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? 

In his article “Subscripts as Partial Differentiation Operatuuors” , rlopez 1228 showed us a way to denote partial derivatives by repeat subscripts. For example, the sixth derivative of u(x,y) with respect to x will be denoted by u_{x,x,x,x,x,x}.

Is there a way to make the notation u_{x,x,x,x,x,x} even shorter by u_{6x}?

In the same way mixed derivatives u_{x,x,x,y,y,y,y} will be denoted as u_{3x,4y}, etc.

Thank you very much!

superposition said that a vector is a linear combination of other vectors

but even if i calculated the coefficient, i do not know which vector is which other vectors's linear combination

how to prove?

InputMatrix3 := Matrix([[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) , close3(t+6)],
[close3(t+2) , close3(t+3) , close3(t+4) , close3(t+5) , close3(t+6) , 0],
[close3(t+3) , close3(t+4) , close3(t+5) , close3(t+6) , 0 , 0],
[close3(t+4) , close3(t+5) , close3(t+6) , 0 , 0 , 0],
[close3(t+5) , close3(t+6) , 0 , 0 , 0, 0],
[close3(t+6) , 0 , 0 , 0, 0, 0]]):
EigenValue1 := Eigenvalues(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)):
Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)):
AEigenVector[tt+1] := Asso_eigenvector;

Matrix(6, 6, {(1, 1) = .514973850028629+0.*I, (1, 2) = .510603608194333+0.*I, (1, 3) = .469094659512372+0.*I, (1, 4) = .389872713818831+0.*I, (1, 5) = .279479324327359+0.*I, (1, 6) = -.154682461176604+0.*I, (2, 1) = .493994413154560+0.*I, (2, 2) = .306651336822139+0.*I, (2, 3) = -0.583656699197969e-1+0.*I, (2, 4) = -.417550308930506+0.*I, (2, 5) = -.566122865008542+0.*I, (2, 6) = .404579494288380+0.*I, (3, 1) = .449581541124671+0.*I, (3, 2) = -0.266751368453398e-1+0.*I, (3, 3) = -.529663398913996+0.*I, (3, 4) = -.359719616523673+0.*I, (3, 5) = .313717798014566+0.*I, (3, 6) = -.537405340038665+0.*I, (4, 1) = .386952162293470+0.*I, (4, 2) = -.351332186748244+0.*I, (4, 3) = -.390816901794187+0.*I, (4, 4) = .470032416161955+0.*I, (4, 5) = .231969182174424+0.*I, (4, 6) = .547134073332474+0.*I, (5, 1) = .306149178348317+0.*I, (5, 2) = -.530611390076568+0.*I, (5, 3) = .192717713961280+0.*I, (5, 4) = .291213691618787+0.*I, (5, 5) = -.562991429686901+0.*I, (5, 6) = -.431067688369314+0.*I, (6, 1) = .212576094920847+0.*I, (6, 2) = -.489443150196337+0.*I, (6, 3) = .553283259136031+0.*I, (6, 4) = -.488381938231088+0.*I, (6, 5) = .363604594054259+0.*I, (6, 6) = .195982711855368+0.*I})

Matrix(6, 6, {(1, 1) = .515428842592397+0.*I, (1, 2) = .515531996615269+0.*I, (1, 3) = .468108280940919+0.*I, (1, 4) = -.392394120975052+0.*I, (1, 5) = -.280467124908196+0.*I, (1, 6) = -.129613084502380+0.*I, (2, 1) = .494563493180197+0.*I, (2, 2) = .301273494494509+0.*I, (2, 3) = -0.622136916501293e-1+0.*I, (2, 4) = .438383262732459+0.*I, (2, 5) = .571041594120088+0.*I, (2, 6) = .377494770878435+0.*I, (3, 1) = .450886315308369+0.*I, (3, 2) = -0.323387895921418e-1+0.*I, (3, 3) = -.527636820417566+0.*I, (3, 4) = .332744872607714+0.*I, (3, 5) = -.322934536375586+0.*I, (3, 6) = -.549772001891837+0.*I, (4, 1) = .385916641681991+0.*I, (4, 2) = -.352066020655722+0.*I, (4, 3) = -.389655495441319+0.*I, (4, 4) = -.450049711766943+0.*I, (4, 5) = -.221529986447276+0.*I, (4, 6) = .568916672007495+0.*I, (5, 1) = .305485655770791+0.*I, (5, 2) = -.528766119966973+0.*I, (5, 3) = .201065789602278+0.*I, (5, 4) = -.310329356773806+0.*I, (5, 5) = .555973984740943+0.*I, (5, 6) = -.425730045170186+0.*I, (6, 1) = .210210489500614+0.*I, (6, 2) = -.488744465076970+0.*I, (6, 3) = .553484076328700+0.*I, (6, 4) = .494245653290329+0.*I, (6, 5) = -.364390406353340+0.*I, (6, 6) = .183130120876843+0.*I})
mm1 := 1;
solve(
[AEigenVector[mm1][2][1][6] = m1*AEigenVector[mm1][2][1][1]+m2*AEigenVector[mm1][2][1][2]+m3*AEigenVector[mm1][2][1][3]+m4*AEigenVector[mm1][2][1][4]+m5*AEigenVector[mm1][2][1][5],
AEigenVector[mm1][2][2][6] = m1*AEigenVector[mm1][2][2][1]+m2*AEigenVector[mm1][2][2][2]+m3*AEigenVector[mm1][2][2][3]+m4*AEigenVector[mm1][2][2][4]+m5*AEigenVector[mm1][2][2][5],
AEigenVector[mm1][2][3][6] = m1*AEigenVector[mm1][2][3][1]+m2*AEigenVector[mm1][2][3][2]+m3*AEigenVector[mm1][2][3][3]+m4*AEigenVector[mm1][2][3][4]+m5*AEigenVector[mm1][2][3][5],
AEigenVector[mm1][2][4][6] = m1*AEigenVector[mm1][2][4][1]+m2*AEigenVector[mm1][2][4][2]+m3*AEigenVector[mm1][2][4][3]+m4*AEigenVector[mm1][2][4][4]+m5*AEigenVector[mm1][2][4][5],
m1^2 + m2^2 + m3^2 + m4^2 + m5^2 = 1], [m1, m2, m3, m4, m5]);

[m1 = .4027576723+.5022235499*I, m2 = -.5922841426-1.043213223*I, m3 = -.1130969773+.9150300317*I, m4 = .9867039883-.5082455178*I, m5 = -1.400123192+.1536850673*I], [m1 = .4027576723-.5022235499*I, m2 = -.5922841426+1.043213223*I, m3 = -.1130969773-.9150300317*I, m4 = .9867039883+.5082455178*I, m5 = -1.400123192-.1536850673*I]

mm1 := 2;
solve(
[AEigenVector[mm1][2][1][6] = m1*AEigenVector[mm1][2][1][1]+m2*AEigenVector[mm1][2][1][2]+m3*AEigenVector[mm1][2][1][3]+m4*AEigenVector[mm1][2][1][4]+m5*AEigenVector[mm1][2][1][5],
AEigenVector[mm1][2][2][6] = m1*AEigenVector[mm1][2][2][1]+m2*AEigenVector[mm1][2][2][2]+m3*AEigenVector[mm1][2][2][3]+m4*AEigenVector[mm1][2][2][4]+m5*AEigenVector[mm1][2][2][5],
AEigenVector[mm1][2][3][6] = m1*AEigenVector[mm1][2][3][1]+m2*AEigenVector[mm1][2][3][2]+m3*AEigenVector[mm1][2][3][3]+m4*AEigenVector[mm1][2][3][4]+m5*AEigenVector[mm1][2][3][5],
AEigenVector[mm1][2][4][6] = m1*AEigenVector[mm1][2][4][1]+m2*AEigenVector[mm1][2][4][2]+m3*AEigenVector[mm1][2][4][3]+m4*AEigenVector[mm1][2][4][4]+m5*AEigenVector[mm1][2][4][5],
m1^2 + m2^2 + m3^2 + m4^2 + m5^2 = 1], [m1, m2, m3, m4, m5]);

[m1 = .4262845394-.5114193433*I, m2 = -.6313720018+1.072185334*I, m3 = -0.7337582213e-1-.9580760394*I, m4 = -1.036525681-.5400714113*I, m5 = 1.412710014+.1874839516*I], [m1 = .4262845394+.5114193433*I, m2 = -.6313720018-1.072185334*I, m3 = -0.7337582213e-1+.9580760394*I, m4 = -1.036525681+.5400714113*I, m5 = 1.412710014-.1874839516*I]