Dear all

I can I obtain the sigma-algebra generated by a given set. 

sigma_algebra.mw

thanks

I am attempting to use the pdsolve function in Maple to explicitly solve a PDE which is basically a perturbation of the Laplace equation.  Nothing happens when I enter pdsolve, however, is this because a boundary condition is also needed to produce a solution?  The BC which I have is that f(x, y, z) goes to zero as sqrt(x^2 + y^2 + z^2) goes to infinity but I am not sure how to enter such a BC in Maple.

PDE := diff(diff(f(x, y, z), x), x) + diff(diff(f(x, y, z), y), y) + diff(diff(f(x, y, z), z), z) - exp(-t*exp(sqrt(x^2 + y^2 + z^2)))*(diff(diff(f(x, y, z), x), x) + diff(diff(f(x, y, z), y), y) + diff(diff(f(x, y, z), z), z))/(1 + m/(2*sqrt(x^2 + y^2 + z^2)))^4 = 3/2*exp(sqrt(x^2 + y^2 + z^2) - t*exp(sqrt(x^2 + y^2 + z^2)))*(diff(f(x, y, z), x)*tx/sqrt(x^2 + y^2 + z^2) + diff(f(x, y, z), y)*ty/sqrt(x^2 + y^2 + z^2) + diff(f(x, y, z), z)*tz/sqrt(x^2 + y^2 + z^2))/(1 + m/(2*sqrt(x^2 + y^2 + z^2)))^4;

pdsolve(PDE);

Good day everyone,

I am running a maple code for a pde and is given the error code "Error, (in pdsolve/numeric/process_IBCs) initial/boundary condition must be given in terms of the dependent variables of the problem only ([W]), got ((D@@2)[1](W))(0, tau) = 0". The link is attached below.

pde.mw

Thanks in advance.

Clifford http://math.tntech.edu/rafal/cliff12/index.html

I read really good reviews from fellow Maple users about Clifford Package( above link).

I couldn't access the link provided. What is the best way to install Clifford Package or get access to the link.

Thank You.

Hey everyone!

I have a complex function stored in a file (Comp-func.txt). The function is continues everywhere on the real axis (X-axis.txt). However, its log shows a jump somewhere close to x=-1.5. I would like to understand how Maple interprets this "jump" and how to avoid such numerical artifact.

thank you.

 Comp-func.txt

Jump-Log-Func.mw

X-axis.txt

Dear all

Can I compute using maple some Riemann Stieltjes integrals 

RSI.mw

Thanks 

This also looks like an applyrule bug.

Download applyrule-bug2.mw

This looks like a bug to me but please correct me if it is not.

Download applyrule-bug1.mw

How to trace the 2 parabolas that pass through 4 cocyclical points. Thank you

Hello all. I'm using version 2021.2 to try to make some simple energy plots for my research. The math is pretty straightforward, but for some reason I cannot get the results to plot properly. My code is below:

restart;
A := 7.17;
B := 2.56*10^(-3);
C := 0.08*10^5;
_local(D);
1;
D := 0*10^(-6);
                           A := 7.17

                      B := 0.002560000000

                          C := 8000.00

                             D := 0

T_0 := 298; 

G0 := -71.398;

S0 := 45.106;

Hf := -57.95;

cp := A + B*T + C/T^2 + D(T)^2;             

`ΔH` := int(cp, T = T_0 .. T);

`ΔS` := int(cp/T, T = T_0 .. T);
           
G := -S0*T - T*`ΔS` + Hf + `ΔH`;

plot(G, T = T_0 .. T_max);

Which yields the following error message:

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

I've looked through everything I can find on this issue, and I'm coming up empty. Anyone know what's happening here?

Dear colleagues.

I use gradplot for a displacement vector in x-direction only, as foolows

gradplot(u1(x), x = 0 .. a, y = 0 .. b, grid = [10, 10], arrows = SLIM, color = u1(x), T, caption = typeset("The displacement field"), fieldstrength = fixed, size = [0.3, 0.5])

I need to make color legend to show the minimum and maximum value and in between for the displacement.

Amr

I need to use convert of complex exponentials to trig, but only to convert exp(I*x) to cos/sin using Euler formula.

The problem is that, since this is done in code without looking at what is inside the exp(), Maple will also convert non complex exponentials as exp(x) to hyperpolic trig which I do not want.  An example will make this clear

For an example, given exp(3*I*x - x)  and applying convert/trig to this it gives 

             (cosh(x) - sinh(x))*(cos(3*x) + sin(3*x)*I)                       --(1)

But I only want to conver the exp(3*I*x) part of the of the above to obtain

          exp(-x) *  (cos(3*x) + sin(3*x)*I)                          ---(2)

I can break  exp(3*I*x - x) first using expand command and obtain  exp(-x) * exp(3*I*x) and then parse this and filter out the complex exponentials (may be using select with has I) and then use convert on those terms only leaving the non-complex exponentials alone. But this gets messy for more complex exponentials.

Is there an easy way to tell Maple  to convert expression of the form exp(I*f(x) + g(x)) to trig but only to sin/cos, hence leaving the exp( g(x) ) as a factor? I looked at help but see nothing there so far.

Maple 2021.2

We have just issued a critical fix to Maple, MapleSim, and Maple Flow running on macOS.

We have heard from some users who were experiencing serious problems with doubled characters while using Maplesoft products on macOS, including these reports on MaplePrimes. Further investigation determined that these problems appear specifically on macOS 11 and macOS 12.  I am happy to report that we have now corrected the problem, and a patch is available. 

Anyone who uses macOS 11 or macOS 12 should install this update immediately. We also strongly recommend that all macOS users install this update, to avoid problems that may be triggered by future updates to your operating system.

To obtain this update:

• If you have Maple only, follow the instructions on the Maple 2021.2.1 update page.
• If you have MapleSim, visit the MapleSim 2021.2.1 update page.
• If you have Maple Flow, follow the instructions for Maple Flow 2021.2.1.

For those who have experienced problems, we apologize for the inconvenience and thank you for your patience while we worked to find a solution.

I try to know an equation of the tangent on the point [0.504244923, 0.3781836925] on the hyperbola7*x^2 - 7*y^2 - 12.0*x + 9.0*y + 2.25 - 2*x*y=0.How can I do that? Thank you.

I see that one of the parameters of the  function Graph accepts a Array of neighbors.

So I gave it a try. 

G := GraphTheory:-Graph([1,2],[[2],[1]])

G := `Graph 10: an undirected unweighted graph with 2 vertices and 1 edge(s)`

It looks pretty good. But there's something wrong with the following codes.

G := GraphTheory:-Graph([0,1],[[1],[0]])

Error, (in GraphTheory:-Graph) invalid vertex 0 in list of neighbors

G := GraphTheory:-Graph(["0","1"],[["1"],["0"]])

Error, (in GraphTheory:-Graph) cannot determine if this expression is true or false: 1" < 1 or 2 < "1
 

G := GraphTheory:-Graph(["a","b"],[["b"],["a"]])

Error, (in GraphTheory:-Graph) cannot determine if this expression is true or false: b" < 1 or 2 < "b
 

How to use  Array of neighbors in  Graph  correctly?

PS: The source of the problem is that I got the following list of adjacencies of a graph  in Python and I want to convert it to  a graph in Maple. Its vertices are [0,1,2, ..., 9].

[[1, 2, 3, 4, 5, 6], [0, 2, 3, 4, 7, 8],
 [0, 1, 3, 5, 7, 9], [0, 1, 2, 6, 8, 9],
 [0, 1, 5, 6, 7, 8], [0, 2, 4, 6, 7, 9], 
[0, 3, 4, 5, 8, 9], [1, 2, 4, 5, 8, 9], 
[1, 3, 4, 6, 7, 9], [2, 3, 5, 6, 7, 8]]

G := GraphTheory:-Graph([$0..9],[[1, 2, 3, 4, 5, 6], 
[0, 2, 3, 4, 7, 8], [0, 1, 3, 5, 7, 9],
 [0, 1, 2, 6, 8, 9], [0, 1, 5, 6, 7, 8],
 [0, 2, 4, 6, 7, 9], [0, 3, 4, 5, 8, 9],
 [1, 2, 4, 5, 8, 9], [1, 3, 4, 6, 7, 9], 
[2, 3, 5, 6, 7, 8]])

Error, (in GraphTheory:-Graph) invalid vertex 0 in list of neighbors