AIM Chat with Bill Abrams , Anne Collins , Benjamin Collins , Matt Goeke , Tom Hoffman , Julianne Rainbolt , Jen Roche , Daniel Shown , Gordon Williams , Shaochen Yang .
2:23 PM
Russell Blyth: Hi
Julianne Rainbolt: hi
2:25 PM
Matt Goeke: hello
Benjamin Collins: Hello.
Julianne Rainbolt: hi QT and vnc not up yet
Julianne Rainbolt: vnc up: 165.134.13.231
Russell Blyth: QT up: rtst://165.134.240.35/GAP060714pm1.sdp
Julianne Rainbolt: rtsp
Russell Blyth: rtsp of course
Russell Blyth: not rtst
Julianne Rainbolt: rtsp://165.134.240.35/GAP060714pm1.sdp
2:30 PM
Daylene Zielinski has joined this chat.
Russell Blyth: any problems?
Julianne Rainbolt: Any problems?
Gordon Williams: all good here
Bill Abrams: It is not coming up for me.
Jen Roche: fine here
Russell Blyth: starting gordon W and Anne's project
Julianne Rainbolt: Bill?
Gordon Williams: everyone in?
Julianne Rainbolt: Video?
Bill Abrams: restarting
Julianne Rainbolt: OK
Gordon Williams: The files you will need are available atGAP Workshop 2006. We recommend that you start by viewing the QuickTime introductory presentation (a slideshow).
Gordon Williams: To complete the worksheet you will need to download into a convenient location the routines.
Gordon Swain has joined this chat.
Bill Abrams: Rebooting?
Julianne Rainbolt: rtsp://165.134.240.35/GAP060714pm1.sdp
Gordon Swain: Oops, time got away from me!
Julianne Rainbolt: Is ok
Julianne Rainbolt: Just started
Julianne Rainbolt: Bill, are you going to reboot?
Bill Abrams: Hello
Gordon Williams: sounds good
Julianne Rainbolt: Hi, do you have video?
Anne Collins: okay
Julianne Rainbolt: Bill?
Gordon Williams: The existing software has some limitations. While the functions described in the worksheet are reasonably good for humans who want to work with elliptic curve groups
Gordon Williams: over prime order finite fields of characteristic \ne 2 or 3, they don't work for finite fields in general.
2:35 PM
Gordon Williams: Caveat emptor: we have not made significant attempts to improve the efficiency of the computations, rather, this is a proof of concept.
Gordon Williams: Many of the workhorse functions, which may be approached by students depending on their level of gap sophistication should work in a more general setting.
Bill Abrams has left this chat.
Gordon Williams: They will work more generally (e.g. over fields not of prime order) but they are not as human readable in their output.
Gordon Williams: Also, full integration of the functions with each other has not been tested yet.
Bill Abrams has joined this chat.
Gordon Williams: While GAP may not be the most natural tool in the world for doing the cryptography, we hope that this worksheet and supporting functions give people the core set of tools they need to
Gordon Williams: work with elliptic curve cryptography in a course where GAP has been the central computational tool.
Tom Hoffman: Is elliptic curve cryptography covered in Gallian?
Gordon Williams: I don't know
Anne Collins: no, not in gallian
Gordon Williams: There are some nice exercises in Koblitz's A Course in Number Theory and Cryptography (e.g. pb. 3 pg. 168)
Gordon Williams: that could be done using these tools. This book also includes a very nice discussion of methods for encoding messages using elliptic curves.
Tom Hoffman: thanks
Gordon Williams: note: Computation of bP is done by adding P to itself b times.
Gordon Williams: you may run into trouble using our routines if you have version 4.4.6 of gap installed
Gordon Williams: yer good
Julianne Rainbolt: 
Anne Collins: functions
2:45 PM
Anne Collins: oops, text should point out that ecL[1], the first element, is the identity
Gordon Williams: this corresponds to the geometric point at infinity
2:50 PM
Gordon Williams: you did great
Anne Collins: sounded great!
Anne Collins: okay, so here's where the worksheet peters out...
Gordon Williams: yeah well
Gordon Williams: thus some of the earlier commentary
Gordon Williams: oops, needed to change point
2:55 PM
Gordon Williams: yeah!
Gordon Williams: it worked!
Gordon Williams: (whew!)
Anne Collins: both get [18,10]
Anne Collins: and x = 18 is the key
Gordon Williams: it's a directive
Gordon Williams: right
Anne Collins: i am personally fond of it... no deeper meaning!
Anne Collins: will eventually include a discussion of how large numbers need to be to ensure security
Benjamin Collins: It is a really great application. I don't know if I could get my students to get it....
Gordon Williams: some of them are cyclic, but not all by any means
Anne Collins: and would be fun to add coding at the end
Gordon Williams: pictures like those at the beginning help
Russell Blyth: qt down
Gordon Williams: it's a nice nontrivial example of a group
Russell Blyth: will be right back with qt
Julianne Rainbolt: on pm2
Julianne Rainbolt: is up
Gordon Williams: it's less obviously a permutation group than a lot of geometric examples
Russell Blyth: we will start section 19 now - after any more comments on GandA project
Gordon Williams: I'd like to incorporate some of the functions we saw demonstrated this morning, but I don't know where to find the links
Anne Collins: it was really fun to put together!
Julianne Rainbolt: which functions?
Gordon Williams: where?
Russell Blyth: they are on the transcript page with the logs of aim etc
3:00 PM
Gordon Williams: the stuff for the other encryption
Tom Hoffman: http://euler.slu.edu/GrantWebPages/PREP06AlgebraGap/subs/MAAPrepGap
Russell Blyth: http://euler.slu.edu/GrantWebPages/PREP06AlgebraGap/transcripts.html
Gordon Williams: thanks
3:05 PM
Russell Blyth: 19.1
Julianne Rainbolt: rtsp://165.134.240.35/GAP060714pm2.sdp
Jen Roche: hello!
Julianne Rainbolt: Hello?
Jen Roche: to the new IT person
Matt Goeke: Hi! 
Julianne Rainbolt: Oh, yes!
Tom Hoffman: Filtered might speed things up
Bill Abrams: Hello, I am back.
Julianne Rainbolt: OK, do you have video now?
Bill Abrams: YEs.
Julianne Rainbolt: Great!
Russell Blyth: 19.3 conjecture?
Gordon Swain: Irred if 3 mod 4
Benjamin Collins: The irreducible primes are those congruent to 3 mod 4.
Benjamin Collins: He only got it first because he didn't type a complete sentence. 
Julianne Rainbolt: 
3:10 PM
Julianne Rainbolt: -1 for grammart!
Julianne Rainbolt: grammar
Benjamin Collins: That's fine with me.
Jen Roche: sounds good
Russell Blyth: let's do section 21 first since it is more likely something in semester one of aa
Gordon Swain: Hey, I was trying to be a student!
Julianne Rainbolt: 
Gordon Swain: Yes, please interpret my answer so it is correct!
Julianne Rainbolt: You DO have the answer, after all ...
Gordon Swain: The art of brown-nosing...
3:15 PM
Julianne Rainbolt: the police are after us again!
Russell Blyth: 21.1
3:20 PM
Julianne Rainbolt: Conjecture?
Jen Roche: size of orbit is n
Jen Roche: size of stabilizer is 2
Gordon Swain: one flip
Russell Blyth: that cuts through that vertex
3:25 PM
Russell Blyth: video down - any comments?
Russell Blyth: we'll start section 20 when back up
Julianne Rainbolt: Video will be up on pm3
Julianne Rainbolt: Now
Russell Blyth: up
Julianne Rainbolt: OK, we're starting Section 20
Russell Blyth: any problems?
Bill Abrams: Just me, but that is to be expected this afternoon
Bill Abrams: And it is working.
Julianne Rainbolt: OK
3:30 PM
Russell Blyth: 20.1
3:35 PM
Julianne Rainbolt: video down
Russell Blyth: going to go to QT pm4
Julianne Rainbolt: pm4 will be the video
Julianne Rainbolt: we're up
3:40 PM
Russell Blyth: comments?
Russell Blyth: try section 16 and let russell know the coded sentence
Benjamin Collins: How many credits of Abstract Algebra do you teach? One semester? Two?
Julianne Rainbolt: We have a one semester UG class
Julianne Rainbolt: The second semester is a second course in linear algebra
Julianne Rainbolt: One 3 hour class
3:45 PM
Benjamin Collins: One thing that I worry about is this taking up a lot of time. I'm rushed as it is.
Gordon Swain: Do you have trouble with students doing just everything, even simple calculations, in GAP?
Anne Collins: do you get all of groups/rings/fields in one term??
Julianne Rainbolt: yes, more or less
Gordon Williams: do you have students install it on their own machines or do you use a dedicated lab?
3:50 PM
Gordon Swain: At what point do they first see GAP? Have they already played with Zn, Sn, and Dn by hand?
Benjamin Collins: Another concern is that current students are visually oriented, and this is not a very visual program. Comments?
Jen Roche: are we free to use any of these exercises we've seen this week?
Jen Roche: so do we need to notify you when we do or something because of the copyright?
Russell Blyth: yes please do! and send me comments
3:55 PM
Gordon Swain: Any ideas on UG research projects that would use GAP (yes, difference sets!)... is the a website?
Gordon Swain: Thanks.
Benjamin Collins: I think that everything has gone very smoothly. Thanks to everyone!
Anne Collins: thanks everyone! this was awesome!
4:00 PM
Jen Roche: Thanks, I think this had been great.
Jen Roche: has
Shaochen Yang: Thank you all!
Bill Abrams: Thanks!
Daylene Zielinski: I've got so many great ideas my head is spinning, but that's a good thing!
Gordon Swain: I enjoyed it tons, and still got to go home each night.
Julianne Rainbolt: Thank YOU all!
Julianne Rainbolt:  the beauty of doing this remotely
Gordon Williams: thanks!
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Daylene Zielinski: Bye Ben and Anne. It was nice to "see" you again.
Daylene Zielinski has left this chat.
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