
ezz-yoonit

ganithashaasthrathil, beejaganita samkhyaa sidhaanthathinte mekhalayil, oru "s"-yoonit feeldinte poornnasamkhyakalude valayathinte yoonit enna ashayathe saamaanyavalkkarikkunnu. yoonittukalkulla pala phalangalum "s"-unitukalkkum saadhuthayullathaanu.
nirvachanam.
k" ennathu "r" enna poornnasamkhyakalude valayamulla oru samkhya feeld ayirikkatte. s" ennathu "r"-nte prime idealukalude oru parimithamaaya koottamaayirikkatte. s" (positteev allengil negatteevu powerukal) leeii praimukalude gunanafalamaanu pradhana fraakshanal ideal ("x") engil "k" yude oru ghadakam "x" ennathu oru "s"-yoonittaan. yukthisahamaya poornnasamkhyakalude valayathinu z oraalkk "s" neey oru parimithamaaya prime nambarukalaayi edukkaam, koodaathe "s"-yoonittine oru yukthisahamaya samkhyayaayi nirvachikkukayum, athinte numeratorum denominatorum "s" leeii praimukalaal maathram vibhajikkappedunnu.
swathukkal.
s"-unitukal "r" yude unitukal adangiya oru gunana grouppaanu. 
diriklettinte yoonit sidhaantham "s"-unitukalkku anusrithamaann "s"-yoonittukalude group parimithamayi srishtikkappedunnu, rank (gunanaparamaayi swatantra gadakangalude paramavadhi ennam) "r" + "s" nuu thulyamaanu, ivide "r" ennathu yoonit grouppinte rankum "s" = umm aanu. |"ezz"|.
ezz-yoonit samavaakyam.
s"-yoonit samavaakyam oru diophantine samavaakyamaan.
yuu", "vii" enniva "keey" yude "ezz" unitukalaayi parimithappedutthiyirikku (allengil kooduthal pothuve, swabhaavasavisheshathakalulla poojyatthinte eathenkilum feeldinte gunana grouppinte parimithamayi srishtikkappetta upavibhaagathinte gadakangal). eee samavaakyathinte parihaarangalude ennam parimithamaanu, koodaathe divyasankhya sidhaanthathil vikasippicheduthathu logarithamukalile rekheeya roopangalkkulla esttimettukal upayogichu pariharangal phalapradamaayi nirnnayikkunnu. vividha diophantine samavaakyangal thathwathil "s"-yoonit samavaakyathinte eathenkilum roopathilekku kuraykkaan kazhiyum deerghavrithaakrithiyilulla valavukalile avibhaajya poyintukalekkurichulla seagalinte sidhaanthavum kooduthal saadhaaranayaayi "y" "n" = "f" ("x") enna roopathilulla superalliptic vakrangalumaanu sradheyamaaya udaaharanam.
s"-yoonit samavakyathinulla oru computational solver software sagemathil labhyamaan.

