Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am installing maple 2019 on Linux 64 bit. I used the option

--mode text

The installer has not proceeded after answering Y to the following. 

Activate Maple 2019 now (requires an Internet connection). [Y/n]:

Any suggestions? 

I can  this equation.

CV.mw
 

restart; c__v := 1.2; `τ__q` := 8.5*10^(-12); `τ__T` := 90.0*10^(-12); rho := 1000; k := 10

1.2

 

0.8500000000e-11

 

0.9000000000e-10

(1)

k*(diff(T(x, t), x, x))+k*`τ__T`*(diff(T(x, t), t, x, x)) = rho*c__v*(diff(T(x, t), t))+(diff(T(x, t), t, t))*c__v*rho*`τ__q`+(1/2)*c__v*rho*`τ__q`^2*(diff(T(x, t), t, t, t))

10*(diff(diff(T(x, t), x), x))+0.9000000000e-9*(diff(diff(diff(T(x, t), t), x), x)) = 1200.0*(diff(T(x, t), t))+0.1020000000e-7*(diff(diff(T(x, t), t), t))+0.4335000000e-19*(diff(diff(diff(T(x, t), t), t), t))

(2)

Boundary condition:

T(0, t) = 300; T(10, t) = 300

#####################################

INITIAL CONDITIONS:

 

T(x, 0) = 300; (D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(D[1](T))(x, 0) = 0, (D[2](T))(x, 0) = 0

(3)

``


 

Download CV.mw

 

 

i) D(X,Y) , D(X,Z) ,D(Y,Z) COVARİANT DERİVATİVE ?

İİ) [X,Y] LİE OPERATOR ? 

İİİ) R(X,Y)Z = D DZ - DDZ - D[X,Y] Z

My Maple Worksheets (not Maple Documents) have lots of explanetory Text blocks [..... surounding executable Math blocks ([> ..... I often insert mathematical symbols, most commonly subscripted variables, in these Text blocks.  For a simple example, consider the text block entered as

[This is a test of a subscripted variable "CTL-R" h__0 "CTL-T" in a text block.

The "CTL-R" (quotes are not actually entered) is the short cut to go into math mode, and "CTL-T" exits math mode and returns to text mode and the double underscore produces an atomic subscripted variable.

The text block actually will look like

[This is a test of a subscripted variable h0 in a text block.

The problem occurs when I reexecute the worksheet. The Text block actually produces output labeled with an equation number. For my simple example above the Text block becomes

[This is a test of a subscripted variable h0 in a text block.

[                                              h0                                                   (1)

 

where the two lines started by [ are actually merged with one expanded [ for the Text block with its output. To get rid of the unwanted output, I have to put my curser over the h0 that is in the Text body (not the output h0) and hit "Shift-F5". The output h0 with its equation number disappears.  If there are a number of simple math expressions in a text block, I have to process them one at a time with "Shift-F5". This takes up a lot of time. With earlier Maple versions (~2015 or earlier) I used to fly through Text blocks using the shortcuts "Ctl-R" and "Ctl-T" and these Text blocks produced no output when the worksheet was reexecuted. 

Starting with Maple 2016 I could enter math expressions in Text blocks using the shortcuts, but I could not copy and paste  a Text block with inline math expressions without the expressions becoming "live" in the copied block.  Starting with Maple 2017 all my Text boxes with math expressions began executing the math and producing output.

I gave up on Maple 2017 and 2018.  I have finally made the jump from Maple 2016 to Maple 2019, in part, because I finally discovered the "Shift-F5" trick to make math expressions in a Text block inactive.

Does anyone know how to make the default behaviour of Maple with math expressions in a Text block to be "Don't execute the math and produce output in the Text block"?

I would post an actual example worksheet, except I have never been successful whenever I have tried to upload a worksheet. I hope my description above is adequate.

Any help will be greatly appreciated.  Neill Smith

 

 


 

restart; with(VectorCalculus)

r := `<,>`(sin(t), cos(t), t)

Vector(3, {(1) = 0.2739493386e-115+0.2739493386e-115*I, (2) = 1.0-0.7504824014e-231*I, (3) = t})

(1)

``


what??

Download problem.mw

How I can take Laplace Transform from equation.

Thanks

LAPLACE

The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

EllipseRoll.mw

Earlier smoothly working generation of normal distribution in v. 2019 unexpectedly shows the error:

RandV  := Statistics[RandomVariable](Normal(0, 1));
Statistics[Sample](RandV, 10);

Error, (in p) unable to convert Float(undefined) to an integer

 

Help create file Excel in ExcelTools, but error row 564?

thu_file.mw

Please help me? 

Hii,

I am using a command -NLPSolve(Ecost1, Q = 10 .. 20, initialpoint = {Q = 10}, assume = nonnegative, maximize = false). I am looking for solution that find the Q value at the minimum value of Ecost1. But Ecost1 should not go below 0. 

and also I am getting an error -Warning, initialpoint option ignored by solver.

Kindly tell how to deal with these issues.

 

Thanks

How I can do ?

Thank you.

 

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and q = {`u__m,n`(t), `v__m,n`(t), `w__m,n`(t)}^T.

\where the elements of the vector,q_i are the time-dependent generalized coordinates.

L_Maple
 

U = (1/2)*(int(int(int(E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x))+v(x, y, t)*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y))))*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x)))/(-nu^2+1)+E*(`&PartialD;`(nu(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y))+v(x, y, t)*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x))))*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y)))/(-nu^2+1)+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(y)+`&PartialD;`(v(x, y, t))/`&PartialD;`(x)+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))+`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y))+`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y))-2*z*(diff(w(x, y, t), x, y)))^2/(2*(1+nu))+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), y, y)-(diff(w(x, y, t), x, x)))^2/(2*(1+nu))+E*l^2*(diff(v(x, y, t), y, y)-(diff(u(x, y, t), x, x)))^2/(8*(1+nu))+E*l^2*(diff(v(x, y, t), x, y)-(diff(u(x, y, t), y, y)))^2/(8*(1+nu)), z = -(1/2)*h .. (1/2)*h), y = 0 .. b), x = 0 .. a))

U = (1/2)*(int(int((1/12)*(-E*(-v(x, y, t)*(diff(diff(w(x, y, t), y), y))-(diff(diff(w(x, y, t), x), x)))*(diff(diff(w(x, y, t), x), x))/(-nu^2+1)-E*(-v(x, y, t)*(diff(diff(w(x, y, t), x), x))-(diff(diff(w(x, y, t), y), y)))*(diff(diff(w(x, y, t), y), y))/(-nu^2+1)+4*E*(diff(diff(w(x, y, t), x), y))^2/(2+2*nu))*h^3+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2+v(x, y, t)*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2))*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2)*h/(-nu^2+1)+E*(`&PartialD;`(nu(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2+v(x, y, t)*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2))*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2)*h/(-nu^2+1)+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(y)+`&PartialD;`(v(x, y, t))/`&PartialD;`(x)+`&PartialD;`(w(x, y, t))^2/(`&PartialD;`(x)*`&PartialD;`(y))+2*`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y)))^2*h/(2+2*nu)+2*E*l^2*(diff(diff(w(x, y, t), x), y))^2*h/(1+nu)+E*l^2*(diff(diff(w(x, y, t), y), y)-(diff(diff(w(x, y, t), x), x)))^2*h/(2+2*nu)+E*l^2*(diff(diff(v(x, y, t), y), y)-(diff(diff(u(x, y, t), x), x)))^2*h/(8+8*nu)+E*l^2*(diff(diff(v(x, y, t), x), y)-(diff(diff(u(x, y, t), y), y)))^2*h/(8+8*nu), y = 0 .. b), x = 0 .. a))

(1)

T = rho*h*(int(int((`&PartialD;`(u(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(v(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(w(x, y, t))/`&PartialD;`(t))^2, y = 0 .. b), x = 0 .. a))

T = rho*h*(int(int(`&PartialD;`(u(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(v(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(w(x, y, t))^2/`&PartialD;`(t)^2, y = 0 .. b), x = 0 .. a))

(2)

F = (1/2)*c*(int(int((`&PartialD;`(u(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(v(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(w(x, y, t))/`&PartialD;`(t))^2, y = 0 .. b), x = 0 .. a))

F = (1/2)*c*(int(int(`&PartialD;`(u(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(v(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(w(x, y, t))^2/`&PartialD;`(t)^2, y = 0 .. b), x = 0 .. a))

(3)

W = int(int(w(x, y, t)*f__1(x, y, t)*cos(omega*t), y = 0 .. b), x = 0 .. a)

W = int(int(w(x, y, z)*f__1(x, y, z)*cos(omega*t), y = 0 .. b), x = 0 .. a)

(4)

u(x, y, t) = sum(sum(`u__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

u(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(5)

v(x, y, t) = sum(sum(`v__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

v(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(6)

w(x, y, t) = sum(sum(`w__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

w(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(7)

diff(`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), t)-`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(F(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`) = `&PartialD;`(W(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), j = 1, () .. (), N

(D(`&PartialD;`))(T(x, y, t))*(diff(T(x, y, t), t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)-`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+2*`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(F(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`) = `&PartialD;`(W(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), j = 1, () .. (), N

(8)

NULL


 

Download L_Maple

 

 

I want to made a comparison via plots of RK-4, NSFD and LWM.

https://stackoverflow.com/questions/39617250/nesting-mpi-calls-with-mpi4py

Is cmaple or maple in linux MPI executable?

can it be call by the python program in above answer at stackoverflow?

any one have tried?

 

I have noticed a few times now with Maple 2019. It looses kernel connection when it is sitting there idly. This time I observed it. Had saved a document after an intensive calculation. The memory used was about 30Gig. shortly after saving the cpu fan was running hard. I checked task manager and cpu was cycling to 100%, it was mserever. Then the memory usage droped to about 6gig and message as shown. During this time Maple screen down in the LH corner displayed "Ready", so it didn't think it was doing anything.
 

Hello,

How I can take variation from left-hand side of  5, and reach to right-hand side of  5. After by using integral by part obtained  7?

Thank you

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