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

Using library is very easy to plot the graph. But how to do this question by using spacecurve rather than the library

I do not quite understand why prof asks this question. Or I am doing right? Where can I improve? Or I understand this question completely wrong. To be honest, I did not get the point 

Why the least square of my calculation is different from the library. Where I am wrong? And how to plot this graph without the library? just use the function mentioned in the content

Hi,

I am struggling with an issue of the solutions produced by the "fsolve" command for a polynomial with multiple solutions. I am running the commands that are represented as follows:

f := x^2-x+0.25:

fsolve({f=0}, x=0..1);

It produces multiple solutions as follows:

{x = 0.5000000000}, {x = 0.5000000000}

What I am looking for is as follows:

1. Store multiple solutions separately.

2. For each solution, separate the variable "x=" and the numerical value "0.50000000". 

I would appreciate inputs from the team. 

Thank you,

Omkar

# uname -a

Linux p9x79 5.4.0-48-generic #52-Ubuntu SMP Thu Sep 10 10:58:49 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux

I use X with TWM.

When minized, the maple icon is about 1/4" diameter.  How do I change this to a larger icon?

Hi, 

I'm trying to calculate the inner product of these two vectors. 

|a> = (1 + i) i, (1) j, (i) k

|b> = (4 - 1) i, (0) j, (2 -2i)k

where bold i, j, k, are the orthonormal bases. 

I can calculate it on paper, the problem I'm having is figuring out how to calculate it using maple. I want to be able to use dirac notation. I've tried using the physics library but none of the example use actual vectors but instead use quantum numbers. 

Thanks, 

Poiseuill's law: the formula is correct if both sides has the same dimension, so it is required that 

     [v]=[(P*R^m*nⁿ)/L]

find n and m that make the above equation dimensionally correct

It might seem like a small thing, but is there a way to separate the text from the numbers? It's only for optical purposes, as i think it looks better. 

Thank you,

MO