Week 7: 7/9/01-7/13/01

Day 1:

-made a few more large examples--300 points

-met with Ileana and reviewed last weeks' work

-organizing and writing explanations to share the files with Ileana, etc.

-files copied to the 112b-ba account on hermite

-looking into reading and exporting in Mathematica some more

-created functions to automatically extract the data for example cases

-took a look at the Mathematica functions FindRoot and Solve, FindRoot definitly seems better

Day 2:

-printed papers by Bruce Hendrickson for Ileana

-tried replacing Solve with FindRoot in the code I have, but had wierd errors

-started reading Cox, Little and O'Shea Chapter 8: Robotics and Automatic Geometric Theorem Proving

-dealt with the first round of wierd errors, but found even wierder ones at the next step

-it seems the wierder errors are due to the questions of imaginaries, so we need a new way to deal with imaginaries if we're going to use FindRoot

-0.I is classified as an Imaginary number by Mathematica, but when FindRoot is told to begin with guesses with +0.I, it fails to look for imaginary roots, while giving imaginary numbers (ones that end with +0.I) as answers. Still not sure how to get FindRoot to look for imaginary answers, without getting extraneous answers as well

-tried to replace Solve with FindRoot in a version of code.nb from Ileana. So far I can only get the variables and guesses generally as a list; FindRoot does not accept this information in the form of a list. Bypassed this problem for the time being, next there were problems with the functions to make graphics since they expect allSol to contain the solutions for a number of configurations, some kind of loop based on t is needed, in addition to some way to make a list not a list (so far my only idea for doing this requires exporting and reading from the exported files)

-so far FindRoot will find the proper numbers for the code I had, only if 0.05I is added to each guess

Day 3:

-Borrowed from Young Science Library:
I. M. Gelfand, M. I. Graev, and A. Postnikov, "Hypergeometric functions associated with positive roots," in Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory
R. Connelly, "On generic global rigidity," in Applied Geometry and Discrete Mathematics

A. Postnikov, "Intransitive Trees," Journal of Combinatorial Theory Series A
B. Roth, "Questions on the rigidity of structures," Topologie Structurale
B. Roth, "Rigid and flexible frameworks," Amer. Math. Monthly
T.-S. Tay and W. Whiteley, "Generating isostatic frameworks," Topologie Structurale
W. Whiteley, "Infinitesimal motions of a bipartite framework," Pacific Journal of Mathematics

-requested on ILL:
G. M. Crippen and T. F. Havel, Distance Geometry and Molecular Conformation
A. Fogelsanger, "The generic rigidity of minimal cycles," PhD thesis
G. Laman, "On graphs and rigidity of plane skeletal structures," Journal Eng. Math.
N. Linial, L. Lovasz, and A. Wigderson, "A physical interpretation of graph connectivity, and its algorithmic applications," in Proceedings 27th Annual Symposium on Foundations of Computer Science
J. B. Saxe, "Embeddability of weighted graphs in k-space is strongly N-P-hard," Proceedings 17th Allerton Conference in Communications, Control and Computing
K. Sugihara, "On redundant bracing in plane skeletal structures," Bull. Electrotech. Lab.

-Found that the ILL request had been cancelled for Deza and Laurent

-working on changing the files from Ileana from Solve to FindRoot

-can make them work, though I have the same syntax problem as I ran into with FindRoot yesterday

-photocopied the articles from the books I borrrowed this morning

-Convinced the FindRoot with complex solutions to work, including the detection (at least all appears to be working)

-met briefly with Ileana

-dealt with the syntax problem with FindRootby onverting things to string and then using Evaluate, it seems to work

Day 4:

-checked the solutions to the FindRoot problems

-don't know what to do about the Working Precision error messages

Goodrich and Tamassia, "Dynamic Ray Shooting and Shortest Paths in Planar Subdivisions via Balanced Geodesic Triangulations"

Blumenthal, Leonard M., "Theory and Applications of Distance Geometry"

Day 5:

-web search for schools with computer engineering programs

-the list I found: programs