Maple Questions and Posts

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I’m having trouble solving this. Any suggestions would be helpful.

NULL

restart

``

with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)

``

ineq := simplify((Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*(Cr*b-1))*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2 > (((alpha*Cr*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*rho0+(2*(Cr*b-1))*(delta+Cn-Pr-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(delta+Cn-Pr-1))^2)

(((alpha*Cr*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*rho0+2*(Cr*b-1)*(delta+Cn-Pr-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(delta+Cn-Pr-1))^2 < (Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+2*(Cr*b-1)*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2

(1)

  

``extra := indets(ineq,And(name,Not(constant))) >~ 0;

{0 < Cn, 0 < Cr, 0 < Crm, 0 < Pr, 0 < a, 0 < alpha, 0 < b, 0 < c, 0 < d, 0 < delta, 0 < g, 0 < i2, 0 < rho0, 0 < sigma, 0 < t}

(2)

 

(solve({ineq}, t) assuming extra[]);

 

``

Download Q_solve.mw

I require the condition for equations  C1<C2<C4​, with all parameters strictly positive and subject to the constraint t > t1​.
I want to solve for the variables t and s. Specifically, what are the analytical conditions on t that ensure C2>C1​, and what are the analytical conditions on s that ensure C4 > C2 >C1​ ?

I attempted to solve this , but I keep encountering errors.
Q_solving_t_and_s.mw

Hi,
I’m taking the liberty of getting back to you once again regarding the animation of a procedure (here, for fractals). I’m able to use the Explore command correctly, but I’m having difficulty with animate.
Thank you very much for your help — it is truly invaluable.

Q_Fractales.mw

In the plot shown below, one of the axes is not visible, and one of the lines inside the graph is also missing. Is there an error in the plotting syntax that is causing this issue? Could anyone please identify the mistake and suggest how to correct it

All_plots_Question.mw

I do not use table data struct in Maple and could not find anything in help on how to do this.

given a table T such as the following, typing indices(T) shows there are more than entry in each index

indices(T)

[[-0.687272727272727, -0.687272727272727, 1.],   [2.25818181818182, 2.25818181818182, 1.]], 

  [[-2.47, -1.47, 2.], [0.53, 1.53, 2.]], 

  [[0.245, -2.755, -2.], [2.745, -0.255, -2.]], 

  [[-2.6, -0.6, 3.], [0.379, 2.379, 3.]], 

  [[2.659, -1.341, -3.], [4.652, 0.652000000000001, -3.]], 

  [[-3.178, 0.822000000000001, 5.], [-1.185, 2.815, 5.]], 

  [[0.0672727272727271, -0.932727272727273, 0.], [3.06181818181818, 2.06181818181818, 0.]], 

  [[2.8895, -2.1105, -4.], [4.3895, -0.6105, -4.]], 

  [[1.01, -0.99, -1.], [4.02571428571429, 2.02571428571429, -1.]], 

  [[-3.63, -0.63, 4.], [-1.13875, 1.86125, 4.]]

In the above each entry in table has 2 indices. I want to keep only the first index in each entry so that it has only one, to become this

[[-0.687272727272727, -0.687272727272727, 1.]], 

[[-2.47, -1.47, 2.]], 

[[0.245, -2.755, -2.]],

 [[-2.6, -0.6, 3.]], 

[[2.659, -1.341, -3.]],

 [[-3.178, 0.822000000000001, 5.]],

 [[0.0672727272727271, -0.932727272727273, 0.]], 

[[2.8895, -2.1105, -4.]], 

[[1.01, -0.99, -1.]], 

[[-3.63, -0.63, 4.]]

And keep everything else as in in the Table. Just need to adjust the indices to be one entry instead of 2 or more.

Here is an example of such table


T:=table([([-.687272727272727, -.687272727272727, 1.], [2.25818181818182, 2.258181\
81818182, 1.])=COLOR(RGB,.63529412,.60392157,.60000000),([-2.47, -1.47, 2.], [.\
53, 1.53, 2.])=COLOR(RGB,.60784314,.47450980,.46274510),([.245, -2.755, -2.], [
2.745, -.255, -2.])=COLOR(RGB,.44705882,.52549020,.67058824),([-2.6, -.6, 3.],
[.379, 2.379, 3.])=COLOR(RGB,.57647059,.34509804,.32549020),([2.659, -1.341, -3\
.], [4.652, .652000000000001, -3.])=COLOR(RGB,.34901961,.46666667,.70980392),([
-3.178, .822000000000001, 5.], [-1.185, 2.815, 5.])=COLOR(RGB,.47058824,0.,.\
54901961e-1),([.672727272727271e-1, -.932727272727273, 0.], [3.06181818181818,
2.06181818181818, 0.])=COLOR(RGB,.62352941,.63529412,.65490196),([2.8895, -2.11\
05, -4.], [4.3895, -.6105, -4.])=COLOR(RGB,.22745098,.40392157,.78039216),([1.0\
1, -.99, -1.], [4.02571428571429, 2.02571428571429, -1.])=COLOR(RGB,.53725490,.\
57647059,.65490196),([-3.63, -.63, 4.], [-1.13875, 1.86125, 4.])=COLOR(RGB,.537\
25490,.20392157,.18823529)])

Is it possible to do this in code?

Maple 2025.2

I want to convert the Chebyshev T(n,x) and U(n-1,x) polnomials into their inverse trigonometric definitions. Is there a simple conversion process available in Maple?  There is a command "invtrig" which I have tried with the "convert" command , but this does not seem to work.

Hi,
I’d appreciate your insights on how to animate this sequence (family) of functions in order to obtain a rendering like the one shown below.


Any suggestions or best practices would be very welcome. Thank you!

AnimQ.mw

Suppose I am plotting a 2D plot and want to highlight the point where two lines intersect. I would like to display this intersection point inside the plot in black font, mark it with an arrow or some visual highlight, and clearly label it. How can I do this?

Additionally, instead of using different colours (blue, green, red) for the lines, I want to distinguish them using different line styles such as solid, dotted, and long-dashed lines. How can I make these changes?

restart

with(Optimization); with(plots); with(Student[VectorCalculus]); with(LinearAlgebra)

 

_local(Pi)

Pi

(1)
 

M_w := b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*((Cr*b-1)*d+b))*(delta+Cn-Pr-1))^2*d/(8*(Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))

(1/8)*b*(((Cr*alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr)*alpha-(-g*i2+a)*Cr)*d+alpha*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr)*b+2*g*i2-2*a)*rho0+(2*(Cr*b-1)*d+2*b)*(delta+Cn-Pr-1))^2*d/((Cr*b*d+b-d)^2*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))

(2)
 

 

M_D := (Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*(Cr*b-1))*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*(((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+rho0^2*b*alpha))*((Cr*b-1)*d+b)^2)

(Cr*rho0*t*(Cr*alpha*b-alpha-1)*d^2+((alpha*((-g*i2+a)*Cr+2*Crm+2*c+3*t-2*Pr)*Cr*b+((g*i2-a)*Cr-2*Crm-2*c-2*t+2*Pr)*alpha+(g*i2-a)*Cr-2*t)*rho0+(2*Cr*b-2)*(sigma*t+Cn-Pr+delta-1))*d+(alpha*((-g*i2+a)*Cr+2*Crm+2*c+2*t-2*Pr)*b+2*g*i2-2*a)*rho0+2*b*(sigma*t+Cn-Pr+delta-1))^2*d*b/((8*((Cr*alpha*b-alpha+1)*rho0^2-2*b*(delta-1))*d+8*rho0^2*b*alpha)*((Cr*b-1)*d+b)^2)

(3)

M_S := ((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+3*t)*alpha*b+((g*i2-a)*Cr+2*Pr-2*Crm-2*c+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr-2*Pr+2*Crm+2*c-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(2*(-sigma*t-Cn+Pr-delta+1))*((Cr*b-1)*d+b))^2*b*d/((8*(((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-2*b*d*(delta-1)))*(Cr*b*d+b-d)^2)

((t*Cr*(Cr*alpha*b-alpha-1)*d^2+(Cr*((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+3*t)*alpha*b+((g*i2-a)*Cr-2*Crm-2*c+2*Pr+2*s-2*t)*alpha+(g*i2-a)*Cr-2*t)*d+((-g*i2+a)*Cr+2*Crm+2*c-2*Pr-2*s+2*t)*alpha*b+2*g*i2-2*a)*rho0-(-2*sigma*t-2*Cn+2*Pr-2*delta+2)*((Cr*b-1)*d+b))^2*b*d/((8*((Cr*alpha*b-alpha+1)*d+alpha*b)*rho0^2-16*b*d*(delta-1))*(Cr*b*d+b-d)^2)

(4)
 

``

DATA1 := [delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]

[delta = .9, a = 0.1e-1, g = .25, c = 0.5e-1, rho0 = .4, Cn = .4, Crm = .1, i2 = 0.6e-1, t = 0.1e-1, alpha = .95, s = 0.1e-1, Pr = .35, upsilon = .95, b = .5, d = .3, Cr = 0.1e-1]

(5)

P11 := subs(DATA1, M_w); P21 := subs(DATA1, M_D); P31 := subs(DATA1, M_S)

0.9301486586e-2

 

4.251178959*(-0.4764573140e-1+0.4030e-2*sigma)^2

 

4.251178959*(-0.4917713136e-1+0.4030e-2*sigma)^2

(6)

``

A1 := plot([P11, P21, P31], sigma = 0 .. .7, color = ["Red", "Blue", "Green"], labels = [sigma, `&pi;__m`], labeldirections = ["horizontal", "vertical"], legend = [`#msubsup(mi("&pi;"),mi("n"),mn("W"));`, `#msubsup(mi("&pi;"),mi("n"),mn("D"));`, `#msubsup(mi("&pi;"),mi("n"),mn("DS"));`], axis[2] = [color = "#600000"])

 
 

display(A1, pointplot([[X, Y]], symbol = circle, symbolsize = 25, color = blue))

Error, (in plots:-pointplot) points cannot be converted to floating-point values

 
 

NULL

Download Manf_profit__t_graph_changes_needed.mw

Hi !

When I use the "expand" command on a summation, I've noticed that sometimes the command works and

sometimes it doesn't. I looked through the previous commands to see which one might be causing this problem.

I found that if I use the "changevar" command  from the "student" package,  (deprecated package,I know )

the "expand" command works correctly.     Strange behavior, isn't it ?       I have Maple 2018 on Windows 10.

Regards  !

There is a small  example in the file.

expand-problem.mw

I am facing three issues while plotting my plot.I need help modifying the syntax:

  1. I am unable to correctly display superscripts and subscripts for Pi[m]^WD < Pi[m]^D inside the graph region

  2. I cannot format the subscript for i__2 on the x-axis.

  3. A horizontal dotted line appears parallel to the x-axis at y=0.5; how can I remove this line?

    Question_1_regional.mw

Hello all,

This will be my LAST (I swear) question about translating a little function from Mathematica to Maple.

rand := RandomReal[{-5, 5}, 20]

ListPlot[rand]

 

ListListLinePlot[rand]

In[16]:= line = Fit[rand, {1, x}, x]

Out[16]= 0.247498 - 0.0131912 x

In[17]:= parabol = Fit[rand, {1, x, x^2}, x]

Out[17]= -1.82858 + 0.31249 x - 0.0082569 x^2

In[18]:= cos = Fit[rand, {1, x, Cos[x]}, x]

Out[18]= 0.483172 - 0.0302095 x - 0.271457 Cos[x]

Plot[{ListLinePlot[rand], line, parabol, cos}, {x, 0, 20}]

#graph omitted by request of users here.

So, then, my LAST question will be :

How to translate this to Maple ?

Thank you very much.

JM

Hello again,

I think I have not been clear enough in my question.

I reformulate :

Is it possible in Maple to create matrices whose elements are also matrices

and this to any level ?

For the Dimensions of a matrix it's ok for me.

thank you 

JM

Hello all,

I just need a hint how to enter "matrices" in Maple which are lists of lists and so on.

Since I gave up on "math"ematica I would like to be able to enter what is just

below (with the dimension).

Is it doable in Maple...I guess yes :)

M = {{a, {1, a, -0.5}}
, {{b, {1}}}, c + d}
Out[5]= {a, {1, a, -0.5}, {{b, {1}}}, c + d}
In[8]:= MatrixForm[M]
Out[8]//MatrixForm=
a
{1, a, -0.5}
{{b, {1}}}
c + d
In[9]:= Dimensions[M]
Out[9]= {4}

PS: Is a moderator ready to make me with a reputation of 100 in order I can enter tags.

Thank you for everything.

Regards,

JM

I am not able to find place in help which lists which changes interface(typesetting = extended); makes compared to interface(typesetting = standard);

Reason  I am asking, is that in interface(typesetting = extended); Maple adds a small annoying "dot"  between each term for multiplication, which is not there in standard.

Is there a place in documentation that mentions this as part of extended? Where to find it?

in Matlab and Mathematica it is possible to put the labels in contour plot, directly on the lines (with nice positioning).

This makes it much much easier to see the level of each contour line since the values are on the lines,  without having to jump to the legend and guess the color and try to visually match colors with the plot.

For example, in Matlab

clear; close all;
x = 0:0.05:20;
y = 0:0.05:15;
[x,y] = meshgrid(x,y);
z = (11-x-y).^2 + (1+x+10*y-x.*y).^2;
[C,h] =contour(x,y,z,10);
clabel(C,h)

gives

In Maple

f:=(11 - x - y)^2 + (1 + x + 10*y - x*y)^2:
plots:-contourplot(f, x=0..20, y=0..15,
         legend=true,
         contours=10,
         'axes'='boxed',
         legendstyle=[location=right], 
         colorscheme="DivergeRainbow");

Is there a way to tell Maple to put contour labels on the "middle" of the level lines (contour lines) similar to what Matlab does?

I see no such option in https://www.maplesoft.com/support/help/maple/view.aspx?path=plots/contourplot

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