Programming for Mathematicians

434 Pages·2000·4.408 MB·English

by  Raymond Seroul

Raymond Seroul
Programming
foMra thematicians
Translfartoetmdh Fer ench
by Donal O'Shea
Wit4h0 F igures
Springer
RaymonSde roul
UniversLiotueiP sa steur
U.F.dRe.M athematiqeutde 'sI nformatique
7,r ueR eneD escartes
6708S4t rasbo,uF rrgance
e-maisle:r [email protected]
Translator:
DonaOl' Shea
DepartmeonfMt a thematics
MountH olyokCeo llege
ClapLpa boratory
SoutHha dleMyA, 0 1075-1U4S6A1 ,
e-maidlo:s [email protected]
Titolfte hF er ench original edition:
math-Iinnffoor.m paotumiraq tuhee mat© IinctieernEsPd.ai rt1ii9so9,n5 s.,
LibraorfyC ongreCsast aloging-in-PuDbaltiaacp aptliifoeondr
DieD eutscBhieb lio-thCeIkP-Einheitsaufnahme
Seroul, RParyomgornamdm:if nogrm athematicIiR aanysm onSde rouTlr.a nsf!r.o m
theF rencbhy D onaOl' She-aB.erliHne;i delbeNregwY; o rkB;a rceloHnoan;g K ong;
LondonM;i lanP;a riSsi;n gapoTroek;y oS:p ring2e0r,0 0
(UniversiItSeBxN3t )- 540-66422-X
MathemSautbijCcelsca ts sifica0t4i-o0n4 ,(6189-9011) :
ISBN3 -540-6642S2p-rXi nger-VBeerrllaign HeidelYboerrkg New
©Springer-VBeerrllaign Heidelberg 2000
PrintiendG ermany
Preafce
Wea raesd wravseist otnti ehns gh lodueorfg si saW.ne ts eteih ntgahst
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Berndad reC hartrecse ntury)
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coullaedr init n e igdhyats!
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in this way.
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thwaetr feo irgetno amnetd h Ian te edteoud nd erasntd.
Aftaenra pepnrticoefss ehviaeplyr erasI,b egtaont eapcrho gmrianmtgo
studientn htiesr dty heiaorrfm athecms(a wthiiwcech a tlhlLe i ce)nI.wc aes
veryp rssieutdro fi ndt hamta nwye rfear nkhloys ttiocl oem pusticeern ce.
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progrkanmosnw goi nlvyey r ftecewh niqfuroecmso mpeurst cience.
1A nyi dniivdual hawbshe oe enxl ieodr w hoh arsda iclaycl hagnedp reosfsiwoinl l
knowwh ta amt alkaibnogu t.
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whicphr etetnodt eeda rcihn sgt ructtous rteusd ewnhtohs ad not myasette rtehde ir
multiicpalttialobens .
Them odemma thteimcaiisca onn demtnope rdo g.rB aumhto w doonees
lerna top roagmr?T his aisd sifi fcualslt er ainnhgo wt od op ro!oA fnsd, in
botcha stehsee,i r sn om ethod.
Litbtyll eti ltmey,i edabse cacmlere eaarn d bmayc okugnradsa m athe­
matibceigatanon h elTphi.sb o oikst hferi uotf t haaptep nrticaenstdhh iapt
syhnestiIsit.ts h beo ok Iwt ohuahtla dv leie kdt oh avhea wdh eInb eg.aI nits
meant for thaonis tner uowcdhtoti opow rnao angmtrm iwnight ournteo uncing
thierma themabtaicockuaglnra dn d wwhaont toh ramnoiouistnleaygt rteh is
newd isciipnolt tihneei ro ftw haoyu ght.
Howe,v emara thteimcaciaarnnpa idcloyvn etrt haebi ilttyoc eratper oofs
tot haer otfp rogmrianmigf ftolhloew itnwgco ondiatrifeoul nllsfie ld:
he sohrhe a asc laeri deoafw haatc ompeurit sw,ht ai cta n adnowd,h at
•
icta nndoot.
he orl ersanhtseot hidnyakn mcilaly.
•
Mathemartseiuclcatalsbn e r oguhldyi veidid not twcoa lsses:
starteiscuC lratemsrf:'o smr ul"at,he ee xrixss tu cthh Patx( ")t,h dee fin­
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itiooftn hg eer atceosmtm odni ovri satnhBdee zout tI=h eauo+ rbvee,mt c.
dynamriseclu tGsa:u sspiiavno tainen xgip,cl ciotsn turctioofn e alne ­
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menxti nas eEts astyfiinpgr opePr,Etu cyl iadn'Bdsl n akihnispag'lostr hims
thcaotm peut htGeC Da ntdh neu bmerusv, i nB ezuott'hsee omre,t .c
A trdaiitonmaalt hteimcatiihannks tsa tliysc;ya sltedmyaanmtiitccha iln king
isan ewd isicniweph losdee velohpamcseo niitnd cewdih tt hoaftc omputer
scieCnocvneet.ri fnrgo m sttoda ytniacm tihcianlik sni onetga sy s(oamned
winlelv meark teh ter saiinot)n.
Expieernscheo wthsaw tri tiang go opdr ogriaesmv emno rdeifi fcutlhta n
writianp gr oboefc atuhseej ceotbtsh aotn ceo nesriasdr leki et ibnayr osf
westo :at phesiyld bee twoene'ens g efi.rnP srogmrianmigos f tseynn onymous
wiht "foolianorgu ndw"h icmha keistd iassttuelaf ndof tena lzypianfrgo r
mathteimcaiaacnusst toomo etdh er dsst.a ndar
Weu saev eyrs tridpopwepndor garmmilnnagg ugea( asseingttnsem,sa tnsd
looapnstd)h e res tarndpd raogmrianmtgce hniques:
reycclianngrd we riticnogd e
•
desncdeianngla ysainssd u cscseirvfieene ment
•
thues oefs equetnoac lelsoo nwte o t ransafd oyrnma mpiorcballie mno t
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as taptriolcbe mmo erf mailrti oma athteimcasi.a n
Ip lcae eeqmupahla osnti hsae e sthseitdAie mc.a thteimncaa ilawaeyxs­
peirencpreoosuf nsdas tfitaicoonns tudayb ienuagtu iltf heyoo rrp rooTfhi.s
isw hyh eo r sphrcaet imcaetsh eimcaIswt .a nttoc onnvcimea thteimcaians
that they will efeexlpgiesunr pioeannn ycazeli antnghd e t issuenaptgam ne
algiotrhemv,ea nv eyrs impolnee .
Theu soef c ompeurctser atneeswo ri,ns omiesn tanrcseeusst,ca itoelsd
porbleimnms a theimc(asht omwu cshp ascheo uolndre se erivnem emyo r
fotrh dei ovriss ag oifv ienengt enr? a)n d ceorms pcuite(nicenesv tigating
algtohrmipsor,v ipnorgg ra)m.Tsh isb oobke awrist nteots hsii tsne crtai:o n
tot hpel eeat shuee rrisp roignmr ianmmga tmhaetiacnstd ot hpel eraeos fu
reoansiwnhge onn per oagmrs.
Sicnef omre p rogmrianmdgo ensom te adne niynmgy fi rlsotv tehr,ei gorous
sidtea kpersi oorvietarm y o rdeea tidl setuodfya p roagmrminlgna guage.
Whenepvosesri bItl aek,te h oep ptonuriy ttop ersemnatht emattihcamsty
studenntoskt n od.Fwo o trh riaess ,oo nnfien dmsa nmya themarsteuiclatls
anpdr ooifnts h bioso k.
Mosotfa llt,h bioso iksa m ieda tu ndgerruaadtweihsts ommea thematical
bacokugnrIdwt.i alllbs eoo fi nertetsott h owsihets ommea htemattirncaiainlg
whow ihs( onre e)t dob egipnr oagmrmnig.
Fohrsi tcoarrlies aonPsa,s ictashl le ag nuaugsee Bdu.tti h bso oiaksb soyl utel
noat troenat thPieas selc aanlg uCoavngeseri.ot noam oerm odelma unagge
isis ntantsao:nn eneoe ued hoanvalesy s igntmeesantntslds o ,o ps.
Acknoewdlmgeents
A bookl ieia ksni cegb.Te hrea uthiosr otnhlepy a rtth aetm egresO.u to f
sightth oawsrheeoi s npeidar nd hwehelodp oitnhw eayrs A.m ong lttatheirs
groaurpte h feol lowiwnhgo mIw ouelsdp iealclyl iet kot hank.
The IaRtES rMtsa boguw rhiacllohw emde a ccetsots hc eo luomfnt sh e
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rveielOw'u evtrt,h eraelblyo mwei nrgtfieo n mey i deas.
Altlh ceo elalguaensfdr e indwsh oh avfeol lwoedt hceo urisnpeo rsg ram­
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mintgh aIht a ve ttahuogwshiehtt w,h omIh avdei scedum sasttaebrosu t
whiIcc ha rdee e,pa lnytdh owsheo hgaivveme ena dvicaeb otuhtbi oso k.
Thset undtmesaj roiingnm a theimcaastSt r tsabogu,or nw hoImt eesdat nd
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rfiened mieyda fso orv etrey ne aWrist.h outf eetdhbeaitcrhkb i oso k would
nevhearv e tshelegei hnot f day.
FinlayIl,w oullkdie t o tthhatenrk sa alntoDro,n aOl' Sehao,f M ount
•
HoylokCeol elgfeo hri esxe cllweonrtk .
Raymond Seroul
UnviesreiL toiuPsa st,e ur
UFRd eM atheqmuaeetstid I'nofrmtaique
7r uRee nDee stceas6r,7 08S4ta rsbgoC uErDE(XrF nace)
seoru@lm at.hus-tasrbgr .f
Contents
1.P rogrammiPnrgo ver.bs . . . . . . . . . .
1.1A.bo vaeln lot, ir c!k s. . . . . . . . . .
12..D on octh ewgiunmgw hicllebi imnsgts a ir 2
13..N ame wthhiayctoh su i tldlo' nktn ow. . 2
14..T omorrotwh,ni gwsi blelb etttehre ;a dfatybe ert,st lteilr 2
15..N eveexre caunot red beerf oirteg viiesn 3
16..D oucmetnotd taoay v otieda trosm orrow 3
17..D estcsea'Dr iscsoeou ntr hMee thod 3
2.R evieowf A rithmetic 5
21..E ucleiadDni viiosn 5
2.2N.um ertaiSoyns tems 6
2.3P.rm ieN umber.s . 7
2.13T..h en umbeorfp irmessm altlheaarng ivreenan lum be.r 8
2.4T.h eG resatt eComDmiovonir s 9
2.14T..h eB ezoTuhte orem 10
2.4G.au2s.s L'esm ma. . . . 10
2.5C.o nugenrce.s . . . . . . . 11
2.6T.h eC hinReesmea iTnhdeeorr em 12
2.7T.h eE ulpehrFi u ncti.o n. . . 14
2.8T.h eT heeomrso fF ermaantEd u ler 15
2.9W.il osn'Tsh eor.e m . . . . . . . 16
21.0 .Q uaadtrRiecs id.u es. . . . . . 17
21..1 PrmieN umbaenrSd u mo fT woS qursae 18
21..2T heM obeiuFsu nct.i on 19
21..3T heF ibcoicnN aumbers 21
21..4R eaosnibnygI nduction 22
21..5S olutoifto hnEesx ceriess 25
3.A n AlgorithDmeiscc riptLiaonng uage 29
31..I ednteirfis. . . . . . 30
3.2A.ri thmEextpeirscs i.o ns 31
3.12N..u mebrs. 31
3.2O.p2e.ir aotns 31
3.2A.rr3a.y s 32
32..F4u.n ctcialolsann pda erntheses 32
3.3B.oo leane sEsxip.or ns 32
34.. Satetmenatnstd h eira xS ynt 33
34.1.A.s siegnntms 34
3.4C.o2n.d itionals 34
3.4F.o3lr.oo ps. 35
34..W4h.i llooep .s 35
34...R5 epelaootp s 35
34..S6e.q ueonfcs etesam tents 36
3.4B.l7co.ko sfs a ttmeents 36
34..C8o.m lpesxt maetents 37
34..L9a.y oount paangcdeo tnrols ytonaf.x 38
34.1.0 .To w hadto etshe ele bs elong? 40
3..41S1e.mo ilcosnosm:ce ls asiecrarlo rs 40
3.5T.h eS emanotfSi atcetsm ents 42
3.15A..s siegnntms 42
3.5C.o2n.d ist ional 42
3.5F.i3rt.sr stal tnaio.n s 43
3..54T.h eb outorsphedorodne r 45
3.5T.h5ef. ol ro op 47
3..56T.h ew hile loop 48
3.5T.h7er.p e ealto op 50
3.5E.m8b.e dldoeodp s 51
3.6W.h icLho otpoC hoose? 51
3.16C..h oionsag flooorp 52
36..C2h.o ionsagw hilloeo p 52
3.6C.h3o.io nsagr peealotop 52
36..I4sn.p cetienntgar ncaensed x its 52
3.6L.o5o.pw sih t caicdents 54
36..G6a.u sseilainnma ition 55
3.6H.o7wt. o g arbd ata 56
4.H ow toC reataen Algorithm 59
41..T heT raocfea nA lgoirthm 59
4.2F.i rMsett h:Ro edclyicKnngo wCno de 60
4.12P..o tsagset amps 60
4.2H.o2w.t o d etmeirnweh etahp eors tiasrgae eil azble 61
4.2C.al3c.ut iltnahgte he rshovladl ue 62
4.3S.e coMnedt h:Uo dsiSnegq uences 64
4.13C..re atoifoa ns ipmlaegl otrhim. 66
4.3T.h2ee. x poinaeslne tries 67
43..D3e.c oomspitiinoop tnrm ief atcors 69
4..34T.h e ldeiavosrift snu ction 71
43..C5a.dr ilniyato fa ni nertsteicon 71
4.3T.h6eC. O RDIAClg otrhim. . . . 74
4.4T.h diM reth:o dDefWerirteid.n g . . . 78
4.14C..al culatwtboi inrzgra fenu ctions 80
4.4S.ot2r.a ogfet hfier Ns tp rinmumeb ers 81
4.34.L.a srcteo mmetnidoans 84
4.5H.o w Ptorov aen A lgotrhim 85
4.15C..ra she.s . . . . . 85
4.5I.n2fi.enl iotop.s . . . 85
4..53C.al culathtGeiC nDgo ft won umebrs 86
4..54A. m orceo pmlitecedax amp.l e . . 86
4..55T.h ev aildyio tfa r seuflutirn hsed abl yo op 87
4.6S.o lutoifto hnEesx ceriess . . . . 88
5.A lgorithamnsd C lassiCcoanls tructions 91
51..E xcnhgaitnhgCe o nteonfTt wsoV aarbiles 91
5.2D.iv esreS um.s . . . . . . . . 9.2
5.12A.. v eyri mpotracnotn vention 92
52..D2o.u bsluem s. . . . 93
52..S3u.m wsih te xceptions 94
5.3S.e rcahifnogarM aximu.m 95
54.. SolvaiT nriga ngrC urlaamSeyres mt 96
5.5R.ap iCdal ctuilooafnP ower.s . . 97
56..C alctuilooafn Ftihbeo nNaumcbceir s 98
5.7T.h eN otioofan S atck. . . . 99
5.8L.ni eaTrra verosfaaF lni ieS tet 101
59..T heLe xcioagphriOcr de.r . . 120
59.1.W.o rdosffi xeldeg nth 120
59..W2o.r dosfv aarbilleeg nth 140
51.0 .S oluttioto hnEexs ce riess 150
6.T heP ascaLla nguage. . . . 190
61..S taogre tohUfes uOabjlc ets 190
6.2I.ne tgeArri thmienPt aiscc al 101
6.12S..ot raogfei netgeirnPs a scal 101
6.3A.rr ayisnP ascal 131
6.4D.e lcraaitoonfa nA rray 141
6.5P.r oudcSte tasnT dy pes 151
6.15P..or duocfet q usaelt s 151
6.5P.r2ou.dc otfu neqsueatls 161
6.5C.o3m.p otsyiptees 161
6.6. TheC oRnosltea notfs 171
6.7L.ti te.r . . . . . . 191
6.8P.r eodceusr. . . . . 191
6.18T..h ed eacrltaipvaero tfa p reodceu r 102
6.8P.r2eo.cd euc rlals 121
6.8C.o3m.mn uciatoifoap n r eodceuw ritthhe exe trior 122
6.9V.is ilbyiio tf Vtaharebi lienasP orceed ur 142
61. 0C.o ntEefxeftc t.s . . . . . . 152
61.0 1.F.un ctio. ns. . . . . . . 1.72 .
61.. 02P.or ceedo urfr nuction? 182
61.1P.r eocdeusrW:h at Ptrhoeg rSaeme mTosD o 192
61..11U.si tnhge mo.d el 133
61..2S olutoifto hnEesx ceriess 143
7.H ow toW ritae Program. . . 153
71..I nrvseea no fdO er4rM atirx 153
71..T1h.ep rolbem 163
71..2T.h eeotrisctauld y 163
71.3..Wr ititnhpger ogram 183
71 4...T hefun ctdieo.tn . 104
71.5..Ho wt ot ypaep rogram 134
7.2C.ha rcatsetrPiiocl ynoomfai M aalt rix 144
7. 21.T.h ep rogrLaevmer rier 174
7.3H.o wt oW rtiea P rogr.a m . 125
7.4A. P oorWlrtyit Peornc eed ur 165
8.T heI nteger.s . . . . . . . . 195
81..T he lEieudacAnl ogirth.m . 195
81..C1o.m pleoxfti htEeyuc leiadanl gorithm 106
8.2T.h eB lnakinAslghoitrphi m. 161
8.3P.e rfNeucmteb rs. . . . . 136
8.4T.h eLo weDsitvo irFs unction 156
8.5T.h eM oeibuFsu nct.i o.n . 176
8.6T.h eSe ivoef E rasttohenes 196
8.16F..o mrultaioofnt hael gorithm 171
8.6T.r2a.n sifnotgrh mael giotrhtmoa p rogram 127
8.7T.h eF unctpiio(nx. ). . . . ... . . . 157
8.17L..e gneder'fso rumla. . . . .. . . 157
8.7I.m2ep.ml entaotfL ieognnede r'fsom rula 187
8.7M.e3i.s' sfseo mlrula 197
8.8E.g yptFircaatni ons 181
8.18T..h ep rogram 138
8.8N.um2e.cr airlse ults 168
8.9O.p eartioonnL sa rIgtnee gers 178
8.19A..d dit.i on. 178
8.9S.ub2ta.rtc io.n 188
8.9M.u3l.ti icpaltion 198
8.9D.e4ac.rlt aions 109
8o59oToheprogr0a m 0 0 0 0 0 0 0 109 10 0
81000D isviioinnB aseb 0 0 0 0 0 0 0 01 490 0 0
810O oloDe sicprtoifot hnde i sviioanl gorithm 149
80010J20u sctaitfioifot nhd ei vioiansl giotrhm 169
81000E3f0ef cteisvmteai toefsi netgepra rts 179
8100.04 A gdoioivdoia nsl giotrh0m 0 200
81001 SumosfF ibonNaucmcebir s0 0 0 0 200
81020O dd mPersai sa S umo fT woS qursae 203
81003 SumosfF ouSrqu are0s 0 0 0 0 0 0 207
81004 HighCloymo pseiN tumber0s 0 0 0 208
81004.1S eevrparlo tpieoerfsh igcholmyp eon sumibters 210
810402P0rc atiicneavslt igoafht iigochnol myp eoi sneitgters2 12
81005 PermtuitoaJnosh:n 'ssAo'lgn oirthm 213
81005.1T hep rogJraomh nson 215
81006T heC ouinGtso od 218
810061S0y antctitcr ees 219
9.T heC ompleNxu mbers0 0 225
90 .1 The GauIsnestgiearns 225
910.1E.ulc ieaddni ivsion 226
910.2I0rre duicbl0e s0 0 226
9103.0T hep rogram 231
902B0a soefsN umertaioinn Gtauhes sIitnaeng ers 234
9012T00h em odulboe tmaa p 0 0 0 0 0 0 02 34
902H0o2w0t ofi nadn e xact osfyr pseertseemtn itva0e s 235
902N0u3m0e riaotsny stienbm a se 0b et0a 0 0 236
90.24A0n a lgorfioterhx emps rsiionbn a sbee ta 237
903M0a chFionru mla0s 0 0 0 0 0 0 0 02 400
90013U.n iqueonfea Ms asc hifnomr ul0a 242
903P0r2o0oo fPf r poosi9t30i10o n0 0 0 243
903T0h3eT0 o dcdo ndiitsnie ocsnea sry 244
90.34T0h eTo dcdo ndiitssi ufiofcni ent 244
903K0e5rn'0a sgl ori0t hm0 0 0 0 0 0 245
903H0o6w0t og erti odft hAerc tanfgunecntti on 249
903E0x7a0m ples 251
10P.o lynomia0ls 0 0 253
1001D0efi niiotn0s 0 253
1002D0e gereo fa P olynomial 254
1003H0o w Stotor aeP olynolm ia 254
1.04T0h Ceo nvenwteiA odnosp t 256
1.05E.uc leiadDni sviion 259
1006E0v aluoaftP ioloynn olmsHi:oa me'rMse thod 261
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