) and certain bloc triangular matrices

-finishing running the last examples

-went to the UMASS Engineering and Physical Sciences library and copied:
Carl Lee, "The associahedron and triangulations of the n-gon"
Dantzig, Hoffman and Hu, "Triangulations (tilings) and certain block triangular matrices

-creating a bugs file on FindRoot and the examples

Day 2:

-beginning to experiment with Mathematica functions for eliminating variables

-things started to seem to work, now I have no idea what's going on, but trying to figure it out

-looking at how the speed of the GroebnerBasis function varies depending on the order of the equations using a function that I found in the Mathematica help GroebnerBasis entry

-all of the possible orders of polynomials I tried took less than 0.1 seconds to be evaluated, though there was a variation of about 25 percent, so there the order of the polynomials does make a difference, though not sure what separates the quick evaulaters from the slower

Day 3:

-retrieved from the ILL office:
Fogelsanger, "Generic Rigidity of minimal cycles

-looking at speed vs polynomial order to try to figure out what makes certain orders evaluate faster than others

-took a quick look at notes on Cox, Little and O'Shea to see if I could find any info about polynomial order, but I think looking at the book itself would be more useful. Unless the book has some useful information I don't think I can figure out much of anything about which orders evaluate faster than others, since there are 2520 different orderings based on types of equations and 362,880 total possibel orderings

-looking at the aborted examples from Ileana using solve (from when I replaced the solve code with FindRoot) to see if changing the order of the polynomials has any effect on the time it takes the code to run

Fogelsanger, "Generic Rigidity of minimal cycles"
Crippen and Havel, "Distance Geometry and Molecular Conformation" pg i-191

Day 4:

-looking at Cox, Little and O'Shea for information about how polynomial order affects the time it takes to find a Groebner basis

-trying changing the order of variables

-changing the order of variables has huge results for GroebnerBasis but does nothing for Solve

-trying evaluating a system of polynomials in GroebnerBasis and then inputing the results into Solve

-this worked very well, so I added it to the code from Ileana, and the examples that made solve run forever are now done evaluating in a minute or two

Day 5:

-stuck in traffic

-trying another example with the GroebnerBasis code

-returned an ILL book

-this example, the simplified version of the 6 armed star polygon forces abortions of GroebnerBasis, while Solve works quickly and easily for it by steps of dt

-helped sort legos for the robotics class, after looking at the robots

-Solve uses too much memory if asked to solve for the colinear as well as the rest

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