# Revision history [back]

### Finding all admissible ideals with SAGE

Let $A=k[x,y,z]$ for a finite field $k$ and let $J=<x,y,z,&gt;$ be="" the="" ideal="" generated="" by="" x,y="" and="" z.="" call="" an="" ideal="" $i$="" of="" $a$="" $r$-admissible="" in="" case="" $j^r="" \subseteq="" i="" \subseteq="" j^2$.="" 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?<="" p="">

### Finding all admissible ideals with SAGE

Let $A=k[x,y,z]$ for a finite field $k$ and let $J=<x,y,z,&gt;$ be="" the="" ideal="" generated="" by="" x,y="" and="" z.="" call="" an="" ideal="" $i$="" of="" $a$="" $r$-admissible="" in="" case="" $j^r="" \subseteq="" i="" \subseteq="" j^2$.="" 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?<="" p="">

### Finding all admissible ideals with SAGE

Let $A=k[x,y,z]$ A=k[x,y,z] for a finite field $k$ k and let $J=<x,y,z,&gt;$ J=<x,y,z,&gt; be="" the="" ideal="" generated="" by="" x,y="" and="" z.="" call="" an="" ideal="" $i$="" i="" of="" $a$="" $r$-admissible="" a="" r-admissible="" in="" case="" $j^r="" \subseteq="" i="" \subseteq="" j^2$.="" 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?<="" p="">

### Finding all admissible ideals with SAGE

Let A=k[x,y,z] for a finite field k and let J=<x,y,z,&gt; be="" the="" ideal="" generated="" by="" x,y="" and="" z.="" call="" an="" ideal="" i="" of="" a="" r-admissible="" in="" case="" $j^r="" \subseteq="" j^r="" is="" contained="" in="" i="" \subseteq="" j^2$.="" 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?<="" p="">

### Finding all admissible ideals with SAGE

Let A=k[x,y,z] for a finite field k and let J=<x,y,z,&gt; 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?<="" p=""> 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?

### 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 $J^r$ is contained in I and I is contained in J^2. $J^2$. 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?

### 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?principle? (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)

### 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)