How to delete the following items([yr , y3 ,y4 ,y11, y111, yr1 ,yr11, yn1 ,yn11, fn, fnr, fn1, fn2])

syms  y yr y1 y2 y3 y4 y11 y111 yr1 yr11 yn1 yn11 h fn fnr fn1 fn2

r=1.7585889236061132562137339518147
 eq1=-y2-(r - 2)/r*y+ 2/(r*(r - 1))*yr+ (2*r - 4)/(r - 1)*y1 -(h^3*(r^4 - 8*r^3 + 22*r^2 - 23*r + 6))/(120*r)*fn+ (h^3*(- r^2 + 2*r + 3))/(60*r)*fnr -(h^3*(- r^3 + 4*r^2 + 9*r - 26))/60*fn1+ (h^3*(- r^3 + 2*r + 1))/120*fn2
 eq2=-h*y3-(r - 3)/r*y+ 3/(r*(r - 1))*yr+ (r - 4)/(r - 1)*y1 -(h^3*(3*r^4 - 24*r^3 + 66*r^2 - 67*r + 12))/(240*r)*fn -(h^3*(r^4 - 5*r^3 + 5*r^2 + 5*r - 4))/(40*r*(r^2 - 3*r + 2))*fnr -(h^3*(- 3*r^4 + 15*r^3 + 15*r^2 - 137*r + 116))/(120*(r - 1))*fn1+ (h^3*(- r^4 + 2*r^3 + 2*r^2 + 3*r - 12))/(80*(r - 2))*fn2
 eq3=-h^2*y4+2/r*y+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h^3*(- r^4 + 8*r^3 - 22*r^2 + 18*r + 5))/(120*r)*fn -(h^3*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h^3*(- r^4 + 5*r^3 + 5*r^2 - 75*r + 77))/(60*(r - 1))*fn1+ (h^3*(- r^4 + 2*r^3 + 2*r^2 + 42*r - 81))/(120*(r -2))*fn2
 eq4=-h*y11-(r - 1)/r*y+ 1/(r*(r - 1))*yr+ (r - 2)/(r - 1)*y1 -(h^3*(r^4 - 8*r^3 + 22*r^2 - 21*r + 6))/(240*r)*fn+ (h^3*(- r^2 + 2*r + 3))/(120*r)*fnr-(h^3*(- r^3 + 4*r^2 + 9*r - 8))/120*fn1 -(h^3*(r^3 - 2*r + 1))/240*fn2
 eq5=-h^2*y111+2/r*y+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(r^4 - 8*r^3 + 22*r^2 - 28*r + 10))/(120*r)*fn -(h^3*(r^4 - 5*r^3 + 5*r^2 + 5*r - 10))/(60*r*(r^2 - 3*r + 2))*fnr -(h^3*(- r^4 + 5*r^3 + 5*r^2 - 35*r + 22))/(60*(r - 1))*fn1+ (h^3*(- r^4 + 2*r^3 + 2*r^2 - 8*r + 4))/(120*(r - 2))*fn2
 eq6=-h*yr1-(r - 1)/r*y+ (2*r - 1)/(r*(r - 1))*yr -r/(r - 1)*y1+ (h^3*(2*r^4 - 13*r^3 + 28*r^2 - 22*r + 5))/240*fn+ (h^3*(4*r^3 - 15*r^2 + 10*r + 5))/(120*(r - 2))*fnr+(h^3*r*(- 2*r^3 + 7*r^2 + 2*r - 3))/120*fn1+ (h^3*r*(2*r^4 - 5*r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2
 eq7=-h^2*yr11-2/r*y+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h^3*(4*r^4 - 22*r^3 + 38*r^2 - 22*r + 5))/(120*r)*fn -(h^3*(- 14*r^4 + 55*r^3 - 55*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h^3*(4*r^4 - 15*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h^3*(4*r^4 - 8*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2
 eq8=-h*yn1-(r + 1)/r*y -1/(r*(r - 1))*yr+ r/(r - 1)*y1+ (h^3*(r^3 - 8*r^2 + 22*r - 5))/240*fn+ (h^3*(r^3 - 5*r^2 + 5*r + 5))/(120*(r^2 - 3*r + 2))*fnr+ (h^3*r*(- r^3 + 5*r^2 + 5*r - 3))/(120*(r - 1))*fn1 -(h^3*r*(- r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2
 eq9=-h^2*yn11-2/r*y+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h^3*(r^4 - 8*r^3 + 22*r^2 + 22*r - 5))/(120*r)*fn -(h^3*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h^3*(- r^4 + 5*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h^3*(- r^4 + 2*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2

[Walter Roberson]

Eliminate them how? They do not appear to be used on any line other than their defining line.

Answer 1

[Mark Sherstan]

Refer to the documentation located here for examples and more info. Your answer should look something like this as I dont know what your final system is.

eliminate(put your final system here,[y3,y​4,y11,y111​,yr1,yr11,​yn1,yn11])

[sadeem alqarni]

When I use the command (eliminate) I get the following''Undefined function 'eliminate' for input arguments of type 'sym'''.

[Mark Sherstan]

Do you have the Symbolic Math Toolbox installed? What is your final system?

[sadeem alqarni]

I own it and my issue is 2013

[Mark Sherstan]

As per MATLAB documentation (look at the bottom of this page) the function was only introduced in the 2018a version, hence the reason you are getting the error.

[Walter Roberson]

eliminate() is similar to solve() except that in some cases where MATLAB does not know how to isolate down to a single formula for the variable, eliminate() can leave a formula for the variable on the left hand side.

[sadeem alqarni]

I downloaded version 2018 and found that the (eliminate) command already exists. Thank you so much

[Walter Roberson]

I am not sure if this topic is complete?

Answer 2

[Walter Roberson]

syms lambda y yr y1 y2 y3 y4 y11 y111 yr1 yr11 yn1 yn11 h fn fnr fn1 fn2
eqn = [fn == -lambda^3* y;
    fnr == -lambda^3 *yr;
    fn1 == -lambda^3 *y1;
    fn2 == -lambda^3 *y2;
    y2 ==(11873623479661898*h*yr1)/6751790211048401 - (6751790211048399*yr)/6751790211048401 - (10440411367201446*h^2*yr11)/6751790211048401 - (2889565507028359*h^3*lambda^3*y)/356208704389857024 - (7342686635091253*h^3*lambda^3*y1)/16005728964417182 + (5339343182411891*h^3*lambda^3*y2)/35562696925852424 - (8706461403438649*h^3*lambda^3*yr)/14763750126578948
    y3 ==(6751790211048400*yr)/6751790211048401 - (5121833268613498*h*yr1)/6751790211048401 + (1942682993063747*h^2*yr11)/6751790211048401 - (1257507243186803*h^3*lambda^3*y)/1424834817559428096 + (1792921480642179*h^3*lambda^3*y1)/128045831715337456 - (3830792419005201*h^3*lambda^3*y2)/195594833092188320 + (584804158233843*h^3*lambda^3*yr)/7381875063289474
    y4 ==(43167539827785635825456172186119148836985614192053456001506197137954110424426612991748655767304149263607370309797879857807360*yr - 25877663013519854714470496995117795354155173250789893980969949273885414104510842702177789859752182314519978124787172805443584*h*yr1 + 28793743615551275434440862209221214364974544635519705088102372831449747642274602026677149127351489284201642179293173138849792*h^2*yr11 + 564074675178466355101711290800115861817243764985287256222857716345096203958245125626607547653918459395601616191204104339456*h^3*lambda^3*y + 15832787617005697588434375587757371943889008049899387788824557377011019590949034231422318079968551816365187213551983537422336*h^3*lambda^3*y1 - 2319610773252914476123117303456760589342682505662780858848875411593890375817837452211793010584702974409979367137796381736960*h^3*lambda^3*y2 + 10654903642375954129417618567659624353082040712631808656956086399963989953536858084783926616542748322610469617555153918885888*h^3*lambda^3*yr)/(50036294386949720075122873848065946429852285073834511840830933442747581829881736280125487071322810498157168988377858038562816*h)
    y11 ==-(184941409074869723143011153977547744705000799495528952419552992180316180577386501665091027843353175309357741831490785796685824*yr - 325235913515173100637850865702098903551699562142465396192194404494983677846338253725708812066911190472255653342320174164869120*h*yr1 + 204669159154556337715365818206448148121157905497136549571998858900754343915908961575983565701637326134212774971626273210630144*h^2*yr11 + 2544239049986467843275698707469541587011076301108202518846002894457145153718354182392064237859142356152722923878193259610112*h^3*lambda^3*y + 56960355964623952886449815035122011802205454531308046094532329690451260856351545014108571256622324380312126963300571862269952*h^3*lambda^3*y1 - 10867289606177968030398005216262262624314164827051937911138705883308322424174554035003444561475672567602097329711242100604928*h^3*lambda^3*y2 + 57321932556903558062451263007272771674558625698224552077575708460206921639867262182843376350264452700814000762954736004497408*h^3*lambda^3*yr)/(81308978378793293947803378616190549003769664850312568053508992390304885119912335689099403933595345327655900413729667796697088*h^2)
    y111 ==(4898080204627391*yr)/6751790211048401 + (4889870827304708*h*yr1)/6751790211048401 - (2669679394946458*h^2*yr11)/6751790211048401 - (6360597615414401*h^3*lambda^3*y)/2849669635118856192 - (6045437207393777*h^3*lambda^3*y1)/48017186893251544 + (7473264660850309*h^3*lambda^3*y2)/183370156023926560 - (1595109723498111*h^3*lambda^3*yr)/9736262791308784
    yr1 ==-(3656952743101927561873653388742649804572793146241237208560353764920619345312510488995751047097418440437207549211760709683551898108472363045856625779802112*yr - 9021305042894063509662111463324531926608641864842826517956074152070290216294230272796622879875699046835427066502247989166870185429774054007066284812926976*h*yr1 + 5029500188048214479556985278091714608080330818463726410165702687652766951595717627870238826463288790834676722511765881545798892345080349410935579097432064*h^2*yr11 + 29843458106253468279896449564935568327098082672813290340772153968234129022336404918653394675006606293830230778041522366235830359941216129630143416107008*h^3*lambda^3*y + 1675847518853807729553772716414912346139041058758022076318220032935667060675256165414685723350885189837487011941469304161737101696313566977379650911600640*h^3*lambda^3*y1 - 528226690998423947287456530198178660967928782233914394961892269068436873409947017852795681116900697111069743049349180859211887363868041682655946710450176*h^3*lambda^3*y2 + 2212842834504469631040082841046644325316210504684789319517696385877979379759791070866324138643353194742598897461893965137675446634147851503383627765383168*h^3*lambda^3*yr)/(2590228454724021167298540239562159380210594447176338763657167365081379551368213541236473496190485690292166627866427246740419000711665995158325912842272768*h)
    yr11 ==-((4483276372902422121252827339784500974390938166325802075449289330620287050723124856599873348751764684756930639853833905002632079350743565336576*yr)/6960333539652369 - (7884240170851191051670901276753862560541347708215063109845977705700858654477343345765648733312436288457892430756205821040655020076806659112960*h*yr1)/6960333539652369 + (5820136678752962014731900670872368723684821573546161455974874777304286876135288935641464495235013666284891143121407819587699946046962926616576*h^2*yr11)/6960333539652369 + (36855892950410567687688032341209926912370306203108056850434388327089196295721764000773191995205554174505402843473570613037644228004044341248*h^3*lambda^3*y)/6960333539652369 + (2051864898530281139352872432993150367700482399240988954374153250078933381979672371302699918186693920515297168145855293428675277913431230906368*h^3*lambda^3*y1)/6960333539652369 - (594516744422630071479400031212554948307672310904984072885673008613003945752567242071812444717390425243751519247393786011866532357077278392320*h^3*lambda^3*y2)/6960333539652369 + (2772230651025598422384595569630867544018311195714175579549498029253878601879598597155117881002906166340333653510425700667432620542834602147840*h^3*lambda^3*yr)/6960333539652369)/(81308978378793293947803378616190549003769664850312568053508992390304885119912335689099403933595345327655900413729667796697088*h^2)
    yn1 ==-((10089458209651429634349407042754439154023982561846151652927777619167270954725918561245531100486776970906198655872121936745784734007963959443252865708324394131405660198273024*yr)/10040581717853480547665465150553 - (18416528412108833831970843480151705099149617314448866767380108038599393049489655797240902251440471306113391660788088082978674081157430006261534277701781964727442429557342208*h*yr1)/10040581717853480547665465150553 + (15509059322515879541487087184376114237383069093407429014061866422852064703944913737964892469356535977842241695378082126526635021266358699576036387759819492017138049136721920*h^2*yr11)/10040581717853480547665465150553 + (133737146246997048055656138391986356990304748578754718264431563700982856487768510452868020900347193799127200137324179322046583951767106289907831006976955874759133863346176*h^3*lambda^3*y)/10040581717853480547665465150553 + (5281242795924637016904503232340138610700336217981118661131280595788763740498073021689300304719984384704088842153183447808668479365921599535790221142122493355414520026103808*h^3*lambda^3*y1)/10040581717853480547665465150553 - (1311381349264776716130409994241646014607549823027166808001430537759678355915467538085622405042110029710789333488338905603985242532264089317313398086850728516524448361218048*h^3*lambda^3*y2)/10040581717853480547665465150553 + (6739894048643283664780508899940759266683384143239594983655920137934231621389524734286434984414987317773232508555523750210490232068690780311689497821156614252894103411884032*h^3*lambda^3*yr)/10040581717853480547665465150553)/(67059755933444642789957577328069600325395872462837409421483070028311630099623020462997353045366833109671298039887005256129957923299044360192*h)
    yn11 ==(267096347221571*h*lambda^3*y)/802700718349700 - ((4483276372902422121252827339784500974390938166325802075449289330620287050723124856599873348751764684756930639853833905002632079350743565336576*yr)/6960333539652369 - (7884240170851191051670901276753862560541347708215063109845977705700858654477343345765648733312436288457892430756205821040655020076806659112960*h*yr1)/6960333539652369 + (5820136678752962014731900670872368723684821573546161455974874777304286876135288935641464495235013666284891143121407819587699946046962926616576*h^2*yr11)/6960333539652369 + (36855892950410567687688032341209926912370306203108056850434388327089196295721764000773191995205554174505402843473570613037644228004044341248*h^3*lambda^3*y)/6960333539652369 + (2051864898530281139352872432993150367700482399240988954374153250078933381979672371302699918186693920515297168145855293428675277913431230906368*h^3*lambda^3*y1)/6960333539652369 - (594516744422630071479400031212554948307672310904984072885673008613003945752567242071812444717390425243751519247393786011866532357077278392320*h^3*lambda^3*y2)/6960333539652369 + (2772230651025598422384595569630867544018311195714175579549498029253878601879598597155117881002906166340333653510425700667432620542834602147840*h^3*lambda^3*yr)/6960333539652369)/(81308978378793293947803378616190549003769664850312568053508992390304885119912335689099403933595345327655900413729667796697088*h^2) + (2859387800382007*h*lambda^3*y1)/2135237996049923 + (1847821385343585*h*lambda^3*y2)/8154141252679642 - (1521963013521259*h*lambda^3*yr)/10878000162683446];

sol = solve(eqn, [y3, y4, y11, y111, yr1, yr11, yn1, yn11, y, y1, y2, yr, h]);

Because you have more equations than variables you wanted to eliminate, I had to choose a set of additional variables to solve for.

The above gives three solutions per variable. The variable I happened to look at, the three solutions were the same, but perhaps they were distinct for a different variable.

[sadeem alqarni]

I have modified my question above

[sadeem alqarni]

example:

syms x y

eqns = [2*x+y == 5, y-x == 1];

eliminate(eqns,x)