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Sample 1. Find all rational roots: f(t) = 21*t**5 + 43*t**4 - 113*t**3 - 46*t**2 + 49*t + 10 = 0
Exact rational root found:
2 / 3
Exact rational root found:
-5 / 7
Sample 2. Solve four NxN linear systems having small integer coefficients.
FM_LIN_SOLVE approximate solution for 25 x 25 system in 0.00 seconds.
Determinant =
1.3275295830832253644589821934885937545600000000000M+39
X(1) =
9.3083551683215158466781562960258778085200474385667M-1
RM_LIN_SOLVE exact solution for 25 x 25 system in 0.00 seconds.
Determinant =
1327529583083225364458982193488593754560 / 1
X(1) =
61785584278962239966328767305853567729 / 66376479154161268222949109674429687728
FM_LIN_SOLVE approximate solution for 50 x 50 system in 0.02 seconds.
Determinant =
1.1767184343659156222752852783560329851053606155163M+96
X(1) =
3.5303049329519547561629707875935880799507280777575M+0
RM_LIN_SOLVE exact solution for 50 x 50 system in 0.01 seconds.
Determinant =
11767184343659156222752852783560329851053606155163488895788435691668352034065582132074616350
72576
/
1
X(1) =
25963593084609330776709791442696628826847720293700388633522222228150017901730670155927899716
9577
/
73544902147869726392205329897252061569085038469771805598677723072927200212909888325466352192
036
FM_LIN_SOLVE approximate solution for 75 x 75 system in 0.06 seconds.
Determinant =
8.6458009593884304466497176868141409874368043584159M+158
X(1) =
2.9750132881254852984855831293192972451289680164345M+0
RM_LIN_SOLVE exact solution for 75 x 75 system in 0.05 seconds.
Determinant =
86458009593884304466497176868141409874368043584158866038219932847609525405426856440508224293
3565302035872155986139687147265810578576164567759071518906480556629
/
1
X(1) =
25721372740668649846282483377402421160424829187005510002972382131652046402176164613557871069
30590389338790663688723108863858876450359702135304213902948210749838
/
86458009593884304466497176868141409874368043584158866038219932847609525405426856440508224293
3565302035872155986139687147265810578576164567759071518906480556629
FM_LIN_SOLVE approximate solution for 100 x 100 system in 0.12 seconds.
Determinant =
3.5174880717168312154288707650879389969977895366159M+225
X(1) =
1.4924010285917821877921723787844039624726137239165M+0
RM_LIN_SOLVE exact solution for 100 x 100 system in 0.13 seconds.
Determinant =
35174880717168312154288707650879389969977895366158547505148577242920191340769931706369819276
730223286545704368964604599010306390683318215201585975464681858519281784956518719677989877102
07513890431647108591774875947523578232356
/
1
X(1) =
26247514081447617087109961525952201308903241664234875372811273534387363907406582563402338186
461489580081056230681325067709646965776871627144530436160075768021306183129663332064854752404
81446842890477718390604869011108433027129
/
17587440358584156077144353825439694984988947683079273752574288621460095670384965853184909638
365111643272852184482302299505153195341659107600792987732340929259640892478259359838994938551
03756945215823554295887437973761789116178
Sample 3. Solve four NxN linear systems, this time having non-integer rational coefficients.
FM_LIN_SOLVE approximate solution for 10 x 10 system in 0.00 seconds.
Determinant =
9.7147804132661796673973639165495117524247426918594M+10
X(1) =
7.1366229035259644464643707839561989917846508277142M+0
RM_LIN_SOLVE exact solution for 10 x 10 system in 0.00 seconds.
Determinant =
9488975856813825989769837906769 / 97675659697423500000
X(1) =
67719242430742463099690931373465 / 9488975856813825989769837906769
FM_LIN_SOLVE approximate solution for 20 x 20 system in 0.00 seconds.
Determinant =
1.5162699369855124181273199328179802380674602563495M+32
X(1) =
1.2748020093337303573759042602207355000203323897259M+1
RM_LIN_SOLVE exact solution for 20 x 20 system in 0.00 seconds.
Determinant =
33988304350356347801570082038451656918825878595293565659147937740479981921060992907486688452
1525140105573756356537749326446418195880575661
/
22415734508281751674995501663953835740509667217835334706831545206093360200328970417083514880
00000000000000
X(1) =
43328358679680641000789699368925045140980714732362183448810928232325766790944234339438009916
12524550387282251544904227599138960275433183424
/
33988304350356347801570082038451656918825878595293565659147937740479981921060992907486688452
1525140105573756356537749326446418195880575661
FM_LIN_SOLVE approximate solution for 30 x 30 system in 0.01 seconds.
Determinant =
6.8420051547927149709909603699901855334922095228697M+54
X(1) =
2.0592160520035187446278473421908223303954891668065M+1
RM_LIN_SOLVE exact solution for 30 x 30 system in 0.01 seconds.
Determinant =
26310818318413061211038829543669848011158301350149686656024083167777252417151712622323617481
665745795472830375106163899387071318288470741954437703318011120096338056562535457703062717062
028828241883048718616776883928057559825006977175234979431781723368784086225308782518865266400
42429493084255510114768125448118158507706153
/
38454835568170764381231224210330002105983020302073302932601494563596775180431889388929689096
460529346626127438414699828413081414220438668377036704772837632806579649553695150213987523259
0742787430557265110011302455345757605068800000000000000000000000000000000000000000
X(1) =
16253897826787321158852570237706801030130158894261737255054278558804998750223027578666123242
508540503145531500405969063022741830818837490142277205006958380997613472375710895073749738768
873271253607044432030423727818216965570025603752029776335299094337831209300874852356133285072
1461268992563912874760770784933952740247801060
/
78932454955239183633116488631009544033474904050449059968072249503331757251455137866970852444
997237386418491125318491698161213954865412225863313109954033360289014169687606373109188151186
086484725649146155850330651784172679475020931525704938295345170106352258675926347556595799201
27288479252766530344304376344354475523118459
FM_LIN_SOLVE approximate solution for 40 x 40 system in 0.01 seconds.
Determinant =
1.0104158744671292591358067723537792785230665098268M+80
X(1) =
2.8924744805054610434682096862674953604437000143334M+1
RM_LIN_SOLVE exact solution for 40 x 40 system in 0.04 seconds.
Determinant =
14202810339562305502320102394317789871274700282301725713529255197301430629669174331575192763
630110460373139826847574473203547917865788960849668653386273272430125911044732363205448662380
001529247559076668776873691279308816024751960482003309323830504905737368611444142751133580594
766697712368115183160604044680108137270259871571880706702209141952747965063781456567185246795
830531692324561572185712375153685465958057784915347553699342834557753349840470095533669681853
3970943671897877469475179792329288510164145122017790047407915402446211972932439654106798679
/
14056400635087557509548358356056196925598913483043847389078983373729501145541485353760410604
500958167765094782898009145354771282431132848534987952919144176200385307721037353308598241893
957438434597616444217511900736415954735880586153902228126832468527642075816442416921279259506
219620951302183618568576383592195866551621163275364984202820428998750477045029359573084566910
499837225263597246313683582685339650873592161239040000000000000000000000000000000000000000000
00000000000
X(1) =
53405646396235991480792932675174168915495914304199752534356447021065730270921701262786055574
819565756472969243473977430479958767814138684784208342940301806453698270410525602976052495561
858779241934496568912879610448330364360688750335147005567155035596251259999627630131463509903
307912032325348702591842389429409254164557302347483090066418612303862436261954117179164963327
365054009614292681927325384512241036651012504330653146936915413850878749507407168880481267592
729542412933131067915924268893565918644677258636908785863770527656617075931669041609326201535
/
18463653441430997153016133112613126832657110366992243427588031756491859818569926631047750592
719143598485081774901846815164612293225525649104569249402155254159163684358152072167083261094
001988021826799669409935798663101460832177548626604302120979656377458579194877385576473654773
196707026078549738108785258084140578451337833043444918712871884538572354582915893537340820834
579691200021930043841426087699791105745475120389951819809145684925079354792611124193770586409
41622267734672407103177337300280750632133886586231270616302900231800755648121715503388382827
Sample 4. Examine determinants of several small Hilbert matrices.
FM_INVERSE approximate inverse for 1 x 1 matrix in 0.00 seconds.
Determinant =
1.0000000000000000000000000000000000000000000000000M+0
RM_INVERSE exact inverse for 1 x 1 matrix in 0.00 seconds.
Determinant =
1 / 1
FM_INVERSE approximate inverse for 2 x 2 matrix in 0.00 seconds.
Determinant =
8.3333333333333333333333333333333333333333333333333M-2
RM_INVERSE exact inverse for 2 x 2 matrix in 0.00 seconds.
Determinant =
1 / 12
FM_INVERSE approximate inverse for 3 x 3 matrix in 0.00 seconds.
Determinant =
4.6296296296296296296296296296296296296296296296296M-4
RM_INVERSE exact inverse for 3 x 3 matrix in 0.00 seconds.
Determinant =
1 / 2160
FM_INVERSE approximate inverse for 4 x 4 matrix in 0.00 seconds.
Determinant =
1.6534391534391534391534391534391534391534391534392M-7
RM_INVERSE exact inverse for 4 x 4 matrix in 0.00 seconds.
Determinant =
1 / 6048000
FM_INVERSE approximate inverse for 5 x 5 matrix in 0.00 seconds.
Determinant =
3.7492951325150871636132407107463796806200434318348M-12
RM_INVERSE exact inverse for 5 x 5 matrix in 0.00 seconds.
Determinant =
1 / 266716800000
Sample 5. Examine determinants of several larger Hilbert matrices.
FM_INVERSE approximate inverse for 10 x 10 matrix in 0.00 seconds.
1 / Determinant =
4.6206893947914691316295628839036278726983680000000M+52
RM_INVERSE exact inverse for 10 x 10 matrix in 0.00 seconds.
Determinant =
1 / 46206893947914691316295628839036278726983680000000000
FM_INVERSE inverse matrix largest relative error was in row 1 column 10. Error = 1.08884M-50
FM_INVERSE approximate inverse for 20 x 20 matrix in 0.04 seconds.
1 / Determinant =
2.3774547167685345090916442434276164257430508782136M+225
RM_INVERSE exact inverse for 20 x 20 matrix in 0.02 seconds.
Determinant =
1
/
23774547167685345090916442434276164401754198377534864930331853312344197593106445851875857668
165737734405657598672655589717656384197107933033865823241498112410235544891661547178096352577
97836800000000000000000000000000000000000
FM_INVERSE inverse matrix largest relative error was in row 1 column 20. Error = 7.09674M-36
FM_INVERSE approximate inverse for 30 x 30 matrix in 0.12 seconds.
1 / Determinant =
2.9398328102395524505848666971400446401362203256340M+518
RM_INVERSE exact inverse for 30 x 30 matrix in 0.07 seconds.
Determinant =
1
/
29398328102395524505544541496714576627047090970174537902378508631336083748868372540222442367
087154324086785080173361110767763803018593535788457415930995086244543066188795733864785271238
542192536704391385464881437021692658344115588315760214041402277212015907525207053450623712821
445582088278053092134614891698230513496009924077208615417827905985550365857258899775072310828
300746368350942171223049176635399789456250078556766280573896317425157669643532780392171962368
0000000000000000000000000000000000000000000000000000000
FM_INVERSE inverse matrix largest relative error was in row 1 column 30. Error = 1.15448M-20
FM_INVERSE approximate inverse for 40 x 40 matrix in 0.30 seconds.
1 / Determinant =
9.1150185983421653630696439604125792349968213233423M+931
RM_INVERSE exact inverse for 40 x 40 matrix in 0.16 seconds.
Determinant =
1
/
91148445317566258751264876699754732527370841154734052886449926733556811479408912156059842334
588941578780273098553144167949448489528336803141772953236332459194497243601609507296388946266
233062528595411175820228799938417775022913338714288588552485278925773157515869431921894493828
321447577822636684274663059529149740493580999891430869202808515756322607727305994484227852766
479158044297125202406142856301182540876335667576022316556769150079984456601875532363261652353
495277151420824528221223209590100339041009139702891426368118406174050396400813767873460036972
335023242261321455435085108585664753779398559394807080194265190638932894157867287281594472593
028619718609003524355718945963579220161775267375998926853659378105451672709373388656591062091
850744065803164410251281367091228073142835765650074817926193321512072501454051242014007288414
616186752903472586959093760000000000000000000000000000000000000000000000000000000000000000000
000
FM_INVERSE inverse matrix largest relative error was in row 1 column 40. Error = 2.18693M-5
Sample 6. Find four NxN inverse matrices, having random 2-digit numerators and denominators.
FM_INVERSE approximate solution for 10 x 10 system in 0.00 seconds.
Determinant =
1.8539495869937354383304358956415053043572030501134M+8
RM_INVERSE exact solution for 10 x 10 system in 0.01 seconds.
Determinant =
1740747236392189345058845844768282633080044232800016068193142549169318416453484615517
/
9389398981527275973091698992735861515294458055836988712435724032409600000000
FM_INVERSE approximate solution for 20 x 20 system in 0.02 seconds.
Determinant =
5.3928065157779394054042391503936119727649242527872M+20
RM_INVERSE exact solution for 20 x 20 system in 0.08 seconds.
Determinant =
13279277328259490303866379541406302912368825456963217445156141961445101033465257113767429685
694219324326632931280963016657142001176436426993024331776714164411323431060807954586977229376
453941883460980104478546571042899152544485585258945569765874757671326584914552844769154935325
03363
/
24624056675142716302359864037161280411077902294640718230962714453529440429012521504691224614
209594203732557526955888802011239876236493895217578726471537030422375074102299064286679434745
79657209183922814517281982046915962652362664837120000000000000000000000000000
FM_INVERSE approximate solution for 30 x 30 system in 0.07 seconds.
Determinant =
-1.6420170614081804846846996954559085193588212654284M+33
RM_INVERSE exact solution for 30 x 30 system in 0.39 seconds.
Determinant =
-70504054183000021545270607166665243507327937573923985632382464788272729613281052964825758581
295708128367269717949976917735423744173780672793146912340172528336528206453146199141196019142
540115842731377410148892062165143090224412178473046524254401643198094065010668129553548616199
294676990571939397610726411665190081664231512721236419016389998635333313538203623691280396644
168044613190115026238485743710419480129309997415990153169180834610774089809831873304908383412
5826503131441056648483597711328076173767668293907542510935279407360011259895385569283293439
/
42937467484373346140503689560711885261160709204013857450006774608182073578778014225188964929
467176090831910064807291997688182230302181980090145842211409260942191842139126592524017323548
896829973399092358380371532091453817642479074181135285771742082102375729719504644370160606054
517584611485047979559746528048152878582311600185116281909667649759869932388432480314981298778
609813238580056790654439031525416118764541196895604401636637439338863786705638105248668883914
0172820738211840000000000000000000000000000000000000000000
FM_INVERSE approximate solution for 40 x 40 system in 0.15 seconds.
Determinant =
3.9967110834808415637227948118221860364913475793044M+50
RM_INVERSE exact solution for 40 x 40 system in 1.36 seconds.
Determinant =
56794218550718469916064662030617264022627539702562932513218538542267743163734778077452107129
702937857552206659237746285751297185368145519858263887130029093351460767777276357578652418470
965268708881903377609568799050771834365146396653409275712412992667578065255347856952116733996
965110244846208517524739580829681340063745481925750557968220307036645752850271988478245073204
899254961900288486777325241560830288569691266976239151291781636378296314219743086236320090996
527074291754679839904340966219967364055325344702660087628083911004209132324623297011704906044
067753326437253688426714493110123671023746247515168296626097400728333924864760084865538360095
472369017058811844562083484067387137464986693391228994019305758622117003274613950653779448903
270922498653417526414189629867407146004108851548200488783278022955226538873742201
/
14210238709888151430816810164504120742169147097883882509158860618120735659521700673491670559
732222265621244444668498806660093829107734489385698292984198294676350657137151028407801813676
869256431304934498409480097122681805725417607453188971034379285656940732070123189773903960205
927121765514042238534422164844885719833247326978831184180300727186488545315231514809439301559
308664247701083378220971730850732294673081060395620725066351974319477841967327198257795402320
320027934691913236437247641165763076515911661615516104246024972081401704483228839681256712367
506806720180474979133508723100479787189931329948396691898271953997750296592808258513333350438
158018791090015050002545717198427961777684031422005664913817600000000000000000000000000000000
0000000000000000000000000000000
All results were ok -- no errors were found.
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