Post a reply
Username:
Note:If not registered, provide any username. For more comfort, register here.
Subject:
Message body:
Enter your message here, it may contain no more than 60000 characters. 

Smilies
:D :) :( :o :shock: :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:
Font size:
Font colour
Options:
BBCode is ON
[img] is ON
[flash] is OFF
[url] is ON
Smilies are ON
Disable BBCode
Disable smilies
Do not automatically parse URLs
Confirmation of post
To prevent automated posts the board requires you to enter a confirmation code. The code is displayed in the image you should see below. If you are visually impaired or cannot otherwise read this code please contact the %sBoard Administrator%s.
Confirmation code:
Enter the code exactly as it appears. All letters are case insensitive, there is no zero.
   

Topic review - Dimension of a finite-dimensional quotient ring
Author Message
  Post subject:  Dimension of a finite-dimensional quotient ring  Reply with quote
I would like to compute the dimension of a coinvariant algebra. I'm not familiar with Singular so I have a few naive questions, listed after my code :

Code:
LIB "finvar.lib";
ring R = 0, (a,b,c,d), dp;
matrix A[4][4] = -1,3,0,0,0,1,0,0,0,0,-1,0,0,0,3,1;
matrix B[4][4] = 1,0,0,0,1,-1,0,0,0,0,1,1,0,0,0,-1;
matrix P,S,IS = invariant_ring(A,B,intvec(0,0,1)); 
ideal I = S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[8],S[9],S[10],S[11],S[12],P[1],P[2],P[3],P[4];
qring Q = groebner(I);


1) How can I compute the dimension of Q as a vector space ?
2) When I ask explicitly the generators of I, I obtained a lot of "gen(1)" as a variable, what does it mean ?
3) If I want to repeat the process with a bigger vector space and a bigger group, how can I directly get the ideal generated by all the components of P and S without copying everything ?
Post Posted: Wed Mar 06, 2019 6:30 pm


It is currently Fri May 13, 2022 10:54 am
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group