Maple 2022 Questions and Posts

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

Hi everyone, I am seeking help regarding the graphs for analytic and numeric solutions and their errors separately?

Hi everyone, Could anyone help me to draw horizontal and vertical line in a plot? Also, How to add command for legends to show inside the plot at empty space. I every time edit legends in paint manually. For reference, I am attaching a picture


When I look for petrov type II vacuum solutions in the Metric search, one of the metrics i get is Stephani [33,8,3].

But when I load the metric and calculate the Ricci or the Einstein tensor, they are not identically zero.
Am I using the metric search wrong or is there a glitch in the program?


How can an equation containing a logarithmic function be converted into a polynomial?


I have a data structure/plotting question. How do I plot the 3 lambdas (singleaxis) and the 6 betas (dualaxis) for 12 calibrations (1000 runs each)? All the details are in the script Thank you!

For the beta plots and subplots, please follow the dualaxis example output format at the bottom of my script for each of the 12 calibrations.

For the lambda plots, I'd like to combine a few of them as follows (each plot with lambda_1 subplot, lambda_2 subplot, and lambda_3 subplot - note that the lambda plot example at the bottom of the script is dualaxis but I just need singleaxis):

PLOT 1 (singleaxis): lambda_1, _2, _3 for ncal2 and ncal3 (superimposed, 2 data series for each subplot)

PLOT 2 (singleaxis):  lambda_1, _2, _3 for ncal7 and ncal8 (superimposed, 2 data series for each subplot)

PLOT 3 (singleaxis):  lambda_1, _2, _3 for ncal4, ncal5, ncal6 (superimposed, 3 data series for each subplot)

PLOT 4 (singleaxis):  lambda_1, _2, _3 for ncal9, ncal10, ncal11 (superimposed, 3 data series for each subplot)

 I run the attached code, but after waiting for a few minutes, there is no response, does anyone know the reason?

 It only shows Evaluating!!!!

I know trig functions are hard to simplify in general but was wondering if there was any simplification command that comes in handy for trig functions of the following form.

sin(theta)^(A - 2)*cos(theta)^2 - sin(theta)^(A - 2) + sin(theta)^A

I am trying to make a very rough animation of a rotating pulsar magnetosphere that would very roughly resemble this gif.
I was able to make a sphere and the dipolar field lines. I was wondering if anyone could provide any possible suggestion regarding.

1. How do i animate the rotation such that the rotation axis is not z but slightly misaligned to z.

2. Is there a better way to make the field likes from the poles (jets).


[1.1, cos(theta), theta]

[1.1, cos(theta), theta]


sph := [.5, theta, phi]; c1 := [A*sin(phi)^2, 0, phi]; c2 := [A*sin(phi)^2, (1/6)*Pi, phi]; c3 := [A*sin(phi)^2, (1/3)*Pi, phi]; c4 := [A*sin(phi)^2, (1/2)*Pi, phi]; c5 := [A*sin(phi)^2, 2*Pi*(1/3), phi]; c6 := [A*sin(phi)^2, 5*Pi*(1/6), phi]

[A*sin(phi)^2, (5/6)*Pi, phi]





A := 2; plot3d([c1, c2, c3, c4, c5, c6, sph], phi = 0 .. 2*Pi, theta = 0 .. 2*Pi, coords = spherical, plotlist = true, scaling = constrained)





s1 := [sqrt(theta), 1, 1/10]; s2 := [sqrt(theta), 3, -1/10]; s3 := [sqrt(theta), 2, 1/10]; s4 := [sqrt(theta), 1.7, 1/7]

p := plot3d([sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], phi = 0 .. 2*Pi, theta = 0 .. Pi, coords = spherical, orientation = [-75, 58, 10], scaling = constrained, color = ["SkyBlue", "yellow", "yellow", "yellow", "yellow", "yellow", "yellow", "red", "red", "red", "red", "red", "red"])




plots[animate](plot3d, [[sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], theta = 0 .. Pi, phi = 0 .. 2*Pi, orientation = [B, 45, 52], coords = spherical], B = -180 .. 180)




3. Any other suggestions that could help with the aesthetics.

Last execution block is not producing any output. Why?

The 3x3 nonlinear system I am trying to solve is already a stylized version of my problem, as I already:

  1. Calibrated my equations before attempting to solve for them (search for "Calib_1" in my script)
  2. Split the original 6x6 system into two 3x3 sub-systems (since 3 out of 6 variables only appear in 3 out of 6 equations) and solved for one sub-system

What else can you think of? Should I instead use the parallel solver on the whole 6x6 system rather than just the unsolved 3x3 sub-system?

How to find, if exist, singular solutions? That is, some valuation of some parameters that will yield a solution that cannot be obtained by applying the same valuation to a general solution. Carl Love (who I cannot tag) once mentioned: "The parameter valuations that lead to singular solutions can often be guessed by using valuations that would produce zeros in denominators in the general solution. A singular solution can't be expressed as any instantiation of a generic symbolic solution. By instantiation I mean an assigment of numeric values to some parameters. Here's an example:"

#2x2 matrix and 2x1 vector. 5 parameters (a, b, d, x, y). The 2 decision variables are
#unseen and unnamed in this pure matrix-vector form. Their values are the two entries 
#in the solution vectors S0 and S1.

A:= <a, b; 0, d>;  B:= <x, y>;

#Get a generic solution:
S0:= LinearAlgebra:-LinearSolve(A, B);

#Instantiate 3 parameters (a, d, y) to 0 and solve again:
S1:= LinearAlgebra:-LinearSolve(eval([A, B], [a, d, y]=~ 0)[]);

#Note that no possible instantiation of S0 can produce S1.

Thank you!

Hello Everyone;

Hope you are fine. I I have make a code but there is error and dsolve comand is working. I also need to plot. Kindly help me. I am waiting kind response. Code is attached.

restart; Cm := 1.0; ENa := 50.0; EK := -77.0; ELeak := -54.387; gNa := 120.0; gK := 36.0; gLeak := .3; II := piecewise(`and`(t >= 10, t <= 40), 10.0, 0.); alpha_m := proc (V) .1*(V+40.0)/(1.0-exp((-1)*(V+40.0)/10.0)) end proc; beta_m := proc (V) 4.0*exp((-1)*(V+65.0)/18.0) end proc; alpha_h := proc (V) 0.7e-1*exp((-1)*(V+65.0)/20.0) end proc; beta_h := proc (V) 1.0/(1.0+exp((-1)*(V+35.0)/10.0)) end proc; alpha_n := proc (V) 0.1e-1*(V+55.0)/(1.0-exp((-1)*(V+55.0)/10.0)) end proc; beta_n := proc (V) .125*exp((-1)*(V+65.0)/80.0) end proc; eq1 := diff(V(t), t) = (II-gNa*m(t)^3*h(t)*(V(t)-ENa)-gK*n(t)^4*(V(t)-EK)-gLeak*(V(t)-ELeak))/Cm; eq2 := diff(m(t), t) = alpha_m(V(t))*(1-m(t))-beta_m(V(t))*m(t); eq3 := diff(h(t), t) = alpha_h(V(t))*(1-h(t))-beta_h(V(t))*h(t); eq4 := diff(n(t), t) = alpha_n(V(t))*(1-n(t))-beta_n(V(t))*n(t); ics := {V(0) = -65, h(0) = .6, m(0) = 0.5e-1, n(0) = .32}

















proc (V) .1*(V+40.0)/(1.0-exp((-1)*(V+40.0)/10.0)) end proc


proc (V) 4.0*exp((-1)*(V+65.0)/18.0) end proc


proc (V) 0.7e-1*exp((-1)*(V+65.0)/20.0) end proc


proc (V) 1.0/(1.0+exp((-1)*(V+35.0)/10.0)) end proc


proc (V) 0.1e-1*(V+55.0)/(1.0-exp((-1)*(V+55.0)/10.0)) end proc


proc (V) .125*exp((-1)*(V+65.0)/80.0) end proc


diff(V(t), t) = 3.683900000-120.0000000*m(t)^3*h(t)*(V(t)-50.0)-36.00000000*n(t)^4*(V(t)+77.0)-.3000000000*V(t)


diff(m(t), t) = .1*(V(t)+40.0)*(1-m(t))/(1.0-exp(-.1000000000*V(t)-4.000000000))-4.0*exp(-0.5555555556e-1*V(t)-3.611111111)*m(t)


diff(h(t), t) = 0.7e-1*exp(-0.5000000000e-1*V(t)-3.250000000)*(1-h(t))-1.0*h(t)/(1.0+exp(-.1000000000*V(t)-3.500000000))


diff(n(t), t) = 0.1e-1*(V(t)+55.0)*(1-n(t))/(1.0-exp(-.1000000000*V(t)-5.500000000))-.125*exp(-0.1250000000e-1*V(t)-.8125000000)*n(t)


{V(0) = -65, h(0) = .6, m(0) = 0.5e-1, n(0) = .32}


sol := dsolve({eq1, eq2, eq3, eq4, ics})

Error, (in dsolve) invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {{V(0) = -65, h(0) = 3/5, m(0) = 1/20, n(0) = 8/25}}





I think some form of simplify() would do but I am not sure how.

See the following script for more details:


#Define the assumptions ex-ante (variances as real and positive, correlations in between -1 and +1 and so on...) - or Maple wouldn't know

assume(`#msub(mi("mu",fontstyle = "normal"),mi("1"))`::real, `#msub(mi("mu",fontstyle = "normal"),mi("2"))`::real, `#msub(mi("mu",fontstyle = "normal"),mi("3"))`::real, `#msub(mi("lambda",fontstyle = "normal"),mi("1"))`::real, `#msub(mi("lambda",fontstyle = "normal"),mi("2"))`::real, `#msub(mi("lambda",fontstyle = "normal"),mi("3"))`::real, `#msub(mi("sigma",fontstyle = "normal"),mi("epsilon1"))`::real, `#msub(mi("sigma",fontstyle = "normal"),mi("epsilon2"))`::real, (`#msub(mi("nu",fontstyle = "normal"),mi("0"))`[1])::real, (`#msub(mi("nu",fontstyle = "normal"),mi("0"))`[2])::real, (`#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 2])::real, (`#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 3])::real, (`#msub(mi("rho",fontstyle = "normal"),mi("u"))`[2, 3])::real, (`#msub(mi("rho",fontstyle = "normal"),mi("v"))`[1, 2])::real, (`#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[1])::real, (`#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[2])::real, (`#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[3])::real, (`#msub(mi("sigma",fontstyle = "normal"),mi("v"))`[1])::real, (`#msub(mi("sigma",fontstyle = "normal"),mi("v"))`[2])::real)

assume(0 <= `#msub(mi("mu",fontstyle = "normal"),mi("1"))`, 0 <= `#msub(mi("mu",fontstyle = "normal"),mi("2"))`, 0 <= `#msub(mi("mu",fontstyle = "normal"),mi("3"))`, 0 <= `#msub(mi("lambda",fontstyle = "normal"),mi("1"))`, 0 <= `#msub(mi("lambda",fontstyle = "normal"),mi("2"))`, 0 <= `#msub(mi("lambda",fontstyle = "normal"),mi("3"))`, 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("epsilon1"))`, 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("epsilon2"))`, 0 <= `#msub(mi("nu",fontstyle = "normal"),mi("0"))`[1], 0 <= `#msub(mi("nu",fontstyle = "normal"),mi("0"))`[2], -1 <= `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 2] and `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 2] <= 1, -1 <= `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 3] and `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[1, 3] <= 1, -1 <= `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[2, 3] and `#msub(mi("rho",fontstyle = "normal"),mi("u"))`[2, 3] <= 1, -1 <= `#msub(mi("rho",fontstyle = "normal"),mi("v"))`[1, 2] and `#msub(mi("rho",fontstyle = "normal"),mi("v"))`[1, 2] <= 1, 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[1], 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[2], 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("u"))`[3], 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("v"))`[1], 0 <= `#msub(mi("sigma",fontstyle = "normal"),mi("v"))`[2])


t__1 := (`&sigma;__v`[2]^2*(`&rho;__v`[1, 2]^2-1)-`&sigma;__&epsilon;2`^2)*`&sigma;__v`[1]^2/((`&sigma;__v`[2]^2*(`&rho;__v`[1, 2]^2-1)-`&sigma;__&epsilon;2`^2)*`&sigma;__v`[1]^2-`&sigma;__&epsilon;1`^2*(`&sigma;__&epsilon;2`^2+`&sigma;__v`[2]^2))

t__2 := -`&sigma;__v`[1]*`&rho;__v`[1, 2]*`&sigma;__v`[2]*`&sigma;__&epsilon;1`^2/((`&sigma;__v`[2]^2*(`&rho;__v`[1, 2]^2-1)-`&sigma;__&epsilon;2`^2)*`&sigma;__v`[1]^2-`&sigma;__&epsilon;1`^2*(`&sigma;__&epsilon;2`^2+`&sigma;__v`[2]^2))

t__3 := (`&sigma;__v`[1]*`&rho;__v`[1, 2]*`&sigma;__v`[2]*`&sigma;__&epsilon;1`^2*`&nu;__0`[2]-`&nu;__0`[1]*`&sigma;__&epsilon;1`^2*(`&sigma;__&epsilon;2`^2+`&sigma;__v`[2]^2))/((`&sigma;__v`[2]^2*(`&rho;__v`[1, 2]^2-1)-`&sigma;__&epsilon;2`^2)*`&sigma;__v`[1]^2-`&sigma;__&epsilon;1`^2*(`&sigma;__&epsilon;2`^2+`&sigma;__v`[2]^2))

See for example that they share the same denominator...
# I want Maple to automatically/smartly choose the most compact way...e.g., (i) t2=t1+... or (ii) t2=t3*... (i) is equivalent to (ii) but I want Maple to pick (ii) if more compact than (i)
# I have 9 expressions like t1,t2,t3 and I want Maple to re-write them as function of each other smartly





It must be something similar to this, but my case is slighty different.

Dear all:

    I am using maple2022 to learn Fourier Series package - Maple Application Center ( . the author provide the package here:  I use the lastest version: Package FourierTrigSeries version 0.41 

there is no .mla so I do not know how to use this package.(the package is a little old). 

please enlight me if you know how to install this old package.

but the author provide the code inside fourierseries-structs.mws 

here is what I do:

1. first delete some lines which is not useful(which I shared in the attachment as

and remain everything inside module and save as .mw (maybe the orginal .mws is a old version of maple files)

2. export as .FourierTrigSeries.mpl (also attached)

3. use the examples.mws (the code also from author)

I got error as:

the package can be recognized, but the first line wil give some error which is out of my knowledge field.

everything mentioned above is here, including the original author's files.

Could you please have a look. your idea is valuable to me.

PS: this package is not available The Fourier Series package for Maple - Maple Application Center ( whenI try to learn  Teaching Fourier Series with Maple II 

if anyone keep it before, please share it.

thanks for your help.


Hi every one, I am trying to find a relation from an equation by putting it is equal to zero but could not get the solution.

Hi all, I am trying to draw a streamline for an ODE, but my worksheet is not working. Could anyone please have a look and help regarding the removal of the error? The value of unknown parameters such as k can be fixed randomly like 0.1,0.2 ,0.3 etc ?

Hello everyone; I am trying to extract ODE of a different order from the differential equation by considering the power of beta, but my file is not working.
Note: My file is working by fixing the value of n=2,3,4 etc., in the exponent, but I am interested in finding ODEs with n in power.

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