Dear All,
Does Maple have built-in Finite Fourier Sine/Cosine Transformation which is defined as below?
2/L*int(f(x)*sin(n*Pi/L*x),x=0..L);

How can I get the finite Fourier transform for the derivatives of a function in terms of its own Fourier transform? 

I know that the fouriersin/fouriercos commands of the inttrans package have the Fourier sine/cosine transformation for the interval from x=0 to infinity?

Best wishes

I am facing a kind of strange problem.  y'=y/x-5^y/x ,   y(0)=5 Cauche equation  it gives empty round brackets () . If I restart Maple engine and perform the same. Kindly help, what is this? 

restart;
with(DEtools);

de1 := diff(y(x), x) = y(x)/x - 5^(-y(x)/x)

de1 := diff(y(x), x) = y(x)/x - 5^(-y(x)/x)

an := dsolve({de1, y(0) = 5}, y(x))

an := ()

I have two expressions, wo_theta and with_theta, which depend on multiple variables.

I would need your help to:

1. Verify, as formally as possible, that wo_theta > with_theta always, i.e., for any value of theta different from zero (and regardless of the values taken up by the other variables)
2. Show the above in a way that is easy and immediate to interpret (perhaps using some type of plot?)

In other words, I want to verify that as soon as I introduce any theta in my expression such expression becomes smaller:

Download inequality.mw

When I annotate a MapleFlow worksheet, I would like to typset some text as a superscript or a subscript for clarity, and to match the math expression. Is there a method to format text using superscripts and subscripts?

Does the Premium version of Maple Calculator for Android Smartphones come with Maple 2023 or does it have to be purchased separately. Thanking you in advance.

Dear All,
I want to simplify the following trigonometric expression, considering that m is an integer number. For this, I use the following command:

expr:= 4*cos(Pi*m)/(Pi*(2*m + 1)); 
simplify(%, assume=integer);
factor(%);

However, if I want to simplify the following trigonometric expression, m is an integer number, and alpha is a real number, using the following command will lead to the wrong answer because alpha is also considered an integer number. Please guide me.

4*cos(Pi*m+2*alpha*Pi)/(Pi*(2*m + 1));
simplify(%, assume=integer);
factor(%);

Best wishes

I have noticed over a few questions I have asked recently.
I ask a question.                   It goes to top of active converstaions
Some  one answers                                            "

I Reply                                                                *

A bit of time passes  so slides  of the top six/seven that show

Another Reply/Answer from someone                possibly does not show in active conversations.  I catch this by the orange flag or email notification

I reply                                 Does not appear in active conversations..

       This can kill the conversation chain.

I have even tried changing one of me replys to an answer but did not go to top active conversations again.

Has anyone else expperienced this?  

If a type is not known, an error is thrown

type([],foo)
Error, type `foo` does not exist

Since no error is thrown, these types are known

type({},'{}');# why that output?
                             false

type([],'[]')
                              true

I would have expceted {} and [] to be listed as subtypes of set and list since their counterparts (nonemptylist and nonemptyset) exist. Technically the types {} and [] are not needed since negating

not(type([],nonemptylist));
not(type({},nonemptyset));
                              true

                              true

works.  However, the types exist, hence my question

How can I make a legend for this plot?

plot([17.85*(2.65*t^2 + 1 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 47 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 97 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 147 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 197 + 3*t)^2/t^2], t = 0 .. 25, labels = ['t', 'x'], labelfont = [Times, 12])

 I got the following figure.

Now I want to put a legend box in this plot for each color line. How can I do it?
 

I need help trying to remove some null elements from a listlist, that i converted from an Array. 

Example: I have a list of coordinates r:=[[1,2],[1,3]], which i converted to an array, and nulled the first element.

r:=convert(r,Array): 
r[1]:=NULL:
r:=convert(r,listlist):

I now have r=[[],[1,3]] after converting it back to a listlist. How do i remove the first element, which is an empty entry, such that i end up with r=[[1,3]]

Thanks 

Hi guys!

I'm looking for a way to type in the same "calculation" in Maple instead of the Word-package WordMat.
This is a screenshot from Word of the calculation I wanna do in Maple. But I can't figure out how to type it correct. Maybe you guys could post a screenshot of the same entered in Maple. 
Note: (I'm a Maple-rookie, it might be a simple "trick")
I know how to assign/define fx IP, U and ZP. It's about calculating with the angle symbol in line, and getting a "readable" result.

Looking forward to hear from all of you...

I have a surface defined by C(x, y, x) = 0 that I visualize with implicitplot3d.
Using shading=shue does not suits me and I would like to define my own coloring function F(x, y, z).

The first error I got made me think that a coloring function cannot depend on 3 parameters.
But a simpler (and not visually satysfying function) F(x, y) already leads to an error, which makes me wonder if it is possible to use a colorig function with  implicitplot3d?

implicitplot3d_coloring.mw

Thanks in advance

restart;
_local(D, O);
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
D := [0, b, 0];
S := [0, 0, h];
O := [x, y, z];
lineSC := Line(S, C);
lineSD := Line(S, D);
H := Projection(A, lineSC);
K := Projection(A, lineSD);
OH := H - O;
OK := K - O;
OC := C - O;
M := Matrix([OH, OK, OC]);
O := eval(O, %);
R := simplify(Distance(O, H));
                               O

Student:-MultivariateCalculus:-LineApplyFunction([0,0,h],

  [Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(a, 

  rowalign = "", columnalign = "", groupalign = "", 

  rowspan = "1", columnspan = "1"), rowalign = "", 

  columnalign = "", groupalign = ""), Typesetting:-mtr(

  Typesetting:-mtd(b, rowalign = "", columnalign = "", 

  groupalign = "", rowspan = "1", columnspan = "1"), 

  rowalign = "", columnalign = "", groupalign = ""), 

  Typesetting:-mtr(Typesetting:-mtd(uminus0h, rowalign = "", 

  columnalign = "", groupalign = "", rowspan = "1", 

  columnspan = "1"), rowalign = "", columnalign = "", 

  groupalign = ""), foreground = "[0,0,0]", readonly = "false", 

  align = "axis", rowalign = "baseline", columnalign = "center", 

  groupalign = "{left}", alignmentscope = "true", 

  columnwidth = "auto", width = "auto", rowspacing = "1.0ex", 

  columnspacing = "0.8em", rowlines = "none", 

  columnlines = "none", frame = "none", 

  framespacing = "0.4em 0.5ex", equalrows = "false", 

  equalcolumns = "false", displaystyle = "false", side = "right", 

  minlabelspacing = "0.8em")],variables=[x,y,z],parameter=t,id=1)

Student:-MultivariateCalculus:-LineApplyFunction([0,0,h],

  [Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(0, 

  rowalign = "", columnalign = "", groupalign = "", 

  rowspan = "1", columnspan = "1"), rowalign = "", 

  columnalign = "", groupalign = ""), Typesetting:-mtr(

  Typesetting:-mtd(b, rowalign = "", columnalign = "", 

  groupalign = "", rowspan = "1", columnspan = "1"), 

  rowalign = "", columnalign = "", groupalign = ""), 

  Typesetting:-mtr(Typesetting:-mtd(uminus0h, rowalign = "", 

  columnalign = "", groupalign = "", rowspan = "1", 

  columnspan = "1"), rowalign = "", columnalign = "", 

  groupalign = ""), foreground = "[0,0,0]", readonly = "false", 

  align = "axis", rowalign = "baseline", columnalign = "center", 

  groupalign = "{left}", alignmentscope = "true", 

  columnwidth = "auto", width = "auto", rowspacing = "1.0ex", 

  columnspacing = "0.8em", rowlines = "none", 

  columnlines = "none", frame = "none", 

  framespacing = "0.4em 0.5ex", equalrows = "false", 

  equalcolumns = "false", displaystyle = "false", side = "right", 

  minlabelspacing = "0.8em")],variables=[x,y,z],parameter=t,id=2)

               /     2            2         / 2    2\ /
               |    h  a         h  b     h \a  + b / |
        HAssign|------------,------------,------------|
               | 2    2    2  2    2    2  2    2    2|
               \a  + b  + h  a  + b  + h  a  + b  + h \

                          /    2         2  /
                          |   h  b    h b   |
                   KAssign|0,-------,-------|
                          |   2    2  2    2|
                          \  b  + h  b  + h \

        /                2                       2               
        |               h  a                    h  b             
OHAssign|uminus0x + ------------,uminus0y + ------------,uminus0z
        |            2    2    2             2    2    2         
        \           a  + b  + h             a  + b  + h          

       / 2    2\ /
     h \a  + b / |
   + ------------|
      2    2    2|
     a  + b  + h \

            /                      2                    2  /
            |                     h  b               h b   |
    OKAssign|uminus0x,uminus0y + -------,uminus0z + -------|
            |                     2    2             2    2|
            \                    b  + h             b  + h \

          OCAssign(uminus0x + a,uminus0y + b,uminus0z)

M := Matrix(3, 3, {(1, 1) = Typesetting:-mrow(Typesetting:-mo("&\

  uminus0;"), Typesetting:-mi("x"), Typesetting:-mo("+"), 

   Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-msup(Typese\

  tting:-mi("h"), Typesetting:-mn("2")), Typesetting:-mo("&Invis\

  ibleTimes;"), Typesetting:-mi("a")), Typesetting:-mrow(Typeset\

  ting:-msup(Typesetting:-mi("a"), Typesetting:-mn("2")), 

   Typesetting:-mo("+"), Typesetting:-msup(Typesetting:-mi(\

  "b"), Typesetting:-mn("2")), Typesetting:-mo("+"), 

   Typesetting:-msup(Typesetting:-mi("h"), Typesetting:-mn("2"))\

  ))), (1, 2) = Typesetting:-mrow(Typesetting:-mo("&uminus0;"), 

   Typesetting:-mi("y"), Typesetting:-mo("+"), Typesetting:\

  -mfrac(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("h"\

  ), Typesetting:-mn("2")), Typesetting:-mo("⁢"),\

   Typesetting:-mi("b")), Typesetting:-mrow(Typesetting:-msup(Ty\

  pesetting:-mi("a"), Typesetting:-mn("2")), Typesetting:-mo("&p\

  lus;"), Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-m\

  n("2")), Typesetting:-mo("+"), Typesetting:-msup(Typesett\

  ing:-mi("h"), Typesetting:-mn("2"))))), (1, 3) = Typesetting:-\

  mrow(Typesetting:-mo("&uminus0;"), Typesetting:-mi("z"), 

   Typesetting:-mo("+"), Typesetting:-mfrac(Typesetting:-mr\

  ow(Typesetting:-mi("h"), Typesetting:-mo("⁢"), 

   Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Type\

  setting:-mi("a"), Typesetting:-mn("2")), Typesetting:-mo("&plu\

  s;"), Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-mn(\

  "2"))))), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi(\

  "a"), Typesetting:-mn("2")), Typesetting:-mo("+"), 

   Typesetting:-msup(Typesetting:-mi("b"), Typesetting:-mn("2"))\

  , Typesetting:-mo("+"), Typesetting:-msup(Typesetting:-mi\

  ("h"), Typesetting:-mn("2"))))), (2, 1) = Typesetting:-mrow(Ty\

  pesetting:-mo("&uminus0;"), Typesetting:-mi("x")), (2, 2) = 

   Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-\

  mi("y"), Typesetting:-mo("+"), Typesetting:-mfrac(Typeset\

  ting:-mrow(Typesetting:-msup(Typesetting:-mi("h"), 

   Typesetting:-mn("2")), Typesetting:-mo("⁢"), 

   Typesetting:-mi("b")), Typesetting:-mrow(Typesetting:-msup(Ty\

  pesetting:-mi("b"), Typesetting:-mn("2")), Typesetting:-mo("&p\

  lus;"), Typesetting:-msup(Typesetting:-mi("h"), Typesetting:-m\

  n("2"))))), (2, 3) = Typesetting:-mrow(Typesetting:-mo("&uminu\

  s0;"), Typesetting:-mi("z"), Typesetting:-mo("+"), 

   Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi("h"), 

   Typesetting:-mo("⁢"), Typesetting:-msup(Typese\

  tting:-mi("b"), Typesetting:-mn("2"))), Typesetting:-mrow(Type\

  setting:-msup(Typesetting:-mi("b"), Typesetting:-mn("2")), 

   Typesetting:-mo("+"), Typesetting:-msup(Typesetting:-mi(\

  "h"), Typesetting:-mn("2"))))), (3, 1) = Typesetting:-mrow(Typ\

  esetting:-mo("&uminus0;"), Typesetting:-mi("x"), Typesetting:-\

  mo("+"), Typesetting:-mi("a")), (3, 2) = Typesetting:-mro\

  w(Typesetting:-mo("&uminus0;"), Typesetting:-mi("y"), 

   Typesetting:-mo("+"), Typesetting:-mi("b")), (3, 3) = 

   Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-\

  mi("z"))})

Error, invalid input: eval received Matrix(3, 3, {(1, 1) = -x+h^2*a/(a^2+b^2+h^2), (1, 2) = -y+h^2*b/(a^2+b^2+h^2), (1, 3) = -z+h*(a^2+b^2)/(a^2+b^2+h^2), (2, 1) = -x, (2, 2) = -y+h^2*b/(b^2+h^2), (2, 3) = -z+h*b^2/(b^2+h^2), (3, 1) = -x+a, (3, 2) = -y+b, (3, 3) = -z}), which is not valid for its 2nd argument, eqns
       /     1       / 2  2      2        2  2    2  2    2  2
  R := |------------ \a  h  - 2 a  h z + a  x  + a  y  + a  z 
       | 2    2    2                                          
       \a  + b  + h                                           

            2      2  2      2        2  2    2  2    2  2
     - 2 a h  x + b  h  - 2 b  h z + b  x  + b  y  + b  z 

            2      2  2    2  2    2  2\\      
     - 2 b h  y + h  x  + h  y  + h  z /|^(1/2)
                                        |      
                                        /      
Why this error ? Thank you.

I have a problem with the order  of the Eigenvalues and Vectors flipping. It is a bit random. I only found it trying to understand why a procedure sometimes rotated a conic one way and  then the other. This a really causing a quite a problem, I have only tried this in Maple 2024 so far. I have included screen shots to prove the effect.

Download 2024-03-21_Q_Eigenvector_output_flipping.mw

Hi I have an n×4 matrix of answer data to a questionnaire I would like to convert into a pivot table. So I can do a Chi2test. 

How do I construct said table?