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]

any user of the community has material ppt or pdf on presentation of clickable math popup and maple in computaconal applied to mathematics.

any help on the origin of math clickable popup;? place the link if they were so friendly!

If A is a matrix 2*2 then how can decompose A as spectral decomposition.

I want to write maple code of the following algorithm with

the following parameters and initial values please help me.

T₀ = 5.5556 × 10⁷ cells, I₀ = 1.1111 × 10⁷ cells, V₀ = 6.3096 × 10⁹ copies/ml,

A_1=A2=1,

c = 0.67, h = 1, d = 3.7877 × 10⁻³, δ = 3.259d,

λ = 2/3× 10⁸d, R₀ = 1.33,

p = (cV₀δR₀₎/λ(R0−1)

and β = dδcR₀/λp .

Algorithm
step 1 :
T(0) = T₀, I(0) = I₀, V (0) = V₀ λi(100 ) = 0 (i=1, ..., 3), u₁(0) = 0 =
u₂(0).

step 2 :
for i=1, ..., n-1, do _:
T_i+1=(T_i + hλ)/(1 + h[d + (1 − u₁ⁱ)βV_i]),

I_i+1 =(I_i + h(1 − u₁ⁱ)βV_iT_i+1)/(1 + hδ),

V_i+1 =(V_i + h(1 − u₂ⁱ)pI_i+1)/(1 + hc),

λ_{1ⁿ⁻ⁱ⁻¹} =(λ₁ⁿ⁻ⁱ + h[1 + (1 − u₁ⁱ)βVi+1])/(1 + h[d + (1 − u₁ⁱ)βV_i+1]),

λ₂ⁿ⁻ⁱ⁻¹ =(λ₂ⁿ⁻ⁱ+ hλ₃ⁿ⁻ⁱ (1 − u₂ⁱ)p)/(1 + hδ),

λ₃ⁿ⁻ⁱ⁻¹ =(λ₃ⁿ⁻ⁱ + h(λ₂ⁿ⁻ⁱ⁻¹− λ₁ⁿ⁻ⁱ⁻¹ )(1 − u₁ⁱ)βT_i+1)/(1 + hc),

R1ⁱ⁺¹ =(1/A1)(λ_{1ⁿ⁻ⁱ⁻¹}−λ_{2ⁿ⁻ⁱ⁻¹} )βV_i+1T_i+1,

R2ⁱ⁺¹ =−(1/A2)λ_{3ⁿ⁻ⁱ⁻¹} pI_i+1,

u_1ⁱ⁺¹ = min(1, max(R1ⁱ⁺¹ , 0)),

u_2ⁱ⁺¹ = min(1, max(R2ⁱ⁺¹ , 0)),

end for

step 3 :
for i=1, ..., n-1, write
T^∗(t_i) = T_i, I^∗(t_i) = I_i, V ^∗(t_i) = V_i,

u_1^∗(t_i) = u_1ⁱ, u2^∗(t_i) = u_2ⁱ.

end for