In my code, why  does InitState(5,5) return only one element of the vector while Coherent(5) returns 5 elements of the vector?

Download test3.mw

Can I export a Table as an image like .png, where Table is defined (with DocumentTools)? See Maple worksheet for example.

Why would anyone want to do this? It all started because I wanted to include a color bar(with a specific color range) in my 3dplot. There is no native way to do this with plot3d so I searched Maple Primes for alternative strategies. One strategy is to generate the 3d plot and the color bar(with plot3d) seperately, then combine the plots in a table so they sit side by side, using with(DocumentTools). I have been almost successful with this strategy. There remain two outstanding problems. 1. I can't re-size the table cells since there are no such options with(DocumentTools). The color bar should have a smaller cell because the figure itself is tall and thin. 2. I need to export this combined object as an image(.png) but its a table with plot objects inside, and not itself a plot object and therefore one can't simply export it as a .png like one would a typical plot object. Is there a way to export this table as a png? I am beginning to think that my idea of combining  plots with document tools and attempting the export the resulting table is not feasible. How does a normal person add a custom-color-range color bar to their plot? I'm not trying to move the earth here but it certainly feels like it.

with_document_tools_how_to_i_resize_the_cells_and_export_the_table_as_png.mw

 I can't achieve this using StringTools:-RegSplit. The StringTools,Regular_Expressions documentation doesn't seem to address these functionalities.

My goal is to split the string at the occurences of "." that are somewhere between "]" and "["* yet not enclosed between the two digits, and to ignore all other occurences of "."

I want to get the unknown function whose Taylor expansion I have. For example, giving x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 will return sin(x). The following algorithm can be implemented for this simple function:

with(inttrans):

with(numapprox):

convert(taylor(sin(x),x, 10),polynom);

laplace(%, x, s1);

eval(%, s1=1/s2);

pade(%, s2, [3,3]);

eval(%, s2=1/s1);

invlaplace(%, s1, x);

But this approach does not lead to the correct solution for slightly more complex functions. For example, if I have the Taylor expansion of the function sin(x^2), I cannot reach the function sin(x^2) with the above algorithm. Note that before extracting the sin(x^2) function, this function is unknown to us and we only have its Taylor expansion:

with(inttrans):

with(numapprox):

convert(taylor(sin(x^2),x, 15),polynom);

laplace(%, x, s1);

eval(%, s1=1/s2);

pade(%, s2, [3,3]);

eval(%, s2=1/s1);

invlaplace(%, s1, x);

Also, the Taylor expansion of the simple function exp(-x^2) with the above algorithm is returned as a trigonometric function:

with(inttrans):

with(numapprox):

convert(taylor(exp(-x^2),x, 10),polynom);

laplace(%, x, s1);

eval(%, s1=1/s2);

pade(%, s2, [3,3]);

eval(%, s2=1/s1);

invlaplace(%, s1, x);

The importance of solving this problem becomes clear when we want to solve the differential equation or the set of differential equations by applying the ‘series’ option. If the variable t expresses time, it can never be obtained with a polynomial function u(t) in sufficiently large times. For example, the exact solution of the following differential equation is u(t)=exp(-a*t^2):

Order:=12;

ode:=t*diff(u(t),t,t)+8*diff(u(t),t)+18*a*t*u(t)=-4*a*t*u(t)*ln(u(t));

ic1:=u(0)=1;

ic2:=D(u)(0)=0;

dsolve({ode, ic1,ic2}, u(t), series);

Does anyone have an idea to extract the unknown function from its taylor expansion?

Best wishes

This is new:

Maple 2024 frozen on opening recent files

Maple 2023 frozen on opening

Maple 2022 frozen on opening start page

Maple 2021 blinking

Maple 2020 opening start page

The above system state is constant for about 30 min. Maple sessions without start page are working. I can enter code but file opeing and saving does not work. The fact that Maple 2020 is also not working makes it unlikely that the Java environement is part of the problem.

I have several times restarted the system. The rest of the system is working.

Something happened to the system and I have no clue what is was and what I can do about it.

Any ideas or suggestions what I could try? Windows 10.

Not sure what  I did, but now  the typsetting rule assistant pops up every time I executre my document (twice!).  Searching the internet, I found that I should be able to turn it off by "expanding the blocks" (?) and then finding the call to this assistant.  Problem is, I can't find this "Expand block"  -- it is not under View it they claim it is in various posts.  Also, if I step through the worksheet, I can't find it ; it only pops up when I execute the entire worksheet.  I attached it here for someone to guide me on how to find where/why this is happening.

Thanks!coupled_network.mw
 

Download coupled_network.mw

Hello Maple community

I am trying to solve a system of equations, which is a little complicated.

eq1 := w = sqrt(a^2 - (a - y)^2);
eq2 := v + cot(t + arcsin(w/a)) = 0;
eq3 := u = (sqrt(c^2 - (c - z)^2) - v*x - w)/x^2;
eq4 := x = y + z + e;
eq5 := v + cot(T + arcsin((u*x^2 + v*x + w)/c)) + 2*u*x = 0;
eq6 := f = Pi/30*(6*u^2*x^5 + 15*u*v*x^4 + (20*u*w + 10*v^2)*x^3 + 30*v*w*x^2 + 30*x*w^2) - Pi/3*(-z^3 + 3*z^2*c - y^3 + 3*y^2*a);
sols := solve({eq1, eq2, eq3, eq4, eq5, eq6}, {u, v, w, x, y, z});

I tried solving it, but it is running for more than two hours now. I know that the system is very complicated, and Maple will take long to solve this. But my question is

1. Is it reasonable to take this long for this system of equations?

2. Can I speed it up in any way by using additional cores of my system or something? Can someone please tell me how I can achieve this?

Looking forward to any inputs the Community may have.

I have a sum in powers of  cosines : a0 + a1 cos(x) + a2 cos^2(x) + a3 cos^3(x) + ... + ak cos^k(x) . I want to transform it into a sum of the form : b0 + b1 cos(x) + b2 cos(2x)+  ... bk cos(kx). How can I do this in Maple?

How can I get the evaluation of integration inside if-statement?

Thanks for your help in advance,

Download SolnforProjectile_v3_3.mw

restart;
with(geometry);
with(plots);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
cb := color = blue;
t3 := thickness = 3;
l3 := linestyle = 3;
xA := 3;
yA := 0;
xB := -3;
yB := 0;
c := 6;
point(A, xA, yA);
point(B, xB, yB);
R := 5;
alpha := arctan(3/4);
evalf(%*180/Pi);
                          36.86989765

xH := (xA + xB)/2;
yH := (yA + yB)/2;
point(H, xH, yH);
xO1 := 0;
yO1 := 4;
point(O1, xO1, yO1);
xO2 := 0;
yO2 := -4;
point(O2, xO2, yO2);
segment(sAB, A, B);
segment(sHO, H, O1);
segment(sAO, A, O1);
segment(sBO, B, O1);
                              sAB

alpha1 := arctan((yO1 - yA)/(xO1 - xA));
beta := Pi + arctan((yO1 - yB)/(xO1 - xB));
AR1 := plottools[arc]([xO1, yO1], R, alpha1 .. beta, l3);
AR2 := plottools[arc]([xO2, yO2], R, -beta .. -alpha1, l3);
N := 80;
dt := (beta - alpha1)/(N - 1);
dr := draw({O1, O2, sAB, sHO, sAO(cb), sBO(cb)});
tex := textplot([[xA, yA - 0.5, "A"], [xB, yB - 0.5, "B"], [xO1, yO1 + 0.5, "O1"], [xO2, yO2 - 0.5, "O2"], [xH, yH - 0.5, "H"]]);
M1 := seq(plottools[disk]([R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], 0.2, color = orange), t = 0 .. N);
M2 := seq(plottools[disk]([R*cos(dt*t + Pi + alpha1) + xO2, R*sin(dt*t + Pi + alpha1) + yO2], 0.2, color = orange), t = 0 .. N);
P1 := seq(plottools[polygon]([[R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N);
P2 := seq(plottools[polygon]([[R*cos(dt*t + Pi + alpha1) + xO1, R*sin(dt*t + Pi + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N);
for t to N do
    E[t] := display(dr, tex, AR1, AR2, M1[t], P1[t]);
    F[t] := display(dr, tex, AR1, AR2, M2[t], P2[t]);
end do;
display([seq(E[t], t = 1 .. N), seq(F[t], t = 1 .. N)], insequence = true, axes = none, scaling = constrained, view = [-10 .. 10, -10 .. 10]);

NULL;
angle that does not turn on the lower arc. Thank you.

How to verify eq by using (2), (3) and (4)? Since lambda's, A's, B's and a are constant, but they appear as variables i.e., D[2](A1)..., (D[2] -> d/dt (derivative w.r.t 't')). Also q(n+1,t)- q(n,t) = a (const). Therefore, d/dt(q(n+1),t) - d/dt,(q(n,t))=0

verif_May24.mw

OS Linux

I have Maple 2022 open with a worksheet on a specific workspace.

I then move to a different workspace and want to start a new instance of maple for a new problem.

In command line I exacute

$]xmaple22 –standalone  filename.mw

Unfortunately when the new instance is started, the open maple instance on the first workspace is moved automatically to the second workspace together with the new instance opened, completely messing up the organization.

This is not expected behavior.

How can I make Maple execute absolutely independent instances of xmaple22 without indiscressionately and automatically moving existing open maple instances to the current workspace.

Severely annoying. Maple 9.5 e.g. does not have this behavior at all so Maple 2022 is a step backwards in this regard.

Thanks

How do I programmatically control the zoom of a 3d plot ?
SEE THE ATTACHED MAPLESHEET. In the attached code, the 'zoom out' on the blue cylinder is not conserved when I saved the maplesheet but it doesn't change the essential question which is how does one control the zoom programmatically. If you yourself adjust the zoom of the blue cylinder and the run tabulate(), you will see how it resets the plots settings to some default set of values.
How_do_I_programmatically_control_the_zoom_in_a_3d_plot.mw

Download How_do_I_programmatically_control_the_zoom_in_a_3d_plot.mw
1. Plot two cylinders with plottools and plot3d. Zoom out on the blue cylinder a little.
2. Use tablate to embed the 3d plots in a visual array, for reasons not discussed here.

3. Notice how the use of tabulate( ), changes the zoom of the individual plots to some default. There are two questions: 1. How do I programmatically control the zoom of a 3d plot with display( )? I don't want to have to click buttons with the mouse to arrive at my ideal zoom level. 2. How do I programmatically control the zoom of a 3d plot when using Tabulate( ) which envokes the default plot settings

Below is a screenshot of the zoom buttons I want to control programmatically.

Dear all,

I have the following partial differential equation. I want all terms with 'diff' to be moved to the left side of the equation and all source terms to be moved to the right side of the equation.

diff(u(x, t), t, t) + 3 + 2*diff(u(x, t), t) + 4*t + x^2 + x^3/3 + diff(u(x, t), t, x, x) + diff(u(x, t), x, x, x, x) = x*t^2;

Is there a comprehensive solution for such purposes?

The desired result:

diff(u(x, t), t, t) + 2*diff(u(x, t), t) +  diff(u(x, t), t, x, x) + diff(u(x, t), x, x, x, x) = x*t^2-x^3/3 -x^2-4*t -3;

Can anyone guide me?

Best wishes,

Why Maple gives this error on solving first order linear ode using ODESteps? 

Download odesteps_fail_may_10_2024.mw

ps. also reported to Maplesoft customer support.