# 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:

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

-photocopied:
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