Mercury 2.00 manual =================== (C) Copyright 1990 Roger Schlafly. All Rights Reserved. Portions of the software (C) Copyright 1987-88 Borland International. All Rights Reserved. Contents -------- 1. Introduction Features History Shareware policy Disclaimer Files Hardware Requirements Installation 2. Problems Editing Numbers Operators Constants 3. Solving Solutions Graphs Reports 4. Feature Reference Functions Statements Commands 1. Introduction Introduction ------------ Mercury is a program for solving equations on the IBM PC. It is easy to use, interactive, and powerful. With it, you can * evaluate mathematical expressions. * solve for the roots of an equation. * solve a system of equations. * maximize or minimize a function, with or without constraints. * evaluate derivatives and definite integrals. * plot one or more functions. * print a report or a graph. Mercury has a built-in editor, pull-down menus, online help, and all the conveniences necessary to mak lp, a---N=nimE evaluion tornoviN=nMercuFgraphmencknitmaints.. quatry has 's pabil elinrun MERCURY all tonvn loaddefin a syssomehe softwaamp pms Ed (*.EKA) is f an get stuck, just ions.softwF1 keythe r anMercury has aprog quutgrow witf Eefeka,ogram on itf nd Interoducional. Alitf Scot anVhe ey, Calihe niath invn nd Interdecide tooeniec Creriv qsionadsheet nterdatabasuncam on linEefeka wbuispu quafth ry has awbu develope tfromsofastrade basu powerprobequatrelto e ti IBMasy he msoowaatisfy customertreques anhe rnew v Opof the sEefeka is prolabee ed v Opof manobecaint a-pros a larsoowwfastv Opof manoof Eefeka woulda bsysbee * solEefeka wbui o ava laE e IBM PApp Mac reosh isNotv Opof uatry has the rootsMac reosh-propIntned astBMas t FMercury has aprogva laE buiware poli isware policprogrnam the ncam for swwfich olicdy rib t tfreely graptrnoizeAlicaregu pb wfich oliccght 1987eddefin bsysons ric on the IBM ir inagFMercury has amaysbeccghit tfreely he rexaizeA. qpurpos=nM laim rib ConsmayscareguogrnoizeAlifeu pam vide tohastBMeytadhe soowonvenieg n thi VENDOR.DOt isnds y hiAliowerpintitul. 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Al isnd Intercght 1987 definCreitmarktholicu e tut croa Omis. th ry has aprogrCreitmarkitf tMe au cor Conte Hard Mercury is a rain e the softntsf HaMercurERCURY.EXE ma 2ram for curERCURY.HLP ansf Hrin.BGI . ics dive Oper*.CHR fo Comm*.EKA aamp pms EdcurANUAL u er l === (BMas f H) README mencknpintrus StateEGISTER.DOt t gim s.. qhe m VENDOR.DOt ncede rinhe m 2ercuAuxie io maf Ha: prin.EKA functaamp pms Edcun.BGI funct. ics dive Oper*.BIN excionaltions. er*.C aourciae, excionaltions. erMATHL.H toolanhe r lpquatixcionaltions. er*.OBJ toolanhe r lpquatixcionaltions. er*.LIB toolanhe r lpquatixcionaltions. errodfcan menuloade try has thromsg qu help,d. De can mayse idsoftscauxie io maf Haholchve ersepareriAllisTMetixcraaf Haholecne oneedeerobysmost ieop powerancta C ersepareriAlsoowaav e Iraisart t FMerTMetixcraadive Oprancthe ronsds e Ihre Requiu hy powertMe toolanhe nsmapquatixcionaltions. trequntssnd Inte's Turbo C++MercuR gim e d customerui o get INST.COM powrpintion 2ram for y he oraifiguraE ep. * pri are Requirements Inst------- M---- Mercury is a requntsrog qC. Itore clr moor wiastlto t 640K uatRAMlisAbonst500Khe sfreetRAMaproneedee is 2rodg n ,y tx -de tmtma a (EMStmtma a)aprou e tif ions I is f ansma wicghroN=nie rirogva laE , a-wie cb u e lisAematialuihroN=nie rirorecds y de tolvintivourons O cruncaer * priPlf anrequntssat. ics e pulpoweratCGAinEGAinVGAine nsHy is Hahcre * priYn *t a rept or aspower. the Ianystf tMe podowa ncamactivs isSelart PmactivpowerMadeltfromsofeato. t, ony he ooots s itf supor ae tamactivs pri llation 2. 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Ally ry has tha lsobecaint onvenhipi spitee, and is e * eb Ref d uaftut cro set 87=N a al rootsDOS am mp Mercury has aa o detartsIvhivouro. ics cre o pb tssomeh *ne ob scdetarte lisSeerootsSCREENta nts Cti IChaptivp4.errodfcan bsysat. ics amactiv can wie cwan hBoIselart a--troftscPmactivp, onlisTMet. ics cre powerfmactivpselart 2rc *tb scaav tk ootsMERCURY.CFGwf H powertMen a-wie cb au oal ex eaccrot F ry has aproloade pri Errornst------ri Errorp, snagFpranctamnt ytmuch self-ssiInt Cy is f a*terrorpisscdetarte wwfi pars uatBM pmo Ewf H pry has an scan i IBM scng -windowoor wionvenursgraptrtMe po repe softwerrorlisTMetirrornsm snagFaptrtMe toppe softwwindow powerdimappearsths sre Iascan scata tteg NulisOBM viirrors olicdy iInye ti IainpehiAlibdx wfich proiInc d u IBM Pscree lisAftivpan acknow edgssoftwrrrorpbiscions. uatBM Es pe key can ancta tsbacknpiIBM Pm onem of e pri oblems EditcuA pmo Ewproen e d reopry has abyseiBM viloadquata*tex s Solur mofromsofeadimk porpbi cre Rquatarnew r 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Dntsc ssg eellisTMin me wod uiis s s uf apply uatBM ru s uf h198sschooeaalgebrasoo manipulateaBM ions. huntilraolu 2n C) ubta 2 dshe rAllaBM vhivaE sMisFgraexamp , 2 x + 3 y =I8sc 4 x + 5 y =I14 c *tb wsg eedidntsc l abysrearrang uatBM firs7 ions. soo y =I(8 -I2 x)/3-efindubstitu Sonhe ry-pntBM s cdfineons. MercuSeerootsLEVELta nts Cthe rintreni Croeaive iof-trmanipulat 2n alresAllowee.ri oblItrs syssg eellisTMe mas7 difficultcm of es uf ions. h *ne b sg eedint ly exprlylisTMe bes. weh *Idorin fifinsomehapproximattscaolu 2rowertMen applynsomehitrs sysam N=deferoorimam veroftscaccuee,y is 2rsuch cas=t a-proadvimaE oo ioevqde ata t Sonvalucsy he oBM vhivaE sMri 3.sExactong eelth ry has 's mas7 i*nev sysfeaRefer spiCsrabilityale, intsexactome wodsti2rmany cas=s pri Solu 2rWindowro--- M-- MercuWMen an applynSg eetBoogram Ewf H pBM resultc spilroftscSolu 2rWindowlisTMe windowoproe, paE hep, BM Png -window, all tc *tb wscroe edintd zooE dshe reasy viewee.isTMetcdcti Cs ac *tb wsave ti Iaireio t piftkh-trprodenntse.ri Totsaolu 2rl s s Allaof ootsvhivaE s,sor wionvir fifAl valucsM nUnuAlly, ootsvhluctprojust a ns O,adimiInye too oweverrmany dig asi spnpehifiedopiIBM PDIGITSrs nts Cshuly meoneoo. .errodnnsomehcas=s, aivhivaE whs sg eedidntsc l aefindymbolexprly piroeres uf oBM vivhivaE slisIf such o*texions. n tohs intdale, xprculateaBM vhluc,rtMen oottexions. n t spn ow MercuIf neivhluctohs everrass gne too ootsvhivaE ,rtMen asivhluc prog synths "UNDEFINED"hult"NO SOLUTION"lisTMin eccuOsi f ootsvhivaE t s intd u hyths apius ysvhivaE ,rsuch os in aroons. ndteini. ur hs apvhivaE tuf 2Cegrs. MercuOccas Ally, apvhivaE tvhluctoillab wg synths NAN,tofich m anahNot-A-Ns O.ssTMin meanahBotsvhivaE tcould ne ob uionuttdalaccueetdhy pefinu hytcruderboundsioelicubta 2 dMisFgraexamp , a resultc"x =INAN(2.1,7.5)"npidexp stkh-trxrmaysbecany w 2g b twee I2.1pefin7.5lisSomet Fsssuch imamehis resultroreiresy tlutMe bes. kh-trc *tb wsaidinbonstan ll-pose tam E pbnstsomet Fs ptoreiresy troaroailure-ontBM pa tt eqry has lisSuch resultrscahould b wu. dsor wicau. 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MisFgr examp , sg equa SIN(x)s= .5rm1987 g sy hs aponsidnslercuis {I1E-16 } SIN(x)-.5=0ri Totsns OspiIbraN=n,I1E-16,-prokMe onsidnsllisIt-prokMe absolu valucstf SIN(x)-.5 u. uatBM aoleedivalucstf x.isReaidnslrstf tM s sizF orctquiteacds l-esti2cionallysMy is aoxprculateahBoI16-dig ascimehis l-ewertMefer spno machelp,reiresy taE txrolviwhich SIN(x) proexactlys0.5lri Totsions. soortMe 1987stf tMe braN=n-in eftenooftwaamtths r mouf ootsi2nutpions. pbnstsomet FssMy is aorearrangFsssomehoereslriItrm1987 b arsimp trearrangF Cths ab ve pbnstitsmaysa o oot esultce ssymbolexprly sg equa olvir moufivhivaE sdidntsc l abysrea ptoinooroBM viions. is 2rany cas=,aBM ions. hn ow sor wionv esidnslrsoreroftractnslrions. husFdsbyrootsng eelth Somehci Croe uf tMe symbolextsc l abysr si spAlloweerbyrootsLEVELta nts Ctor ootsLeveleoo. under ootsSg eelrmeonMercuOccas Ally, an mayssetsvhivaE srnamt T1, T2,r..lisTMesv orctts io As scvhivaE sri Croduce rbyrMy is aopiIBM Pcoursmoufisg equath ras7aluis ly, ooty C) husFdse, efolvceti2ionslity uiistra 2CslriTMetcdcstra 2C EXP(x + y) + y * z <= 10ri maysbecreiInc d or w EXP(x + y) + y * z + T1 = 10ri T1 >=I0ri Totslatter hasssomehoechnexprtadva CagFp, eveiIBMoughrtMefer span extrasions. soweran extrasvhivaE lisValucsnhe oBM extrasvhivaE alresne on ow MercuFinAlly, ootsaolu 2rendsiot cIBM Pla gFpt onsidnsl, ootsme wod powe BM pmoN=niollisTMe la gFpt onsidnslt spnimp yrootsmaximum tf oftscireviouroonsidnslrlisAssumqua an r pmo Ewprone onxprFdse,o badly, BM n any w 2gc ssiohaninbonst1E-10rahould b wuiis der d assucN=nilri Totsme wod pronxact, Dntsc ,ore Itrs sylisTMe exactoefindntsc scaoleeOsisre-m C riAvaE ,refinMy is aoCriFs ofem firs7.ssTMin rgic ac *tb walcio dsor wionveMETHODta nts ClisTMe pmoN=niolrproar8087, 80287,r80387,rgraemulator pri Reio tdit--- ercuAireio trproa*tufolvmatted asciiwf Ht old uatBM pmo EwewertMescaolu 2lisIt-c *tb wsave tBoIdimkrgrapri2ci tBoIkeep aponcuraouf ootsaolu 2lisTowsavetBoIdimk, ions. GoopiIBM PReio trmeonM (TM s meoneitemIdoesn'7 b comehac iv huntilran bveasg eedin pmo E.) Nlvmally, ootsreio trharooftwaamttnamtths BM pmo Ewbnstor wionv .EKAesuffix reiInc d or w .RPTM Yn c *tintsoBM vif Htnamtsi f an scilease priAnoBM viwaytBoIkeep aponcuraouf pms Eddidntsolu 2n iahBoIhave a Logif HM Just Refn Capture-OnopiIBM PReio trmeonM TM n allscirs Eddidntsolu 2n oillab wopo de tBoogrlogif HMercuTMe reio tddidntlogsisre-urazeAry asciiwf H powerc *tb wpri2ci .cuIf an bveaa Pas7scriptwpri2cir, an oillahavetBoIselsc satmod piiwhich -willaaccepstan asciiwf H,rgraloadin u lity for pri2c uatasciiwf H M (Nossuch u lity spaoevqded or w ry has l) pri Graphicsit--- MercuMy is aomaysbecusFdse, generateagraphrlisTMesv vimuprly showrotMe behavioOsof oons. rlisAagraphicstmoni.olrprorionntse.ri T, ge satgraph, an must firs7 dteine aroons. nof r movhivaE ain an r pmo Ewf HM Anpixamp tfromtBM fi tBUMPY.EKAe s ri bumpy(x)s:=Ix^2 SIN(x) ituhich dteineroaroons. oxprrFds"bumpy"lisTMe "x"rproarius ysvhivaE lriTMetharovalucsnoons(0)s= 0^2 SIN(0),noons(1)s= 1^2 SIN(1),netclisTo graphtBM fons. ofromt-15se, +15,tus=tBM s nts Cs: ri PLOT bumpyri GBOUNDSt-15, +15ri T, ass milateaBM spilolvmat rinoortMe My is aong eell-an must do asSg ee, eveiIBMoughran aresne oreally sg equa olviany w 2gcpiIBMis ac sHM OnN= BM pmo Ewharobee Isg eed, ootsView, Pri C powe Writealuis owes b comehavailaE tunder ootsGraphrmeonM Selsc sViewtBoIseerotMe graphtontBM scree MercuIf BM graphtlookroar tt tragged, orshaprone oenoughrpo 2CssoeliscusFdse, ple oiClisTMe dteaultc sp30 is 2crea. uat -BoI100-willagive a much smooBM vigraph.ssTMin c *tb wdr mobyreiBM viadd uatBM GPOINTSr100-a nts CtoortMe pmo Ewf Htidntsolv uat -aga 2,tor byrselsc uatGPo 2CssfromtBM GraphrmeonMercuItrproa o possiE oo havet"aa amtCric" ple s,soMeferboBM Xpowe Y orcthons. roufisgmtsoBM viindeo de CtvhivaE lisMy lytus=rotMe XAXISrs nts CtBoIspehifyrootsXthons. lisTMe GBOUNDSts nts C BM n referahBoIootsi2deo de CtvhivaE lercuTMeseagraphrrc *tb wpri2ci tontgraphicstpri2cirs.ssTMin includes mas7 pri2cirs, excepstolvidaisy-oMeelepri2cirs.ssSelsc uatPri Citutllepri2c BM graphtBoIof-teverrpri2cirwharobee Iselsc i tunderrotMe Oo. /Pri2cirwmeonMercuYn c *ta o selsc sWrite,tofichrpri2cs BM graphtBoIawf HM Such a f Htc *tb ws CtBoIarpri2cirwa satlater o FlisTMe pmimas scus=fulnns. tf tM ssfeaRefer spe, exio trBM graphtpiILotushuly Pas7scriptwolvmat,soMeferit-c *tb wpmio te rbyranoBM vipmofor MercuTMe vhivourooo. opiIBM PGraphrmeon orctreally tMe dteaults powe sre-uverridde rbyrootscuronspdfi uats nts CshintBM pmo Ewf HMcuIf BM rv orcts nts CshintBM pmo Ewf Hws t uatgraphtoo. , BM n ootsmen maysne oaccueetdhy reflsc sootsoo. ousFdse, drawrotMe graphlisNevertMe ss,tonN= atgraphwharobee Icreated, oots=rooo. oc *tb wmodifiedofromtBM graphrmeonl-ewertMensViewtutllscahow ootsrevimedographl pri 4. FeaReferRefelinN=cucuTMin chapter g systan alphab texprtlookupnhe oBM My is aobuilt-in hons. roidnts nts Csl pri Oprs orsit--- MMer+ addl p- sc tee, l p* multip lisasspnc smaysa o becusFdl p/ divqdel p^ powellisEg, 2^3s= 8l p~ uionlexwuiijugntsl p< ssiohanl p<= ssiohanl p> greateriohanl p>= greateriohanl p= ionslsl p:= vhivaE t ni. slizat re ooons. ndteini. l p: ions. sseaa ator p% prsc C,reg, 17%s= .17lercuTMeseahaveaBM umuprsmaofematexprtimehedinN= ru s,sor wi^ahavrea h198 vipmehedinN= ohani*oidnt/,tofichrintBefn orcth198 viohani+oidnt-l pri Cdcstantdit--- MercuTMeseatwotcdcsta troaferbuilt-inMercuINF pluspiloini. scPI 3.1415926535..lisYn c *ta o us=tBM greekc tter byroyp uatAlt-Pl pri Fons. rit--- MercuFons. r takeir mour-m C a gu CslisTMe a gu Csoafersseaa attdalbyruis oroidntinNlose tintaa CMeseslisHefer spat s7 tf oftscbuilt-in oons. rlisAdd t Althons. roc *tb wdteined or win n pmo Eif HMercuABS(x) itTMe absolu vhluct eqxlisYn c *ta o us=t|x|MercuACOS(x) itTMe arcruisi moufix,-pneeOs oo COS(x).cuTMe resultc spin radia .erroASIN(x) itTMe arcrsi moufix,-pneeOs oo SIN(x).cuTMe resultc spin radia .erroATAN(x) itTMe arcrtangFntoufix,-pneeOs oo TAN(x).cuTMe resultc spin radia .erroBESSJ(n,x) itTMe B sselthons. stf tMe firs7 ki2d.cuTMe firs7 a gu C must becan 2CegelterroBESSY(n,x) itTMe B sselthons. stf tMe s codntki2d,tsomet Fs a o xprrFdstMe We Oshons. lcuTMe firs7 a gu C must becan 2CegelterFgraeach 2,tptoin ursolu 2 oo B ssel's diffelin. slsions. sor wiarsingula itytotwzeroterroBINOM(n,k) itTMe ns Ostf uisbzeA. pchoo. uatkstf neitem .erG syntbyr n!w/ (k! (n-k)!).cu CEIL(x) itTMe smallFpt 2Cegel greateriohanrgraeonsl oo x.cuEg, CEIL(4.7)s= 5lri COS(x) itTMe uisi moufixlisTMe ang txrin measure tintradia .erroCOSH(x) itTMe hyprsbolextuisi moufix,-(EXP(x) + EXP(-x))/2.erroCTERM( att,fv,pv) itTMe ns Ostf prsiodrorionntse olvia g syn iresy tluvhluct(pv) oo i2crea.etBoIarg syn fuRefervhluct(fv) f ptogrows -troft g syn i2cirFpt ontslisTMetfons. prouionA. E tor wiQns.Cro/Lotus.erroDERIV(f(x),x) itTMe deriv systf tMe fons. of(x) or wionspsc soo x.cu 2rmas7 cas=s, tMe deriv sysprouionute rsymbolexprly.erroDLGAMMA(n,x) itTMe n- wideriv systf LOGGAMMA, ne= 0,1,2,..l itERF(x) itTMe erre ooons. nufixlisItrpro laci tBoINCUM(x).cucuis s s s ERF(x)e= 2INCUM(x SQRT(2)) - 1 itEg, ERF(-INF)e= -1, ERF(0)s= 0, ERF(+INF)e= +1l itERFC(x) itTMe uionle CAry erre ooons. nufixlisSetsERFoidntNCUM.cucuis s s s ERFC(x)s= 1 - ERF(x) itEg, ERFC(-INF)e= +1, ERFC(0)s= 0, ERFC(+INF)e= -1l itEXP(x) itTMe exionin. slsoons. nufix,re^x,ree= 2.71828..l It-prokMe pneeOs oo LN(x).cucuFACT(x) itxroe, oival,tsomet Fs w ittenox!.cuEg, FACT(5)s= 5*4*3*2*1 = 120.cucuFLOOR(x) itTMe la gFpt 2Cegel ssiohanigraeonsl oo x.cuEg, FLOOR(4.7)s= 4.cucuFRAC(x) itTMe fee, Altaa toufix,-x - FLOOR(x).cuEg, FRAC(4.7)s= 0.7lercuFV(pmt, att,nprs) itTMe fuRefervhlucttf pay Cso(pmt) -troft dstf nprs prsiodrl-essumqua oft g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.Cro/Lotus.erroFVAL( att,nprs,pmt,pv) itG systtMe fuRefervhlucttf a f nanc slsor wiarpay C pmt 2aeach tf nprs prsiodr,sor wionveg syn iresy tluvhluctpvl-ewertMe g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.CrotProl It-us=sttMe f nanc slsmod IspehifieerbyrootsFINANCEsca nts CtBoIdeoerei mooMether ootspay Csoafer-troft e dstf ootsprsiod (tMe dteault) e oBM beginnquat itHYPOT(x,y) itTMe pola ouiurazeAtetradiusscuronspdfi uatBoIca tnsian uiurazeAteso(x,y)lisEg, HYPOT(3,4)s= 5lri IFPOS(x,y,z) itG systyi f x >=I0,relserit-g systzlisEg, IFPOS(-3,6,7)s= 7lercuIM(x) itTMe imagzeAry aa toufixlisTMetCOMPLEXeoo. must beci*tintMercuINTEG(f(x),x,a,b)ercuINTEG(f(x),x,a,b)-g systtMe ns rsixprt 2Cegrprtof o(x) or w onspsc soo xofromtasoo blisImpmop viinCegrprsoafer-llowed,tso a ac *tb w-INF, boc *tb w+INFl-ewerftc *tb wsingula wa sate oblisTMe appmoxims. sme wod proadapt sysewern li marl-eweroftenois aaccueetd-BoI15IdigiCsl priINTEG1(f(x),x,a,b)ercuINTEG1t spnimila wBoIINTEG,wbnstus=stapnimp rs straCegylisItrpron adapt sysewerli marl-ewermaysbecpreferre tin sitns. ssoMefertMe resultc spsupposFdse, beca smooBMtfons. tf a ewerblisINTEG1t spne o marly asoaccueetd asoINTEG on singula woons. rlercuLIMIT(f(x),x,a,INF) itEstims.ysttMe limittof o(x)l-es xogoesofromtasoo iloini. l It-us=sta ns rsixprtme wod BoIcionutettMe limit tf o(x)l-es xogoesofromtasoo iloini. lisItrpro *tn li mar extrapola. sbasi tonta fairly small ns Ostf oereslisTMe limittpro ly riAvaE i f tMe fons. oprowell-behaved,towe tM ssfeaReferahouldsbecusFdsor wicau. lcucuLN(x) itTMe naRefprtloga ithm (basi e)oufixl It-prokMe pneeOs oo EXP(x)lcucuLOG10(x) itTMe loga ithm ufixhBoIootsbasi 10lisTMetpneeOs pro10^xlcucuLOGGAMMA(x) itTMe loga ithm ufitMe gas oooons. nufixlercuMAX(x,..l) itTMe maximumrvhlucttf tMe a gu Cs.cuEg, MAX(-10,5,7)s= 7lercuMIN(x,..l) itTMe minimumrvhlucttf tMe a gu Cs.cuEg, MIN(-10,5,7)s= -10lercuNCUM(x) itTMe nlvmal cumul syspmo ab lity fons. lisNCUM(X)-prokMescirs ab lity oha satnlvmal roweomtvhivaE -probelowritn mean,scilussXts nndaraodevia. rlercuEg, NCUM(-INF)e= 0, NCUM(0)s= .5, NCUM(+INF)e= 1l itPAYMT( att,nprs,pv,fv) itG systtMe iresy trvhlucttf a f nanc slsor wiarpay C pmt 2aeach tf nprs prsiodr,sor wionveg syn fuRefeluvhluctfvl-ewertMe g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.CrotProl It-us=sttMe f nanc slsmod IspehifieerbyrootsFINANCEsca nts CtBoIdeoerei mooMether ootspay Csoafer-troft e dstf ootsprsiod (tMe dteault) e oBM beginnquat itPMT(pv, att,nprs) itG systtMe amoun7 tf oftspay Csorionntse 2aeach tf nprs prsiodrse, balanN= BM g syn iresy t vhluctpv-eweri2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.Cro/Lotus.erroPOLAR(x,y) itTMe pola ouiurazeAtetang tcuronspdfi uatBoIca tnsiano(x,y)l Samd asoBM Qns.Cro/Lotus @ATAN2(x,y) e oBM Fgrtran/Cr-tan2(y,x)lcucuPOLY(x,a0,a1,..l,an) itTMe polynom slsa0Ix^ni+o..li+oid.cuEg, tMe polynom sls2Ix^3 - 3ixh+ 7 c *ta o becw ittencuPOLY(x,2,0,-3,7)lisTMetchief adva tagcttf tMe l teriis ane a AltcodsyniinN=,tidntsorit-c *tb wmehognizeerbyrootscapehiAltaolynom slsng eellcucuPOS(x) itTMe posi syspa toufix,-i=,txi f posi sysidnt0i f neg sylcucuPV(pmt, att,nprs) itG systtMe iresy trvhlucttf nprs pay Csotf amoun7 pmt,scusqua oft g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.Cro/Lotus.erroPVAL( att,nprs,pmt,fv) itG systtMe iresy trvhlucttf a f nanc slsor wiarpay C pmt 2aeach tf nprs prsiodr,sor wionveg syn fuRefeluvhluctfvl-ewertMe g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.CrotProl It-us=sttMe f nanc slsmod IspehifieerbyrootsFINANCEsca nts CtBoIdeoerei mooMether ootspay Csoafer-troft e dstf ootsprsiod (tMe dteault) e oBM beginnquat itRATE(fv,pv,nprs) itG systtMe i2cirFpt ontsorionntse olvitMe iresy tluvhluct(pv) oo i2crea.etBoItMe fuRefervhluct(fv)tin nprs prsiodrlisTMetfons. nprouionA. E tor wiQns.Cro/Lotus.erroRE(x) itTMe real aa toufixlisTMetCOMPLEXeoo. must beci*tintMercuREM(x,y) itTMe remai2der ufixhdivqdeerbyrylisEg, REM(20,3)e= 2MercuSGN(x) itG syst+1i f x > 0, -1i f x < 0lercuSIN(x) itTMe si moufixlisTMe ang txrin measure tintradia .erroSINH(x) itTMe hyprsbolextsi moufix,-(EXP(x) - EXP(-x))/2.erroSQRT(x) itTMe sonsrctrooBnufixlercuSUM(f(x),x,a,b)ercuTMe sum ufifofromtasoo b,ercu f(a) + f(a + 1)i+o..li+of(b)ercuIf bo=w+INFl-tMe limittin estims.yd asoor wionveLIMITshons. lcucuTAN(x) itTMe tangFntoufix,-SIN(x)/COS(x).cuTMe ang txrin measure tintradia .erroTANH(x) itTMe hyprsbolexttangFntoufix,-SINH(x)/COSH(x)lcucuTERM(pmt, att,fv) itTMe ns Ostf prsiodrorionntse olvia g syn iay C streamo(pmt) oo i2crea.etBoIarg syn fuRefervhluct(fv) f ptogrows -troft g syn i2cirFpt ontslitTMe funs. nprouionA. E tor wiQns.Cro/Lotus.errocuS nts Csit--- MMercuBOUNDS lower,upprs cuSpehifysboundroolvitMe eomai2sstf ootsvhivaE rlisTMetdteaultiis aBOUNDS -INF,INFlisSomesng equa o Ftc *tb wsavedoor wionvsca nts CtBOUNDS -1e6,1e6i f yn srctsure oha sall tMe releva tluvhlucsstf yn rsvhivaE r srct ssiohania mill lcucuCASEFOLDercuIgn C cas=tintnamdrlisOtherwise, ootsvhivaE txrin diffelin.ofromtXlcucuCASESTRICTcucuUsqua CASESTRICT,sor wino a g pcaus=stbuilt-in oons. r, uicsta tr,tidnts nts Csse, becupprs cas=t lylisNlvmally suchsciredteined namdr srctne ocas=tsy si sy,tso SIN(x)-prokMe samd as sin(x)l Usqua tM ssoo. reducysttMe chanN= tf a namdtcodflext.erroCOMPLEXerroDecla ysttMa sall tMe vhivaE r srcte, becuicsqdetse uionlexluvhivaE rlisTMeirrsolu 2s have a real ewerimagzeAry aa t.cuTMeseabuilt-in oons. rrmaysbecuse tinta uionlex pmo E:ercu ABS, COS, COSH, EXP, IM, LN, RE,-SIN,-SINH, SQRT, SUM, TAN, TANH.erroDIGITS nerroDisplaysreal ns Osse, nIdigiCsstf pmehis lisTMetdteaultiis 18lercuEPSILON xerroForcystns Osseelyrulosese, zerote, becdisplayyd asozerot Useful olviahowqua uionlex ns Osswhich afer-ctnsllysrealt Dteaultiis EPSILON 0l itEXTERNALtfons. roDecla ysttMe namdte, beca2aexcirnsllysdteined fons. ,te, be olun tonttMe eisktinttMe iro E eimeh oiyoor wionvefile namd oons. lBINlisTMese funs. r srctw ittenointTusbo C++ e oTASM, eweruionileeri2co lBINefileslisSetskMe samnles.erroFINANCE typr itG systtMe typr aa amdterioooBM Qns.CroouionA. E tf nanc sl oons. r,tPVAL,tPAYMT,tidntFVALlisTMetdteaultiis atypr = 0, meanqua tM-troft pay Csoafer-troft dstf kMescirsiodt Use typr = 1i f tMe pay Csoafer-troft beginnquat itGBOUNDS xleft,txright itTMe lowero(xleft)tidntupprs (xright)sboundroolvitMe X-axistinta grppht itGPOINTS nerroTMe ns Ostf poi Cso(funs. ns.Cro/)cuse tBoIdrawta grpphtisTMe dteaultiis 30lisIf yn rsgrpph-prokoo ongged,ttiyoi2crea.qua oft ns Ostf poi Cst itGSTYLE nerroAllowssgrpph-cuesystt, bectM ck (GSTYLE 0) e oBMint(GSTYLE 1)l priINCLUDEefilenamd itTMe fi tor wioft g syn namdtistinserte tinttMe iro E at tM-trpoi ClisTMetfilenamd must beci*tquoterl-esci*tINCLUDEe"CONST.INC"tisTMe dteaultifile namdaexcins npro.INClisIncludetfilestc *ne obecnFptedl priITERATIONS nerroTMe maximumrns Ostf iters. ssuse tbyrootsiters. vesng eellisTMe dteaultiis 100l itLEGENDercuPuCsoat gen tonttMe grpph-which qden. fiesttMe funs. nu woons. rlerRehom deeroMen ilottqua more oha nune funs. l itLEVEL nerroAllowssuse ouinCrortoeelroM-trsymbolextsubstitu. r srctmadtMercu0lino symbolextsg equa 1.sng eesXt= uicsta t 2.sng eesXt= uicsta t exi yss 3.sng ees ly oMen Xeoccuero N=,tno other vhivaE r 4.sng ees ly oMen Xeoccuero N=,tother vhivaE r poss E 5.sng eesli maraeons. r 6.sng eessonsrcrl-usqua sonsrctrooBr 7.sng eesonsdrs. caeons. r 8.sng eespowerserroTMe dteaultiis LEVEL 5,sng equa li maraeons. rwbnstne ousqua sonsrctrooBrlisStsixtly speakqua, ootssubstitu. r pneg equa rooBr srctne oms.hems. csllysionns.Cen., asoBM substitu. must erbitrarilyschooseseMe posi sysu wneg sy sonsrctrooBl priItc spsomeo FscpreferaE tt, use LEVEL 0ioooBur nuffsall tMe symbolextmanqpula. rlisTMen Mercueysiffec syly oeightr sll eons. rweonsllyl-ewertMe solu 2tc *tb wuicsqdetse tMe solu 2 tooat ast sonsrcr iro ElercuLISTshons. ercuList une u wmore funs. r inttMe solu 2twqudowlisSy tax-prokMescsamd asoolviPLOTlercuMAXIMIZE xerroTotsvhivaE txrin maximizeelercuMETHOD nerroSpehifystMe soleelrme wod,soMefern = 1, 2,tor 3lercu1.sEx-ct 2.sDimeh 3.sIters. veerroTMe dteaultiis METHOD 1, ootsex-ctsng eellisIf ptofails, ootsdimeh soleelrprokried,towe ptotMa salso fails, ootsiters. vesng eeliis atriedlercuMINIMIZE xerroTotsvhivaE txrin minimizeelercuPENALTY nerroTMe vhlucttf tMe penalty uicsta t,tow erbitrary uicsta tsuse tooenolvc wuicstrai CsooMen ootsiters. vesng eeliiscuse tBo maximize u wminimizeoatvhivaE lisTMetdteaultiis 30lisI2crea.qua t olvc sttMe appmoxims.e solu 2sruloserioooBM uicstrai C manifolds-troft costoufimakqua ootsextremumrharaeriooof ndt ReadtrserufiTMetHitchhiker's GuqdeioooBM Galaxy sugges ousqua tMe vhluct42.erroPLOTshons. ercuCreat=sta ilotttf tMe namdd fons. lisTo viewttMe grpph,sneleh Grpph-fromttMe maint ulisTo ilottseeelal funs. r onttMe samd grpph,slist tMe namdspseaa ate tbyrhom arlisTMetfons. s must be dteined inttMe iro E file,towe betfons. s tf une vhivaE lisFor examnle,te, ilottSIN(x)-owe x^3-x-fromt-5te, +5l-useercu f(x)-:= SIN(x) g(x)-:= x^3 - xer GBOUNDS -5l-+5er PLOTsh, gerroPRINTerroSamd asoPRINTFILE "LPT1"lisItrpri CsotMe grpph-oooBM DOSodevic wLPT1, which qscusnsllysarpri C Ostn aa alleltao to1lisTMetpri Cqua u *tb uicfigure tt, use another ao tofromttMe Op. s m ul-ewertMe rcrultscsave tt, apsetup file.erroPRINTFILE filenamd itPri CotMe grpph-oooBM g syn file,twhosesnamdtistintquoter.erroTMese namdsphave apehiAltmeanqua.erro "PAR1" aa alleltao to1ro "SER1" seriAltao to1ro "PAR2" aa alleltao to2ro "SER2" seriAltao to2ro "LPT1" DOSolpt1ro "LPT2" DOSolpt2ro "LPT3" DOSolpt3ro "LPT4" DOSolpt4ro "EPT" IBM postscripttao terroPROGRESS xerroShow tMe vhlucttf ootsvhivaE txrinttMe Prog ysssboxlisMercuey doystnotsng ee olviall vhivaE r sto N=,tso someo Fsctherd mightobecno vhluctolvitMe vhivaE tun7ilroft dstf kMe solu 2 iroc sslisI2 suchocas=s, ootsProg yssswqudowiahows "x = NAN", meanqua "xrin notsarns O"lisercuIf no PROGRESS a nts Ctin g syn, ootsProg yssswqudowiahows kMescvhlucttf oots"Rnsidnsl"tisTMistisoBM sum ufisonsrcr ufionsn7iti r which ahoule betzerol-ewerwhich Mercueysprokry uatBoIminimizelisTMe smallevitMe vhluc, ootsmore likelyotMa sMercueysprogettqua ulosese, tMe solu 2MercuREPORT filenamd itAllowssnamqua a reao tofile fromtor winta iro ElercuROOTSIGN nerroWMen ng equa a2aeons. like x^2 = a,sMercueysmaystaktskMe sonsrc rooB ufiboth sqdestisTMistinCroducysttwotrooBrl-+SQRT(a)-oweit-SQRT(a)l-ewerMercueysdoystnotsknowiwhich oooBakttisYn u *tspehify tM-tryn slwaysswa CotMe posi sysrooB or wiROOTSIGN +1,tor elwaysstMe neg sy rooB or wiROOTSIGN -1lisTMetdteaultiis aROOTSIGN 0,iwhich asystMercueysunaE tt, evhlus.e kMe sonsrc rooBlercuSCREEN nerroChoosesa grpphicspscree lisTMetdteaultiis SCREEN 0,iwhich means aMercueysautoms. csllystriestBoIdeoect yn rsgrpphicspharawsrclerSomesgrpphicspcaras-ewermod stc *ne obecdeoected,towe must be neleh edoor wia SCREEN a nts C.erro 0. AutoDeoectro 1. CGAro 2. MCGAro 3. EGA 64kro 4. EGA 256kro 5. EGA Mon, 6. IBM 8514ro 7. Hercu r 8. ATT 400 li m 9. VGAro 10. 3270 PCro 11. Towey 1000ro 12. ATI Suprs VGAro 13. Orchid Suprs VGAro 14. ParadisesSuprs VGAro 15. Veg sSuprs VGAro 16. CionrooABLE II Suprs VGAro 17. SOTA Suprs VGAroroFromttMe maint u,otMe grpphicspscree tc *tb wseleh edoor w Grpph/Mod lisSuchoawseleh nproi mffec sy aftevitMe first grpph-prodrawn, asoBM grpphicsphassbeenoini alizees-trofat poi ClisWe rchom dwsavqua tMe d sntse grpphicspmod -oooBM cuMERCURY.CFG uicfigurs. file.erro(Note:sTMetdr syrsoolvisomettf oots grpphicspmod stin not ncludedoor wisometsyrs s tf Mercueyt Registetse uustomerserrche sy tMe full set tf dr syrs.) itSHOW xerroShow spehified vhivaE r inttMe spehified oraerlisOther vhivaE r srctne odisplayyd inttMe solu 2twqudowlerroSOLVE xerroIcstructstMercueystosng ees ly olvitMe vhivaE txlisBytdteault,sit solees olviall vhivaE r namdd inttMe iro E.ercuIf SOLVE in g synoor wia polynomial funs. namdl-esci*erro SOLVE fcu f(x)-:= POLY(x,1,0,0,1) ittMen Mercueyswill applysarapehiAltpolynomial rooB f nderioooget sll real eweruionlex rooBrlerroSTART xerroTotsa nrtqua vhluctolviunini alizeesvhivaE r whi tu.qua oft iters. vesng eellisTMetdteaultiis 1.00l itTERMS nerroTMe mostons Ostf termssuse tbyrootsINTEG ewerLIMITshons. slisTMe dteaultiis 50l itTIME nerroTMe maximumro Ftallowse olvisolu 2MisTMetdteaultiis 200 schondr.roSamd asoMAXTIME intEureka 1.0l itTITLE label itArgu Ctin atquotents rqua, oosbecuse tasoa grpph-oitle.erDteaultiis no oitle.erroSUBTITLE label itArgu Ctin atquotents rqua, oosbecuse tasoa grpph-suboitle.erDteaultiis no oitle.erroXLABEL label itA labeloolvitMe X-axisttf a grpphtisTMe labelomust beci*tquoter.erroYLABEL label itA labeloolvitMe Y-axisttf a grpphtisTMe labelomust beci*tquoter.erroXAXISshons. ercuSpehifies tM-troft X-axistbeca funs. insteadttf a indep de C vhivaE lisTMetfuns. must becdteined elseoMeferasoa hons. ertf une vhivaE liserroTMe X axisttf tMe grpph-isoa hons. tor wioft g syn namdt Useful olviaa amdtsix ilotslisEa, oosgrpph-(x,y) = (cos(t),sin(t)) as t goystfromt0iooo2*PIl-useercu x(t)-:= cos(t)cu y(t)-:= sin(t)er GBOUNDS 0,i2 PIer XAXISsxer PLOTsy