When taking notes I sometimes use the palette to insert a matrix into a worksheet. When I do this, the main aspect that is useful to me is being able to visualize matrix expressions as I would write them.

I would like to do the same but for determinants of matrices. Is there a way to get almost the same thing as with the matrix palette, but with vertical bars denoting a determinant rather than the brackets used for matrices?

How do we compute integrals of functions or expressions that have units attached?
For example

The results of the integrals have the wrong units.

Download integration_with_units.mw

I have X=+-1,

and I want to calculate X^n.

 Thank's

Dear members of the forum, please tell me if it is possible to calculate the series presented below by Maple 2022. As far as I understand, first you need to calculate the inner and then the outer sum, but I don’t know how to do this with the help of the program, this series does not converge, as it seems to me, but I can be wrong, if the series diverges, then I need to show it.

Sorry for my ignorance, but maybe I wrong apply such commands for calculation this sums:

Sum(F, a = 1 .. infinity, b = 1 .. infinity) = DefiniteSummation(F, a = 1 .. infinity, b = 1 .. infinity)

I understand, that Sum () not be able to recive more than one args, but I don't understand how to make this calculation...

Any idea? Thanks for advices and help!

Dear All,

I have an executable program which I have generated with Fortran. Is it possible to run such a program from Maple? It sounds a bit weird but that would simplify my computation, since I would not need to use scripts in Linux. Thank you very much.

Cheers.

Let's say we have four equations and four unknowns and we use solve to find a solution.

The return value of solve is a set.

Here is an example

If we want to make the four expressions above procedures, the manual way is to basically copy the right-hand side of each expression and then write

T__1 := (R,m__1, m__2, g, I__s) -> ...

T__2 := (R,m__1, m__2, g, I__s) -> ...

a := (R,m__1, m__2, g, I__s) -> ...

alpha := (R,m__1, m__2, g, I__s) -> ...

Is there a way to do this automatically from the return value of solve?

If the return value were a list, I would use something like

T__1 := unapply(result[1], R, m__1, m__2, g, I__s)

T__2 := unapply(result[2], R, m__1, m__2, g, I__s)

a := unapply(result[3], R, m__1, m__2, g, I__s)

alpha := unapply(result[4], R, m__1, m__2, g, I__s)

But the return value is not a list.

So, in summary my quesions are

1) what, in general, is the best way to obtain the desired procedures?

2) is there a way to use the strategy I suggested if the result were a list, but for sets?

Download solveEqs.mw

i need to differentiate this equation 

Potential energy eq:
p := (m1*a1 + m2*(a123 + z(t)))*sin(theta(t))*g + m3*(sin(theta(t))*(a1234 + z(t)) + cos(theta(t))*a5)*g;

  p := (m1 a1 + m2 (a123 + z(t))) sin(theta(t)) g    + m3 (sin(theta(t)) (a1234 + z(t)) + cos(theta(t)) a5) g

i have tried these 2 methods

diff(p, theta)

diff(p, theta(t))

but both of them comes out 0 

where they should give 

diff((m1*a1 + m2*(a123 + z))*sin(theta)*g + m3*(sin(theta)*(a1234 + z) + cos(theta)*a5)*g, theta);

       (m1 a1 + m2 (a123 + z)) cos(theta) g + m3 (cos(theta) (a1234 + z) - sin(theta) a5) g

how is the syntax for partial differentiating a pre defined equation dependent on time.

I would like to know if there is a difference in the definition of the following words to describe a collection of code in Maple.  Specifically, is there a difference between an internal command, an internal procedure and an internal function?  Or are the folks who wrote Help using the three words interchangeably?  

For example, Help describes "restart" as a command.  That seems reasonable.  It also describes "evalf" as a command. 

Sin, cos and tan are described as functions.  That also appears to be reasonable.  "eval" and "convert" are also labeled as functions. 

However, "unassign" is a procedure as is "animate".  I could understand that since one might assume there is nothing returned. And yet one can assign an animation to a variable/name.

Section 1.4 of the Programming Guide discusses Maple Library Commands under the subheading of "procedures".  However, section 3.15 discusses "function types" which with section 3.8 implies these collections of code might be viewed as functions. (And then there is the function operator of a procedure.) 

I'm trying to compartmentalize the Maple language, but maybe I should not. My inclination is to call everything for which one uses a functional call (section 3.8) as a procedure.  Any assistance would be appreciated.

Dear Maple users

I have encountered a very strange error at one of my students. When using functions from the Expression Palette, she receives an error. It happens every time she is using this Palette. A reinstallation of Maple didn't help solve this issue. When using Command Completion for the very same function (for example cosine or square root), it works properly. 

She did send a Maple file to me in order for me to investigate it. I opened it and reexecuted the entire document. The error messages remained. I tried applying the functions from the Expression Palette myself resulting in the same errors. I even opened a new document and tried it again. Still an error. Then I closed Maple completely and opened it again. Within a new document, I applied a function from the Expression Palette. Now it worked!! I can't seem to understand  the logic behind this behavior. The file sent to me by the student obviously contain some kind of error, but why will this error spread to a new document, which I have opned on my own computer? My own computer does not have any issues with Maple. 

I have attached the Maple file with the errors and a screen shot. I hope someone can explain this strange behavior and tell me how I can help this student make Maple work again. 

Kind regards,

Erik V.

Maple file:

Error.mw

After saving and closing my maple file, it was corrupted when I tried to open it again later. 

I tried searching for a solution without any luck...can someone help me repair it?

Regnede_Eksamenssæt.mw

(When it asks to save it as Regnede_Eksamenssæt_1 only a small part of the document is included)

restart;
with(geometry):
with(plots):
_EnvHorizont:lName = 'x';
_EnvVerticalName = 'y';
Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc;
R := 5;
ang := [3/4*Pi, -(3*Pi)/4, -Pi/6,4*Pi/9];
seq(point(`||`(P, i), [R*cos(ang[i]), R*sin(ang[i])]), i = 1 .. 4);
pts:=[seq(P || i,i=1..4)]:
seq(dsegment(`||`(seg, i), [`||`(P, i), `||`(P, irem(i, 4) + 1)]), i = 1 .. 4);
Triangle(Tr1,[P1,P2,P4]);
EulerCircle(Elc1,Tr1,'centername'=o);
circle(cir, [point(OO, [0, 0]), R]);
dist := proc(M, N) sqrt(Vdot(M - N, M - N)); end proc;
display(draw([P1(color = black, symbol = solidcircle, symbolsize = 12), 
P2(color = black, symbol = solidcircle, symbolsize = 12), 
P3(color = black, symbol = solidcircle, symbolsize = 12), 
P4(color = black, symbol = solidcircle, symbolsize = 12),seg1,
seg2,seg3,seq4,Tr1,Elc1,
cir(color = blue)]), 
textplot([[seq( [ coordinates(`||`(P, i))[], convert(`||`(P, i), string)],i=1..4], 
,align = [above, right]), axes = none);
does not recognize neg4 or tr1? I don't know to manage. Thank you.

When we use Maple input to define a procedure in a worksheet in Document mode, how do we evaluate/execute the command. I am used to just hitting <Enter> when using 2d Math. Today, I've been trying to use Maple input, but when I hit <Enter> nothing happens, or something does happen that messes up the definition such that I get a 

Warning, premature end of input, use <Shift> + <Enter> to avoid this message.

right in the middle of the procedure which then generates a 

Error, global declaration unexpected outside procedure or module
Error, missing operator or `;`

and the only way to even execute and see these errors is by executing the whole worksheet. 

Attached is an example: 
 

I can hit enter on the 2d math version, but not on the first 1d math version. On the 1d version, if I go to right after "end:" and hit <Enter> I get an error: Error, reserved word `end` unexpected.

Download 1dmathproc.mw

The documentation on plots:-densityplot says

Any additional arguments are interpreted as options which are specified as equations of the form option = value. For example, the option grid = [m, n] where m and n are positive integers specifies that the plot is to be constructed on an m by n grid at equally spaced points in the ranges a..b and c..d respectively. By default a 49 by 49 grid is used; thus 2401 points are generated, and 2401 colored cells are displayed.

Consider the following simple example

If we look at the output from the print statement inside of g we see

Download DensityPlotGridQuestions.mw

That is, there are 16 points in the grid, not 5x5=25.

Is the documentation incorrect or did I miss something?

This question is about an aspect of the code below. In fact, the code could be made simpler to get at the question, but I chose to show you how the problem originated. 

We start with a 4x3 matrix A. There is a procedure, convertArrayToTable, that takes this matrix and creates a table. The table is such that the keys are the numbers in the first column of A. For each such key k1, the associated value is another table. The latter table has as keys the values in the second column that have k1 in the first column.

Now, further below, if you are curious I write about why I am doing this (what the exact real problem is). For now, I am generating a matrix B which in is formed by the concatenation of A and 2A, along the column (ie, A on top of 2A).

So for this matrix B, the table T that is generated has, for example a key 1 and the associated value is a table with keys 0.2 and 0.400000000000000.

I wish to be able to access T[1][0.400000000000000] but this is not working and I don't know why.
 

Download tableDecimalIndex.mw

So now just a brief note on why I want to create such a table.

I want to create a density plot based on the values in the rows of B. In the case of the simple example shown above, the grid of values would be based on values of x from 1 to 4 and of y from 0.2 to 0.400000000000000. Then I would specify, say "grid=[5,3]" for an eight point grid. 

In this example I am assuming the points used by the densityplot procedure would be exactly the ones in the rows of B, ie (1,0.2), (2,0.2), (3,0.2), (4,0.2),(1,0.400000000000000),(2,0.400000000000000),(3,0.400000000000000),(4,0.400000000000000).

The function I would pass in the signature

densityplot(f, a..b, c..d)

would be a custom procedure that I am assuming would be called as f(x,y) and would simply look up T[x][y] in the table I created to get the value.

Of course in my real problem the grid has way more points.

I am making a lot of assumptions about this densityplot procedure, but the documentation isn't very clear at all.

Here is a proof of concept of what I am trying to achieve (note that below, I am avoiding the issue of the decimal keys in tables by using integers instead):
 

In the above output, the output from the print statement in the f procedure is not being shown. Locally on my computer it is shown and f is called at the expected values (the ones in the rows of B). So that is all good. The issue seems to always go back to keying in to tables with certain (but not all) decimal numbers

Download DensityPlot.mw

restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':
_EnvVerticalName = 'y':
Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc:
R := 5:
ang := [2/3*Pi, -3*Pi*1/4, -Pi*1/6]:
seq(point(`||`(P, i), [R*cos(ang[i]), R*sin(ang[i])]), i = 1 .. 3):
seq(dsegment(`||`(seg, i), [`||`(P, i), `||`(P, irem(i, 3) + 1)]), i = 1 .. 3):
circle(cir, [point(OO, [0, 0]), R]):
dist := proc(M, N) sqrt(Vdot(M - N, M - N)); end proc:

display*([draw*[P1(color = black, symbol = solidcircle, symbolsize = 12), 
P2(color = black, symbol = solidcircle, symbolsize = 12), 
P3(color = black, symbol = solidcircle, symbolsize = 12), 
cir(color = blue)], 
textplot*([[coordinates(P1)[], "P1"], 
[coordinates(P2)[], "P2"], 
[coordinates(P3)[], "P3"]], align = [above, right])], axes = none);
                /[                
 plots:-display |[geometry:-draw [
                \[                

   P1(color = black, symbol = solidcircle, symbolsize = 12), 

   P2(color = black, symbol = solidcircle, symbolsize = 12), 

   P3(color = black, symbol = solidcircle, symbolsize = 12), 

                                       /[[-5  5  (1/2)      ]  
   cir(color = blue)], plots:-textplot |[[--, - 3     , "P1"], 
                                       \[[2   2             ]  

   [  5  (1/2)    5  (1/2)      ]  [5  (1/2)  -5      ]]  
   [- - 2     , - - 2     , "P2"], [- 3     , --, "P3"]], 
   [  2           2             ]  [2         2       ]]  

                         \]             \
   align = [above, right]|], axes = none|
                         /]             /

no figure drawn, Why? Thank you