Carter Lyons: Good morning! I guess it goes without saying (but I will anyway) that my conjecture yesterday about problem 8.3 was way off base. Sorry about that!
Janet McShane has joined this chat.
Dominic Soda: is qt running?
Juli Rainbolt: vnc started - stand by on video and audio
drvazz has joined this chat.
Ayan Mahalanobis has joined this chat.
Ayan Mahalanobis: Thanks!
Juli Rainbolt: vnc and quicktime have started
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Donna Nonnenkamp: vnc is the same ip as yesterday 165.134.131.27 The quicktime for audio is rtsp://165.134.240.33/audio0717a.sdp and the quicktime for video is rtsp://165.134.240.33/video0717a.sdp
janetlbeery has joined this chat.
10:00AM
Juli Rainbolt: questions?
Dominic Soda: qt problems here again see you shortly
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Carter Lyons: I am still trying toget QT going.
10:05AM
Donna Nonnenkamp: Carter- do you need help?
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Donna Nonnenkamp: Hi Dominic
Carter Lyons: No. I forgot to turn up the volume on myspeaker. I am fine now.
Dominic Soda: qt is back thanks
Donna Nonnenkamp: Good
brooksbankpa: not such a problem here but it's often difficult to see what a list of vectors contains; the Display command is useful. e.g. Display(Elements(V));
Ayan Mahalanobis: can we have some lattice structure on the subspaces.
10:10AM
Ayan Mahalanobis: In Xgap
Ayan Mahalanobis: Ok!
brooksbankpa: I've not used it in years but it would make sense that it could.
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Ayan Mahalanobis: Sound is out.
Donna Nonnenkamp: Tracy The quicktime for audio is rtsp://165.134.240.33/audio0717a.sdp and the quicktime for video is rtsp://165.134.240.33/video0717a.sdp
drvazz: not here
Silvia La Falce: audio is fine her
brooksbankpa: I'm fine.
Tracy Hamilton: fine
Dominic Soda: yes qt is fine
drvazz: I mean, sound fine here
Jim Woeppel: Sound OK
sklarjk: I can hear fine.
Ken Yanosko: i hear you
Carter Lyons: Sound is okayhere.
Robert Talbert: Sound and vid is fine here
janetlbeery: yes, fine
Meral Arnavut: I hear you!
Ayan Mahalanobis: I am fine.
Tracy Hamilton: sorry i was late -- traffic  How far into section 11 are we?
Carter Lyons: The bottom of the GAP window is not visible. Can you shrink that window slightly?
Silvia La Falce: Display(Elements(D)); gave a nice list of
Silvia La Falce: subspaces with generators
10:15AM
Donna Nonnenkamp: Carter is that better?
Math and Computer Science: Tracy - he is taking about the text in Section 11 - he has not gotten to the project yet.
Carter Lyons: I cannot control the scroll onyour screen. Should I be able to do that?
Tracy Hamilton: thanks
Math and Computer Science: taking should have been "talking"
Carter Lyons: Got it.
brooksbankpa: (p^3-1)/(p-1)
10:20AM
drvazz: =p^2+p+1
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Silvia La Falce: there are p^3-1 generators and
Silvia La Falce: each subspace uses p-1 of them
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brooksbankpa: same
brooksbankpa: hyperplanes and points are interchangeable.
Dominic Soda: could you scroll back to Display when you get a chance
brooksbankpa: not really
10:25AM
Dominic Soda: thanks
brooksbankpa: there are some useful commands for elementary linear algebra -- are you going to touch on this topic at some stage?
Dominic Soda: yes
brooksbankpa: will do then
brooksbankpa: they're worth knowing I think -- and easy
10:30AM
Robert Talbert: Question -- I typed in "Int(Z(2))" and it gave back "1" as Juli said, but "Int(Z(2^2))" gives an error message, and so does "Int(Z(4))". Is there a simple explanation for that?
Ayan Mahalanobis: Probably they are not integers but polynomials.
Ayan Mahalanobis: Does GAP look at the field extension as polynomials?
brooksbankpa: Z(4) is a generator of the field GF(4); you can only get integers for elements of the ground field GF(2)
Math and Computer Science: or equivalent representation
Ayan Mahalanobis: Do we knoe ehat representation?
10:35AM
Ayan Mahalanobis: knoe=know & ehat=what 
Math and Computer Science: Donna is going to paste in a link for Allen Hibbard's algebra resources
Donna Nonnenkamp: http://www.central.edu/AlgebraResources/
10:40AM
Dominic Soda: Do your students have linear algebra before abstract algebra?
Math and Computer Science: yes
Ayan Mahalanobis: No way to see the elements in algebraic extension.
Dominic Soda: amen!
brooksbankpa: I tried using some of this stuff yesterday to factor x^2+1 of the Gaussian Rationals, but didn't have much success.
10:45AM
Math and Computer Science: I've just sent out an email to the list which discusses Ayan's question
Math and Computer Science: It's a response to a Q in the GAP forum from 1994
Math and Computer Science: by Alexander Hulpke, again 
10:50AM
Donna Nonnenkamp: changiing tape
Ayan Mahalanobis: How will one do arithmetic inside a finite field?
Donna Nonnenkamp: new tape installed thanks
Ayan Mahalanobis: there is a vector space structure with finite field extension. Is this the same we are talking about?
10:55AM
brooksbankpa: yes -- I'll include a discussion of this in the email I send out later.
Ayan Mahalanobis: So those nasty looking elements are vectors?
brooksbankpa: yes one can easily regard GF(p^k) as a vector space over its prime field GF(p) in GAP.
brooksbankpa: by the way, arithmetic is performed in finite field using "look-up tables" or "Zech logarithm" tables; that's part of the reason why GAP can't handle large finite fields.
Ayan Mahalanobis: No normal basis or polynomial basis!
11:00AM
brooksbankpa: do you use other systems for linear algebra?
Math and Computer Science: Maple
brooksbankpa: thanks.
brooksbankpa: I will do, thanks.
Dominic Soda: why not GAP?
drvazz: Mathematica is nice for linear algebra, too, but the syntax for GAP is closer to Maple syntax
janetlbeery: MATLAB's wonderful for linear algebra.
Dominic Soda: thanks
11:10AM
Carter Lyons: Can you DISPLAY this F? It wold be a good way to see the elements of the factor ring.
11:15AM
Robert Talbert: "Display(F)" gives "Field([ (a) ])"
brooksbankpa: (a) is the primitive element here
brooksbankpa: i.e. the generator of the multiplicative group
brooksbankpa: try r:=PrimitiveElement( F );
brooksbankpa: now, as Russell suggests, you can regard elements as powers of r. For example r^2 returns (a^2)
Tong Wu: Would you want the student to discover one of the irreducible polynomials from the list of above (factors of x^27 - 1? Robert-TSU
Ayan Mahalanobis: Well in a teaching situation that is probably not feasible. It is doing things backward.
11:20AM
brooksbankpa: Again, KnownAttributesOfObject( F ), tells the students what GAP knows about the object he/she has constructed.
brooksbankpa: it's essentially all it knows about ANY field, so you really can compute with it.