Juli Rainbolt: questions?
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Juli Rainbolt: same addresses - let us know if we need to repeat them.
Jim Woeppel: What does ! mean in GAP; as in !1+x^2
2:30PM
Carter Lyons: Has anyone been able to check for a ring homorphism that is not a ring endomorphism? So far, I have not been able to use the command unless R is identical to S.
brooksbankpa: we did that yesterday I think -- at least for the 0 homomorphism.
Math and Computer Science: Jim, in what context?
Silvia La Falce: I did, using the command Peter gave yesterday, for homom. from Z18 to Z6
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Math and Computer Science: welcome back, all
brooksbankpa: regarding "!" the only place I've seen/used it before is in connection with record-type objects in GAP -- never in a GAP session.
Dominic Soda: Some of the x->kx maps from Zm to Zn are not well defined.
Carter Lyons: Using the ByMappingFUnction with R = Integers, S= Z15 taking x to x mod n it didn't workfor me.
Donna Nonnenkamp: same IP for VNC 165.134.131.27 Quicktime setting for video is rtsp://165.134.240.33/video0717p.sdp and the quicktime setting for audio is rtsp://165.134.240.33/audio0717p.sdp
Silvia La Falce: The problem is that for f(x)=k*x to be a homomorphism from Zm to Zn, n must divide n
Silvia La Falce: I mean, n must divide m
Dominic Soda: There are not even mappings
2:35PM
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Tong Wu has joined this chat.
Robert Talbert: "List(factors, Degree)" appears to give the same output without the "ofUnivariateLaurentPolynomial" stuff.
2:40PM
Dominic Soda: Is there a Poly to list function?
Math and Computer Science: Dominic - can you clarify your question
Dominic Soda: Is there a map from a polynomial to its coefficient list?
Dominic Soda: my audio is down again
brooksbankpa: the coefficients can be obtained via CoefficientsOfLaurentPolynomial
2:45PM
Dominic Soda: Thanks
Math and Computer Science: dominic - do you have your sound back?
2:50PM
Robert Talbert: I'm a little confused about the correlation of what we're doing in GAP with how a student would answer the question in 13.2. Specifically....
Robert Talbert: .... where exactly are we adjoining the root of the polynomial?
2:55PM
Robert Talbert: So based on what the students have read, they would automatically (?) know to check THAT particular field (e.g. field of order 125) to see if the poly splits?
brooksbankpa: they can, of course, construct the extension field explicitly using their favourite choice of irreducible (we did this in the morning session didn't we?)
Robert Talbert: So they are not actually using GAp to construct the field by adjoining the element; they just know what that field ends up being and are checking to make sure it all works.
Dominic Soda: yes i can hear thank you
Robert Talbert: Peter just answered my question. 
3:00PM
brooksbankpa: CoefficientsOfUnivariatePolynomial seems to be better actually
brooksbankpa: Yes
brooksbankpa: You can now get integers using IntVecFFE if you wish
3:05PM
brooksbankpa: IntVecFFE( CoefficientsOfUnivariatePolynomial( f ) );
Tracy Hamilton: it's length 7
3:15PM
Jim Woeppel: I have lost Video, audio, and VNC
Math and Computer Science: checking
Math and Computer Science: jim rebut
Donna Nonnenkamp: Jim reboot
Donna Nonnenkamp: Jim is it working?
brooksbankpa: if you just want one power of a as a linear combination, you can also use bas:=Basis( GF( , [a^0,a,a^2] ); Coefficients( bas , a^6 );
3:20PM
Donna Nonnenkamp: changing the tape
Math and Computer Science: how are you doing Jim?
Donna Nonnenkamp: tape changed
Robert Talbert: Incidentally, the Advanced Encryption Standard (AES) protocol the US government uses is based on objects and operations in GF(2^. So GAP could be used to play around with this cryptosystem like we're playing around with coding.
Robert Talbert: There is a good article in Cryptologia on "mini-AES", a shrunken-down version of AES using GF(2^4), that's intended for student investigation
3:25PM
drvazz: Could you send us the reference info?
Robert Talbert: Raphael Chung-Wei Phan, "Mini Advanced Encryption Standard (Mini-AES): A Testbed for Cryptanalysis Students", Cryptologia v. XXVI number 4 (October 2002), pp283--306
drvazz: Thanks!
Robert Talbert: See also www.nist.gov/aes
3:30PM
Tracy Hamilton: The nsa also has some interesting info on the history of cryptology at http://www.nsa.gov/museum/index.html
3:35PM
brooksbankpa: the method I gave earlier gives a quick way of constructing the table since one can loop over all powers of a.
Juli Rainbolt: questions?
Dominic Soda: Is this what is called a BCH code?
Janet McShane: BCH codes are double error-correcting
Donna Nonnenkamp: http://mirrors.ccs.neu.edu/GAP/NEU/Manual/C065S078.htm
Donna Nonnenkamp: This is the site with information on BCH
3:50PM
Tracy Hamilton: n/m
Donna Nonnenkamp: good tracy
3:55PM
Jim Woeppel: Can youshow how to factor the polynomial in first example over the rationals
Jim Woeppel: Over the extension
brooksbankpa: I tried yesterday for a while, but didn't have much joy -- I can look into it some more.
Dominic Soda: au revoir!