
neuton bahubhuj

ganit mein, neuton bahubhuj sthaaniya kshetron parr bahupadon key vyavhaar koo samajhane key liye ack upkaran haye, yaa adhik aam taur parr, atimapi kshetron parr. 
mool mamle mein, ruchi kaa sthaaniya kshetra "anivarya roop seey" anishchit "x", i mein aupchaarik puraskar shrinkhala kaa kshetra thaa.ee. aupchaarik shakti shrinkhala ring sootra key anshon kaa kshetra _ 1,
sootra _ 2 parr, jahan sootra _ 2 vaastavik sankhya yaa jatil sankhya kshetra thaa. yeh abhee bhee puisucs vistaar key sambandh mein kaafee upayogi haye. neuton bahubhuj pramukh shabdon key sootra _ 4 koo samajhane key liye ack prabhaavi upkaran haye.
sameekaran sootra key liye shakti shrinkhala vistaar samadhanon kaa sootra _ 5
jahan sootra _ 6 sootra _ 7 mein gunank key saath ack bahupad haye, bahupad valay; arthaat, nihit roop seey paribhaashit beejganitiya kaary. yahaan ghatank sootra _ 8 kuchh parimeya sankhyaaen hain, joe chuni gaee shakha key aadhar parr hain; aur samadhan swayam sootra _ 9 mein shakti shrinkhala hain.
shakha key anuroop ack bhaajak sootra key liye sootra _ 10 key saath. neuton bahubhuj sootra _ 11 kii ganana key liye ack prabhaavi, algoridmic drishtikon detaa haye.
pee-edic sankhyaon kii shuruat key baad, yeh dikhaaya gayaa kii neuton bahubhuj sthaaniya kshetron key liye parinirdhaaran key prashnon mein utanaa hii upayogi haye, aur isaliye beejganitiya sankhya siddhant mein. neuton bahubhuj dirghvrittakar vakron key adhyayan mein bhee upayogi rahey hain.
paribhasha.
ack kshetra parr ack bahupad diye jaane parr, jadon kaa vyavhaar (yeh maanate hue kii isaki jadein hain) agyaat hoga. neuton bahubhuj jadon key vyavhaar key adhyayan key liye ack takneek pradaan karate hain.
sootra _ 2 koo ack gair-archemian mulyankan sootra _ 14 key saath sampann kshetra honey dein, aur
sootra _ 16 key saath. phir sootra _ 17 key neuton bahubhuj koo sootra _ 18 key bindu samooh key uttal patwar kii nichali seema key roop mein paribhaashit kiya jaataa haye. 
sootra _ 19 key saath ankon kii andekhi karna.
jyaamitiya roop seey punah sthaapit, inn sabhi binduon koo "xy"-tala parr "p" i "mein plot karein. maan leejiye kii ank soochkaank baaen seey daaen badh jaate hain ("pee" 0 "sabse baaen bindu haye," pee "aine" sabse daaen bindu haye). phir, "p" 0 seey shuru karate hue, "y"-aksh key samanantar ack kiran koo seedhe neeche kheenchen, aur iss kiran koo ghadee kii vipareet disha mein ghumaaen jaba taka kii yeh bindu "p" k1 (jaruri naheen kii "p" 1) seey naa takra jaae. yahaan kiran todein. abb "p" k1 seey "y"-aksh key samanantar ack doosari kiran kheenchen, aur iss kiran koo ghadee kii vipareet disha mein ghumaaen jaba taka kii yeh bindu "p" k2 seey naheen takaraata haye. taba taka jaari rakhein jaba taka kii prakriya bindu "p" n "taka naheen pahunch jaati haye; parinami bahubhuj (jisamen bindu" p "0", p "k1", p "k2, hotey hain..., p" km ", p" n ") neuton bahubhuj haye.
iss prakriya koo dekhane kaa ack aur, shayed adhik sahaj tarika yeh haih sabhi binduon "pee" 0 key aspas ack rubber baind parr vichaar karein..., pee" aine. baind koo oopar kii or failaaen, jaise kii baind kuchh binduon dwara apane nichale hisse mein atak jaae (bindu nakhunon kii tarah kaam karate hain, aanshik roop seey xy tala mein hathauda maarte hain). neuton bahubhuj key sheersh thheek vahee bindu hain.
isake ack saaf-suthare aarekh key liye dekhein kii jey. doubleu. aiss. casal, ell. aim. aiss. chhaatr granth 3, cup 1986 dwara "sthaaniya kshetron" kaa chaith6 §3. yeh 1986 key paperback sanskaran key pee99 parr haye.
mukhya pramey.
pichhale khand mein sanketanon key saath, neuton bahubhuj seey sambandhit mukhya parinam nimnalikhit pramey haye, joe bataata haye kii sootra _ 17 kii jadon kaa mulyankan poori tarah seey isake neuton bahubhuj dwara nirdhaarit kiya jaataa haih
sootra _ 21 dein
sootra _ 22 (jaisa kii oopar paribhaashit kiya gayaa haye) key neuton bahubhuj key rekha khandon kii dhalaanen badhate crum mein vyavasthit houn, aur
sootra _ 23
x-aksh parr prakshepit rekha khandon kii sambandhit lambai (i.ee. yadi hamaare paas bindu sootra _ 24 aur sootra _ 25 key beach ack rekha khand haye tou lambai sootra _ 26 haye).
upsamhaar aur anuprayog.
pichhale khandon key sanketan key saath, humm sootra _ 39 dwara sootra _ 2 parr sootra _ 17 key vibhajan kshetra koo darshaate hain, aur sootra _ 42 dwara sootra _ 43 seey sootra _ 39 kaa vistaar.
neuton bahubhuj pramey kaa upayog aksar bahupadon kii aparivartaniyata dikhaane key liye kiya jaataa haye, udaaharan key liye agale upsamhaar menh
vaastav mein, mukhya pramey key anusaar, yadi sootra _ 29 sootra _ 17 kaa mool haye, tou sootra _ 59 
yadi sootra _ 17 sootra _ 2 parr irreducible naheen thaa, tou sootra _ 29 kaa degree sootra _ 11 sootra _ 64 hoga, aur sootra _ 65 hoga. lekin sootra _ 50 coprime key saath sootra _ 66 key kaaran yeh asambhav haye.
ack aur saral upsamhaar nimnalikhit haih
"pramanah" mukhya pramey dwara, sootra _ 17 kaa ack mool sootra _ 29 honah chaahiye jiska mulyankan sootra _ 76 haye, sootra _ 29 sootra _ 2 parr alag kiya jaa sakata haye. 
yadi sootra _ 29 sootra _ 2 seey sambandhit naheen haye, tou sootra _ 29 kaa ack alag gallois sanyugma sootra _ 82 haye, sootra _ 84 key saath, aur sootra _ 82 sootra _ 17 kaa mool haye, ack virodhabhas.
adhik aam taur parr, nimnalikhit kaarak pramey haih
"pramanah"
pratyek sootra _ 33 key liye, sootra _ 92 dwara ekmusht sootra _ 102 key utpaad koo iss tarah seey niroopit karein kii sootra _ 29 sootra _ 17 aur sootra _ 105 kaa mool haye. humm sootra _ 107 key karakkaran koo sootra _ 7 mein sootra _ 107 koo mool monic kaarak sootra _ 109 mein bhee niroopit karate hain.
sootra _ 29 koo sootra _ 92 kaa mool maan lein. humm maan sakate hain kii sootra _ 112 sootra _ 2 parr sootra _ 29 kaa nyuntam bahupad haye. 
yadi sootra _ 82 sootra _ 112 kaa mool haye, tou sootra _ 39 kaa ack k-automorphism sootra _ 117 maujood haye joe sootra _ 29 koo sootra _ 82 parr bhejata haye, aur hamaare paas sootra _ 121 haye kyonki sootra _ 2 henselian haye. isaliye sootra _ 82 bhee sootra _ 92 kaa mool haye.
isake alawa, gunan sootra _ 126 key sootra _ 112 kaa pratyek mool spasht roop seey gunan sootra _ 128 key sootra _ 127 kaa mool haye, kyonki baar-baar mool spasht roop seey ack hii mulyankan saajha karate hain. yeh darshaata haye kii sootra _ 129 sootra _ 130 koo vibhajit kartaa haye
sootra _ 131 koo maan leejiye. sootra _ 133 kaa mool sootra _ 132 chunein. dhyaan dein kii sootra _ 133 key mool sootra _ 112 key mool seey alag hain. sootra _ 2 parr sootra _ 136 key nyuntam bahupad key saath pichhale tark koo doharaaen, maan leejiye kii doubleu.ell.jee. sootra 138 honey key liye, yeh dikhaane key liye kii sootra 139 sootra 140 koo vibhajit kartaa haye. 
iss prakriya koo taba taka jaari rakhein jaba taka kii sootra _ 92 kii sabhi jadein samaapt naheen hoe jaati hain, ack antatah aataa haye 
sootra _ 143 key saath sootra _ 142. yeh sootra _ 90, sootra _ 92 monic koo darshaata haye. 
lekin sootra _ 92 saha-moolya hain kyonki unaki jadon kaa alag mulyankan hotaa haye. isaliye spasht roop seey sootra _ 147, mukhya vivaad koo darshaata haye.
yeh tathya kii sootra _ 148 mukhya pramey seey anusaran kartaa haye, aur isi tarah sootra _ 95, yeh tippani karke kii sootra _ 92 key neuton bahubhuj mein kewal ack khand sootra _ 152 seey sootra _ 152 mein shamil hoe sakata haye. sootra _ 92 kii irraducibility kii sthiti uparokt sahafalan seey anusaran karati haye. (kyu.ee.dee.) 
nimnalikhit uparokt kaarak kaa ack tatkaal parinam haye, aur henselian kshetron parr bahupadon kii kamee key liye ack pareekshan kaa gathan kartaa haih
neuton bahubhuj key anya anuprayog iss tathya seey aatey hain kii ack neuton bahubhuj kabhi-kabhi ack neuton bahubhuj kaa ack vishesh mamla hotaa haye, aur iska upayog dou-charr bahupad samikaranon key asymptotic samadhanon key nirmaan key liye kiya jaa sakata haye jaise 
sootra _ 158
samamit falan vyakhya.
mulyankan key sandarbh mein, hamein ack bahupad key mool key praathamik samamit karyon key mulyankan key roop mein kuchh jaankaari dee jaati haye, aur ack beejganitiya samaapan mein vaastavik mool key mulyankan parr jaankaari kii aavashyakta hoti haye. isamen parigrahan siddhant aur ekatva siddhant donon key pahalu hain. neuton kii pehchaan key madhyam seey shakti raashi key mulyankan key liye sambhav vaidh nishkarsh hain.
itihas.
neuton bahubhuj kaa naam isaq neuton key naam parr rakhaa gayaa haye, jinhone pahali baar unakaa varnan kiya aur varsh 1676 seey heinry oldenberg koo sambodhit patrachar mein unake kuchh upayog kiye.