Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

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

In my Maple program, the voltage output of the system is computed as a time-domain response under different time intervals. The response curve has already been successfully obtained and plotted.

However, I would like to further extract and plot the envelope of this response. I initially attempted to determine the envelope by identifying the extrema of the signal, i.e., by solving the condition that the time derivative of the response equals zero. Unfortunately, this approach consistently leads to error messages, and I am not sure whether the issue is related to symbolic differentiation, numerical noise, or the implementation itself.

Could anyone please advise on:

  1. The correct way to extract an envelope curve from a time-domain signal in Maple?

  2. Whether there are alternative or more robust methods (e.g., based on numerical post-processing, signal processing techniques, or built-in Maple tools) to obtain the envelope, especially for numerically computed responses?

Any suggestions or example commands would be greatly appreciated.

Thank you in advance for your help.
numsolve-1229.mw

How can we determine the solution of the  system

Udot1 := -beta*V;
Vdot1 := beta*U;
Pdot1 := Q;
Qdot1 := 0;

and with initial conditions 

 U(0) := U[0];
V(0) := V[0];
P(0) := P[0];
Q(0) := Q[0];

Ode1.mw

In this maple file i try to find normal form and limit cycle of this jerk system but l don't know find like a paper did?

av.mw

I'm trying to reproduce a manual asymptotic analysis (see the attached pdf file) in Maple for a two-soliton solution. Specifically, I want to evaluate the limit of a function (e.g., r[2]r[2]r[2] or ∂xq[2]\partial_x q[2]∂x​q[2]). How can I properly perform the limit a2→+−∞ as t​→+−∞ in Maple, either by substitution or by reparametrization, in order to study the asymptotic behavior of a multi-variable expression symbolically? 

restart

with(Student[Calculus1])

lambda1 := I*mu1; lambda2 := I*mu2; a1 := -2*x/mu1+mu1*t; a2 := -2*x/mu2+mu2*t

numer_r := lambda2*cosh(a1)-lambda1*cosh(a2)

denom_r := (lambda1^2+lambda2^2)*cosh(a1)*cosh(a2)-2*lambda1*lambda2*(1+sinh(a1)*sinh(a2))

r2 := I*(-lambda1^2+lambda2^2)*numer_r/denom_r

numer_dq := (sinh(a1)-sinh(a2))^2; denom_dq := ((lambda1^2+lambda2^2)*cosh(a1)*cosh(a2)-2*lambda1*lambda2*(1+sinh(a1)*sinh(a2)))^2

dq2 := 1-2*(lambda1^2-lambda2^2)^2*numer_dq/denom_dq

limit_r2 := limit(r2, a2 = -infinity); simplify(limit_r2)

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic,set(name = algebraic),list(name = algebraic)), but received -2*x/mu2+mu2*t = -infinity

 

limit_r2

(1)

limit_r2_pos := limit(r2, a2 = infinity); simplify(limit_r2_pos)

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic,set(name = algebraic),list(name = algebraic)), but received -2*x/mu2+mu2*t = infinity

 

limit_r2_pos

(2)

NULL

Download asymptotic.mw cooocp_(2).pdf

Any suggestions for reformulating the limit or change of variables would be appreciated. 

I checked the ConsistencyTest of the system of equations but no output with 'true' or 'False'. Is it not work in 'DEtools'? Download consistency.mw

I am working with a symbolic expression in Maple that combines exponential terms. How can exponential terms be fully converted into hyperbolic functions? 

restart

with(Student[Precalculus])

interface(showassumed = 0)

assume(x::real); assume(t::real); assume(lambda1::complex); assume(lambda2::complex); assume(a::real); assume(A__c::real); assume(B1::real); assume(B2::real); assume(delta1::real); assume(delta2::real); assume(`&omega;__0`::real); assume(g::real); assume(l__0::real)

expr := A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`&omega;__0`+(1/2)*x))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`&omega;__0`*l__0^2*(delta1+I*delta2)*t)))*(sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)*(((-sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`&omega;__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`&omega;__0`*l__0^2*(delta1+I*delta2)*t))*((sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))))*(-delta1+I*delta2)*(delta1+I*delta2))

A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t)))*((-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(((-(delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))+exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)))*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))+exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t))*(((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))))*(-delta1+I*delta2)*(delta1+I*delta2))

(1)

NULL

Download simplify.mw

  1. Further simplify the expression under three physical scenarios, assuming delta__1 > 0:

    • Case (i): When A__c = 0

    • Case (ii): When delta__1 > g * A__c

    • Case (iii): When delta__1 < g * A__c

I have created an animation of a flexible octahedron (following Bricard) with Maple.   It shows the six vertices and twelve edges.  How do I add the faces (triangles)?  Can the animation show their lines of intersection?

restart;
with(geometry);

triangle(ABC, [point(A, a, b), point(B, c, d), point(C, e, f)]);
AreCollinear: hint: could not determine if a*d-a*f-b*c+b*e+c*f-d*e is zero
Error, (in geometry:-triangle) not enough information: the three points might be AreCollinear

assume(a*d - a*f - b*c + b*e + c*f - d*e <> 0);

triangle(ABC, [point(A, a, b), point(B, c, d), point(C, e, f)]);
                              ABC

area(ABC);
                   

What does the ~ after the point variables supposed to mean?

The workbook includes the excel data file but I also included the worksheet and data file separate for versions that can't load workbooks.

 

Average_World_Temperature_workbook-.maple

Average_World_Temperature_since_1850_worksheet.mw

HadCRUT5.zip

I have just started to use Maple workbook (*.maple). In the workbook, there are 4 worksheets: "main.mw","calc1.mw","calc2.mw","calc3.mw". In "main.mw", I plot variables saved from "calc?.mw". This works. However, when I make changes in one of the worksheet "calc?.mw" and get the new expressions for the variables, they are not updated in "main.mw". I deleted the variables being changed but "main.mw" still run and show the old expressions of these variables.

How do I refresh so that "main.mw" will show the updated variables from "calc?.mw"?

Thanks.

Trying to produce two different font sizes within a plot title.  I can achieve it with Typesetting but I'm getting brackets and fluff I don't want.  Any other ideas?

For example

with(Typesetting):
plot(x^2, title = [cat(mtext("sort of", font = "TimesNewRoman", size = 30), mtext("works", size = 10))])

I’m trying to plot a 3D surface in Maple with variables l and m. I used numerical substitution to evaluate the function and the results are real and positive. However, when I plot the function over a range of l and m, the graph shows complex (imaginary) values instead.

This seems very strange to me and has been quite frustrating. I’ve tried many different approaches to resolve the issue, but nothing has worked so far.

Why is this happening? How can the function evaluate to real numbers with direct substitution, but show complex values during plotting?

Any suggestions or explanations would be greatly appreciated. Thank you!
gra423_Omega.mw

I'm not sure if this is fixed in newer Maples or if there's a work around. 

Whenever I size a 3d plot, that I'm trying to stretch out the width while keeping the height, never seems to work.  For example using the size=[3000,800] produces a plot area that's bigger but NOT actually a plot stretched in the x axis.  Going to size=[3000,3000] of course then makes the plot and the area bigger and so scales both x and y bigger.  However I don't want the y axis scaled up - I'm trying to scale the plot up - not the area.  And what happened to the window zoom, icon - we've lost zoom control to just magnify + and magnify - (at least in 2022) this seems like a regression. 

Is this plot size a bug or just a plot command that fails to function like it should? 

I am very confused by the y-value of the rightmost point on the plot below.

restart

I'd like to find the values of x for which x^2/(10^(-8)-x) = 5*10^(-3).

So I ask Maple to solve this equation.

evalf(solve(x^2/(10^(-8)-x) = 5*10^(-3)))

-0.5000010000e-2, 0.10000e-7

(1)

Do these solutions work?

eval(x^2/(10^(-8)-x), x = 1.0000*10^(-8)) = Float(infinity) 

eval(x^2/(10^(-8)-x), x = -0.5000010000e-2) = 0.5000000000e-2 NULL

Suppose I define the function

f := proc (x) options operator, arrow; x^2/(1/100000000-x) end proc = proc (x) options operator, arrow; x^2/(1/100000000-x) end proc 

f(10^(-8))

Error, (in f) numeric exception: division by zero

 

f(.999999*10^(-8)) = 0.9999980000e-2NULL

f(.99999*10^(-8)) = 0.9999800001e-3NULL

Now, the function seems continuous between these two points

plot(f, .99999*10^(-8) .. .999999*10^(-8))

 

It is late, and perhaps I am just tired and not seeing things clearly. I expected the topmost point on the right to have a y-value of 0.00999998, ie almost 0.01.

I expected that the bottom leftmost point to be 0.0009999800001, ie almost 0.001, and it is.

And I thus expected to show that there must be some x for which we have f(x)=0.005, which if I am not mistaken is between the two numbers. After all, 0.999998e-2-0.5e-2 = 0.499998e-2NULL

0.5e-2-0.9999800001e-3 = 0.4000020000e-2NULL

what am i missing here?


Download plotq.mw

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