Hey there,

I've a numerical solved system of differential equations, which depend on one argument and one index. I can solve it, but when I try plot it I have this error: Error, (in plot) two lists or Vectors of numerical values expected.

Could anyone help me figure out what I'm doing wrong?

> restart;
> A := 115.1558549; B := .3050464658; n := 3; f0 := 0.5e-4;
               
>f:=theta->f0*(cos(arcsin(sin(theta)/n)))^2;
  I0:=Ir(z)+sum(Is[k](z),k=1..20);

> alpha := [0, 1, 2, 3, 4, 5, 6];

Theta := [3*Pi*(1/180), 6*Pi*(1/180), 9*Pi*(1/180), 12*Pi*(1/180), 15*Pi*(1/180), 18*Pi*(1/180), 21*Pi*(1/180), 24*Pi*(1/180), 27*Pi*(1/180), 30*Pi*(1/180), 33*Pi*(1/180), 36*Pi*(1/180), 39*Pi*(1/180), 42*Pi*(1/180), 45*Pi*(1/180), 48*Pi*(1/180), 51*Pi*(1/180), 54*Pi*(1/180), 57*Pi*(1/180), 60*Pi*(1/180)];

>G:= theta->A*sin(theta)*cos(2*arcsin((sin(theta)/n)))/((1+sin(theta)^2/B^2)*cos(arcsin(sin(theta)/n)));

>for j from 1 to 7 do
d1 := diff(Ir(z), z) = -sum(G(Theta[k])*Ir(z)*Is[k](z)/I0,k=1..20)-alpha[j]*Ir(z)-sum(f(Theta[k])*Ir(z),k=1..20):
d2 := diff(Is[1](z), z) = G(Theta[1])*Ir(z)*Is[1](z)/I0-alpha[j]*Is[1](z)+f(Theta[1])*Ir(z):
d3 := diff(Is[2](z), z) = G(Theta[2])*Ir(z)*Is[2](z)/I0-alpha[j]*Is[2](z)+f(Theta[2])*Ir(z):
d4 := diff(Is[3](z), z) = G(Theta[3])*Ir(z)*Is[3](z)/I0-alpha[j]*Is[3](z)+f(Theta[3])*Ir(z):
d5 := diff(Is[4](z), z) = G(Theta[4])*Ir(z)*Is[4](z)/I0-alpha[j]*Is[4](z)+f(Theta[4])*Ir(z):
d6 := diff(Is[5](z), z) = G(Theta[5])*Ir(z)*Is[5](z)/I0-alpha[j]*Is[5](z)+f(Theta[5])*Ir(z):
d7 := diff(Is[6](z), z) = G(Theta[6])*Ir(z)*Is[6](z)/I0-alpha[j]*Is[6](z)+f(Theta[6])*Ir(z):
d8 := diff(Is[7](z), z) = G(Theta[7])*Ir(z)*Is[7](z)/I0-alpha[j]*Is[7](z)+f(Theta[7])*Ir(z):
d9 := diff(Is[8](z), z) = G(Theta[8])*Ir(z)*Is[8](z)/I0-alpha[j]*Is[8](z)+f(Theta[8])*Ir(z):
d10 := diff(Is[9](z), z) = G(Theta[9])*Ir(z)*Is[9](z)/I0-alpha[j]*Is[9](z)+f(Theta[9])*Ir(z):
d11 := diff(Is[10](z), z) = G(Theta[10])*Ir(z)*Is[10](z)/I0-alpha[j]*Is[10](z)+f(Theta[10])*Ir(z):
d12 := diff(Is[11](z), z) = G(Theta[11])*Ir(z)*Is[11](z)/I0-alpha[j]*Is[11](z)+f(Theta[11])*Ir(z):
d13 := diff(Is[12](z), z) = G(Theta[12])*Ir(z)*Is[12](z)/I0-alpha[j]*Is[12](z)+f(Theta[12])*Ir(z):
d14 := diff(Is[13](z), z) = G(Theta[13])*Ir(z)*Is[13](z)/I0-alpha[j]*Is[13](z)+f(Theta[13])*Ir(z):
d15 := diff(Is[14](z), z) = G(Theta[14])*Ir(z)*Is[14](z)/I0-alpha[j]*Is[14](z)+f(Theta[14])*Ir(z):
d16 := diff(Is[15](z), z) = G(Theta[15])*Ir(z)*Is[15](z)/I0-alpha[j]*Is[15](z)+f(Theta[15])*Ir(z):
d17 := diff(Is[16](z), z) = G(Theta[16])*Ir(z)*Is[16](z)/I0-alpha[j]*Is[16](z)+f(Theta[16])*Ir(z):
d18 := diff(Is[17](z), z) = G(Theta[17])*Ir(z)*Is[17](z)/I0-alpha[j]*Is[17](z)+f(Theta[17])*Ir(z):
d19 := diff(Is[18](z), z) = G(Theta[18])*Ir(z)*Is[18](z)/I0-alpha[j]*Is[18](z)+f(Theta[18])*Ir(z):
d20 := diff(Is[19](z), z) = G(Theta[19])*Ir(z)*Is[19](z)/I0-alpha[j]*Is[19](z)+f(Theta[19])*Ir(z):
d21 := diff(Is[20](z), z) = G(Theta[20])*Ir(z)*Is[20](z)/I0-alpha[j]*Is[20](z)+f(Theta[20])*Ir(z):
dsys := {d1, d10, d11, d12, d13, d14, d15, d16, d17, d18, d19, d2, d20, d21, d3, d4, d5, d6, d7, d8, d9}:
dSol[j] := dsolve({op(dsys), Ir(0) = 1, Is[1](0) = 0.1e-1, Is[2](0) = 0.1e-1, Is[3](0) = 0.1e-1, Is[4](0) = 0.1e-1, Is[5](0) = 0.1e-1, Is[6](0) = 0.1e-1, Is[7](0) = 0.1e-1, Is[8](0) = 0.1e-1, Is[9](0) = 0.1e-1, Is[10](0) = 0.1e-1, Is[11](0) = 0.1e-1, Is[12](0) = 0.1e-1, Is[13](0) = 0.1e-1, Is[14](0) = 0.1e-1, Is[15](0) = 0.1e-1, Is[16](0) = 0.1e-1, Is[17](0) = 0.1e-1, Is[18](0) = 0.1e-1, Is[19](0) = 0.1e-1, Is[20](0) = 0.1e-1}, [Ir(z), Is[1](z), Is[2](z), Is[3](z), Is[4](z), Is[5](z), Is[6](z), Is[7](z), Is[8](z), Is[9](z), Is[10](z), Is[11](z), Is[12](z), Is[13](z), Is[14](z), Is[15](z), Is[16](z), Is[17](z), Is[18](z), Is[19](z), Is[20](z)], numeric);
end do:

>for j from 1 to 7 do
dSol[j](0.4);
as:='as':
for l from 1 to 20 do
as[l]:=[Theta[l],rhs(dSol[j](0.4)[2+l])];
od:
plo[j]:=convert(as,listlist);
od:

>plot(plo[2],plo[1]);
Error, (in plot) two lists or Vectors of numerical values expected

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).

Hello everyoene, please i have a problem solving this delay differential equation:

y'(x)=cos(x)+y(y(x)-2)    0<x<=10

y(x)=1      x<=0

tau=x-y(x)+2

please i need the solution urgently

i need to find how many rows and how many columns has a matrix that i just imported so i don't have to use readstat so it will be more automatic.

m1 := ImportMatrix("Matrix1.txt");
F := readstat("rows of the matrix");
C := readstat("columns of the matrix)")

LAG := C-1;
LAGG := F-1

for a to LAG do
for v to F do
for i to C-a do
h := m1(v, i);
r := m1(v, i+a);
..
..
.
.
in mathlab we use 

a=load('BROOKER.dat'); 

[m,n]=size(a);

but in maple? please help

Here my worksheet that at the end of it I have a problem with the dsolve when solving an ode system. and the error is 

Error, (in StringTools:-IsPrefix) second argument must be a string

I know that the dsolve has problem with bracket . Then how can I fix it or how can I change my codes.

 optimal.mwoptimal.mw

why can not draw graph in maple in this case and how to plot graph with matlab in maple

with(StringTools);
with(FileTools);
with(Matlab);
openlink();
evalM(sprintf("load fisheriris;X = meas(:,3:4);figure;plot(X(:,1),X(:,2),'k*','MarkerSize',5);"));
closelink();

Dear, I want to the expression for any r and s. Please help I am waiting your quick responce

Help.mw

With my best regards and sincerely.

Govt. Degree College Taxila

Dear, I am facing a problem which I run the attached file it this answer [Length of output exceeds limit of 1000000]. Please help to overcome this problem.

ytsf3.mw

With my best regards and sincerely.

Govt. Degree College Taxila

Hi, I solved some equations those days and get a group of data, namely, Data1. Then I want to get the function of the data, so I use the CurveFitting package of maple, and get the function easily (the function seems as a*x^3+b*x^2+c*x+d). But the function is not the one I really wanted, because it is hard to generate the complex curve (even the function is known) in some software. 

As I know, it is easily to generate some arcs in the software, so is there any way to fit a group of data with some piecewise of arcs?

 Best regards.

Data1:= [[.690499054221957, .109364306247567], [.679584570047867, 0.955093827253927e-1], [.668476295825779, 0.820785684569687e-1], [.657171143364362, 0.690714704619819e-1], [.645665768347822, 0.564884351571898e-1], [.633956566493958, 0.443305616055764e-1], [.622039668654294, 0.325997176601303e-1], [.609910934797136, 0.212985591645471e-1], [.597565946804089, 0.104305524003572e-1], [.585, 0], [.572208093323944, -0.998792942142104e-2], [.559184918035503, -0.195271676259796e-1], [.545924844835652, -0.286107087732754e-1], [.532421909264435, -0.372305667237386e-1], [.518669795218710, -0.453777271949494e-1], [.504661816411590, -0.530420942817277e-1], [.490390895570740, -0.602124307834357e-1], [.475849541144774, -0.668762917052363e-1], [.461029821255068, -0.730199502124052e-1]]

1. how to eliminate the diff(*(x,y,z),x) terms in an expression, "*" means any function which have independent variables x,y,z?

2. how to get the gradient of a vector, which should be a tensor?

Hi all,

I'm trying to create the 3D animation which can show the idea of rotating 2D function plot, such as:

with(plots):

display(seq(surfdata([seq([seq([x, cos(2*p*Pi*(1/25))*x^(1/2), -sin(2*p*Pi*(1/25))*x^(1/2)], x = 0 .. 4, .1)], p = 0 .. t)]), t = 1 .. 25), insequence = true);

But it's too inconvenient because of too many seq functions in this commond, is there any easier way to plot this animatiton?

Thank you.

Hi,

I am experiencing some problems with the plot3d command. It does not return a nice 3d-graph, but just a bunch of dashed lines. I have entered something like this:

with(plots):

plot3d(x*y,x=-1..1,y=-1..1);

I am using maple 17 on windows 7

Thanks in advance.

Int(ln(1+sqrt((x+1)/x)),x);

value(%);

Does not work.

Int(ln(2+sqrt((x+1)/x)),x);
value(%);

Works.

But with some effect,

Could this possibly be improved in the next release?

Ok guys this is the problem i have a matrix wich is really the result of a semivariogram so it is like this 
thi is my semivariogram so i have to find the best model and fit it to it, i can't just throw a polynomial it has to be
spherical= h:= C((3/2)*x/a-(1/2)*x^3/a^3) 
expotencial=
Lineal= y:= p*x
or y:=p*x^a

so i want the maple to show me the variogram plot and the i select wich one of the models i will apply.
the problem is that i don't know how to apply the models so started something that could maybe lead to the values of C and A for the spherical and the xpotencial becouse the others too are easy.
------------------------------------------------------------------.--------------------------------------------------------
restart;
with(plots);
with(CurveFitting);
m3 := Matrix([[0, 0], [1, 2], [2, 5], [3, 7], [4, 10], [5, 14], [6, 15], [7, 15.4], [8, 15.8], [9, 16], [10, 16.4]]);
plot(m3);
Upsilon := C(1-exp(-x/a));
Upsilon := C((3/2)*x/a-(1/2)*x^3/a^3);
for C to 16 do
for a to 100 do
for x to 11 do
H := m3(x, 2);
R[C, a, x] := abs(Upsilon-H)
end do
end do
end do;
for r to 16 do
for j to 100 do
N[r, j] := sum(R[r, j, X], X = 1 .. 11);
if N[r, j] < 55 then
print(r, j)
end if
end do
end do;
k := 14*(3/2*((1/16)*xx)-(1/2)*xx^3/16^3);
multiple(plot, [m3, color = "Green"], [k, xx = 0 .. 11, color = "Blue"])
----------------------------------------------------------...................---------------------------------------
so in this code i rest the values of the model and the values of the matrix for differents C and a so i pick the min of the Sum to see wich C and a give me the min value but i didn't work quite well first is difficult to get the C and a and sometimes the new curve is just not similir to the semivariogram (Matrix) please help i tried 
k := NonlinearFit(C((3/2)*x/a-(1/2)*x^3/a^3), X, Y, x)
and 
k:=LeastSquares`(m3, v, curve = C*(1-exp(-x/a)))
but they don't let me because they aint linear on the parameters
please help 
if you are interested in this topic here is what i am trying to do but explained really well is for geological matters
http://www.kriging.com/PG1979/index.htm#Chapter_2+Part1

if want to help me use this matrix 
m3:= Matrix([[0, 0], [1, 1], [2, 3], [3, 5], [4, 7], [5, 8], [6, 9], [7, 10], [8, 10.5], [9, 10], [10, 9.8], [11, 9.8], [12, 10.5], [13, 10.89], [14, 11.2], [15, 10.6], [16, 9.85], [17, 9.45], [18, 9.77], [19, 10.15], [20, 10.7], [21, 10.04], [22, 10], [23, 10.85], [24, 10.7], [25, 10.94], [26, 10.81], [27, 10.33]])
for that matrix the spherical model is the best i know

goodbye

Developed and then implemented with open code components. It is very important to note this post is held for students of civil engineering and mechanics. Using advanced mathematical concepts to concepts in engineering.

Metodos_Energeticos_full.mw

(in spanish)

Atte.

L.Araujo.C