In [1]:

# Generátor projektov - Numerická matematika. 
# Tento program generuje vstupy a výstupy semestrálneho projektu z numerickej matematiky.
# V projekte treba aplikovať : 
# Numerickú interpoláciu, výpočet numerických chýb, numerické riešenie nelineárnych rovníc
# numerické integrovanie a grafické a výpočtové funkcie programov
# Použité programové systémy: SageMath (Python) a MATLAB
# P. Szabó

import random
x=var("x")
for i in [1,2,..,100]:
    f(x) = 1
    n=random.randint(4,5)
    z=random_vector(QQ,n,20)
    
    # generátor polynómu f(x) s náhodným koreňom z[j]
    for j in [0,1,..,n-1]: 
        k=random.randint(0,4)
        z[j]=(z[j])+k/5 
        f(x)=f(x)*(x-z[j])
          
    t=sorted(z.list())
 .......

# Každý študent za reťazcom "Študent x:" môže nájsť svoju úlohu podľa priradenia študentov 
# zo súboru "Študenti - priradenie úloh".

# Tu sú uvedené kroky realizácie projektu: 
# 0) Pripraviť, konvertovať body B = {[xi,yi],i=0,1,..,k} do systému SageMath (MATLAB).
# 1) Nakresliť body B = {[xi,yi],i=0,1,..,k} v danom programovom systéme.
# 2) Spojiť body [xi,yi] a [xi+1,yi+1] s úsečkami (lineárna interpolácia), i=0,1,..,k-1.
# 3) Nájsť Lagrangeov interpolačný polynóm f(x),  f(xi)=yi, i=0,1,..,k.
# 4) Vykonať test správnosti výpočtu,  porovnanie koeficientov polynómu.(v riadku za bodmi [xi,yi], sa nachádza interpolačný polynóm)
# 5) Nájsť intervaly [ai,bi], i=1,2,..,m  kde funkcia f(x) má jeden koreň. 
# 6) Nájsť korene na intervaloch [ai,bi], i=1,2,..,m, s presnosťou 0.0001 (Používajte bisekciu).
# 7) Na intervaloch [ai,bi], i=1,2,..,m, vypočítajte určité integrály funkcie f(x) (Lagrangeov polynóm, viď bod 3.).
# 8) Vypočítané úlohy nahrajte do súboru Priezvisko_num_mat.ipynb. Súbor odovzdajte v systéme Moodle.
# 9) Súbor musí obsahovať hlavičku s informáciami: 

# Fakulta, AR, 
# Názov predmetu, 
# názov projektu
# Meno a priezvisko riešiteľa
# číslo úlohy
# SageMath, verzia programu
# Dátum odovzdania
xStudentx1:
B={[xi,yi],i=1,..,4}={[−13/9,140447209/6196500];[7/360,−182430343589/285534720000];[1321/2040,21209990809/230918860800];[467/204,−1166435747939/108243216000];[143/30,243115061/2754000]}
f(x)=x4−141293060x3+102713400x2+11905631377000x−75371114750=0
(29/60,x-4/9,x113/30,x69/85)
xStudentx2:
B={[xi,yi],i=1,..,5}={[−19/10,−113008783/532000];[−47/380,669133808233/79235168000];[137/152,−126463821459129/253552537600000];[433/280,1642187247921/1307987968000];[25/7,−35218080477/420175000];[31/5,563088433/665000]}
f(x)=x5−214012660x4+834095320x3−73693325x2−2266471166250x+2836314415625=0
(-9/10,x68/35,x23/20,x26/5,x62/95)
xStudentx3:
B={[xi,yi],i=1,..,4}={[−34/5,353683/1350];[−65/18,−8986961321/131220000];[−59/72,43144024847/16796160000];[23/120,−1002991339/622080000];[8/5,137122/3375]}
f(x)=x4+1231180x3+72231350x2−5536313500x−60325625=0
(-13/60,x3/5,x-64/45,x-29/5)
xStudentx4:
B={[xi,yi],i=1,..,4}={[−14/5,1960497/72200];[−107/80,−16614535833/14786560000];[−33/1520,7643525368287/5337948160000];[91/95,−6569388/81450625];[198/95,98755839/6859000]}
f(x)=x4+577760x3−3823914440x2−218611361000x+512631361000=0
(103/95,x-7/8,x79/95,x-9/5)
xStudentx5:
B={[xi,yi],i=1,..,5}={[−102/5,−143894256/625];[−433/40,76637690265731/405504000];[−47/120,−48901717854239/54743040000];[274/165,60707762944/4891924125];[1241/330,−9080781595288097/7827078600000];[20/3,215920757/37125]}
f(x)=x5+8357660x4−6405174950x3+290125149500x2+25019414125x−84099125=0
(17/3,x22/15,x-9/4,x-97/5,x102/55)
xStudentx6:
B={[xi,yi],i=1,..,4}={[−19/5,12214/375];[−2,−1792/975];[−64/65,5943896/53551875];[−17/78,−713124169/925376400];[4/3,193192/8775]}
f(x)=x4+17339x3+4726975x2+428975x−5665=0
(-14/5,x-10/13,x-6/5,x1/3)
xStudentx7:
B={[xi,yi],i=1,..,5}={[−83/30,−726894721/8002800];[−101/60,336260491/1536537600];[−6/13,−213611871192/22045521875];[487/494,28319442089246819/22983955650175000];[389/190,−267398468337/24760990000];[19/5,36307971/154375]}
f(x)=x5−104117410x4−25345337050x3+51823192625x2+90962892625x−5354272771875=0
(123/95,x44/65,x14/5,x-8/5,x-53/30)
xStudentx8:
B={[xi,yi],i=1,..,4}={[−123/35,23411091/171500];[−109/70,−2003849199/96040000];[41/80,1092884133/57344000];[289/80,−29231080407/286720000];[33/5,571329/1750]}
f(x)=x4−1151280x3−166491400x2+305211750x+1716125=0
(-88/35,x13/8,x-3/5,x28/5)
xStudentx9:
B={[xi,yi],i=1,..,5}={[−68/35,−64478843/979608];[−617/1190,206305646261/286362439188];[1/340,−4390348149/141985700000];[53/120,1027809592199/2961100800000];[157/60,−431579291/5287680];[109/20,7220681/8160]}
f(x)=x5−76691785x4−6819347600x3+22681768000x2−407037140000x−460131487500=0
(1/10,x-33/35,x47/60,x-8/85,x89/20)
xStudentx10:
B={[xi,yi],i=1,..,4}={[−39/5,2787626/1625];[−223/65,−17491040973/17850625];[15/104,413960840407/73116160000];[79/8,−500281273629/33280000];[102/5,3626644/325]}
f(x)=x4−3351260x3−1667991300x2+1245573250x+230868125=0
(7/20,x-34/5,x-4/65,x97/5)
xStudentx11:
B={[xi,yi],i=1,..,5}={[−11/3,−5054267729/12960000];[−19/10,1443753677/57600000];[−127/240,−1973742059/235929600];[53/40,28261/1152];[11/4,−15881047/9216000];[157/40,110911647/640000]}
f(x)=x5−7140x4−294292880x3+7358311576000x2+20988559960000x−6828940000=0
(3/40,x-8/3,x117/40,x-17/15,x103/40)
xStudentx12:
B={[xi,yi],i=1,..,5}={[−68/5,−8992676/375];[−41/5,25812688/2625];[−221/70,−5059606653/67228000];[−187/210,19741808755097/81682020000];[19/15,−401649664/5315625];[14/5,697686/625]}
f(x)=x5+34421x4+22322525x3−30152375x2−8196214375x+4965843125=0
(-19/5,x-63/5,x-88/35,x9/5,x11/15)
xStudentx13:
B={[xi,yi],i=1,..,5}={[−131/70,−4705469329/144060000];[−239/420,142470473123/816820200000];[−5/24,−176194139/24883200000];[5/8,13485452569/15052800000];[11/7,−23861169/105043750];[96/35,25363503/600250]}
f(x)=x5−779420x4−118119800x3+2340912250x2+642391735000x+372143750=0
(-61/70,x61/35,x-3/20,x7/5,x-4/15)
xStudentx14:
B={[xi,yi],i=1,..,4}={[−101/20,24261307/152000];[−287/120,−125250161603/3939840000];[−2/15,23923/9500];[302/285,−3400558343/1055600100];[252/95,34027637/685900]}
f(x)=x4+30371140x3−10937317100x2−22275185500x+10880147500=0
(7/15,x157/95,x-11/15,x-81/20)
xStudentx15:
B={[xi,yi],i=1,..,5}={[−66/65,−1207074528/17850625];[−1/130,425663/297034400];[87/130,−27803184993/7425860000];[269/130,14816211457/1485172000];[23/5,−4739472/21125];[37/5,161611708/105625]}
f(x)=x5−68465x4+1270534225x3−49686221125x2−38976105625x=0
(14/5,x87/65,x-1/65,x0,x32/5)
xStudentx16:
B={[xi,yi],i=1,..,5}={[−24/19,−1275735491707/27367410000];[733/2660,1877760425307549263/4314725718186240000];[459/560,−300813966697/9417513369600000];[769/720,216358171141/5882149601280];[19/9,−1154722/455625];[176/45,100568327717/969570000]}
f(x)=x5−26804947880x4+425210414309200x3−13122818321546000x2+204815911970000x+85019126000=0
(131/45,x59/45,x33/40,x-5/19,x57/70)
xStudentx17:
B={[xi,yi],i=1,..,4}={[−9/5,412/45];[−53/120,−22352561/207360000];[7/120,2887399/207360000];[8/15,−37/405];[28/15,26/3]}
f(x)=x4−1160x3−158225x2+41500x+131125=0
(-1/12,x13/15,x1/5,x-4/5)
xStudentx18:
B={[xi,yi],i=1,..,4}={[−112/55,414963752/11679525];[−61/330,−8190545569/3700073520];[361/390,10217556223/69403230000];[1889/1170,−9572786030777/20612759310000];[137/45,47032064/2606175]}
f(x)=x4−36801287x3+5185396525x2+1508854482625x−2447214625=0
(-57/55,x92/45,x77/65,x2/3)
xStudentx19:
B={[xi,yi],i=1,..,5}={[−103/35,−18899031996/77389375];[−27/35,42132893304/3792079375];[149/190,−81004834053/866634650000];[112/95,18204444/379152659375];[3387/2660,−55145889811323/26634109371520000];[33/14,14464131063/1238230000]}
f(x)=x5−28891330x4−848678442225x3+357422374422250x2−7160749111055625x+852924581875=0
(111/95,x113/95,x2/5,x-68/35,x19/14)
xStudentx20:
B={[xi,yi],i=1,..,5}={[−4,−54708211/227500];[−39/20,5940837/520000];[−23/35,−253817429/1092455000];[1/56,150219749251/344207360000];[341/520,−13716258189839/53228564480000];[121/65,21555976577/499817500]}
f(x)=x5+1093364x4−869910x3−149195200x2+187569910000x+704716250=0
(-3,x-9/10,x56/65,x-29/70,x9/20)
xStudentx21:
B={[xi,yi],i=1,..,5}={[−27/10,−40578381/1330000];[−27/20,180274437/1033600000];[−74/85,−519660999/47210245250];[−382/595,23104794332577/2833794971131250];[334/665,−794707122288087/176867132545250];[242/95,593637816339/3877049750]}
f(x)=x5+5509322610x4−3366256525x3−1511609282625x2−883137201875x−13231250=0
(-17/10,x-19/35,x147/95,x-1,x-63/85)
xStudentx22:
B={[xi,yi],i=1,..,5}={[−41/5,−128536681/23750];[−73/19,3206007475187/3095123750];[−23/95,−10395309701/15475618750];[9/20,2639709/2432000];[21/20,−3636171/12160000];[11/5,342771/4750]}
f(x)=x5+1061190x4−5496475x3+23222375x2+4471211875x=0
(-36/5,x9/10,x-46/95,x0,x6/5)
xStudentx23:
B={[xi,yi],i=1,..,5}={[−91/10,−49791189/5000];[−161/40,94819898873/40960000];[7/40,−433279/1638400];[123/160,62565129/33554432];[267/160,−422086088403/104857600000];[31/10,445361/2500]}
f(x)=x5+35380x4−417391600x3+47477716000x2−1237437160000x+5051971600000=0
(99/80,x3/10,x-81/10,x21/10,x1/20)
xStudentx24:
B={[xi,yi],i=1,..,4}={[−31/20,9081553/168000];[−17/120,−428202229/207360000];[74/105,514912201/243101250];[149/28,−3981459339/7683200];[21/2,8887957/8400]}
f(x)=x4−4351420x3+1539200x2+1623350x−836525=0
(-11/20,x8/7,x19/2,x4/15)
xStudentx25:
B={[xi,yi],i=1,..,5}={[−63/85,−3150805032/352876225];[33/85,5449027848/749861978125];[241/340,−57419901/10690688000];[253/260,419833073583/343371766400000];[177/130,−4584092043/107303677000];[174/65,78053924256/5158830625]}
f(x)=x5−97232210x4+174662272442050x3−325368516105125x2+109242326105125x−18992168978125=0
(22/85,x109/65,x9/10,x44/85,x68/65)
xStudentx26:
B={[xi,yi],i=1,..,4}={[48/85,407628/122825];[143/85,−50264/14616175];[67/35,3328/1500625];[31/14,−3788473/408170000];[17/5,59904/14875]}
f(x)=x4−4637595x3+9599425x2−42920714875x+14569210625=0
(9/5,x12/5,x71/35,x133/85)
xStudentx27:
B={[xi,yi],i=1,..,4}={[−19/10,245487/1960];[−67/140,−2716130313/384160000];[69/70,177439713/6002500];[61/7,−5656595958/1500625];[82/5,25061472/6125]}
f(x)=x4−115370x3+178971225x2+35530912250x+70294375=0
(-9/10,x77/5,x-2/35,x71/35)
xStudentx28:
B={[xi,yi],i=1,..,4}={[−6/5,74589/3500];[43/140,−242285583/384160000];[67/70,13851/240100];[9/4,−744303/160000];[22/5,190509/3500]}
f(x)=x4−17935x3+4439700x2−1369875x−1065917500=0
(-1/5,x57/70,x11/10,x17/5)
xStudentx29:
B={[xi,yi],i=1,..,4}={[−127/45,37063684/833625];[−85/117,−6865654692314/2225241061875];[1067/2470,40499760311/4823839112976];[1601/1710,−271139391157/889237524240];[107/45,105938/6669]}
f(x)=x4−466311115x3−271288100035x2+56276682500875x−19115844168125=0
(-82/45,x24/65,x62/45,x47/95)
xStudentx30:
B={[xi,yi],i=1,..,4}={[−103/20,9264567/59840];[−1173/440,−59246589607127/1911528960000];[−489/1870,27610468397983/4585616103750];[227/204,−67330944841/27060804000];[77/30,485051203/10098000]}
f(x)=x4+3485311220x3−665257112200x2−27599951000x+35499170125=0
(-83/20,x56/85,x47/30,x-13/11)
xStudentx31:
B={[xi,yi],i=1,..,5}={[−3/2,−234946883/9690000];[−17/60,63142277029/552562560000];[227/570,−1628314063792/14064551832375];[2023/2090,888583590096033/169480743520825000];[1101/935,−11744790386084/1629269401662375];[194/85,11128105794/991811875]}
f(x)=x5−282631106590x4+1690910450x3+99817156750x2−146099261250x−2636716661875=0
(109/85,x-1/2,x-1/15,x82/95,x59/55)
xStudentx32:
B={[xi,yi],i=1,..,4}={[−29/10,146091699/2261000];[−213/380,−15243396198291/2481311840000];[643/646,693813908601/13605675301250];[1537/1190,−418214871/40106784200];[83/35,21848229/2769725]}
f(x)=x4−3305922610x3−306823113050x2+1607047282625x−18292874375=0
(103/85,x74/95,x48/35,x-19/10)
xStudentx33:
B={[xi,yi],i=1,..,5}={[−3/2,−351816129/31790000];[−151/340,36759544473/9995793280000];[−159/1870,−100387461045249/2858367371337500];[9/22,1044816759/46543739000];[79/85,−1418933376/9761516875];[192/85,567783594/22968275]}
f(x)=x5−22231870x4−707914450x3+368079794750x2+18459233750x−5778180625=0
(-1/2,x107/85,x12/55,x3/5,x-33/85)
xStudentx34:
B={[xi,yi],i=1,..,4}={[−12/5,187187/21375];[−47/45,−84992/820125];[−4/9,1649351/77911875];[−13/95,−45312/16290125];[88/95,32656507/7716375]}
f(x)=x4+404171x3+442285x2+2895x+1519106875=0
(-1/5,x-7/95,x-31/45,x-7/5)
xStudentx35:
B={[xi,yi],i=1,..,4}={[−29/60,80321549/24624000];[193/360,−5216687/39890880000];[566/855,38370270211/17100721620000];[2123/1520,−1684604697271/5764984012800];[121/40,91783027/6566400]}
f(x)=x4−264416840x3+1985621410400x2−633619256500x+678915200=0
(31/60,x81/40,x5/9,x73/95)
xStudentx36:
B={[xi,yi],i=1,..,4}={[−49/40,178143/2560];[47/80,−6945731/983040];[13/6,27176317/6480000];[97/24,−5607413/405000];[123/20,62339/640]}
f(x)=x4−1111120x3+11659480x2−18244912000x−237935000=0
(-9/40,x44/15,x7/5,x103/20)
xStudentx37:
B={[xi,yi],i=1,..,5}={[−111/35,−15310930283/39016250];[−53/63,39149358796921/1612709382375];[67/90,−50826643219/214938360000];[167/130,28746134683/133665480000];[993/520,−32525512527827/53228564480000];[13/4,23549493/416000]}
f(x)=x5−5137916380x4−14906981900x3+20404714625x2−46899134125x+4263611375=0
(-76/35,x1,x9/4,x22/45,x102/65)
xStudentx38:
B={[xi,yi],i=1,..,5}={[−88/35,−1070169167/3601500];[−311/420,482884559027/28752071040];[371/660,−1733431195654171/438316401600000];[911/440,2983671579667549/346324070400000];[127/40,−64845131/135168000];[43/10,52244/525]}
f(x)=x5−5507924x4+6840111550x3+538153696x2−13181293770000x+969917500=0
(33/10,x-53/35,x1/30,x12/11,x61/20)
xStudentx39:
B={[xi,yi],i=1,..,5}={[−9/5,−36186/125];[31/90,300160002031/20667150000];[287/180,−89363846441/1322697600000];[319/140,2313447237/2151296000];[113/35,−232872874/157565625];[23/5,10614/125]}
f(x)=x5−5573630x4+11561450x3−1765377875x2−747045625x+18224875=0
(-4/5,x20/7,x18/5,x17/10,x67/45)
xStudentx40:
B={[xi,yi],i=1,..,4}={[−46/5,76167/100];[−21/5,−7052/25];[−3/20,161/32000];[0,−41/2500];[11/10,3627/250]}
f(x)=x4+425x3+163100x2−21250x−412500=0
(-41/5,x-1/5,x-1/10,x1/10)
xStudentx41:
B={[xi,yi],i=1,..,4}={[−88/45,513006538/25001055];[−206/855,−15040356448/21375902025];[111/190,15869091/1303210000];[183/190,−88183437/1303210000];[212/95,2657638/308655]}
f(x)=x4−139x3−1422127075x2+1101051857375x−332046857375=0
(66/95,x117/95,x-43/45,x9/19)
xStudentx42:
B={[xi,yi],i=1,..,5}={[−83/5,−267942983/4750];[−158/15,26702895944/759375];[−319/120,−569093010081707/472780800000];[217/760,527793607280981/354973552640000];[1059/1330,−77750020792096479/8323159178600000];[76/35,13693766644/28511875]}
f(x)=x5+1542077980x4+65574113300x3−664583249875x2+506026183125x−52447283125=0
(8/19,x-82/15,x-78/5,x3/20,x41/35)
xStudentx43:
B={[xi,yi],i=1,..,4}={[2/15,478667/57375];[137/120,−58433/3525120000];[791/680,7656903/213813760000];[78/17,−866136649/6264075];[9,1231979/2550]}
f(x)=x4−116891020x3+1615075100x2−426491275x+18415=0
(23/20,x8,x17/15,x20/17)
xStudentx44:
B={[xi,yi],i=1,..,4}={[−9/2,2187801/34000];[−97/40,−296093313/43520000];[−7/8,6997263/8704000];[7/170,−1281357/1336336];[126/85,3262644/122825]}
f(x)=x4+1621340x3+140513400x2−2252317000x−77498500=0
(41/85,x-2/5,x-7/2,x-27/20)
xStudentx45:
B={[xi,yi],i=1,..,5}={[−2,−1377376/95625];[−77/80,30361769/11141120000];[−143/240,−920125215217/13536460800000];[−5/51,33504003883/862563127500];[46/51,−605242095116/215640781875];[41/15,2086567/19125]}
f(x)=x5+7912040x4−7322330600x3−7955338250x2−51443191250x+96231875=0
(26/15,x6/85,x-1,x-4/15,x-37/40)
xStudentx46:
B={[xi,yi],i=1,..,4}={[−17/10,222343/24000];[−21/32,−11892643/1966080000];[−169/1440,12369126139/34398535680];[25/18,−560847287/131220000];[17/5,74579/1500]}
f(x)=x4−211144x3−1109480x2−77200x+583115000=0
(12/5,x17/45,x-49/80,x-7/10)
xStudentx47:
B={[xi,yi],i=1,..,4}={[−67/45,10106404/91125];[31/180,−2017333577/209952000];[17/12,10874129/1555200];[71/10,−9277189/7500];[66/5,6399008/3375]}
f(x)=x4−130990x3+389931350x2−1768675x−1342135=0
(5/6,x-22/45,x61/5,x2)
xStudentx48:
B={[xi,yi],i=1,..,4}={[−2/5,22784/1625];[51/65,−83472/714025];[527/390,7734317777/23134410000];[46/15,−242128/26325];[27/5,25344/325]}
f(x)=x4−1502195x3+17387975x2−252441625x+2772625=0
(26/15,x22/5,x63/65,x3/5)
xStudentx49:
B={[xi,yi],i=1,..,4}={[−31/5,3151/8];[−91/40,−582371127/5120000];[131/160,110218239/655360000];[223/160,−4243421/5242880];[14/5,1247/40]}
f(x)=x4+14180x3−228571600x2+5603320x−12015920000=0
(9/5,x79/80,x-26/5,x13/20)
xStudentx50:
B={[xi,yi],i=1,..,5}={[−106/45,−1357053376/17660025];[−128/153,7813091821157546/4978067449584375];[13/646,−3064078178865367867/10678958487198112500];[983/1140,32352120900853/94268297954304];[247/180,−8807655709/61033046400000];[107/45,9073616552/441500625]}
f(x)=x5−83095814x4−1239517654075x3+5463427119622250x2+520674249055625x−155062534375=0
(-61/45,x62/45,x-27/85,x41/30,x34/95)
xStudentx51:
B={[xi,yi],i=1,..,4}={[−19,15122891/2250];[−559/60,−4090887311/608000];[−289/1140,185861407991/187662240000];[37/285,−149843/879666750];[17/15,4365557/128250]}
f(x)=x4+3491190x3+281244275x2−188547125x+24125=0
(2/15,x-18,x12/95,x-19/30)
xStudentx52:
B={[xi,yi],i=1,..,5}={[−21/5,−2505258/6875];[−329/180,8311618402451/415704960000];[−41/180,−29168491789/415704960000];[1/22,468503/120788250];[71/110,−1353450493/1610510000];[11/5,41586/625]}
f(x)=x5+2341990x4−52011650x3−1835312375x2+6564125x=0
(1/11,x0,x-41/90,x-16/5,x6/5)
xStudentx53:
B={[xi,yi],i=1,..,5}={[−23/10,−547833889/1235000];[−11/30,1530399409/75026250];[833/1140,−1349559351034279/5006077914240000];[1284/1235,846429857620519/3447593347526250];[831/130,−3535032910888/529092525];[63/5,544774916/24375]}
f(x)=x5−9593741x4+21358914820x3+10561650x2−510659091852500x+64533771250=0
(58/5,x17/30,x17/19,x-13/10,x77/65)
xStudentx54:
B={[xi,yi],i=1,..,5}={[−53/10,−2935641/3400];[−809/340,1228389775789113/17265461120000];[−129/340,−444935462319/17265461120000];[1/20,50887431/206720000];[129/190,−18164069847/42093683000];[186/95,73661307291/1384660625]}
f(x)=x5+59771615x4−199336460x3−168568075x2+403143807500x+4578212018750=0
(-3/10,x-39/85,x2/5,x91/95,x-43/10)
xStudentx55:
B={[xi,yi],i=1,..,4}={[−63/80,100512377/19968000];[669/2080,−462512503859/56153210880000];[3/5,71269/5070000];[257/195,−6831354973/23134410000];[43/15,380779/28080]}
f(x)=x4−787240x3+6536320280x2−7382963375x+166612675=0
(28/15,x17/80,x10/13,x28/65)
xStudentx56:
B={[xi,yi],i=1,..,5}={[−9/5,−288788/2625];[−9/35,857107499/315131250];[71/105,−10891199/20420505];[37/30,1978657/13608000];[107/40,−15560277021/716800000];[99/20,248459317/672000]}
f(x)=x5−2479420x4+161872100x3+23571750x2−7352613125x+25281875=0
(7/5,x79/20,x16/15,x-4/5,x2/7)
xStudentx57:
B={[xi,yi],i=1,..,4}={[−57/5,23731864/16625];[−191/30,−19786681937/21546000];[−143/210,1968249944921/36951390000];[764/665,−49525774336/39112590125];[221/95,482200784/6001625]}
f(x)=x4+208191995x3−648175x2−2803887125x+742562375=0
(-52/5,x34/35,x-7/3,x126/95)
xStudentx58:
B={[xi,yi],i=1,..,5}={[−8/5,−82582016/5386875];[−11/26,67639140301/1893594300000];[98/1105,−371400741264/13179574127525];[472/1105,6524931584/988468059564375];[464/585,−16373382526976/232947603793125];[97/45,1863352588/94248765]}
f(x)=x5−115739945x4−2753271825x3+15579683232125x2−1216215475x−21504690625=0
(36/85,x52/45,x-16/65,x-3/5,x28/65)
xStudentx59:
B={[xi,yi],i=1,..,4}={[−93/10,51349439/52000];[−761/180,−12685711902377/27293760000];[79/720,724394716927/698720256000];[1163/1040,−4652192888351/701915136000];[186/65,220759493/2636400]}
f(x)=x4+5821936x3−26398315600x2+8818929250x+7030178000=0
(-83/10,x3/8,x-7/45,x121/65)
xStudentx60:
B={[xi,yi],i=1,..,4}={[−123/70,609554053/58653000];[−1791/2660,−1466887194709/90115407648000];[−637/1710,32296025251/427518040500];[82/45,−106165163/4363065];[24/5,22207232/149625]}
f(x)=x4−55012394x3−302395985x2−207138550x−14845625=0
(-7/45,x-53/70,x19/5,x-56/95)
xStudentx61:
B={[xi,yi],i=1,..,4}={[−73/90,220206481/11664000];[151/360,−4276078079/33592320000];[113/160,1436211/131072000];[653/160,−19280775141/131072000];[42/5,13997399/28800]}
f(x)=x4−6481720x3+605414800x2−27530948000x+498797720000=0
(61/80,x13/20,x37/5,x17/90)
xStudentx62:
B={[xi,yi],i=1,..,5}={[−8/5,−2794526/24375];[−17/140,559803397999/262189200000];[169/280,−6828649749669/22373478400000];[557/520,1489869335053/4562448384000];[776/195,−739850892721754/1973654353125];[23/3,4838319079/1842750]}
f(x)=x5−467715460x4+547134200x3−464147273000x2−888175x+10265=0
(84/65,x17/20,x-3/5,x20/3,x5/14)
xStudentx63:
B={[xi,yi],i=1,..,5}={[−19/12,−52771213/14580000];[−31/60,9017/43740000];[−2/5,−583/7776000];[−17/72,2200429/5374771200];[1/30,−1209271/437400000];[107/90,307591603/52488000]}
f(x)=x5+7960x4+1648732400x3+356291944000x2−997994860000x−91634320000=0
(-7/20,x-9/20,x-7/12,x-11/90,x17/90)
xStudentx64:
B={[xi,yi],i=1,..,5}={[−127/70,−106542969/6530720];[−163/280,7991848111/234061004800];[−37/120,−4032797/3622993920];[23/255,13984973366/215640781875];[2007/2210,−199739399606309429/369028075570700000];[154/65,13309944933/303460625]}
f(x)=x5−3576792820x4−1291517928200x3−46279357000x2+30913136500x+32129690625=0
(-57/70,x-7/20,x-4/15,x38/85,x89/65)
xStudentx65:
B={[xi,yi],i=1,..,5}={[−94/15,−85068664/55125];[−703/210,1954567466423/9075780000];[−89/105,−4129893248/850854375];[1/10,31862567/18900000];[22/21,−1967039672/283618125];[92/35,8123483744/40516875]}
f(x)=x5+7315x4−4980711025x3−2018833165375x2+2374138826875x+120087875=0
(7/15,x57/35,x-4/15,x-79/15,x-10/7)
xStudentx66:
B={[xi,yi],i=1,..,4}={[−67/40,7198599/64000];[−17/112,−662566184841/98344960000];[117/140,31954689/6146560];[181/20,−90840447/17920];[89/5,1487607/280]}
f(x)=x4−4983280x3+9013560x2+15635114000x−136892500=0
(-27/40,x84/5,x13/10,x13/35)
xStudentx67:
B={[xi,yi],i=1,..,4}={[−101/5,8963436/875];[−583/60,−34478280173/2592000];[353/420,1552807778819/31116960000];[86/35,−15460547/900375];[4,537718/2625]}
f(x)=x4+3049210x3−44771525x2+1567771750x+3216125=0
(-7/30,x-96/5,x67/35,x3)
xStudentx68:
B={[xi,yi],i=1,..,4}={[−23/10,2246779/39000];[−131/260,−23423820057/4569760000];[343/390,945878317/462688200];[38/15,−1286528/131625];[23/5,77644/975]}
f(x)=x4−1583390x3−4011950x2+353244875x−1254625=0
(-13/10,x22/15,x19/65,x18/5)
xStudentx69:
B={[xi,yi],i=1,..,4}={[−13/5,67562/1235];[−62/95,−116571312/22806175];[1037/1235,15374429417482/16284179104375];[321/182,−370150319979/521169703600];[22/7,10060928/423605]}
f(x)=x4−192118645x3−130226175x2+184083325x−17281235=0
(15/7,x-8/5,x28/95,x18/13)
xStudentx70:
B={[xi,yi],i=1,..,4}={[−24/19,936775028/69447375];[−31/380,−4755314837/37532448000];[161/180,3481176413/3989088000];[17/9,−29624/192375];[139/45,2698339/192375]}
f(x)=x4−61811710x3+22201776950x2+129857192375x−1882025=0
(1/10,x76/45,x94/45,x-5/19)
xStudentx71:
B={[xi,yi],i=1,..,5}={[−32/5,−13667129/16875];[−131/30,318549397/3645000];[−479/210,−3826726880587/122523030000];[−13/28,32412428123/2323399680];[137/180,−14115931841759/1322697600000];[20/9,9214499/32805]}
f(x)=x5+5317630x4+1316579450x3−84888147250x2−36427715750x+1419175=0
(-10/3,x-43/35,x-27/5,x11/9,x3/10)
xStudentx72:
B={[xi,yi],i=1,..,5}={[−139/65,−727191370117/4948193250];[−821/780,378771578979449/889249705344000];[25/132,−38501585426359321/1628032348800000];[886/385,22686642847105024/989667957403125];[409/105,−18548576725111/730033053750];[83/15,214858849/519750]}
f(x)=x5−422276006x4+14569320475x3+261579741126125x2−790348125630625x−2051747689384375=0
(114/35,x74/55,x-29/30,x68/15,x-74/65)
xStudentx73:
B={[xi,yi],i=1,..,4}={[−11/6,771589/36000];[−41/60,−60401/320000];[143/240,13325649127/3317760000];[181/80,−921824497/368640000];[19/5,149981/3600]}
f(x)=x4−379120x3−131144x2+413099000x+16175=0
(14/5,x69/40,x-8/15,x-5/6)
xStudentx74:
B={[xi,yi],i=1,..,4}={[−19/5,6981/50];[−27/20,−4078009/160000];[99/140,49522751/15366400];[79/35,−29105703/3001250];[21/5,4141/50]}
f(x)=x4−12770x3−1446175x2+11042875x−736625=0
(46/35,x16/5,x1/10,x-14/5)
xStudentx75:
B={[xi,yi],i=1,..,5}={[−47/5,−176701492/14875];[−156/35,607361084226/178574375];[−201/1190,−19481259600756/2982942074875];[1229/1020,7532349736323721/309142624896000];[29/12,−44177823943/18506880000];[18/5,3436128/14875]}
f(x)=x5+139393570x4−429411275x3+1559694250x2+146035274375x−4703410625=0
(-42/5,x-18/35,x67/30,x13/5,x3/17)
xStudentx76:
B={[xi,yi],i=1,..,4}={[−19/5,137747/875];[−1,−5184/175];[23/20,116683/160000];[291/140,−802128177/384160000];[128/35,68252/1715]}
f(x)=x4−15170x3−2299350x2+15123875x−1116125=0
(4/5,x93/35,x3/2,x-14/5)
xStudentx77:
B={[xi,yi],i=1,..,4}={[−113/70,4567147/156408];[−37/1260,−65813229947179/47889001440000];[1573/1710,917896814951/2137590202500];[1434/665,−47507733416/14080532445];[141/35,2595515/58653]}
f(x)=x4−5092111970x3+1380341418950x2+17807921047375x−278038209475=0
(106/35,x122/95,x-43/70,x5/9)
xStudentx78:
B={[xi,yi],i=1,..,4}={[−17/5,6149/84];[−19/20,−8104717/1120000];[18/35,2312/4501875];[1201/1260,−1104817051/4032758016];[107/45,1693211/102060]}
f(x)=x4−2315x3−85972100x2+5782315750x−22942625=0
(37/70,x-12/5,x1/2,x62/45)
xStudentx79:
B={[xi,yi],i=1,..,5}={[−19/5,−170969/140];[−43/40,2988132147/20480000];[37/40,−264070763/143360000];[27/14,14948344953/1680700000];[103/28,−341102346013/6722800000];[57/10,3291489/5600]}
f(x)=x5−897140x4+15391400x3+3249377000x2−1242811750x+1704696250=0
(6/5,x-14/5,x13/20,x93/35,x47/10)
xStudentx80:
B={[xi,yi],i=1,..,4}={[−63/65,97117681/9886500];[311/780,−16748006401/123383520000];[1,1029/32500];[17/12,−130801/4320000];[13/5,75317/11700]}
f(x)=x4−23665x3+4979911700x2−36912250x+340473125=0
(23/30,x37/30,x8/5,x2/65)
xStudentx81:
B={[xi,yi],i=1,..,4}={[−4/5,2343/500];[29/90,−3086347/459270000];[667/1260,6384843973/2016379008000];[1387/1120,−505294270321/1573519360000];[229/80,155626249/10752000]}
f(x)=x4−157315040x3+14258950400x2−3446936000x+640763000=0
(1/5,x149/80,x4/9,x43/70)
xStudentx82:
B={[xi,yi],i=1,..,5}={[−67/5,−14300737/400];[−63/10,1420688963/120000];[−1/6,−128083/9720000];[11/60,66448909/124416000];[143/160,−9711186471/4194304000];[183/80,777075299/4915200]}
f(x)=x5+2627240x4−430972400x3+43674000x2+39131875x+319315000=0
(103/80,x-62/5,x-2/15,x1/2,x-1/5)
xStudentx83:
B={[xi,yi],i=1,..,5}={[−56/5,−1175273269/44000];[−113/20,74051625193/6400000];[17/220,−145951721673877/1030726400000];[315/176,2839227393371301/105546383360000];[273/80,−513695624409/3276800000];[11/2,27934539/20000]}
f(x)=x5+1417440x4−1343192200x3+4448074000x2+4478226875x−294540320000=0
(-51/5,x-11/10,x93/40,x9/2,x69/55)
xStudentx84:
B={[xi,yi],i=1,..,5}={[−13/6,−36404259/286000];[−913/1020,57153769490527703/31576710971520000];[−39/1870,−2584452756151415863/668857964892975000];[758/715,2655841664621826/635344282519375];[1457/390,−68648707003668323/210899065162500];[104/15,3186764688/1519375]}
f(x)=x5−45679172930x4−903242075x3+708556875469750x2+62074210375x−2113216546975=0
(20/13,x-7/6,x-53/85,x89/15,x32/55)
xStudentx85:
B={[xi,yi],i=1,..,4}={[−144/55,2977936/166375];[−421/330,−3261087679/11859210000];[−137/165,4748848/148240125];[25/22,−115960423/5856400];[4,396344/3025]}
f(x)=x4+46165x3−195733025x2−163341815x−99683025=0
(-89/55,x-8/11,x3,x-14/15)
xStudentx86:
B={[xi,yi],i=1,..,4}={[−91/45,77397583/3888000];[−781/1440,−2638765800311/4299816960000];[323/1440,155473814069/859963392000];[1799/1440,−6981986923511/4299816960000];[239/80,313998781/10368000]}
f(x)=x4−509360x3−845291518400x2+24423472592000x+28037432000=0
(-46/45,x23/45,x159/80,x-1/16)
xStudentx87:
B={[xi,yi],i=1,..,5}={[−61/15,−31654441/202500];[−38/15,3875456/759375];[−7/5,−1173/500];[−21/40,43983379/61440000];[7/8,−19680111/819200];[3,22477/60]}
f(x)=x5+24760x4−2950x3−118975x2−34225x−18475=0
(2,x-4/5,x-46/15,x-2,x-1/4)
xStudentx88:
B={[xi,yi],i=1,..,4}={[−36/5,5405049/12920];[−55/16,−106992528227/778240000];[9/272,170755449629373/64999383040000];[1304/1615,−2481622281949/54422701205000];[178/95,2717306891/116603000]}
f(x)=x4+6796112920x3−40501764600x2−744921323000x+43766731615000=0
(-31/5,x63/85,x83/95,x-27/40)
xStudentx89:
B={[xi,yi],i=1,..,4}={[−14/5,50518/1375];[−119/110,−271814273/146410000];[−31/110,4883247/146410000];[7/5,−99328/6875];[4,29232/275]}
f(x)=x4−711x3−1651275x2−861275x−108275=0
(-9/5,x-4/11,x-1/5,x3)
xStudentx90:
B={[xi,yi],i=1,..,4}={[−21/65,1333591/87880];[179/260,−2356461/4569760000];[9/10,667/8125];[28/5,−31752/65];[111/10,1084]}
f(x)=x4−32726x3+351071300x2−26786113000x+8554716250=0
(101/10,x7/10,x44/65,x11/10)
xStudentx91:
B={[xi,yi],i=1,..,4}={[−46/15,19327478/208845];[−599/510,−6432739313/541216080];[2187/2210,1801426554581373/166981029670000];[1236/455,−2163112987572/728608960625];[146/35,12066934/227409]}
f(x)=x4−7156323205x3−19361938675x2+52898138675x+578088138125=0
(-24/85,x111/35,x147/65,x-31/15)
xStudentx92:
B={[xi,yi],i=1,..,4}={[−71/5,24619392/8075];[−225/34,−275752147581/126951920];[−3/170,63552519/15868990000];[91/190,−35748571859/22154570000];[186/95,172435392/2915075]}
f(x)=x4+198281615x3−986138075x2−1801840375x=0
(-66/5,x91/95,x-3/85,x0)
xStudentx93:
B={[xi,yi],i=1,..,5}={[−59/5,−666177589/40000];[−249/40,101721196539/20480000];[−51/40,−14105763/4096000];[−23/40,644968051/307200000];[59/120,−92129539129/4976640000];[67/30,637994309/1620000]}
f(x)=x5+37130x4+187071200x3−332392000x2−98880340000x−9890120000=0
(37/30,x-54/5,x-1/4,x-9/10,x-33/20)
xStudentx94:
B={[xi,yi],i=1,..,5}={[−23/10,−78804571/1170000];[−5/6,13208587/12150000];[−71/780,−511562088551/2887174368000];[677/1560,313597565193463/1847791595520000];[37/24,−1753820607517/323481600000];[17/5,180929837/1170000]}
f(x)=x5−1249780x4−323117x3+8524946800x2+2673748750x−4513125=0
(12/65,x41/60,x-11/30,x12/5,x-13/10)
xStudentx95:
B={[xi,yi],i=1,..,5}={[−39/5,−740243799/190000];[−77/20,21049944657/30400000];[−39/80,−18548434971/12451840000];[11/80,4172226819/12451840000];[577/760,−44423743771173/25355253760000];[206/95,29260421949/260642000]}
f(x)=x5+951152x4−7142915200x3−992721152000x2+1551897760000x+3566431900000=0
(7/20,x-34/5,x111/95,x-9/10,x-3/40)
xStudentx96:
B={[xi,yi],i=1,..,4}={[−22/13,963653436/21146125];[−98/715,−30777255084/10454040025];[177/110,65456670309/13323310000];[207/70,−14283621/62426000];[144/35,143156646/6131125]}
f(x)=x4−282295005x3+2213325x2+513341125125x−4512617875=0
(14/5,x-9/13,x109/35,x23/55)
xStudentx97:
B={[xi,yi],i=1,..,4}={[−13/3,97643/225];[−41/30,−58484281/405000];[83/60,293193943/12960000];[341/60,−1469237521/2592000];[51/5,391384/375]}
f(x)=x4−25930x3−5911450x2+17374225x−59815=0
(-10/3,x46/5,x13/6,x3/5)
xStudentx98:
B={[xi,yi],i=1,..,5}={[−99/10,−4555770543/560000];[−767/140,28301513163291/13445600000];[−407/280,−1806193555777/172103680000];[−49/80,42533724311/22937600000];[211/240,−12437618989019/159252480000];[47/15,3959257031/4536000]}
f(x)=x5+8441840x4+4849800x3−7131997168000x2−2473075000x−544684375=0
(-3/8,x32/15,x-89/10,x-72/35,x-17/20)
xStudentx99:
B={[xi,yi],i=1,..,5}={[−7/5,−58562007/1430000];[−9/80,171742329423/468582400000];[137/240,−250160389187/910924185600];[943/660,6500913856361/26048517580800];[1369/715,−1290462772501/597971089430000];[191/65,59869193083/3141710000]}
f(x)=x5−7843917160x4+1067021171600x3−332461214500x2−14081271072500x+852634375=0
(126/65,x-2/5,x104/55,x7/40,x29/30)
xStudentx100:
B={[xi,yi],i=1,..,4}={[−21/10,235467/22000];[−181/220,−8152711/58564000];[−21/440,1265738751/7496192000];[21/40,−55107/5632000];[8/5,36639/5500]}
f(x)=x4+131220x3−18872200x2−204311000x+81500=0
(3/5,x9/20,x-6/11,x-11/10)
In [2]:

# LaTex - zápis polynómu
# f(x).list()[1]

f(x)=x^3-3*x+5
g(x)=0
for i in [0,1,2,3]:
   g(x)= g(x)+f(x).list()[i]*x^i
r2=LatexExpr(" f(x)=")+latex(f(x))+ LatexExpr("=0")
show(r2)
f(x)=x3−3x+5=0