Relational model

Historyofinvention

Netteddatabaseandhierarchicaldatabasehavesolvedtheproblemofdataconcentrationandsharing,butthereisstillagreatlackofdataindependenceandabstractionlevel.Whenusersaccessthesetwodatabases,theystillneedtoclarifythedatastoragestructureandpointouttheaccesspath.Buttherelationaldatabasethatappearedlatersolvedtheseproblemsbetter.Relationaldatabasetheoryappearedinthelate1960sandearly1970s.Therelationaldatamodelprovidesthecharacteristicsandfunctionalrequirementsofrelationaloperations,butdoesnotgivespecificgrammaticalrequirementsforthelanguageoftheDBMS.Theoperationoftherelationaldatabaseishighlynon-procedural,usersdonotneedtopointoutaspecialaccesspath,andtheselectionofthepathisdonebytheoptimizationmechanismoftheDBMS.

In1970,IBMresearcherDr.EFCoddpublished"RelationalModelofLargeSharedDataBanks"andproposedtheconceptofrelationalmodel,expoundingtheparadigmtheoryand12standardsformeasuringrelationalsystems,suchasthedefinitionCertainrelationalalgebraoperationsstudiedthefunctionalcorrelationofdataanddefinedthethirdparadigmofrelations,thuspioneeringthestudyofdatabaserelationalmethodsanddatanormalizationtheory.Forthis,hewontheTuringAwardin1981.

Later,Coddpublishedmanymorearticles,layingthefoundationofrelationaldatabase.Therelationalmodelhasastrictmathematicalfoundation,arelativelyhighlevelofabstraction,andissimpleandclear,easytounderstandanduse.Butatthattime,somepeoplethoughtthattherelationalmodelwasanidealizeddatamodel,anditwasunrealistictoimplementaDBMS.Theywereespeciallyworriedthattheperformanceofrelationaldatabaseswasunacceptable.Somepeopleevenregardeditasaseriousthreattothenormalizationworkofmeshdatabasesthatwasinprogressatthattime..Inordertopromoteunderstandingoftheproblem,ACMtooktheleadinorganizingaseminarin1974,duringwhichadebatebetweenthetwofactionsforandagainstrelationaldatabasesledbyCoddandBachmanwaslaunched.Thisfamousdebatepromotedthedevelopmentofrelationaldatabases,whicheventuallybecamethemainstreamofmoderndatabaseproducts.

Sincethen,manypeoplehaveturnedtheirresearchdirectionstorelationalmethods,andrelationaldatabasesystemshaveappearedoneafteranother.

Definition

Therelationaldatamodelisdevelopedbasedontherelationalconceptinsettheory.Boththeentitiesandtheconnectionsbetweenentitiesintherelationalmodelarerepresentedbyasinglestructuretype-relationship.Therelationshipintheactualrelationaldatabaseisalsocalledatable.Arelationaldatabaseiscomposedofseveraltables.

Relationalmodelreferstoadatamodelthatusesatwo-dimensionaltabletorepresententitiesandtheirconnections.

Basicterms

Thereare13basicconceptsandbasictermsoftherelationalmodel.Theyare:

(1)Relation:arelationCorrespondstoatwo-dimensionaltable,andthetwo-dimensionaltableisthenameoftherelationship.

(2)Tuple:Arowinatwo-dimensionaltableiscalledatuple.

(3)Attribute:Thecolumnsinthetwo-dimensionaltablearecalledattributes.Thenumberofattributesiscalledthedegreeordegreeoftherelationship.Thevalueofthecolumniscalledtheattributevalue;

(4)(Value)Domain:Thevaluerangeoftheattributevalueisthevaluedomain.

(5)Component:theattributevalueofthecolumncorrespondingtoeachrow,thatis,anattributevalueinthetuple.

(6)Relationshipmode:Therowdefinitioninthetwo-dimensionaltable,thatis,thedescriptionoftherelationshipiscalledtherelationshipmode.Generallyexpressedas(attribute1,attribute2,...,attributen),suchastheteacher'srelationshipmodelcanbeexpressedasateacher(teachernumber,name,gender,age,title,department).

(7)Key(code):Ifthereisanattributeorattributesetthatuniquelyidentifiesanentityinarelationship,itiscalledthekeyoftheentity.Atuple,thecombinationofvalues​​ontheattributearealldifferent.

(8)Candidatekey(candidatecode):Ifthevalueofanattributeintherelationshipcanuniquelyidentifyatuple,ifnoattributecanberemovedfromakeyintherelationship,otherwiseitisnotThekeyofthisrelationshipiscalledthespecifiedcandidatekeyasthecandidatekeyorcandidatecodeoftherelationship.

Forexample,the"studentnumber"or"librarycardnumber"inthefollowingstudenttablecanuniquelyidentifyatuple,andthe"studentnumber"and"librarycardnumber"canbothuniquelyidentifyatuple.Then"studentnumber"and"librarycardnumber"canbeusedascandidatekeysforstudentrelations.

Inthecourseselectiontable,onlytheattributegroups"studentnumber"and"coursenumber"canuniquelyidentifyatuple,andthecandidatekeyis(studentnumber,coursenumber).

(8)Primarykey(primarycode):Specifyatupletouniquelyidentifytherelationshipamongthecandidatekeysofarelationship,thenthespecifiedcandidatekeyiscalledtheprimarykey,orsimplytheprimarykey,keyWord,maincode.Eachrelationshiphasandonlyoneprimarykey,usuallyasmallercombinationofattributesisusedastheprimarykey.Forexample,inthestudenttable,if"studentID"isselectedasthebasisfordataoperation,the"studentID"isthemainkey.Inthecourseselectiontable,theprimarykeyis(studentnumber,coursenumber).

(9)Primaryattributesandnon-primaryattributes:Theattributesincludedinanycandidatekeyintherelationshiparecalledprimaryattributes,andtheattributesnotincludedinanycandidatekeyarenon-primaryattributes.

(10)Fullkeyorfullcode:acollectionofallattributesinarelationalmodel.

(11)Foreignkeyorforeigncode:Althoughanattributeinarelationshipisnottheprimarykeyofthisrelationship,oronlytheprimarykey,butitistheprimarykeyofanotherrelationship,itiscalledforeignKeyorforeigncode.

(12)Superkeyorsupercode:Ifanattributeisremovedfromakeyofarelationship,itisstillthekeyoftherelationship,thensuchakeyiscalledthesuperkeyorsupercodeoftherelationship.

(13)Referencerelationshipandreferencedrelationship:refertotworelationshipsthatareconnectedbyforeignkeysandcanbetransformedintoeachother.

Two-dimensionaltable

Relationalmodel,fieldsarecalledattributes,fieldvalues​​arecalledattributevalues,andrecordtypesarecalledrelationalmodels.ThenameoftherelationalschemaisR.Arecordiscalledatuple,andacollectionoftuplesiscalledarelationshiporinstance.Generally,uppercaselettersA,B,C,...areusedtoindicateasingleattribute,andlowercaselettersareusedtoindicateattributevalues.Thenumberofattributesintherelationshipiscalled"elementnumber",andthenumberoftuplesiscalled"cardinality".Therelationshipelementoftheexampleis5,andthebaseis2.Sometimesitisalsocalledarelationshipasatable,withtuplesasrowsandattributesascolumns.

Key

Key,alsoknownascode,consistsofoneorseveralattributes,dividedintothefollowingtypes:

a.Superkey:IfinrelationIfanattributeisremovedfromakeyof,itisstillthekeyofthisrelationship,andsuchakeybecomesasuperkey.

b.Candidatekeys:Superkeyswithoutextraattributesarecalledcandidatekeys.Thatis,ifyouwanttodeletetheattributeinthecandidatekey,itisnotasuperkey.

c.Primarykey:Acandidatekeyselectedbytheuserasatupleidentifieriscalledtheprimarykey.Ingeneral,thekeyreferstotheprimarykey.

Definitionandnatureofrelationship

RelationshipisacollectionoftupleswithelementnumberK(K>=1).

Relationshipisastandardizedform,andithasthefollowinglimitations:

a.Eachattributevalueintherelationshipisnotdecomposable.

b.Thesametuplesarenotallowedintherelationship.

c.Theorderoftuplesisnotconsideredintherelationship.

d.Theattributesinthetuplearealsounordered.

Relationalmode,relationalsub-mode,andstoragemode

Relationalmodel,theconceptualmodeisacollectionofrelationalmodes.Amodeisacollectionofrelationalsub-modes,andaninnermodeisacollectionofstoragemodes.

1.Relationalmode

Relationalmodeisactuallytherecordtype,including:modename,attributename,valuedomainname,andtheprimarykeyofthemode.Hedoesnotinvolvethedescriptionofphysicalstorage,onlythedescriptionofdatacharacteristics.

2.Relationshipsub-mode

Thesub-modeisthedescriptionofthepartofthedatausedbytheuser.Inadditiontopointingouttheuser'sdata,thecorrespondencebetweenthemodeandthesub-modeshouldalsobepointedout.

3.Storagemode

Thebasicorganizationofrelationalstorageisfiles,andtuplesarerecordsinfiles.Sincetherelationalmodelhaskeys,storingarelationcanberealizedbyhashingorindexing.

Threetypesofintegrityrulesoftherelationshipmodel

1.Entityintegrityrules

ThisrulerequirestuplesintherelationshipTherecanbenonullvalues​​ontheattributesthatmakeuptheprimarykey.Ifthereisanullvalue,thentheprimarykeyvaluewillnotbeabletouniquelyidentifythetuple.

2.Referentialintegrityrules

IftheattributesetKistheprimarykeyoftherelationalpatternR1,andKisalsotheforeignkeyoftherelationalpatternR2,thenintherelationshipofR2,thevalueofKistakenThereareonlytwopossibilitiesforthevalue,eithernullvalueorequaltoaprimarykeyvalueintheR1relationship.

Attentionshouldbepaidwhenusing:

a.Theforeignkeyandthecorrespondingprimarykeycanhavedifferentnames,aslongastheyaredefinedinthesamevaluerange.

b.R1andR2canalsobethesamerelationalmodel,whichrepresentstheconnectionbetweenattributes.

c.Whethertheforeignkeyvalueisallowedtobeemptyornotdependsonthespecificproblem.

3.User-definedintegrityrules

Thisisaconstraintforspecificdataanddependsontheapplicationenvironment.

Formaldefinitionofrelationalmodel

One,threecomponents:datastructure,dataoperationandintegrityrules.

1.Thebasicdatastructureoftherelationalmodelistherelation.

2.Relationaloperationsaredividedintorelationalalgebraandrelationalcalculus.

3.ThreetypesofintegrityrulesofRelationalModel.

Second,relationalalgebra

Dataoperationsinrelationaldatabasesaredividedintotwotypes:queryandupdate.Querystatementsareusedforvariousretrievaloperations,andupdateoperationsareusedforinsert,delete,andmodifyoperations.

Relationalquerylanguages​​aredividedintotwocategoriesaccordingtotheirtheoreticalbasis:

1.Relationalalgebralanguage:queryoperationsareDMLlanguages​​basedonsetoperations.

2.Relationalcalculationlanguage:queryoperationisbasedontheDMLlanguagepredicatecalculation.

Fivebasicoperationsofrelationalalgebra

Relationalalgebraisasetofadvancedoperationswithrelationastheoperationobject.Arelationshipisdefinedasacollectionoftuplesofthesamenumber.Theelementsinthesetaretuples,andtheoperationsinrelationalalgebracanbedividedintotwocategories:

Traditionalsetoperations:union,difference,intersection,andCartesianproduct.

Expandedrelationaloperations:projection,selection,connectionandnaturalconnection,division.

1.Union

TherearetworelationsRandSthathavethesamerelationmode.TheunionofRandSisasetoftuplesbelongingtoRandS,rememberItisR∪S.

Note:RandShavethesameelementnumber.

2.Difference

TherearetworelationsRandSthathavethesamerelationmode.ThedifferencebetweenRandSisasetoftuplesthatbelongtoRbutnotS,DenotedasR-S.

Note:RandShavethesameelementnumber.

3.Cartesianproduct

SupposetheelementsoftherelationsRandSarerands,respectively.DefinetheCartesianproductofRandStobeasetof(r+s)tuples.Thefirstrcomponents(attributevalues)ofeachtuplecomefromatupleofR,andthelastscomponentscomefromatupleofS.,DenotedasR×S.

IfRhasMtuplesandShasntuples,thenR×Shasm×ntuples.

4.Selection

Findingalltuplesthatmeetthegivenconditionsfromtherelationshipiscalledselection.Theconditionisgivenbyalogicalexpression,andthetupleisselectedifthevalueofthelogicalexpressionistrue.Thisisanoperationperformedfromtheperspectiveofrows,thatis,tuplesareextractedinthehorizontaldirection.Theresultoftheselectionoperationcanformanewrelationship,andtherelationshipmoderemainsunchanged,butthenumberoftuplesislessthanorequaltothenumberoftuplesintheoriginalrelationship,whichisasubsetoftheoriginalrelationship.

Recordedas:δF(R)≡{t?tbelongstoR∧F(t)=true}

5.Projection

SelectfromtherelationshipThenewrelationshipcomposedofseveralattributesiscalledprojection.Thisisthecalculationfromtheperspectiveofthecolumn.Afterprojectionoperation,anewrelationshipcanbeobtained.Thenumberofattributescontainedintherelationshipisoftenlessthanthatoftheoriginalrelationship,ortheattributesarearrangedinadifferentorder.Ifthenewrelationshipcontainsduplicatetuples,theduplicatetuplesmustbedeleted.

Recordedas:∏A(R)={t[A]?tbelongstoR}AistheattributecolumninR.

Forexample:∏3,1(R)

Fourcombinationoperationsofrelationalalgebra

1.Cross

RelationshipRandTheintersectionofSisasetoftuplesthatbelongtoRandS,denotedasR∩S.RandSrequirementsaredefinedonthesamerelationalmodel.

R∩S≡{t?tbelongstoR∧tbelongstoS},RandShavethesamearity.

2.Connections

Therearetwokindsofconnections:θconnectionandFconnection(θisanarithmeticcomparisonsymbol,Fisaformula).

⑴Thetajoin

Thetajoinistoselecttupleswhoseattributevalues​​satisfyacertainθoperationfromtheCartesianproductoftherelationsRandS,denotedas:

R?×iθj?S,whereiandjaretheserialnumbersofthei-thandj-thattributesintherelationsRandS,respectively.

R?×iθj?S≡δiθ(r+j)(R×S)

Ifθistheequalsign"=",theconnectionoperationiscalled"equalValueconnection".

⑵Fjoin

TheFjoinoperationistoselecttupleswhoseattributevalues​​satisfyacertainformulaFfromtheCartesianproductoftherelationsRandS,denotedas:

R?×F?S,whereFisaformulaoftheformF1∧F2∧...∧Fn,eachfisaformulaoftheformiθj,andiandjarethefirstintherelationsRandS,respectivelyTheserialnumberofthei-thattributeandthej-thattribute.

3.Naturalconnection

ThenaturalconnectionofthetworelationsRandSisrepresentedbyR?×?S.Thespecificcalculationprocessisasfollows:

①CalculateR×S

②LetthecommonattributesofRandSbeA1,...,Ak,andselectR×SthatsatisfiesR.A1=S.A1,...,R.Ak=S.Aktuples

③RemovethesecolumnsofS.A1,...,S.Ak.

Ifthereisnocommonattributeinthetworelations,thenthenaturalconnectionistransformedintoaCartesianproductoperation.

4.Division

GivenrelationsR(X,Y)andS(Y,Z),X,Y,Zareattributegroups.YinRandYinScanhavedifferentattributenames,buttheymustcomefromthesamedomainset.ThedivisionoperationofRandSresultsinanewrelationshipP(X),wherePistheprojectionofthetupleinRthatmeetsthefollowingconditionsontheattributeX:theimagesetYXofthecomponentvaluexofthetupleonXcontainsSonYAcollectionofprojections.

Relationalalgebraexpressionsandexamplesoftheirapplications

Inrelationalalgebraoperations,theformulathatiscompoundedbyfivebasicoperationsthroughafinitenumberoftimesiscalledRelationalalgebraicexpressions.Theresultofthisexpressionisstillarelationship.Canuserelationalalgebraicexpressionstoexpressvariousdataqueryoperations.

Samplequestion:Supposetherearethreerelationshipsintheteachinglibrary:

StudentrelationshipS(S#,SNAME,AGE,SEX)

LearningrelationshipSC(S#,C#,GRADE)

CurriculumRelationshipC(C#,CNAME,TEACHER)

Thefollowingusesrelationalalgebraexpressionstoexpresseachquerystatement

1.SearchandlearnThestudentIDandgradeofthestudentwhosecoursenumberisC2.

2.RetrievethestudentIDandnameofthestudentwhosestudycoursenumberisC2.

3.RetrievethestudentIDandnameoftheelectivecoursenamedMATHS.

4.RetrievethestudentIDofthestudentwhoseelectivecoursenumberisC2orC4.

5.RetrievethestudentIDofatleasttheelectivecoursenumberC2orC4.

6.SearchforthenamesofstudentswhodonotstudyC2withage.

7.Retrievethenamesofstudentsstudyingallcourses.

1.∏S#,GRADE(δC#='C2'(SC))

or∏1,3(δ2='C2'

Relationshipmode

Relationshipmodeisthedescriptionoftherelationship.

R(U,D,dom,F)

Risthenameoftherelationship,andUconstitutestherelationshipAttributenamecollection,thedomainfromwhichtheattributesintheDattributegroupUcomefrom,themappingcollectionfromthedomattributetothedomain,andthedatadependencycollectionbetweentheattributesF.Forexample:thetutorandthegraduatestudentcomefromthesamedomain-people,takedifferentattributesName,anddefinethemappingofattributestodomainsinthepattern,thatis,whichdomainstheycomefrom:

dom(SUPERVISOR-PERSON)=dom(POSTGRADUATE-PERSON)=PERSON

Relationshipmodecanusuallybeabbreviatedas:

R(U)orR(A1,A2,...,An)

Rrelationname,A1,A2,...,AnattributeName,note:Themappingofdomainnamesandattributestodomainsisoftendirectlydescribedasthetypeandlengthofattributes.

Relationaldatabasesystemsaredatabasesystemsthatsupportrelationalmodels.

Thecharacteristicsare:singleconcept,standardized,expressedintwo-dimensionaltables.

Introduction

TherelationalmodelwasproposedbyEFCoddin1970.

ItComparedwiththehierarchicalandmeshmodel,ithasthefollowingcharacteristics:

1.Simpledatastructure(two-dimensionaltable)

2.Solidtheoreticalfoundation.

a.Relationaloperationtheory

b.Relationalmodeldesigntheory

Thebasicassumptionoftherelationalmodelisthatalldataareexpressedasmathematicalrelations,thatistosaynasubsetoftheCartesianproductofaset.Thereasoningaboutthisdataiscarriedoutthroughbinary(thatis,noNULL)predicatelogic,whichmeansthatthereareonlytwopossibleevaluationsforeachproposition:Eithertrueorfalse.Dataismanipulatedbyamethodofrelationalcalculusandrelationalalgebra.Relationalmodelisadatamodelthatusesatwo-dimensionaltablestructuretoexpressentitytypesandconnectionsbetweenentities.

RelationalmodelAllowsthedesignertobuildamodelofinformationconsistencythroughthestandardizationofthedatabase.TheaccessplanandotherimplementationandoperationdetailsareprocessedbytheDBMSengineandshouldnotbereflectedinthelogicalmodel.ThisisthecommonpracticeofSQLDBMSOpposite,whereperformanceadjustmentsoftenrequirechangestothelogicalmodel.

Thebasicbuildingblocksofrelationshipsaredomainsordatatypes.Tuplesareorderedmultisetsofattributes,andattributesaredomainsandAnorderedpairofvalues.Arelationalvariable(relvar)isacollectionoforderedpairs(orderedpairs)offieldsandnames,whichactastheheaderoftherelation.Arelationshipisacollectionoftuples.Althoughtheserelationalconceptsaremathematicallydefined,theycanbelooselymappedtotraditionaldatabaseconcepts.Tablesarerecognizedvisualrepresentationsofrelationships;tuplesaresimilartotheconceptofrows.

Thebasicprincipleoftherelationalmodelistheprincipleofinformation:allinformationisexpressedasdatavalues​​intherelation.Therefore,relationalvariablesarenotrelatedtoeachotheratdesigntime;instead,thedesignerusesthesamedomaininmultiplerelationalvariables.Ifoneattributedependsonanotherattribute,referentialintegrityisusedtoenforcethisdependency.

Advantages

(1)Singledatastructure

Intherelationalmodel,whetheritisentitiesortheconnectionsbetweenentities,theyareallexpressedbyrelations,andrelationsAllcorrespondtoatwo-dimensionaldatatable,thedatastructureissimpleandclear.

(2)Therelationshipisstandardizedandestablishedonastricttheoreticalbasis

Thebasicnormsthatconstitutetherelationshiprequirethateachattributeintherelationshipcannotbeseparated,andtherelationshipisestablishedonasolidbasis.Thetheoreticalbasisisbasedonstrictmathematicalconcepts.

(3)Simpleconceptandeasyoperation

Thebiggestadvantageoftherelationalmodelissimplicity,whichiseasyforuserstounderstandandmaster.Arelationshipisatwo-dimensionaltable,andusersonlyneedtousesimplequeries.Thelanguagecanoperatethedatabase.

Composition

Relationaldatastructure

Singledatastructure-relationship

Real-worldentitiesandvariousconnectionsbetweenentitiesAllarerepresentedbyrelations.Fromtheuser'spointofview,thelogicalstructureofthedataintherelationalmodelisatwo-dimensionaltable.

Collectionofrelationaloperations

Commonlyusedrelationaloperationsincludequeryoperationsandinsert,delete,andmodifyoperations.Amongthem,theexpressionabilityofqueryoperationisthemostimportant,including:selection,projection,connection,division,union,intersection,difference,etc.

Intheearlystage,therelationaloperationabilityinrelationalmodelsisusuallyexpressedbyalgebraicmethodsorlogicalmethods,whicharecalledrelationalalgebraandrelationalcalculus,respectively.Relationalalgebraisawayofexpressingqueryrequirementsbyalgebraicoperationsonrelations;relationalcalculusisawayofexpressingqueryrequirementsbypredicates.ThereisalsoalanguagebetweenrelationalalgebraandrelationalcalculuscalledStructuredQueryLanguage,orSQLforshort.

Dataintegrityoftherelationship

Includes:domainintegrity,entityintegrity,referentialintegrityanduser-definedintegrity.

Domainintegrity:referstothevaluerangeoftheattribute,suchasgendershouldbemaleorfemale.

TheEntityIntegrityrule:IftheattributeAistheprimaryattributeofthebasicrelationshipR,thentheattributeAcannottakeanullvalue.Forexample:Inthecoursetable(coursenumber,coursename,teacher,weeklyclasshours,remarks),the"coursenumber"attributeistheprimarykey,thenthe"coursenumber"cannottakethesamevalue,norcanittakeanullvalue.

Referentialintegrityrules:Iftheattribute(orattributegroup)FistheforeignkeyofthebasicrelationshipR,itcorrespondstotheprimarykeyKsofthebasicrelationshipS(therelationshipRandSarenotnecessarilydifferentrelationships),ThenthevalueofeachtupleintherelationshipRontheattributeFmustbe:

1.Ortakeanullvalue(eachattributevalueinFisempty);

2.OrequaltotheprimarykeyvalueofatupleinS.

Forexample:employee(employeenumber,name,gender,departmentnumber,boss,salary,commission)

department(departmentnumber,name,location)

Theemployeenumberistheprimarykeyofthe"employee"relationship,thedepartmentnumberistheforeignkey,andthedepartmentnumberinthe"department"relationshipistheprimarykey,thenthedepartmentnumberattributeofeachtupleintheemployeerelationshipcanonlytakethefollowingtwotypesofvalues:

Type1:Nullvalue,whichmeansthattheemployeehasnotbeenassignedadepartment;

Type2:Non-emptyvalue,butthevaluemustbethedepartmentnumberofatupleinthedepartmentrelationshipValuemeansthattheemployeecannotbeassignedtoanon-existentdepartment,thatis,theremustbeatupleinthereferencedrelationship"department",anditsprimarykeyvalueisequaltotheforeignkeyvalueofthereferencerelationship"employee".

Domainintegrity,entityintegrityandreferentialintegrityaretheintegrityconstraintsthatmustbemetintherelationalmodel.Aslongasitisarelationaldatabasesystem,itshouldsupportdomainintegrity,entityintegrityandreferentialintegrity.Inaddition,differentrelationaldatabasesystemsoftenrequiresomespecialconstraintsaccordingtotheirapplicationenvironments,anduser-definedintegrityisaconstraintoncertainspecificrelationaldatabases.Forexample:courseselectiontable(coursenumber,studentnumber,grade).Whendefiningtherelationshipselectiontable,wecandefinetheconstraintthattheattributeofgrademustbegreaterthanorequalto0.