Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi!

Somebody know how Maple computes (numerically) the values of the Z function? That is, if we run the command evalf(Z(3)), How compute Maple this number?

Many thanks in advance for your comments.

I am having trouble calculating exterior derivatives for one forms, maple does not seem to recognize them as one forms.

 

Sigma2 := (R^2+a^2)^2-Delta*a^2*sin(Theta)^2;
rho2 := R^2+a^2*cos(Theta)^2;
z := 2*M*R/rho2;
interface(typesetting = extended);
with(DifferentialGeometry); with(Tensor);
DGsetup([T, R, Theta, Phi], BlackHole, verbose);
         The following coordinates have been protected:
                       [T, R, Theta, Phi]
  The following vector fields have been defined and protected:
   [Typesetting:-mcomplete(D_T, Typesetting:-_Hold([

     _DG([["vector", BlackHole, []], [[[1], 1]]])])), 

     Typesetting:-mcomplete(D_R, Typesetting:-_Hold([

     _DG([["vector", BlackHole, []], [[[2], 1]]])])), 

     Typesetting:-mcomplete(`D_Θ`, Typesetting:-_Hold([

     _DG([["vector", BlackHole, []], [[[3], 1]]])])), 

     Typesetting:-mcomplete(`D_Φ`, Typesetting:-_Hold([

     _DG([["vector", BlackHole, []], [[[4], 1]]])]))]
   The following differential 1-forms have been defined and 

      protected:
[Typesetting:-mcomplete(dT, 

  Typesetting:-_Hold([_DG([["form", BlackHole, 1], [[[1], 1]]])])), 

  Typesetting:-mcomplete(dR, 

  Typesetting:-_Hold([_DG([["form", BlackHole, 1], [[[2], 1]]])])), 

  Typesetting:-mcomplete(`dΘ`, 

  Typesetting:-_Hold([_DG([["form", BlackHole, 1], [[[3], 1]]])])), 

  Typesetting:-mcomplete(`dΦ`, 

  Typesetting:-_Hold([_DG([["form", BlackHole, 1], [[[4], 1]]])]))

  ]
g := evalDG((-1+z)*`&t`(dT, dT)+`&t`(dT, dR)+`&t`(dR, dT)+rho2*`&t`(dTheta, dTheta)-z*a*sin(Theta)^2*(`&t`(dPhi, dT)+`&t`(dT, dPhi))-a*sin(Theta)^2*(`&t`(dR, dPhi)+`&t`(dPhi, dR))+Sigma2*sin(Theta)^2*`&t`(dPhi, dPhi)/rho2);


ON := evalDG(DGGramSchmidt([D_T, D_R, D_Theta, D_Phi], g, signature = [-1, 1, 1, 1]));
e0 := evalDG(ON[1]);

oneform:=RaiseLowerIndices(g,e0,[1]);

ExteriorDerivative(oneform);

  1. I use both Maple and Matlab
  2. I also install (a stripped down version of) Maple as the "symbolic toolbox" for Matlab using the executable MapleToolbox2022.0WindowsX64Installer.exe, which lives in C:\Program Files\Maple 2022. This gives me acces to (some) symbolic computation capability from within Matlab.
  3. This installation process has been working for as long as I remember, certainly more than 10 years
  4. With Maple 2022 and Matlab R2022a, this installation process ran with no problems and I can perform symbolic computation within Matlab
  5. However, although the Matlab help lists the Maple toolbox as supplemental software (as in all previous releases), I can no longer acces help for Maple from within Matlab - I just get a "Page not found" message
  6. The relevant Maple "help" is at the same place within the Matlab folder structure which is C:\Program Files\MATLAB\R2022a\toolbox\maple\html
  7. I have just spoken to support at Matlab and they claim tha this must be a Maple (or Maple toolbox installer issue) - so nothing to do with them!
  8. Has anyone else had a similar problem andd found a workaround?

Hello,

Im a tax student and tring to figure out Maple. I plotted the following graph with the code:

implicitplot([Vth = Vps, V1 = 25000, V1 = 50000, V1 = 75000, V1 = 100000], E = 0 .. 1000000, T = 0 .. 15, color = [black], labels = ["E in (EUR)", "T (in Jahren)"], labelfont = [times, bold, 12], view = [0 .. 1000000, 0 .. 15])

I would like to color the intermediate areas and attach a legend. A colleague has plotted this for me, but unfortunately has not provided me with the source code and has now lost the file. Can someone help me to re-plot the last shown chart?

Thanks so so much in advance!! Best regards Rebekka

Hello,

Im a tax student trying to use Maple for my studies. I plotted two surfaces in a 3D coordinate system, the surfaces intersect = indifference area.

The current formula is like this:

plot3d([Vth/E, Vps/E], E = 0 .. 1000000, T = 0 .. 15, labels = ["E", "T", ""], color = [gray, white], labels = ["E (in EUR)", "T (in Jahren)", ""], labelfont = [times, bold, 12])
It looks like this:

I would like to draw in the same graph, the indifference area (Vth/E = Vth/E), it looks like this:


A colleague has plotted this for me, but unfortunately has not provided me with the source code and has now lost the file. Can someone help me to re-plot the last shown chart?


Thanks a lot in advance!!

Rebekka

Switching font to Arial apparently makes the sign disappear in MathContainers.

Vorzeichen.mw

If i want to do mathematical modelling for planetary motion, how can maple help me with it?

Does maple software support Benders decomposition technique for Mixed Integer Linear Programming? If no, how we can implement it in maple? Any suggestions. 

Thank you

hello 
i have a Table in my worksheet; 

it countains 3 coulmns, and each coulmns cointains a loop that requires about a day to evaluate. 

is there a way to excute the 3 coulmns in parallel, there is no interaction between them and i cant seprete them into different worksheets.

thanks in advance.

Anyone experience a delay in typing as the screen fills with text/math etc.?

I'm using Maple 2021 and as the space is filled typing slows. I can finish typing and watch the last 4 keys enter on the screen.


Hi !

Looks like there is a bug in the inert "Diff" command.

I have Maple 2018 on Windows 10 ,64 bits.

Does Maple consider Diff(f(x),x) to be equal to Diff(f(x),[x]) ?

It should be the same.

Maple displays  that it is equal but keeps in memory something else.

In the attached file, I give a very simple example.

I don't like to say this but my old version of Maple V Release V (1997) is more consistent i.e.

this version shows it's different and  keeps in memory that difference.

diff-problem.mw

 

I wonder if newer versions have this problem ?


Best regards !

When using the built-in fsolve function to find the roots of a polynomial, how does exponentiation occur? For example, x3 is found​​​​​​first, and then to find x4, will he start again from the beginning, that is, x*x*x*x, or will he take the value of x3​​​​​​ and multiply by x? The teacher is interested in finding out this, but I don't know how to find out myself. 

Hello Everyone;

Hope you are fine. I am solving system of odes using rk-4 method. For this purpose I formulate the "residual" (on maple file) which is further function of "x" and "y". With the help of discritization point further I convert "residual" into system of ode's. Then i used "sys111 := solve(odes_Combine, `~`[diff](var, t))" to simplify the system. Finnally i applied RK-1. Code is pasted and attached. This all process is for "N=4". When i increase the value of "N", number of Odes increase accordingly. With increasing value of "N" the comand "sys111 := solve(odes_Combine, `~`[diff](var, t))" taking a lot of time due to heavy computation. Is that any way to proceed without this comand for rk-1?

Question1.mw

 


 

restart; with(PDEtools, Solve); with(LinearAlgebra); with(plots); DD := 30; Digits := DD; N := 4; nu := 1.0; t0, tf := 0, 1; Ntt := 10; h := evalf((tf-t0)/(Ntt-1)); xmin := 0; xmax := Pi; `Δxx` := 1.0*xmax/N; ymin := 0; ymax := xmax; `Δyy` := 1.0*ymax/N

0, 1

 

.111111111111111111111111111111

 

.785398163397448309615660845820

 

.785398163397448309615660845820

(1)

residual := 1.000000000*(diff(A[0, 0](t), t))-32.00000000*A[2, 0](t)-32.00000002*A[0, 2](t)+(diff(A[1, 1](t), t))*(4.000000001-8.000000003*y-8.000000003*x+16.00000000*x*y)+(diff(A[1, 0](t), t))*(-2.000000000+4.000000000*x)+(diff(A[0, 3](t), t))*(-4.000000000+40.00000000*y-95.99999994*y^2+64.00000001*y^3)+(diff(A[0, 2](t), t))*(3.000000000-16.00000001*y+16.00000001*y^2)+(diff(A[0, 1](t), t))*(-2.000000001+4.000000000*y)-A[3, 3](t)*(768.0000000-7680.000000*y+18432.00000*y^2-12288.00000*y^3-1536.000000*x+15360.00000*x*y-36863.99998*x*y^2+24576.00000*x*y^3)-A[3, 2](t)*(-576.0000002+3072.000000*y-3072.000000*y^2+1152.000000*x-6144.000000*x*y+6144.000000*x*y^2)-A[3, 1](t)*(384.0000000-768.0000000*y-768.0000006*x+1536.000000*x*y)-A[3, 0](t)*(-192.0000000+384.0000000*x)-A[2, 3](t)*(-128.0000000+1280.000000*y-3072.000000*y^2+2048.000000*y^3)-A[2, 2](t)*(96.00000000-512.0000002*y+512.0000002*y^2)-A[2, 1](t)*(-64.00000002+128.0000000*y)-A[3, 3](t)*(767.9999998-1536.000000*y-7679.999998*x+15360.00000*x*y+18432.00000*x^2-36864.00000*x^2*y-12288.00000*x^3+24576.00000*x^3*y)-A[2, 3](t)*(-575.9999998+1152.000000*y+3072.000000*x-6144.000000*x*y-3072.000000*x^2+6144.000000*x^2*y)-A[3, 2](t)*(-128.0000000+1280.000000*x-3072.000000*x^2+2048.000000*x^3)-A[1, 2](t)*(-64.00000002+128.0000000*x)-A[1, 3](t)*(384.0000000-768.0000000*y-767.9999998*x+1536.000000*x*y)-A[2, 2](t)*(96.00000004-512.0000002*x+512.0000002*x^2)+(diff(A[3, 3](t), t))*(16.00000000-160.0000000*y+383.9999999*y^2-256.0000000*y^3-160.0000000*x+1600.000000*x*y-3839.999999*x*y^2+2560.000000*x*y^3+384.0000000*x^2-3840.000000*x^2*y+9215.999998*x^2*y^2-6144.000001*x^2*y^3-256.0000000*x^3+2560.000000*x^3*y-6143.999998*x^3*y^2+4096.000000*x^3*y^3)+(diff(A[3, 2](t), t))*(-12.00000000+64.00000002*y-64.00000002*y^2+120.0000000*x-640.0000002*x*y+640.0000002*x*y^2-288.0000001*x^2+1536.000000*x^2*y-1536.000000*x^2*y^2+192.0000000*x^3-1024.000000*x^3*y+1024.000000*x^3*y^2)+(diff(A[3, 1](t), t))*(8.000000003-16.00000000*y-80.00000003*x+160.0000000*x*y+192.0000000*x^2-384.0000000*x^2*y-128.0000001*x^3+256.0000000*x^3*y)-A[0, 3](t)*(-191.9999999+384.0000000*y)+(diff(A[3, 0](t), t))*(-4.000000000+40.00000000*x-96.00000002*x^2+64.00000001*x^3)+(diff(A[2, 3](t), t))*(-12.00000000+120.0000000*y-287.9999999*y^2+192.0000000*y^3+64.00000000*x-640.0000000*x*y+1536.000000*x*y^2-1024.000000*x*y^3-64.00000000*x^2+640.0000000*x^2*y-1536.000000*x^2*y^2+1024.000000*x^2*y^3)+(diff(A[2, 2](t), t))*(8.999999999-48.00000002*y+48.00000002*y^2-48.00000000*x+256.0000001*x*y-256.0000001*x*y^2+48.00000000*x^2-256.0000001*x^2*y+256.0000001*x^2*y^2)+(diff(A[2, 1](t), t))*(-6.000000002+12.00000000*y+32.00000001*x-64.00000000*x*y-32.00000001*x^2+64.00000000*x^2*y)+(diff(A[2, 0](t), t))*(3.000000000-16.00000000*x+16.00000000*x^2)+(diff(A[1, 3](t), t))*(8.000000003-80.00000003*y+192.0000000*y^2-128.0000000*y^3-16.00000000*x+160.0000000*x*y-383.9999999*x*y^2+256.0000000*x*y^3)+(diff(A[1, 2](t), t))*(-6.000000000+32.00000001*y-32.00000001*y^2+12.00000000*x-64.00000002*x*y+64.00000002*x*y^2):

for i2 from 0 while i2 <= N-1 do odes11[0, i2] := simplify(eval(residual, [x = 0, y = i2*ymax/(N-1)])) = 0; odes11[N-1, i2] := simplify(eval(residual, [x = xmax, y = i2*ymax/(N-1)])) = 0 end do:

8

(2)

odes_Combine := {seq(seq(odes11[i, j], i = 0 .. N-1), j = 0 .. N-1)}:

sys111 := solve(odes_Combine, `~`[diff](var, t)):

ICS1 := {A[0, 0](0) = .444104979341173495851499233536, A[0, 1](0) = .198590961107083475045046921568, A[0, 2](0) = -0.167999146492673347540059075790e-1, A[0, 3](0) = -0.869171705198864625153083083786e-3, A[1, 0](0) = .198590961107083475045046921567, A[1, 1](0) = 0.888041604305848495880917177172e-1, A[1, 2](0) = -0.751243816645416714455046298805e-2, A[1, 3](0) = -0.388668563362181391196975707953e-3, A[2, 0](0) = -0.167999146492673347540059075793e-1, A[2, 1](0) = -0.751243816645416714455046298835e-2, A[2, 2](0) = 0.635518954643030408055028178047e-3, A[2, 3](0) = 0.328796368925226898150257328603e-4, A[3, 0](0) = -0.869171705198864625153083083734e-3, A[3, 1](0) = -0.388668563362181391196975707910e-3, A[3, 2](0) = 0.328796368925226898150257328592e-4, A[3, 3](0) = 0.170108305076655667148638268230e-5}:

f, diffs := eval(GenerateMatrix(`~`[`-`](`~`[rhs](sys222), `~`[lhs](sys222)), var1))