## How to write loop?...

I want write loop for this code:

V := 24;

eq := {Eq2, Eq3};

ans := fsolve(eq, {a1 = 0, a3 = 0});

r := 0;

W1 := rhs(ans[1])*phi11(r)+rhs(ans[2])*phi21(r)

V and W1 is Variable, I change V and solve eq and determinen a1 and a3 after i calculated W1

I want write Loop for this,

can you help me????????/

## Solving numerically a system of non-linear equatio...

Hi, I'm trying to solve without success numerically the following system of 15 nonlinear equations. Could anyone help, please? Thanks

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## error with rule solve or fsolve...

hi.i am a problem with rule solve or fsolve in maple....please see attached file and say your comments

thanks

equ.mw

## Possible bug in "fsolve"...

As part of a project, I am numerically estimating the roots of many large polynomials. Occasionally, "fsolve" fails with strange errors related to "fsolve/refine2". Searches for these error messages have turned up nothing.

I've inluded the code below that causes the error on Maple 18.02. I apologize for the polynomial in question being so long, it's the shortest example I have. The error it generates is:

Error, (in fsolve/refine2) invalid input: evalf expects its 2nd argument, n, to be of type posint, but received undefined

Is this a bug? Or am I missing some fsolve option to prevent this? Note that it only happens when the "complex" flag is used.

=========

P := x^14-22702264347017701018473605850972699930097274504938699916055555261201515180511538865331807292689345943133521696082918467714371257277276696385067641909170155322906230250853577229812913946663078548646992393337618113886746876557117483839533553328895358682670189394678910311793504505447628428181885141769168591937690303328913335175451328463754619536253583902806843310134957600949886784187209785783810122275010505534415815566439121541947044486358488039865870455952098827525405324562601732796858645293515431747164008309785658410612354201118685855495413079021176507985235094746401708925593687656572387531020719291601076812080687859808747213536777976702071405128537760507468013438105233313663196919816564525291458692028177366393652501832447863872200682143768513389322886600569382594287138458765510827267842205096062437750804878586024353928794905249283675708441066101095406513448522689302522442783437142289641259057413952301148939774149714785/3195755849586795631956816504521213454239300164039404772924331154185577854140658969534719471406093912112781063157828311505891258148739680804289213024862131311540960306206602785748866445362483281617891374949555209869677857419473553982132073059025609434698683760348542259396937054082293168625919023158753310878489047944378154369352523436731294817697449949932655665007647918855300664365159027040571937825740235967492228453331261542499260943085539271304638576578246276634403350307801994081681247214869084246168101721298760198550961832560608341435638093413744839736250679074198753022491225840288065341597851066663786665723409977381822591654466626645542917017628998630902708076612502066607817250779545511895971357711983287763127653752300554550391349040027472903180009282594974618980021621163037989247901106508257414514187962209356325857887950302223210328647697948055097831009797738621154319922212951316644741457327450027692469090867369598*x^13+19088859498864751331345860430721481446264521641744903691362655800372349704990331481604867685549645823662978708926030541236042951546550966879612333115396628902751820387999904934599090760358886795430484312266737008386396041896213971568537362589851823779617430207078749426022658232278071527361264481524611089324107754031784837527081637219350016169914382322455035364613935875393571579561406195287363628553419822536428710010055920488818415526206620047517917895155637033562338042275152771173240104076821411360366799172066699958543868065037999702280159896040588223787643434915579465270491451613199185385049196526456210057933748521047167538262357063585093474544299142560492581751607753970282443057122762426600024763892341448332834018680513343674283251162037067303651651086278409136799357849452879897251530675098741236156640469815784447341282424004221641529187217962536022784563163918511210513153785881467158114512281634789894107114727680109/1065251949862265210652272168173737818079766721346468257641443718061859284713552989844906490468697970704260354385942770501963752716246560268096404341620710437180320102068867595249622148454161093872630458316518403289892619139824517994044024353008536478232894586782847419798979018027431056208639674386251103626163015981459384789784174478910431605899149983310885221669215972951766888121719675680190645941913411989164076151110420514166420314361846423768212858859415425544801116769267331360560415738289694748722700573766253399516987277520202780478546031137914946578750226358066251007497075280096021780532617022221262221907803325793940863884822208881847639005876332876967569358870834022202605750259848503965323785903994429254375884584100184850130449680009157634393336427531658206326673873721012663082633702169419138171395987403118775285962650100741070109549232649351699277003265912873718106640737650438881580485775816675897489696955789866*x^12-127688837609696458957114129756229560761957972259253280819996356067917173759565012901801561924391178368568146719627801670086606489531437386224078360185442651606983719684283163392876990522586784115059551865746707609765679864632874671595399416688286257053075135779925094175440416074968471245768830366824397599424731191899057489251725430472639828977416853808059394673266682604308077331301860791811476274942568803494246399367164616630866928631772760003749091917886558963952047434319195736393271420111064778587861639539510320744497931007588784407172972776901653630399291814617861650330433072614870207218474263898528043868017109168847074788133295715653324601280999334137328493510780499508083274179117783232296907665583279993325725716354393277745170409349317876378784871325009748734263290375761397883657890413900529632709410443413043575189427898559331856967020187201932742096158736566419271039506140015010172468151681141071869870925420155369/639151169917359126391363300904242690847860032807880954584866230837115570828131793906943894281218782422556212631565662301178251629747936160857842604972426262308192061241320557149773289072496656323578274989911041973935571483894710796426414611805121886939736752069708451879387410816458633725183804631750662175697809588875630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fsolve(P,complex);

## Strange behavior of fsolve...

 > Let us define a piecewise-linear continuous function:
 > restart; VP := Vector[row](16, {(1) = 10, (2) = 177.9780267, (3) = 355.9560534, (4) = 533.9340801, (5) = 711.9121068, (6) = 889.8901335, (7) = 1067.868160, (8) = 1245.846187, (9) = 1423.824214, (10) = 1601.802240, (11) = 1779.780267, (12) = 1957.758294, (13) = 2135.736320, (14) = 2313.714347, (15) = 2491.692374, (16) = 2669.670400}); VE := Vector[row](16, {(1) = 5.444193931, (2) = .4793595141, (3) = .3166653569, (4) = .2522053489, (5) = .2123038784, (6) = .1822258228, (7) = .1544240625, (8) = .1277082078, (9) = .1055351619, (10) = 0.8639065510e-1, (11) = 0.6936612570e-1, (12) = 0.5388339810e-1, (13) = 0.3955702170e-1, (14) = 0.2612014630e-1, (15) = 0.1338216460e-1, (16) = 0.1203297900e-2}); for i to 15 do p[i] := VE[i+1] < x and x <= VE[i], (VP[i+1]-VP[i])*(x-VE[i])/(VE[i+1]-VE[i])+VP[i] end do; g := unapply(piecewise(seq(p[i], i = 1 .. 15)), x);
 > for i to 15 do print(fsolve(g(x) = VP[i])) end do;
 > Why doesn't the fsolve command work if i = 4, 7, 9, 11, 14? There are workarounds:
 > print(DirectSearch:-SolveEqutions(g(x) = VP[i]));
 > and/or
 > VP := convert(VP, rational); VE := convert(VE, rational); print(solve(g(x) = VP[i]));
 > How to explain such behavior of the fsolve command? That was asked but not answered in http://forum.exponenta.ru/viewtopic.php?t=13524&sid=025a140e7e00b99803c86060a5c0c33c .
 >

strange_behavior.mw

Edit. Replaced worksheet.

## Time-consuming fsolve ...

I know 1st root of a function locates in a small interval (by drawing plots of function).

but fsolve command uses unreasonable time to find roots.

Also NextZero dosent work.

--------------------------------------------------------------------------------------------------

restart; s := sqrt(n)*Pi*(sqrt(n)*Pi-tan(sqrt(n)*Pi))/(sqrt(n)*Pi*tan(sqrt(n)*Pi)+2*(1-sec(sqrt(n)*Pi)));

C := (tan(sqrt(n)*Pi)-sqrt(n)*Pi*sec(sqrt(n)*Pi))/(sqrt(n)*Pi-tan(sqrt(n)*Pi));

S := s*(-C^2+1);

Gamma[b] := E[b2]/E[b1];

Gamma[c] := E[c2]/E[c1];

alpha[b] := t[b1]*t[b2]/(t[b1]+t[b2])^2;

alpha[c] := t[c1]*t[c2]/(t[c1]+t[c2])^2;

EIb := b*E[b1]*(t[b1]^4+2*Gamma[b]*alpha[b]*(2-alpha[b])*(t[b1]+t[b2])^4+Gamma[b]^2*t[b2]^4)/(12*(Gamma[b]*t[b2]+t[b1]));

EIc := b*E[c1]*(t[c1]^4+2*Gamma[c]*alpha[c]*(2-alpha[c])*(t[c1]+t[c2])^4+Gamma[c]^2*t[c2]^4)/(12*(Gamma[c]*t[c2]+t[c1]));

b := 1;Lb := 2; Lc1 := 2.5; Lc2 := 3; E[b1] := 180; E[b2] := 200; t[b1] := 0.3e-1; t[b2] := 0.4e-1; E[c2] := 220; t[c1] := 0.5e-1; t[c2] := 0.2e-1;

for k from 0 by 10 to 100 do

E[c1] := 150+k; nce := (1/2)*(Lc1/Lc2)^2*n; nb := (1/2)*(Lb/Lc2)^2*n; q[k] := 1000*fsolve((subs(n = nce, C*s)*EIc/Lc1)^2/(S*EIc/Lc2+subs(n = nce, s)*EIc/Lc1+subs(n = nb, s*(1-C))*EIb/Lb)-subs(n = nce, s)*EIc/Lc1-2*EIb/Lb, n = 1.45 .. 1.56)*evalf(Pi^2)*EIc/(2*Lc2^2); print(q[k], k)

end do;

with(CurveFitting); F := PolynomialInterpolation([seq([10*i, q[10*i]], i = 0 .. 10)], z)

## Fsolve fails for some values of parameters...

Hi, the fsolve works perfectly fine when otaining SOL2 below. However, as soon as I change the values of paramters (from 0 values in SOL2 to t_prof = .16, t_r = .16, t_w = .16 in SOL3) fsolve simplmy reproduces the eval results and would not solve! Please your help is highly appreciated. Thanks in advance!

restart;
eq1 := ((1-s)*w)^(1-gamma)*r^gamma-P_v = 0;
eq2 := (1-s)*w*H/M-(1-gamma)*P_v*q/phi = 0;
eq3 := r*(K+K_f)/M-gamma*P_v*q/phi = 0;
eq4 := prof-M*p_d*q+(1-s)*w*H+r*(K+K_f) = 0;
eq5 := -tau*y_x+q-y_d-y_g = 0;
eq6 := p_d-sigma*P_v/((sigma-1)*phi) = 0;
eq7 := y_d-M^(lambda-1)*Y*(p_d/P)^(-sigma) = 0;
eq8 := y_x-F_f*(tau*p_d)^(-sigma_x) = 0;
eq9 := y_f-M_f^(lambda-1)*Y*((1+z)*tau*p_f/P)^(-sigma) = 0;
eq10 := (G*alpha_g+Y)^(-alpha_c)/P-A*H^alpha_h/((1-t_w)*w) = 0;
eq11 := P*Y-(1-t_w)*w*H-(1-t_r)*r*K-(1-t_prof)*prof+T = 0;
eq12 := P*Y-M*p_d*y_d-M_f*(1+z)*tau*p_f*y_f = 0;
eq13 := (1-t_r)*r-r_f = 0;
eq14 := G-y_g*M^((lambda_g-1+sigma_g)/(sigma_g-1)) = 0;
eq15 := s*w*H+M*p_d*y_g-T-t_w*w*H-t_r*r*(K+K_f)-t_prof*prof-z*M_f*tau*p_f*y_f = 0;

SOL2 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = 0, t_r = 0, t_w = 0, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

SOL3 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = .16, t_r = .16, t_w = .16, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

## How can I find all the roots ?...

If there is  an equation or are several equations, I need to obtain all the roots, how can I do???

fsolve ? rootfindings? or what?

If an examples of actual is given,  That will be perfect  !!!

Thanks

## fsolve returns its own statement...

Hi Everyone,

I have a bunch polynomial systems of equations (all form zero-dimensional ideals, i.e. there is a finite number of complex solutions), and I would like to get a real solution for each of them, if available.

fsolve would be the tool to use. But it lead to some strange behaviour for me. Among some other inputs, the input

fsolve({81*x3^12+72*x3^10-614*x3^9+16*x3^8-384*x3^7+1884*x3^6+480*x3^4-2760*x3^3+1600, 81*x2*x3^11+72*x2*x3^9-452*x2*x3^8+16*x2*x3^7-240*x2*x3^6+980*x2*x3^5+32*x2*x3^4-144*x2*x3^3-800*x2*x3^2-220*x3^3+160*x2^2+480*x2+520, 81*x3^11+72*x3^9-452*x3^8+16*x3^7-240*x3^6+980*x3^5+32*x3^4-144*x3^3-800*x3^2+160*x1+160*x2+480},{x1, x2, x3});

somehow outputs itself, i.e.

fsolve({81*x3^12+72*x3^10-614*x3^9+16*x3^8-384*x3^7+1884*x3^6+480*x3^4-2760*x3^3+1600, 81*x2*x3^11+72*x2*x3^9-452*x2*x3^8+16*x2*x3^7-240*x2*x3^6+980*x2*x3^5+32*x2*x3^4-144*x2*x3^3-800*x2*x3^2-220*x3^3+160*x2^2+480*x2+520, 81*x3^11+72*x3^9-452*x3^8+16*x3^7-240*x3^6+980*x3^5+32*x3^4-144*x3^3-800*x3^2+160*x1+160*x2+480},{x1, x2, x3})

I know that this system has no real solutions, but only complex ones. But wouldn't the expected output then be just nothing (as e.g. "solve" does)?

I am confused by this output. Furthermore, how can I "check" with Maple if the output was a solution? By checking the type? There must be less hacky solutions. Thank you all in advance for your help.

Albert

PS.: When I add the keyword "complex" to the function call, then I receive a complex solution; hence, the syntax at least is correct (if someonw might have doubted that).

## Is this a bug with fsolve...

When I use fsolve with equation

-x^2 + 2*x + 5 + (x^2 + 2*x - 1)* sqrt(2 - x^2)=0

I got only one solution.

fsolve(-x^2 + 2*x + 5 + (x^2 + 2*x - 1)* sqrt(2 - x^2)=0,x);

In fact, it have two reals solutions.

I posted at here

http://mathematica.stackexchange.com/questions/83985/does-the-equation-have-two-roots/83991#83991

## ODE- convergence problem...

Dear Colleges

I have a problem with the following code. As you can see, procedure Q1 converges but I couldn't get the resutls from Q2.

I would be most grateful if you could help me on this problem.

Sincerely yours

Amir

restart;

Eq1:=diff(f(x),x\$3)+diff(f(x),x\$2)*f(x)+b^2*sqrt(2*reynolds)*diff(diff(f(x),x\$2)^2*x^2,x\$1);
Eq2:=diff(g(x),x\$3)+diff(g(x),x\$2)*g(x)+c*a^2*sqrt(2*reynolds)*diff(diff(g(x),x\$2)^2*x,x\$1);
eq1:=isolate(Eq1,diff(f(x),x,x,x));
eq2:=subs(g=f,isolate(Eq2,diff(g(x),x,x,x)));
EQ:=diff(f(x),x,x,x)=piecewise(x<c*0.1,rhs(eq1),rhs(eq2));
Eq11:=diff(theta(x),x\$2)+pr*diff(theta(x),x\$1)*f(x)+pr/prt*b^2*sqrt(2*reynolds)*diff(diff(f(x),x\$2)*diff(theta(x),x\$1)*x^2,x\$1);
Eq22:=diff(g(x),x\$2)+pr*diff(g(x),x\$1)*f(x)+pr/prt*a^2*c*sqrt(2*reynolds)*diff(diff(f(x),x\$2)*diff(g(x),x\$1)*x^1,x\$1);
eq11:=isolate(Eq11,diff(theta(x),x,x));
eq22:=subs(g=theta,isolate(Eq22,diff(g(x),x,x)));
EQT:=diff(theta(x),x,x)=piecewise(x<c*0.1,rhs(eq11),rhs(eq22));
EQT1a:=eval(EQT,EQ):
EQT2:=eval(EQT1a,{f(x)=G0(x),diff(f(x),x)=G1(x),diff(f(x),x,x)=G2(x)}):
bd:=c;
a:=0.13:
b:=0.41:
pr:=1;
prt:=0.86;
reynolds:=12734151.135786774055543653356602;     #10^6;   #1.125*10^8:

c:=88.419896050808975395120916434619:
;
Q:=proc(pp2) local res,F0,F1,F2;
print(pp2);
if not type(pp2,numeric) then return 'procname(_passed)' end if:
res:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=pp2},numeric,output=listprocedure);
F0,F1,F2:=op(subs(subs(res),[f(x),diff(f(x),x),diff(f(x),x,x)])):
F1(bd)-1;
end proc;
fsolve(Q(pp2)=0,pp2=(0..1002));
se:=%;
res2:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=se},numeric,output=listprocedure):
G0,G1,G2:=op(subs(subs(res2),[f(x),diff(f(x),x),diff(f(x),x,x)])):
plots:-odeplot(res2,[seq([x,diff(f(x),[x\$i])],i=1..1)],0..c);

Q2:=proc(rr2) local solT,T0,T1;
print(rr2);
if not type(rr2,numeric) then return 'procname(_passed)' end if:
solT:=dsolve({EQT2,theta(0)=1,D(theta)(0)=-rr2},numeric,known=[G0,G1,G2],output=listprocedure):
T0,T1:=op(subs(subs(res),[theta(x),diff(theta(x),x)])):
T0(bd);
end proc;
fsolve(Q2(rr2)=0,rr2=(0..100));

shib:=%;
sol:=dsolve({EQT2,theta(0)=1,D(theta)(0)=-shib},numeric,known=[G0,G1,G2],output=listprocedure):
plots:-odeplot(sol,[x,theta(x)],0..c);
#fsolve(Q2(pp3)=0,pp3=-2..2):

Amir

## how do i solve this problem?...

Hi,

we want to know what is the meaning of this statement?

We expect to have the following statement . But unfortunately we don,t get it

> with(difforms);
> sol := fsolve({diff(S, x) = 0, diff(S, y) = 0}, {x, y});

I do not take values above code.

## fsolve fail to evaluate non-linear system...

Hello there

I'm quite an amature so please don't judge.  I'm trying to use fsolve to solve a system of non-linear equations but Maple is just "spitting" on me the equations with no intention to solve them:

> delta5 := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+zeq^2)*(sqrt(x^2+zeq^2)*x))+x*zeq/sqrt(x^2+zeq^2)^3)/(2*Pi*E5);
print(`output redirected...`); # input placeholder
> shrinkage := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Zb^2)*(sqrt(x^2+Zb^2)*x))+x*Zb/sqrt(x^2+Zb^2)^3)/(2*Pi*E5)-P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Za^2)*(sqrt(x^2+Za^2)*x))+x*Za/sqrt(x^2+Za^2)^3)/(2*Pi*E5);
> eq10 := subs(x = 1800, delta5)+subs(x = 1800, Zb = z2, Za = z1, shrinkage)+subs(x = 1800, Zb = z3, Za = z2, shrinkage)+subs(x = 1800, Zb = z4, Za = z3, shrinkage)+subs(x = 1800, Zb = z5, Za = z4, shrinkage) = 36.7*10^(-3);
print(`output redirected...`); # input placeholder
> eq9 := subs(x = 1500, delta5)+subs(x = 1500, Zb = z2, Za = z1, shrinkage)+subs(x = 1500, Zb = z3, Za = z2, shrinkage)+subs(x = 1500, Zb = z4, Za = z3, shrinkage)+subs(x = 1500, Zb = z5, Za = z4, shrinkage) = 47.2*10^(-3);
print(`output redirected...`); # input placeholder
> eq8 := subs(x = 1200, delta5)+subs(x = 1200, Zb = z2, Za = z1, shrinkage)+subs(x = 1200, Zb = z3, Za = z2, shrinkage)+subs(x = 1200, Zb = z4, Za = z3, shrinkage)+subs(x = 1200, Zb = z5, Za = z4, shrinkage) = 63.8*10^(-3);
> eq7 := subs(x = 900, delta5)+subs(x = 900, Zb = z2, Za = z1, shrinkage)+subs(x = 900, Zb = z3, Za = z2, shrinkage)+subs(x = 900, Zb = z4, Za = z3, shrinkage)+subs(x = 900, Zb = z5, Za = z4, shrinkage) = 91.1*10^(-3);
print(`output redirected...`); # input placeholder
> eq6 := subs(x = 600, delta5)+subs(x = 600, Zb = z2, Za = z1, shrinkage)+subs(x = 600, Zb = z3, Za = z2, shrinkage)+subs(x = 600, Zb = z4, Za = z3, shrinkage)+subs(x = 600, Zb = z5, Za = z4, shrinkage) = 137.9*10^(-3);
> eq5 := subs(x = 450, delta5)+subs(x = 450, Zb = z2, Za = z1, shrinkage)+subs(x = 450, Zb = z3, Za = z2, shrinkage)+subs(x = 450, Zb = z4, Za = z3, shrinkage)+subs(x = 450, Zb = z5, Za = z4, shrinkage) = 175.2*10^(-3);
> eq4 := subs(x = 300, delta5)+subs(x = 300, Zb = z2, Za = z1, shrinkage)+subs(x = 300, Zb = z3, Za = z2, shrinkage)+subs(x = 300, Zb = z4, Za = z3, shrinkage)+subs(x = 300, Zb = z5, Za = z4, shrinkage) = 230.9*10^(-3);
print(`output redirected...`); # input placeholder
> sys := {eq10, eq5, eq6, eq7, eq8, eq9};
print(`output redirected...`); # input placeholder
> fsolve(sys, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400});

and this is what Maple gives after the fsolve

fsolve({(3937.500000*(.2/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(450*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3888888889e-2/E5+(3937.500000*(.2/(202500+(650+h4)^2)+(450*(650+h4))/(202500+(650+h4)^2)^(3/2)))/E5 = .1752000000, (3937.500000*(.2/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(600*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2187500000e-2/E5+(3937.500000*(.2/(360000+(650+h4)^2)+(600*(650+h4))/(360000+(650+h4)^2)^(3/2)))/E5 = .1379000000, (3937.500000*(.2/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(900*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.9722222220e-3/E5+(3937.500000*(.2/(810000+(650+h4)^2)+(900*(650+h4))/(810000+(650+h4)^2)^(3/2)))/E5 = 0.9110000000e-1, (3937.500000*(.2/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1200*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.5468750000e-3/E5+(3937.500000*(.2/(1440000+(650+h4)^2)+(1200*(650+h4))/(1440000+(650+h4)^2)^(3/2)))/E5 = 0.6380000000e-1, (3937.500000*(.2/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1500*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3500000000e-3/E5+(3937.500000*(.2/(2250000+(650+h4)^2)+(1500*(650+h4))/(2250000+(650+h4)^2)^(3/2)))/E5 = 0.4720000000e-1, (3937.500000*(.2/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1800*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2430555555e-3/E5+(3937.500000*(.2/(3240000+(650+h4)^2)+(1800*(650+h4))/(3240000+(650+h4)^2)^(3/2)))/E5 = 0.3670000000e-1}, {E1, E2, E3, E4, E5, h4}, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400})

## fsolve more equations than variables...

Hi everyone,

i'm trying to find out the euler angles from a rotation matrix.

I have a matrix that contains the result of multpilying the 3 axis rotation R(z,c)*R(y,b)*R(x,a) without knowing the values of the angles a,c,b (that's what I want to find out), so there are sinus and cosinus everywhere. There is another matrix containing the expected values that each equation in the first matrix will match.

My problem is that I eventually will change the order of the multiplication of the axis (i.e. R(x,a)*R(z,c)*R(y,b)) and I'm try to make maple compute this for me.

I defined R(x,a), R(y,b) and R(z,c) as follows:

Rx := Matrix (3,3, [1,0,0,0,cos(a),-sin(a),0,sin(a),cos(a)]);
Ry := Matrix (3,3, [sin(b), 0, cos(b), 0, 1, 0, -sin(b), 0, cos(b)]);
Rz := Matrix (3,3, [cos(c), -sin(c), 0, sin(c), cos(c), 0, 0, 0, 1]);
and
RT := Multiply(Multiply(Rx,Rz),Ry);

Since here is alright. Now I want to match RT to the solution matrix.

g1 := RT[1,1] = mat[1,1];
g2 := RT[1,2] = mat[1,2];
g3 := RT[1,3] = mat[1,3];
g4 := RT[2,1] = mat[2,1];
g5 := RT[2,2] = mat[2,2];
g6 := RT[2,3] = mat[2,3];
g7 := RT[3,1] = mat[3,1];
g8 := RT[3,2] = mat[3,2];
g9 := RT[3,3] = mat[3,3];

soll := fsolve({g1,g2,g3,g4,g5,g6,g7,g8,g9},{a,b,c});

At this point I'm getting an error. I know that there are more equations than variables but the system is solvable anyway.
What maple trick can I do to solve this system or to find the good 3 equations?

Extra question:

Is there any method to match RT to mat without all those gX equations?

Thank you everyone.

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