Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

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

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 keep getting an error: invalid subscript selector on specifically this part of my code:

MuligIndgange := subsop(RemoveList\[i\]=NULL, MuligIndgange).
Whenever I comment out the MuligIndgange := part it works.

I can't for the life of me see why it's happening, and whenever I use this code outside my proc it works aswell.

Any help is appreciated, and if you need more context I'll be happy to give it.

for i to numelems(MuligIndgange) do
     if M1[MuligIndgange[i][1], MuligIndgange[i][2]] =/= 0 then
         RemoveList := [op(RemoveList), i];
      end if;
end do;
for i from numelems(RemoveList) by -1 to 1 do
    MuligIndgange := subsop(RemoveList[i] = NULL, MuligIndgange);
end do;

I have seen this quite a bit in blocks of code. The `>` symbol seems to appear erratically. I don't know how to specifically reproduce this. Does it mean something? I would post the worksheet but it will not run without the package.

Hello

I have the following procedure that uses the Lie Derivatives of a vector field to build a set of equations.

LieDerList:=proc(h::symbol,f::list,vars::list)
description "This function returns the system of equations based on the Lie derivative.":
local i,n:=numelems(vars),L:=Array(0..n):
L[0]:=h:
for i from 1 to n do
    L[i]:=inner(f,map((a,b) -> diff(b,a),vars,L[i-1])):
end do:
return(zip((w,v)->simplify(w-v),[seq(L)],[seq](cat(h,i),i=0..n))):
end proc:

Below it is an example on how to call the procedure.

I used CodeTools:-ThreadSafetyCheck to check all the procedures used within LieDerList and LieDerList itself, but nothing wrong came out. However when I try to run 

LieEq4:=Threads:-Map(w->LieDerList(x,w,[x,y,z]),models4):

where models4 is a list of 1765 elements, maple returns "Error, (in factors) attempting to assign to `LinearAlgebra:-Modular:-Create` which is protected". If I change Threads to Grid, there is no problem at all.  

What am I overlooking? Is there a method to ensure the procedure is thread-safe?

Many thanks.   

PS.  I found one problem - inner, which is related to LinearAlgebra package, is not thread-safe.  

For a lesson I'm preparing, I want to illustrate some probability concepts using Maple.
In particular, I need to use the fact that the Expectation operator(let say the Mean operator) is a linear operator with respect to random variables. 
However, I don't want to particularize my demonstration by using this or that statistical distribution but simply the notion of random variable.
I have therefore created a specific Distribution named  MinimalAbstractDistribution in which only the mean and variance are defined.

When Statistics:-Mean is applied to the expression (A*p+q) where p and q are names and A is a random variable with distribution MinimalAbstractDistribution, linearity is effectively used.
But not when it is applied to A/p or A-q.

Why that?
Is there a way of defining a statistical distribution so that Mean behaves as expected?

(You will easily understand that no workaround of the form

Mean(A+q);
eval(%, q=-q);

# or
add(Mean~([op(A-q)]))

can be accepted in a lesson).

Thanks for your attention
 

restart

with(Statistics):

 

MinimalAbstractDistribution := proc(i)
  Distribution(Mean=mu[i], Variance=sigma[i]^2)
end proc:

A := RandomVariable(MinimalAbstractDistribution(1))

_R

(1)

[Mean, Variance](A);

[mu[1], sigma[1]^2]

(2)

Mean(p*A+q);
Mean(p*(A+q))

p*mu[1]+q

 

p*(mu[1]+q)

(3)

# But

Mean(A-q);
Mean(A/p)

FAIL

 

FAIL

(4)
 

 

Download Mean_operator.mw

Can I draw such figures using Maple?

If possible please guide how I can do it.

How to evaluate the right eigenvector of a given matrix in maple?

Simple question (I'm sure) here.  I have one worksheet where the variable does not show up in the ouput of an assignment like this:

whereas I was expecting the output to include the variable being assigned like this in most other worksheets:

I am having some difficulting locating the cause (and therefore the setting) to have the behavior set back to including the variable name in the ouput.  Thanks in advance for your help.

det_roots.docx

How to find the roots of the equation ?

like if the roots of the equations are m ,n,o,p then the value of these roots in terms of λ0  λ1  λ2  λ3  µ1  µ2 and  µ3

Calculate the values of the following determinants

Windows 10 64bit

If I double click on a  file to open it from explorer  i.e. launch Maple, it is 50/50 whether Maple hangs on opening the file and I have to kill it in the Task Manager. This only happens the 1st time I try to open the file. Subsequent clicks on it will open it. If Maple is already open the problem does not happen.  The problem willl also be there after the PC is restarted. Has anyone else noticed this?

Dear Users!

I hope everyone here is fine. In the attached file I have a list of points in three dimensions. I want to plot surfaceplot (also in Dimension=2) of only those points which are less than 1.

But I want to plot the density plot for all points with the range on x-axes 5 to 15 and the range on y-axes 50-1000

Help.mw

May be someone can come up with a way to simplify this ode solution? I used the option useInt but the solution can be written in much simpler way than Maple gives.  Below is worksheet showing Maple's 2024 solution and my hand solution.

(having trouble uploading worksheet, will try again).


 

144036

ode:=diff(y(x),x)^3=y(x)+x

(diff(y(x), x))^3 = y(x)+x

maple_sol:=dsolve(ode,useInt):
maple_sol:=Vector([maple_sol]);

Vector(3, {(1) = x-Intat(3*_a^2/(_a+1), _a = (y(x)+x)^(1/3))-_C1 = 0, (2) = x-Intat(3*_a^2/(_a+1), _a = -(1/2)*(y(x)+x)^(1/3)-((1/2)*I)*sqrt(3)*(y(x)+x)^(1/3))-_C1 = 0, (3) = x-Intat(3*_a^2/(_a+1), _a = -(1/2)*(y(x)+x)^(1/3)+((1/2)*I)*sqrt(3)*(y(x)+x)^(1/3))-_C1 = 0})

mysol1:= Intat(1/(_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol2:= Intat(1/( -(-1)^(1/3)*_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol3:= Intat(1/( (-1)^(2/3)*_a^(1/3) + 1), _a = (y(x) + x))=x+_C1:
mysol:=Vector([mysol1,mysol2,mysol3]);

 

Vector(3, {(1) = Intat(1/(1+_a^(1/3)), _a = y(x)+x) = x+_C1, (2) = Intat(1/(-(-1)^(1/3)*_a^(1/3)+1), _a = y(x)+x) = x+_C1, (3) = Intat(1/((-1)^(2/3)*_a^(1/3)+1), _a = y(x)+x) = x+_C1})

map(X->odetest(X,ode),mysol)

 

Vector(3, {(1) = 0, (2) = 0, (3) = 0})

 


 

Download simpler_solution.mw

I keep losing the edits I do. I post screen shot. Click submit, then find all my changes are lost. Will try one more time and give up:

This is Maple solution

This is implified version

 

Both versions are verified correct by odetest. The question is there is a way to obtain the simpler form from Maple.

 

When I calculate the edge values of a matrix the result is lengthy expression that could be simplified if evaluated numerically, Why is that not done? 

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