@Markiyan Hirnyk 

same error even if using <= and >=

x11 := [0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]:
y11 := [ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]:
z11 := [ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]:
u11 := [7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7,8,7];
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) >= k9*x1(t)+ k10*y1(t)+ k11*z1(t)+k12*u1(t);
d1 := Diff(u1(t),t) >= 0;
a2 := Diff(x1(t),t) <= k1*x1(t)+ k2*y1(t)+ k3*z1(t)+k4*u1(t);
b2 := Diff(y1(t),t) <= k5*x1(t)+ k6*y1(t)+ k7*z1(t)+k8*u1(t);
c2 := Diff(z1(t),t) <= k9*x1(t)+ k10*y1(t)+ k11*z1(t)+k12*u1(t);
d2 := Diff(u1(t),t) <= 0;

ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1],u1(1)=u11[1];
sol:=dsolve({a1,b1,c1,d1, a2,b2,c2,d2,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,.003,.003,.003);
result1 := Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance=0.01);

@Markiyan Hirnyk 

is it only for equation has <= ? can not use = ?

Error, (in Optimization:-NLPSolve) feasibilitytolerance option is accepted for constrained problems only

result1 := Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003], feasibilitytolerance = 0.01);
Error, (in Optimization:-NLPSolve) feasibilitytolerance option is accepted for constrained problems only

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) = k9*x1(t)+ k10*y1(t)+ k11*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[1];

@Kitonum 

i still do not know the calculation of representation after reading wiki

i googled some homormophism algorithms however difficult, 

how to do these in maple?

just expect one of application such as fourier analysis on finite group

@Kitonum 

find representation of a matrix group

homomorphism

G -> GL(V) where V is vector space

any book teach how to calculate this? so far, i find no books mention it clearly

which algorithm can do this?

i do not understand what is GL, how vector space input into GL?

after this, does this arrow represent  Hom(G, GL(V))?

@Preben Alsholm 

how about how to set feaibility tolerance as i can not find an example in google

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

@Preben Alsholm 

success,

thank you very much

@Preben Alsholm 

when meeting non-numeric result encountered

how to deal with this error?

> Optimization:-Minimize(ans, initialpoint = [0.1e-2, 0.2e-2, 0.3e-2, 0.1e-2, 0.2e-2, 0.3e-2, 0.1e-2, 0.2e-2, 0.3e-2]);
Error, (in Optimization:-NLPSolve) non-numeric result encountered
> Optimization:-Minimize(ans, initialpoint = [0.1e-2, 0.2e-2, 0.3e-2, 0.1e-2, 0.2e-2, 0.3e-2, 0.1e-2, 0.2e-2, 0.3e-2], method = nonlinearsimplex, evaluationlimit = 1000);
Error, (in Optimization:-NLPSolve) non-numeric result encountered

@Preben Alsholm 

Error, (in ans) unable to execute add

Error, (in Optimization:-NLPSolve) unable to execute add

in maple 12, does it need maple 17?

x11 := [0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]:
y11 := [ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]:
z11 := [ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]:
a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t);
b1 := Diff(y1(t),t) = k4*x1(t)+ k5*y1(t)+ k6*z1(t);
c1 := Diff(z1(t),t) = k7*x1(t)+ k8*y1(t)+ k9*z1(t);
ICS:=x1(1)=x11[1],y1(1)=y11[1],z1(1)=z11[1];
sol:=dsolve({a1,b1,c1,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9]);
tim := [seq(n, n=1..27)];
ans:=proc(k1,k2,k3,k4,k5,k6,k7,k8,k9)
sol(parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9]);
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)
end proc;
ans(.001,.002,.003,.001,.002,.003,.001,.002,.003);
Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003]);

@Carl Love 

https://skydrive.live.com/redir?resid=E0ED7271C68BE47C%21443

@Carl Love 

After tried your method, it succeed, you are really a Maple expert of expert

Then, i try my own idea
1.
Error [Length of output exceeds limit of 1000000] when i try my own method with subs after permutate, how to increase this limit?

> with(combinat); list6 := permute([seq(k, k = 1 .. 512)], 2);
[Length of output exceeds limit of 1000000]

list7 := Matrix(nops(list6), 1);
for n from 1 to nops(list6) do
temp1 := list6[n];
for k from 1 to nops(list1a)*nops(list3) do
temp1 := subs(k=list5[k],temp1);
od;
list7[count] := temp1;
count := count + 1;
od;

2.
Only 3*3 matrix already got so much limitation, i feel that my computer's computation power is not enough for dimension more than 3 such as 5*5, 6*6 ....etc

what is the maximum dimension of maple that can do in my whole question?

i see that it seems i can use your method to revise previous steps

are there distribution computing for maple running on several computers?

 3.

in order to get all combination for dimension 5, it runs a very long time

i do not prove whether permutate n*n items to get all combinations, 

by observation, dimension 3 work for it.

with(combinat):
list1 := permute([a, b, a, b, a, b], 3);
list1a := subs(b=1,subs(a=0, list1));
n := 5;
list1a := permute([seq(seq(k,k=0..1),k2=1..n)], n);
list2 := permute([a, b, c, d, e, f, g, h, a, b, c, d, e, f, g, h, a, b, c, d, e, f, g, h], 3);
list3 := permute([seq(seq(k,k=11..18),k2=1..3)], 3);
Iter:= iterstructs(Permutation([seq(seq(k,k=11..(10+nops(list1a))),k2=1..n)]), size=n):
list3b := [];
while not Iter[finished] do
p:= Iter[nextvalue]();
list3b := [p, op(list3b)];
end do:

@Carl Love 

how to use these command in this case? any example?

@acer 

list6 := permute(convert(list5,list), 2);

Kernel connection has been lost

Execution stopped : Memory allocation failed

Please see ?alloc for more detail

what should i do for intel Core i5 3317U CPU @ 1.7HGHz 8GB memory 7.71 can used

64bits opearating system window 8

@nm I used maple 15

this example I copy a Chinese book, may be example is wrong, you can do with similar direction, not need exactly the same

@Thomas Richard 

i just set number formating to decimal places 5, and then i set back to None now.

actually there is no setting i made.

you can look at the picture i uploaded, it is a real bug in maple 12.0

@acer 

after using [] , it is correct now.

i never dare to use {} any more