ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 23 Sep 2017 11:29:43 -0500Finding all admissible ideals with SAGEhttp://ask.sagemath.org/question/38952/finding-all-admissible-ideals-with-sage/Let A=k[x,y,z] for a finite field k and let J=(x,y,z) be the ideal generated by x,y and z. Call an Ideal I of A r-admissible in case $J^r$ is contained in I and I is contained in $J^2$.
Can SAGE find all 4-admissible ideals for a given finite field (lets say with 2,3 or 5 elements for a start)? This is one of the easiest special cases of a more general problem, which is probably too hard and too slow for todays computer. But maybe SAGE can do it in principle? Note that this is a finite problem as it is equivalent to finding all ideals in $A/J^4$ that are contained in $J^2/J^4$, which are all finite rings. (More general it would be more interesting to do the same with A replaced by the non-commutative polynomial ring in x,y,z, which is the quiver algebra with 1 point and 3 loops)Sat, 23 Sep 2017 11:29:43 -0500http://ask.sagemath.org/question/38952/finding-all-admissible-ideals-with-sage/