FirstEigenVector := Matrix(3, 1, {(1, 1) = -.736895432967255+0.*I, (2, 1) = -.588906969844997+0.*I, (3, 1) = -.331924240964690+0.*I});
SecondEigenVector := Matrix(3, 1, {(1, 1) = -.589856901397123+0.*I, (2, 1) = .320280857681335+0.*I, (3, 1) = .741275257969058+0.*I});
ThirdEigenVector := Matrix(3, 1, {(1, 1) = .330233185410229+0.*I, (2, 1) = -.742030156443046+0.*I, (3, 1) = .583384341736151+0.*I});
LHS := ProjOfEigenVector;
LHS := Matrix(3, 3, {(1, 1) = -.736895432967255+0.*I, (1, 2) = -.589856901397123+0.*I, (1, 3) = .330233185410229+0.*I, (2, 1) = -.588906969844997+0.*I, (2, 2) = .320280857681335+0.*I, (2, 3) = -.742030156443046+0.*I, (3, 1) = -.331924240964690+0.*I, (3, 2) = .741275257969058+0.*I, (3, 3) = .583384341736151+0.*I});
RHS := c1*FirstEigenVector+c2*SecondEigenVector+c3*ThirdEigenVector;
RHS := Matrix(3, 1, {(1, 1) = (-.736895432967255+0.*I)*c1+(-.589856901397123+0.*I)*c2+(.330233185410229+0.*I)*c3, (2, 1) = (-.588906969844997+0.*I)*c1+(.320280857681335+0.*I)*c2+(-.742030156443046+0.*I)*c3, (3, 1) = (-.331924240964690+0.*I)*c1+(.741275257969058+0.*I)*c2+(.583384341736151+0.*I)*c3});
solve([LHS[1][1] = RHS[1][1], LHS[2][2] = RHS[2][1], c1^2+c2^2+c3^2 = 1], [c1, c2, c3]);

after calculated the projection matrix, 

it is a 3*3 matrix on left hand side

however, combination of eigenvectors on right hand side is 3*1 matrix

when calculated c1,c2,c3 under the condition c1^2+c2^2+c3^2 = 1

how to know whether LHS[1][1] = RHS[1][1], or LHS[1][2] = RHS[1][1] or

LHS[1][3] = RHS[1][1]

How to create a borel set from a list of decimal

if i interpolate three decimal number and solve it, 

if any number substitute into this result which is a inverse function, can the results be said borel set?

with(LinearAlgebra):
t:=1;
NewMatrix3 := Matrix([[test10, close3(t) , close3(t+1)],
[close3(t) , close3(t+1) ,0],
[close3(t+1) , 0,0]]);

Matrix(3, 3, {(1, 1) = test10, (1, 2) = 5.59, (1, 3) = 5.74, (2, 1) = 5.59, (2, 2) = 5.74, (2, 3) = 0, (3, 1) = 5.74, (3, 2) = 0, (3, 3) = 0})

NewEigenMatrix := Eigenvalues(NewMatrix3);
solve([MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[1][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[2][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[2][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[x],[y],[z]]))[3][1] = NewEigenMatrix[1]* Matrix([[x],[y],[z]])[3][1]]
, [x,y,z]);

When i look into 'maple help' for Pade approximation, it only show a code for solving equation involving 1 variable only..what is the code for equation involving 2 or more variable for pade approximation?

Hi everyone

I'd be pleased if you could give a hand with the exploration assistant.

1. I want the exploration assistant to appear on the same document I am working on, but everytime I use it (either by right-clicking or by the explore command) it automatically appears on a new document.

2. can I manipulate a piecewise function when using embedded components? i.e.: plot the function and varying the parameters using sliders.

thanks

cesar

I have made a maplet. The aim is to take two numbers in textboxes and find their Jacobi symbol. The result should appear in a third textbox. Now I have done all the steps and called a procedure on buttonclick. Following is the procedure I have made

jacob := proc (x, y)

local A, B;

A := x;

B := y;

with(numtheory);

jacobi(A, B)

end proc:

Problem: The problem is that when I make any small modification to the code it runs and shows the result in the 3rd textbox but as soon as I save it, restart maple and recompile the program, the textbox 3 will show jacobi(value of textbox1, value of textbox2) instead of the result. What should I do, actually I am new to maple. Please guide me.

k := a*x6^7 + b*x6^6 + c*x6^5 + d*x6^4 + e*x6^3 + f*x6^2 + g*x6;
discrim(k, x6);

after know the discriminant equation, how to do next?

solve(Max(Min(x, 1), Min(x, 2)));
solve(Min(Max(x, 1), Max(x, 2)));

i do not know how to use Rootof something

any other expression

Please, I solved a pde system of equation problem numerically, using maple 17.

But I dont know how to plot multiple solutions on one graph.

I want to vary one of the parameters....

e.g Pr=0.71, Pr=7, Pr=10 where other parameters are kept constant

My working is attachedtobi_msc_solution.mw

Download tobi_msc_solution.mw

Please, Any help will be gracefully appreciated

I am solving a system of 8 boundary value differential equations with boundary conditions:

> restart; with(plots);
 eq1 := alpha*(F(eta)+(1/2)*eta*(diff(F(eta), eta)))+F(eta)*F(eta)-G(eta)*G(eta)+H(eta)*(diff(F(eta), eta))-(diff(F(eta), `$`(eta, 2)))-beta*(f(eta)-Q(eta)*F(eta)) = 0;

 eq2 := alpha*(G(eta)+(1/2)*eta*(diff(G(eta), eta)))+2*F(eta)*G(eta)+H(eta)*(diff(G(eta), eta))-(diff(G(eta), `$`(eta, 2)))-beta*(g(eta)-Q(eta)*G(eta)) = 0;

 eq3 := (1/2)*alpha*(H(eta)+eta*(diff(H(eta), eta)))+H(eta)*(diff(H(eta), eta))+diff(P(eta), eta)-(diff(H(eta), `$`(eta, 2)))-beta*(h(eta)-Q(eta)*H(eta)) = 0;

 eq4 := alpha*((Q(eta)*Q(eta))*f(eta)+((1/2)*eta*Q(eta)*Q(eta))*(diff(f(eta), eta))-(1/2)*eta*Q(eta)*f(eta)*(diff(Q(eta), eta)))+Q(eta)*f(eta)*f(eta)-Q(eta)*g(eta)*g(eta)+h(eta)*Q(eta)*(diff(f(eta), eta))-h(eta)*f(eta)*(diff(Q(eta), eta))+beta*((Q(eta)*Q(eta))*f(eta)-(Q(eta)*Q(eta))*Q(eta)*F(eta)) = 0;

 eq5 := alpha*((Q(eta)*Q(eta))*g(eta)+((1/2)*eta*Q(eta)*Q(eta))*(diff(g(eta), eta))-(1/2)*eta*Q(eta)*(diff(g(eta), eta))*(diff(Q(eta), eta)))+2*Q(eta)*f(eta)*g(eta)+h(eta)*Q(eta)*(diff(g(eta), eta))-h(eta)*g(eta)*(diff(Q(eta), eta))+beta*((Q(eta)*Q(eta))*g(eta)-(Q(eta)*Q(eta))*Q(eta)*G(eta)) = 0;

 eq6 := (1/2)*alpha*((Q(eta)*Q(eta))*h(eta)+(eta*Q(eta)*Q(eta))*(diff(h(eta), eta))-eta*h(eta)*Q(eta)*(diff(Q(eta), eta)))+Q(eta)*h(eta)*(diff(h(eta), eta))-(h(eta)*h(eta))*(diff(Q(eta), eta))+beta*((Q(eta)*Q(eta))*h(eta)-(Q(eta)*Q(eta))*Q(eta)*H(eta)) = 0;

 eq7 := 2*F(eta)+diff(H(eta), eta) = 0;

 eq8 := 2*f(eta)+diff(h(eta), eta) = 0;
bc := {F(0) = 1, G(0) = 1, H(0) = 0, F(8) = 0, G(8) = 0, f(8) = 0, g(8) = 0, h(8)-.2*H(8) = 0, Q(8) = .2, P(8) = 0};

sys:={bc, eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8};

para:= {alpha=0.5, beta=0.5};

A1 := dsolve(subs(para, {bc, eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8}), numeric, method = bvp[midrich], output = array([seq(0.1e-1*i, i = 0 .. 100*N)]))

But i am getting the error

"Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system".

I can't understand where is the problem. Please help

Hi,
i am trying to built a maplet which can encode and decode.  for example i have Ceasar encryption codes and i want to built a maplet that can do it. 

you can see below one of my try: encode is working but decode didnt work :/ what should i do?

restart:
with(Maplets[Elements]):
with(StringTools):

alphabet := convert([97, 98, 99, 231, 100, 101, 102, 103, 240, 104, 253, 105, 106, 107, 108, 109, 110, 111, 246, 112, 114, 115, 254, 116, 117, 252, 118, 121, 122],bytes): 

code:= letter -> SearchText(letter,alphabet)-1:
char := i -> alphabet[i+1]:
modulus := Length(alphabet): 
shift := proc(key);
i -> (i+key) mod modulus;
end:

CaesarEnc :=()-> Action(Evaluate('cpmessage'= 'Implode(map(char,map(shift('ky'),map(code,Explode('text')))))')):

CaesarDec := () -> Action(Evaluate('cpmessage' = 'CaesarEnc(-'ky','text')')):

Caesar := Maplet(Window('title'= "Caesar Encoding And Decoding", BoxLayout['BL1']( BoxColumn('halign'=left,
BoxRow(Label['l1']("Write message: ",'width'=100,'halign'=left), TextBox['text']('background'=white,'foreground'= brown,'height'=6,'editable'=true,'width'=50)),BoxRow(Label['l2']("Key: ",'width'=100,'halign'=left), TextBox['ky']('background'=white,'foreground'= black,'height'=3,'editable'=true,'width'=50)),Button("Encode",'onclick'=CaesarEnc()), Button("Decode",'onclick'=CaesarDec()),BoxRow(Label['l3']("Text: ",'width'=100,'halign'=left), TextBox['cpmessage']("",'background'=white,'foreground'= blue,'height'=6,'editable'=false,'width'=50) ))))):
Maplets[Display](Caesar);

i need to do it for my thesis. waiting for your answers, thank you :)

hey i am new here and i have a question,

i have an partial differential equation diff(u(t,x),t$2)=diff(u(t,x),x$2) with the intial value problem u(0,x)=f(x)=1/(1+x^2) and diff(u(0,x),t)=0

and now my question i have already programm it:

> with(inttrans);

with(DEtools);

with(plots);

> with(PDETools);

> k := diff(u(t, x), `$`(t, 2)) = diff(u(t, x), `$`(x, 2));
bc := u(0, x) = 1/(1+x^2);
v := diff(u(0, x), t) = 0;
d / d \ d / d \
--- |--- u(t, x)| = --- |--- u(t, x)|
dt \ dt / dx \ dx /
1
u(0, x) = ------
2
1 + x
0 = 0

> pdsolve(k, u(t, x));
print(`output redirected...`);
u(t, x) = _F1(x + t) + _F2(x - t)

> c := pdsolve({bc, k, v}, u(t, x));
print(`output redirected...`); # input placeholder

 and now question at the last there is nothing does it means that maple can´t solve it with the intial value problem and how can solve it with Fourier-Transformation to x???

can anyone help me please and sorry my englisch is not so good ;)

expect to calculate a eigenvector in terms of variable test10

close3 are decimal value

> NewMatrix3 := Matrix([[test10, close3(t), close3(t+1), close3(t+2), close3(t+3), close3(t+4)], [close3(t), close3(t+1), close3(t+2), close3(t+3), close3(t+4), close3(t+5)], [close3(t+1), close3(t+2), close3(t+3), close3(t+4), close3(t+5), 0], [close3(t+2), close3(t+3), close3(t+4), close3(t+5), 0, 0], [close3(t+3), close3(t+4), close3(t+5), 0, 0, 0], [close3(t+4), close3(t+5), 0, 0, 0, 0], [close3(t+5), 0, 0, 0, 0, 0]]); New_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(NewMatrix3), NewMatrix3));

Error, (in LA_Main:-Eigenvectors) cannot determine if this expression is true or false: abs(149.8198+5.59*Re(test10))+27.38*abs(Im(test10))+abs(118.8174+5.74*Re(test10))+abs(90.3603+5.49*Re(test10))+abs(61.9327+5.19*Re(test10))+abs(31.0804+5.37*Re(test10)) < (1/10)*abs(149.8198+5.59*Re(test10))+2.738000000*abs(Im(test10))+(1/10)*abs(118.8174+5.74*Re(test10))+(1/10)*abs(90.3603+5.49*Re(test10))+(1/10)*abs(61.9327+5.19*Re(test10))+(1/10)*abs(31.0804+5.37*Re(test10))

Hello, 

I have a trigonometric equation.

I would like to isolate gamma[1](t) and to determine gamma[1](t) in fonction of alpha(t), beta(t) and z(t). The others variables in the equations are fixed parameters.

I have tried to use isolate function. But it doesn't work.

Of course, my expressions should be complex but that is not a problem if i manage to expresse gamma[1](t) in fonction of alpha(t), beta(t) and z(t).

Here my program

constraints_2.mw

Thank you for you help

Hello, could you give me ideas with such challenge? I have created my model in MapleSim and want to check correctness of the scheme. I need to get values of block variable. by default maplesim displays results as a graph and i do not see what is real value. How I can get these values?