The center of mass for the density function p(r,θ,φ) = ln(r^2 + θ^2 + φ^2 +1) over the solid sphere radius 2.

I'm not sure how to do this on Maple.  

Many thanks!

Hi friends!

I have the following problem.

I'm trying to generate a matrix given a certain lenght n and a polynomial g(x) of degree r as follows:

If n=10, g(x)=x^4+3x^3+x^2+2x+1 and r=degree(g(x))=4, then the resulting matrix will be

i.e. a matrix with 10 columns, n-r=6 lines, and whose inputs are the coefficients of the polynomial, as follows:

Any help will be very appreciated.

Thank you!

I'm doing som XML readin, and need a bit help in using the HasChild function properly.

The attachment shows that using HasChild on a xmltree works fine, but I can't get i working when using it on a xmldocument. The latter is usually the case when you get when you read in from a file.

HasChild.mw

Hello there, 

Would you please tell me how to re-write the 'PMSM_v_eq' as 'PMSM_flux_eq_desired'? My simple attempt was using the 'solve()' command, but it failed. 

Here is the worksheet:

Thank you!

Download PMSM_eq.mw

Hello

I have no choice but use Grid:-Map and Grid:-Seq in my calculations due to the size of them.  Here is a very small example that is puzzling me (Perhaps I did something really silly and did not realize). 

ansa:=CodeTools:-Usage(Grid:-Map(w->CondswithOnesolutionTest(w,eqns,vars,newvars,tlim),conds5s)):

with the following result:

ansa:=set([{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}])

The same thing but now using only map

ansb:=CodeTools:-Usage(map(w->CondswithOnesolutionTest(w,eqns,vars,newvars,tlim),conds5s)):

ansb:={[{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}]}

(This is what I expected as the result).

Why did Grid:-Map add set to the answer?  What am I missing?  

Many thanks

mwe.mw

I have a system of ODEs, and I am using the DifferentialAlgebra Package. I am getting this error message: Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {-I, I, 2*I} in the given input. What should I do?

Here is the problem. I start Maple 2020 on windows 10. Run a script which takes 1-2 days to complete. 

During this time, I can't use that Maple at all, since it is busy. 

I could start Maple 2019, and that runs as completely separate process. But I want to use Maple 2020 since some things in my scripts do not work on Maple 2019 that work on Maple 2020.

If I start a new instance of Maple 2020, by doing Start->Maple 2020. it does seem to start it OK, but I noticed it seems to be somehow still connected to the one running somehow.  May be they are sharing the same interface?

I can use the new instance now and open new worksheet and use it. But it seems to become very slow, as if it is sharing something with the other Maple 2020 running the long script which uses lots of resources. It is not RAM issue, I have 64 GB RAM, and there is plenty of free RAM left. 

When I close the new Maple 2020 workseet I started, I get a message asking if I want to save the worksheet that I have open from the earlier instance which is still running ! 

I say no ofcourse, as I do not want to terminate that instance, I want to keep it running until the script is completed.

My question is: Could someone may be explain exactly what happens when one starts new Maple 2020, while one is allready running? Why it seems they are sharing either the interface or something else.  How to start completely separate Maple 2020 instance on same PC while one is allready running?

With Mathematica, this issue does not happen. I can start two instances of same version on same PC, and there is nothing shared between them at all.  This does not seem to be the case with Maple.

Maple 2020.1 on windows 10.

sometimes solve returns solution of the form

restart;

#eqs:=.....
#sol:=solve(eqs,{v[1],v[2],v[3]});

sol:={v[1]=t,v[2]=3/2*t,v[3]=v[3]};

And wanted to remove all those that represnt arbitrary solution, which is v[3]=v[3] above.

I could do this using

remove(x->lhs(x)=rhs(x),sol);

which gives

{v[1]=t,v[2]=3/2*t};

But as an excersise, I could not figure how to do the same using subsindent (where I wanted to replace v[3]=v[3] with {} or NULL,. and also using applyrule.

Is it possible to do the same as above but using subsindent and applyrule (which is similar to patmatch)? 

I noticed the other day that the magnitude ||v|| for vector v gives different results based on the library loaded. I have not heard of any reason in my studies for there to be a magnitude calculation that is different from the

m = sqrt(`x__1`^(2)+`x__2`^(2)+...+`x__n`^(2))

Which I've come to understand as the calculation for the length of a vector of size N.
Why does the VectorCalculus library calculate the correct ||v|| whereas LinearAlgebra seemingly returns the largest element?

Sorry I can't make it very easy to understand in the title, this is what I want:

In the forms of Method of Underdetermined Coefficient a*y''+b*y'+c*y=F(x), I want the maple to assume b^2 < 4ac so the homogenous will contain sin and cos. Is there any quick command to do this or I have to develop on my own? 

I want this because I want to set the coefficient unknown and graph them, so if I do what Maple default does, when I plug the coefficients (which b^2<4ac) it returns imaginary numbers and I don't know how do deal with it.

Thank you for everyone helping.

I needed to make symbolic vector, as in  

my_vector:=Vector([v__1,v__2,v__3])

The problem is that, the proc called, has to create this vector on the fly, since the dimension changes on each call. So I used seq command to generate it. But seq did not work. I tried

my_vector:=Vector([seq('v__i',i=1..3)])

After looking more at it, It seems to have nothing to do with evaluation. If the subscript index is variable, it does not work.

f:=proc(v::symbol,i::posint)  
  print("i=",i);
  print("v__i=",v__i); 
  return (v__i);
end proc;

f(v,2)

One way is to use v[i] instead of v__i, and now it works:

[seq('v[i]',i=1..3)]

But since subscripted variable are supposed to be safer than indexed variable, I wanted to use v__i and not v[i].

Why it does not work? And is there a workaround this?  

ps. I could always do this 

V:=[seq(:-parse(cat("v__",convert(i,string))),i=1..3)]
lprint(V[1])

But this seems like a hack to me and I do not know why it should be needed.

ps. any one knows where help on "__" is in Maple? I can't find it. doing ?__ turns out nothing. I do not know under what name help on double subscript is in maple.

Maple 2020.1

Is it possible to determine an analytic solution to the following system of two differential equations for $A$ and $B$ using Maple.  My suspicion is that trial and error would find an analytic solution in theory and so that Maple could find the solution.  M is a constant and \sigma is some arbitrary function of t and the spatial coordinates. 

\[ \Bigg( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} + \frac{1}{2} \Bigg( 1 + \frac{M}{2 \sqrt{x^2 + y^2 + z^2}} \Bigg) \Bigg( \frac{\partial \sigma}{\partial x }\frac{\partial}{\partial x} +\frac{\partial \sigma}{\partial y}\frac{\partial}{\partial y} +\frac{\partial \sigma}{\partial z}\frac{\partial}{\partial z} \Bigg) \Bigg)B=0, \]

\[\frac{d A}{dt} = AB.\]

Furthermore, the boundary conditions are 

\[B \rightarrow -1  \: \text{as}  \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty,\]

\[A \rightarrow e^{-t} \: \text{as} \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty \]

System_of_Equations.pdf

Hi, I have this graph and i am trying to find a method that will only look at the second gradient change. I want it to adjust list A that it takes out the coordinates for the first gradient and the last 2. I have tried to find a way to make it work but i have no idea how to get maple to sense that there is a gradient change (basically i want to split the graph in 4 bits each of which contains a constant gradient if that makes sense!)

Dear Users!

Hope you would be fine. I have some problem in execution the last loops (highlighted as red) where sumation is present. When NN>3 it takes alot of time more than 12 hours. Is there any alternative command to reduce the query. I am waiting for your response. Thanks in advance. 

restart; with(LinearAlgebra); Digits := 30; NN := 2; nu := 1; M1 := NN; M2 := NN; M3 := NN;

for k1 from 0 while k1 <= M1-1 do for k2 from 0 while k2 <= M2-1 do for k3 from 0 while k3 <= M3-1 do

SGP[M3*(M2*k1+k2)+k3+1] := simplify(sum((-1)^(k1-i1)*GAMMA(k1+i1+2*nu)*x^i1*(sum((-1)^(k2-i2)*GAMMA(k2+i2+2*nu)*y^i2*(sum((-1)^(k3-i3)*GAMMA(k3+i3+2*nu)*z^i3/(GAMMA(i3+nu+1/2)*factorial(k3-i3)*factorial(i3)), i3 = 0 .. k3))/(GAMMA(i2+nu+1/2)*factorial(k2-i2)*factorial(i2)), i2 = 0 .. k2))/(GAMMA(i1+nu+1/2)*factorial(k1-i1)*factorial(i1)), i1 = 0 .. k1)) end do end do end do;

SGPxyz := `<,>`(seq(seq(seq(SGP[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

Lambda := `<,>`(seq(seq(seq(chi[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

for i while i <= NN^3 do for j while j <= NN^3 do for k while k <= NN^3 do

q[i, j, k] := int(int(int(SGP[i]*SGP[j]*SGP[k]*(-x^2+x)^(nu-1/2)*(-y^2+y)^(nu-1/2)*(-z^2+z)^(nu-1/2), z = 0 .. 1), y = 0 .. 1), x = 0 .. 1) end do end do end do;

U := Matrix(NN^3, NN^3, 0);

for j while j <= NN^3 do for k while k <= NN^3 do U[j, k] := simplify(sum(chi[i1]*q[i1, j, k], i1 = 1 .. NN^3)) end do end do;

F := simplify(evalm(U));

Special request to @acer @Carl Love @Kitonum @Preben Alsholm