PREP - Professional Enhancement Programs of the MAA


Abstract Algebra with GAP

A PREP Workshop

AIM log - Wednesday July 16, 2:30 pm - 4:00 pm

Donna Nonnenkamp: audio for quicktime is rtsp://165.134.240.33/audio0716p.sdp and for video is rtsp://165.134.240.33/video0716p.sdp
Juli Rainbolt: are you there tracy?
Tracy Hamilton: you invited me twice -- i declined one of them
Dominic Soda: Is qt up?
Meral Arnavut has joined this chat.
Math and Computer Science: yes
Meral Arnavut: Hi again to everybody!
Donna Nonnenkamp: hi
Meral Arnavut has declined the invitation to this chat.
Ken Yanosko has joined this chat.
Dominic Soda: no audio here?
Ken Yanosko has declined the invitation to this chat.
Donna Nonnenkamp: still no audio
drvazz: audio ok here
Robert Talbert: I've got audio
Donna Nonnenkamp: dominic-audio?
Dominic Soda: not yet
Tong Wu: audio ok here
2:30PM
Meral Arnavut: No audio!
Donna Nonnenkamp: Dominic - you may want to quit quicktime and reopen and open the audio link first in file open url in new player .. then open the video link
janetlbeery has joined this chat.
Dominic Soda: still no audio i'm going to reboot see you soon
Math and Computer Science: hi all
Dominic Soda has left this chat.
sklarjk has left this chat.
Donna Nonnenkamp: remember to type in the numbers not click on the link
Meral Arnavut: Audio ok!
Donna Nonnenkamp: audio for quicktime is rtsp://165.134.240.33/audio0716p.sdp and for video is rtsp://165.134.240.33/video0716p.sdp
Carter Lyons: 8.3 Sigma(k_i-1) +1 where K_1 is the power of the ith prime in the facorization of n. 8.4 Phi(n)
Dominic Soda has joined this chat.
Robert Talbert: Technical question -- is there a way to clear the values of the variables you've defined in GAP without quitting and restarting?
2:35PM
Donna Nonnenkamp: audio for quicktime is rtsp://165.134.240.33/audio0716p.sdp and for video is rtsp://165.134.240.33/video0716p.sdp
sklarjk went offline before accepting your invitation.
Robert Talbert: Yes -- say you've been working on a problem and defined a bunch of variables, now you want to clear the memory out to avoid accidentally using a previously-defined variable you'[ve forgotten about
Dominic Soda: audio back
Donna Nonnenkamp: Good Dominic
brooksbankpa: Add(list,x) works
Ken Yanosko: maybe Append(j,[2]);
brooksbankpa: also Concatenate( list1 , list2 ) is useful
Robert Talbert: That wasn't exactly what I was looking for... We don't need to go into it right now though, just curious and I can poke around more in the help files.
Carter Lyons: summation
drvazz: Nilpotents: product $p_i^(n_i-1)$ for all i?
2:40PM
Tracy Hamilton: product p_i^(k_i -1)
janetlbeery: p1^r1-1*p2^r2-1*etc using previous notation and phi(n) (what drvazz and Tracy said)
Tracy Hamilton: where n = product p_i^k_i
Donna Nonnenkamp: can you read the board ok?
sklarjk went offline before accepting your invitation.
2:45PM
brooksbankpa: I guess the difficulty is getting the domain and range correct?
2:50PM
Dominic Soda: isn't z->z^5 the identity map here
brooksbankpa: I think I have a solution to the Z_m --> Z_n problem.
brooksbankpa: try h:=function( x ) return( k*Int(x) mod n ); end;
sklarjk has joined this chat.
sklarjk: Hi!
Donna Nonnenkamp: Hi Jessica
brooksbankpa: then f:=MappingByFunction(Z_m,Z_n,h) should work.
2:55PM
brooksbankpa: need to specify k
brooksbankpa: and n
3:00PM
Carter Lyons: It has to be idempotent in both rings
Dominic Soda: The image must be an idempotent in the ring Z25
brooksbankpa: no
Donna Nonnenkamp: Section 10 coming up
3:05PM
brooksbankpa: Oh dear...the mod n piece returns an integer..should be able to fix it soon!
3:10PM
brooksbankpa: OK, here's a fix: define f:=function(x) return( ZmodnZObj(0*Int(x),25) ); end;
Jim Woeppel: For problem try 9.5, h2:=x->0*(ZmodnZObj(Int(x),25));
Math and Computer Science: ok, that's like what jim proposed
brooksbankpa: yes - that defines the zero homomorphism.
3:15PM
Dominic Soda: does obj have to be a list?
Donna Nonnenkamp: Changing tapes
Donna Nonnenkamp: new tape has been installed
3:30PM
Jim Woeppel: You did not need to define the polynomial rings?
3:45PM
Janet McShane: Juli - you mentioned that you have the students submit their Gap log --- do they do that electronically?
Robert Talbert: This is a bit of a side issue, but I tried some of the factoring using polynomials over the Gaussian Integers (setting R := GaussianIntegers) but it doesn't seem to be doing it right. For example it said z^2 + 1 was irreducible
Robert Talbert: although over Z[i], z^2+1 = (z-i)(z+i).
Robert Talbert: Yes, I did define z := X(R, "z") with R := GaussianIntegers.
Dominic Soda: can GAP factor any poly over the Rationals?
3:50PM
Dominic Soda: Thanks I'll go look too.
brooksbankpa: I suspect that GAP has problems factoring over this ring.
Tong Wu: thanks
3:55PM
brooksbankpa: does anyone know of an algorithm for factoring over the Gaussian Integers?
Robert Talbert: I've seen that as a homework exercise in a textbook before 
Dominic Soda: Perhaps the ring should beQ[i] rather than Z[i] for the factoring to work.
brooksbankpa: yes maybe that would work -- I'll try it.




Back to Home Page
 
 

This PREP workshop is made possible by the NSF grant DUE: 0089005