Hi,

I get the error in the following code

restart:

gama1:=0.01:

zet:=0;
#phi0:=0.00789:
Phiavg:=0.02;
lambda:=0.01;
Ha:=1;


                               0
                              0.02
                              0.01
                               1
rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])*(1-Ha^2*u(eta))+((1/(eta)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta));
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(-2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)+k(eta)/k1[w]/(eta)*diff(T(eta),eta) ));
eq3:=diff(phi(eta),eta)+phi(eta)/(N[bt]*(1+gama1*T(eta))^2)*diff(T(eta),eta);
      /  d   /  d         \\   mu1[w] (1 - u(eta))
      |----- |----- u(eta)|| + -------------------
      \ deta \ deta       //         mu(eta)      

           /             /  d           \\               
           |      mu_phi |----- phi(eta)||               
           | 1           \ deta         /| /  d         \
         + |--- + -----------------------| |----- u(eta)|
           \eta           mu(eta)        / \ deta       /
                                /      /                        
                                |      |                        
/  d   /  d         \\     1    |      |  rho(eta) c(eta) u(eta)
|----- |----- T(eta)|| + ------ |k1[w] |- ----------------------
\ deta \ deta       //   k(eta) |      |         5000 p2        
                                \      \                        

                                /  d           \
     (a[k1] + 2 b[k1] phi(eta)) |----- phi(eta)|
                                \ deta         /
   + -------------------------------------------
                                          2     
         1 + a[k1] phi1[w] + b[k1] phi1[w]      

            /  d         \\\
     k(eta) |----- T(eta)|||
            \ deta       /||
   + ---------------------||
           k1[w] eta      ||
                          //
                                      /  d         \
                             phi(eta) |----- T(eta)|
          /  d           \            \ deta       /
          |----- phi(eta)| + ------------------------
          \ deta         /                          2
                             N[bt] (1 + 0.01 T(eta))
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,eq1):
eq2:=subs(phi(0)=phi0,eq2):
eq3:=subs(phi(0)=phi0,eq3):

#A somewhat speedier version uses the fact that you really need only compute 2 integrals not 3, since one of the integrals can be written as a linear combination of the other 2:
Q:=proc(pp2,fi0) local res,F0,F1,F2,a,INT0,INT10,B;
global Q1,Q2;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve(subs(p2=pp2,phi0=fi0,{eq1=0,eq2=0,eq3=0,u(1)=lambda/(phi(1)*rhop/rhobf+(1-phi(1)))*D(u)(1),D(u)(0)=0,phi(1)=phi0,T(1)=0,D(T)(1)=1}), numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
INT0:=evalf(Int((1-eta)*F0(eta),eta=0..1-zet));
INT10:=evalf(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet));
B:=(-cbf*rhobf+cp*rhop)*INT10+ rhobf*cbf*INT0;
a[1]:=2/(1-zet^2)*B-10000*pp2;
a[2]:=INT10/INT0-Phiavg;
Q1(_passed):=a[1];
Q2(_passed):=a[2];
if type(procname,indexed) then a[op(procname)] else a[1],a[2] end if
end proc;
#The result agrees very well with the fsolve result.
#Now I did use a better initial point. But if I start with the same as in fsolve I get the same result in just about 2 minutes, i.e. more than 20 times as fast as fsolve:

Q1:=proc(pp2,fi0) Q[1](_passed) end proc;
Q2:=proc(pp2,fi0) Q[2](_passed) end proc;
Optimization:-LSSolve([Q1,Q2],initialpoint=[6.5,exp(-1/N[bt])]);


proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
              HFloat(6.5), HFloat(0.006737946999)

the error is :

Error, (in Optimization:-LSSolve) system is singular at left endpoint, use midpoint method instead

how can I fix it.

Thanks

Amir

I have exported Maple code as a Maplet file.  When I click on the file Maplet Launcher opens but nothing "runs".  It looks like it's trying because the icon flashes, but no window opens.  The Maple worksheet from which the Maplet was generated runs fine.

Any suggestions as to how to get Maplet Launcher to run my Maplets?

Thanks,

Rollie

Hello,

In a mechanical problem, i have to deal with a system with trigonometric expression. The variables are gamma[1](t), psi[1](t), phi[1](t), alpha(t), beta(t), x(t). The orthers are parameters.

I would like to have a explicit relations between  gamma[1](t), psi[1](t), phi[1](t) and alpha(t), beta(t), x(t).

In orthers words, i would like to have 

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Of course, the expresions of alpha(t), beta(t), and x(t) should be complex. Nevertheless, it will avoid me to have to solve Newton Raphson algorithm to solve these constraints equations.

Normally, it should be feasible.

When i have only one equation and not a system, isolate function is helpful.

But in this case, i don't manage to have my relations.

Have you some ideas to expression these relations ?

alpha(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

beta(t)= f(gamma[1](t), psi[1](t), phi[1](t)).

 x(t) = f( gamma[1](t), psi[1](t), phi[1](t)).

Here the code of the equations :

restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
eq_liai[1]:= rF[1]*cos(a[1])-cos(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*cos(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*cos(a[1])*sin(gamma[1](t))*sin(psi[1](t))-sin(a[1])*sin(phi[1](t)))-cos(alpha(t))*rBTP[1]*cos(a[1])-sin(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-sin(alpha(t))*cos(beta(t))*h = 0;
eq_liai[2]:= rF[1]*sin(a[1])-sin(a[1])*cos(gamma[1](t))*e[1]-l[1]*(cos(phi[1](t))*sin(a[1])*cos(gamma[1](t))*cos(psi[1](t))-cos(phi[1](t))*sin(a[1])*sin(gamma[1](t))*sin(psi[1](t))+cos(a[1])*sin(phi[1](t)))-cos(beta(t))*rBTP[1]*sin(a[1])+sin(beta(t))*h = 0;
eq_liai[3] := h[1]+sin(gamma[1](t))*e[1]+l[1]*(sin(gamma[1](t))*cos(psi[1](t))+cos(gamma[1](t))*sin(psi[1](t)))*cos(phi[1](t))+sin(alpha(t))*rBTP[1]*cos(a[1])-cos(alpha(t))*sin(beta(t))*rBTP[1]*sin(a[1])-cos(alpha(t))*cos(beta(t))*h-z(t) = 0;

or directly a maple file

constraints.mw

Thanks a lot for your help

Maple Player seems like it could be an outstanding piece of software, yet with the new operating system for Ipad, the program crashes immediately. I am unable to find any solutions. I also stumbled across a post in which Maplesoft is no longer providing support for the APP. Is this true?

When you use the slider without Do(%MathContainer1 = StandardError(Variance, R)):
everything works ok but when you add Do(%MathContainer1 = StandardError(Variance, R)):
Maple Crashes.....

Strange...

LL_102)_Covariance_M.mw

hi,

     there is a common  differential equation in my maple note,the solution of the eq. can be expressed by

associated Legendre function(s),but i get a result by hypergeometric representation.how i can translate the later into a  single Legendre fun？

 Thank you in advance  

Download question_12.19.mw

I have an ipad air 16G running ios 7.0.4 and downloaded the MaplePlayer APP.  t seems to crash on several of the routines for example, "Approximaing Sphere" and "Linear System Tutor". The app was last updated in 2011.  Do you have plans to any upgrades plan in the near future?

I have an ipad air 16G running ios 7.0.4 and downloaded the MaplePlayer APP.  t seems to crash on several of the routines for example, "Approximaing Sphere" and "Linear System Tutor". The app was last updated in 2011.  Do you have plans to any upgrades plan in the near future?

Hi MaplePrimers,

I'm trying to solve a system of algebraic equations using 'solve' [float].  I'd prefer to use 'solve' over 'fsolve', as 'solve' solves my system in about 0.05s, whereas fsolve takes about 5 seconds.  I need to solve the system repeatedly at a different points, so time is important.  I don't know why there is such a large difference in time ... 

I have a few piecewise functions of order 3 to 5.  It solves fine with the other (piecewise) equations, but adding one piecewise function which gives me an error while trying to solve:

Error, (in RootOf) _Z occurs but is not the dependent variable.

I think this is due to solve finding multiple solutions.  Is there a way to limit solve to only real solutions?

Thanks in advance!

I have a TextArea component on the worksheet. Is it possible to create on the worksheet some number of Sliders, where the number of sliders is defined by the number entered in the TextArea?

Why does the following statement not evaluate, or better yet, how can I make it do so?

A:=value(floor(p)) assuming p>0,p<1,p::real;

or

A:=simplify(floor(p)) assuming p>0,p<1,p::real;

or any one of a lot of different attempts along the above lines, all of which seem (to me) that they should yield

A:=0

rather than

A:=floor(p)

which is what I get.

Thanks in advance

I have theoretically 3(could eventually be more) layers with an incident wave with a wave equation for that wave.

It refracts into the 2nd layer from the first and now has a 2nd wave equation, then from the 2nd into the 3rd layer with a 3rd wave equation.

All the wave equations are of the form, Psi(z) = A_1psi_1(z) + B_1psi_2(z); this is just a general solution where psi_1&2 are linearly independant solutions that make up the general equation above and A_1 and B_1 are constant coefficients that would be A_2,B_2 and A_3,B_3 for the 2nd and 3rd layers respectively.

Transfer matrix method gives A_1,B_1 in terms of A_2,B_2(as it transfers from layer 1 to 2 they equate under boundary conditions so you can solve the simultaneous equations for results). You create a matrix of these results and multiply it with the respective matrix of the 2nd layer to 3rd layer to give you the overall transfer matrix from one side of the system to the other.

I think something to do with transfer function but not sure how to use it or set up the problem. 

Thanks in advance for any pointers.

f(f(z,a),b) = f(z, a + b) 

i googled this axiom is diff(x(t),t) = xi(f);

then i think 

diff(x(t),t$2) = xi(f);

is it f(f(f(z,a),b),c) = f(z, a + b+c) ?

then think again

whether  f(f(f(z,a),b),c) + f(f(z,a),b) = f(z, a + b+c)  is diff(x(t),t$2)+diff(x(t),t)= xi(f);

however do not know how to construct right hand side  f(z, a + b+c), this is my guess

any books teaching this?

i think that if any matrix group be created from  f(f(f(z,a),b),c) + f(f(z,a),b)

that can help to convert to differential equations

hope that there is a solvable group which can represent solvable differential equation or differential system

if xi is Infinitesimal in maple,

how to find Infinitesimal from f(f(z,a),b) = f(z, a + b) ?

got error when draw root locus

and would like to know how to set feasibility tolerance, less than 0.1 is also ok

with(DynamicSystems):

x11 := [1.05657970467127, .369307407127487, .400969917393968, .368036162749865, .280389875142339, .280523489139136, .283220960827744, .373941285224253, .378034013792196, .384412762008662, .358678988563716, .350625923673556, .852039817522304, .362240519978640, 1.03197080591829, .343650441408896, .982510654490390, .404544012440991, .422063867224247, 1.20938803285209, .455708586000668, 1.22503869712995, .388259397947667, .472188904769827, 1.31108028794286, 1.19746589728366, .572669348193002];

y11 := [.813920951682113, 10.3546712426210, 2.54581301217449, 10.2617298458172, 3.82022939508992, 3.81119683373741, 3.90918914917183, 10.5831132713329, 10.8700088489538, 11.0218056177585, 10.5857571473115, 9.89034057997145, .271497107157453, 9.77706473740146, 2.23955104698355, 4.16872072216206, .806710906391666, 11.9148193656260, 12.0521411908477, 2.52812993540440, 12.6348841508094, 2.72197067934160, 5.10891266728297, 13.3609183272238, 3.03572692234234, 1.07326033849793, 15.4268962507711];

z11 := [8.93290500985527, 8.96632856524217, 15.8861149154785, 9.16576669760908, 3.20341865536950, 3.11740291181539, 3.22328961317946, 8.71094047480794, 8.60596466961827, 9.15440788281943, 10.2935566768586, 10.5765776143026, 16.3469510439066, 9.36885507010739, 2.20434678689869, 3.88816077008078, 17.9816287534802, 10.1414228793737, 10.7356141216242, 4.00703203725441, 12.0105837616461, 3.77028605914906, 5.01411979976607, 12.7529165152417, 3.66800269682059, 21.2178824031985, 13.9148746721034];

u11 := [5.59, 5.74, 5.49, 5.19, 5.37, 5.56, 5.46, 5.21, 5.55, 5.56, 5.61, 5.91, 5.93, 5.98, 6.28, 6.24, 6.44, 6.58, 6.75, 6.78, 6.81, 7.59, 7.73, 7.75, 7.69, 7.73, 7.79];

a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);

b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);

c1 := Diff(z1(t),t) = k8*x1(t)+ k9*y1(t)+ k10*z1(t)+k12*u1(t);

d1 := Diff(u1(t),t) = 0;

ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1],u1(1)=u11[27];

sol:=dsolve({a1,b1,c1,d1,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12],output=listprocedure);

X,Y,Z,U:=op(subs(sol,[x1(t),y1(t),z1(t),u1(t)]));

tim := [seq(n, n=1..27)];

N:=nops(tim):

ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12) sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);

 add((X(tim[i])-x11[i])^2,i=1..N)+add((Y(tim[i])-y11[i])^2,i=1..N)+add((Z(tim[i])-z11[i])^2,i=1..N)+add((U(tim[i])-u11[i])^2,i=1..N)

 end proc;

ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.001,.002,.003);

result1 := Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.001,.002,.003]);

x11 := [1.05657970467127, .369307407127487, .400969917393968, .368036162749865, .280389875142339, .280523489139136, .283220960827744, .373941285224253, .378034013792196, .384412762008662, .358678988563716, .350625923673556, .852039817522304, .362240519978640, 1.03197080591829, .343650441408896, .982510654490390, .404544012440991, .422063867224247, 1.20938803285209, .455708586000668, 1.22503869712995, .388259397947667, .472188904769827, 1.31108028794286, 1.19746589728366, .572669348193002];

y11 := [.813920951682113, 10.3546712426210, 2.54581301217449, 10.2617298458172, 3.82022939508992, 3.81119683373741, 3.90918914917183, 10.5831132713329, 10.8700088489538, 11.0218056177585, 10.5857571473115, 9.89034057997145, .271497107157453, 9.77706473740146, 2.23955104698355, 4.16872072216206, .806710906391666, 11.9148193656260, 12.0521411908477, 2.52812993540440, 12.6348841508094, 2.72197067934160, 5.10891266728297, 13.3609183272238, 3.03572692234234, 1.07326033849793, 15.4268962507711];

z11 := [8.93290500985527, 8.96632856524217, 15.8861149154785, 9.16576669760908, 3.20341865536950, 3.11740291181539, 3.22328961317946, 8.71094047480794, 8.60596466961827, 9.15440788281943, 10.2935566768586, 10.5765776143026, 16.3469510439066, 9.36885507010739, 2.20434678689869, 3.88816077008078, 17.9816287534802, 10.1414228793737, 10.7356141216242, 4.00703203725441, 12.0105837616461, 3.77028605914906, 5.01411979976607, 12.7529165152417, 3.66800269682059, 21.2178824031985, 13.9148746721034];

u11 := [5.59, 5.74, 5.49, 5.19, 5.37, 5.56, 5.46, 5.21, 5.55, 5.56, 5.61, 5.91, 5.93, 5.98, 6.28, 6.24, 6.44, 6.58, 6.75, 6.78, 6.81, 7.59, 7.73, 7.75, 7.69, 7.73, 7.79];

k1 := result1[2][1];

k2 := result1[2][2];

k3 := result1[2][3];

k4 := result1[2][4];

k5 := result1[2][5];

k6 := result1[2][6];

k7 := result1[2][7];

k8 := result1[2][8];

k9 := result1[2][9];

k10 := result1[2][10];

k11 := result1[2][11];

k12 := result1[2][12];

a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);

b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);

c1 := Diff(z1(t),t) = k8*x1(t)+ k9*y1(t)+ k10*z1(t)+k12*u1(t);

d1 := Diff(u1(t),t) = 0;

diff_eq := [a1, b1, c1, d1];

sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t), u1(t)], [x1(t), y1(t), z1(t), u1(t)]);

sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t)], [x1(t), y1(t), z1(t), u1(t)]);

ResponsePlot(sys6, Step(), parameters = params);

RootLocusPlot(sys6);

> sys6 := DiffEquation(diff_eq, [], [x1(t), y1(t), z1(t), u1(t)]);

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

> sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t), u1(t)], [x1(t), y1(t), z1(t), u1(t)]); sys6 := DiffEquation(diff_eq, [x1(t), y1(t), z1(t)], [x1(t), y1(t), z1(t), u1(t)]);

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

Error, (in DynamicSystems:-DiffEquation) unrecognized diff-equation type: 9

> ResponsePlot(sys6, Step(), parameters = params); RootLocusPlot(sys6);

Error, invalid input: DynamicSystems:-ResponsePlot expects value for keyword parameter parameters to be of type ({set, list})(name = complexcons), but received params

Error, (in Verify:-CommonExports) system object is not a module