### 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 ~~$J=<x,y,z,>$ ~~J=<x,y,z,> 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="">