MaplePrimes Questions

Dear everyone.

Please suggest me how to choose a suitable function (g(x)) so that the convergence property of the following improper integral can be checked by the comparison method:

Hi,

I just started to try out maple, as I'm testing out some software. So far it's been fairly easy to work in. I have ran into this interesting solution however

The issue I'm having is that the solution should not be... whatever that is. It should result in, off the top of my head, 2 or 4 numbers, and I'm only interested in one of them. None of the above is the answer to my question however. I don't know exacty what I'm supposed to do to get to that point. looking up the "RootOf" part on the support page didn't really explain it all that well.

Dear all 
I have Sol=proc(  )
local .... ;
RES:=vector with size fixed 
for k from 1 to 100  # iteration
a:=..
if a < 0.1 then 
break;
end if ;
RES[k]:=a;
end do;
print(RES);
 end proc;

My questions:
1) How can I define the vector RES with no size fixed ( we can not at the begin fix the size of RES)
2) Then how can I plot this vector versus number of iteration  
Thank you

Anybody find Import CAD closes MapleSim 2022.2 when just opening file chooser when attempting to import CAD file?

Regards,
Bill

calculating specific weight I get an answer in kg/m2s2. The context panel does not allow me to change the units to N/m3. Any suggestions how to change the units to N/m3. If I use Maple I get the right units. The problem is with Maple Flow.

How to find the dispersion relation (3) in Maple? I try it by equating the coefficients of cos(kx + wt) and its derivative to zero, but couldn't find it.

restart

with(LinearAlgebra):

alias(E = E(x, t), P = P(x, t), N = N(x, t), Q = Q(x, t));

E, P, N, Q

(1)

d := Matrix([[c*(diff(E, t))+diff(E, x), alpha*P, 0, 0], [N[0]*E, diff(P, t), -sigma[2]*Q[0]*N/N[0], sigma[2]*omega[0]*Q], [0, sigma[1]*sigma[2]*Q[0]*P/N[0], diff(N, t), 0], [0, -omega[0]*P, 0, diff(Q, t)]]) = 0

d := (Matrix(4, 4, {(1, 1) = c*(diff(E(x, t), t))+diff(E(x, t), x), (1, 2) = alpha*P(x, t), (1, 3) = 0, (1, 4) = 0, (2, 1) = N(x, t)[0]*E(x, t), (2, 2) = diff(P(x, t), t), (2, 3) = -sigma[2]*Q(x, t)[0]*N(x, t)/N(x, t)[0], (2, 4) = sigma[2]*omega[0]*Q(x, t), (3, 1) = 0, (3, 2) = sigma[1]*sigma[2]*Q(x, t)[0]*P(x, t)/N(x, t)[0], (3, 3) = diff(N(x, t), t), (3, 4) = 0, (4, 1) = 0, (4, 2) = -omega[0]*P(x, t), (4, 3) = 0, (4, 4) = diff(Q(x, t), t)})) = 0

(2)

re := -c*omega^3-kappa*omega^2+(c*omega[0]*(N[0]^2*sigma[2]+Q[0]^2*sigma[1])/N[0]^2-alpha*N[0])*omega+kappa*omega[0]*(N[0]^2*sigma[2]+Q[0]^2*sigma[1])/N[0]^2 = 0;

-c*omega^3-kappa*omega^2+(c*omega[0]*(Q[0]^2*sigma[1]+N[0]^2*sigma[2])/N[0]^2-alpha*N[0])*omega+kappa*omega[0]*(Q[0]^2*sigma[1]+N[0]^2*sigma[2])/N[0]^2 = 0

(3)

``

``

Download d_relation.mw

Hi everyone 

I have a problem regarding the animation of a flying ball. 

I get the coordinates and rotation in rad/s out of differential equations. Now I want to show the movement of the ball including the rotation in an animation. 

With just the coordinates it works just fine, but when I try do add the rotation the error message "number of elements in lust must be a multiple of 2" appears

I would be grateful for some advice. Thank you in advance.

I added my file, hope it helps.

how_rot.mw

Hi

My third-party soft is fussy: it will only accept pasted plaintext, with no spaces in between, for example:

1407,1411,2,1408,1409,0
1407,1408,2,1409,1411,0

#My input is 
ans1 := [1407, 1408, 2, 1409, 1411, 0], [1407, 1409, 2, 1408, 1411, 0], [1407, 1411, 2, 1408, 1409, 0];

#I am "trying" to remove the whitespace and convert it to plain text

with(StringTools):
for i to 3 do
seq(parse(DeleteSpace(convert(ans1[i][j],string))),j=1..6);
next i
od;

#But the whitespace is still there....

lprint(%%%);lprint(%%);lprint(%)
ans1 := [1407, 1408, 2, 1409, 1411, 0], 

  [1407, 1409, 2, 1408, 1411, 0], [1407, 1411, 2, 1408, 1409, 0]


                  1407, 1408, 2, 1409, 1411, 0

                  1407, 1409, 2, 1408, 1411, 0

                  1407, 1411, 2, 1408, 1409, 0

Dear all

My code give me the following error 
Error, (in SOR) invalid left hand side in assignment
I don't understand its origin.

coore_invalid.mw

Thank you

I'm working on finding the analytic expression of the PDF of a sum of abstract Uniform Random Variables URV).
Here "abstract" means that the supports are not numeric but litteral.

Maple is capable to find such a PDF for numeric supports but unable to determine the PDF of U1+U2 where 

U1 := RandomVariable(Uniform(a1, b1)):
U2 := RandomVariable(Uniform(a2, b2)):

A way to deal with abstract URV is to complute explicitely the convolution product of th PDFs.
Ir seems that this fails (MAPLE 2015.2) for these PDF are piecewise functions.
A workaround is to convert them first into Heaviside(s).

One done the explicit expression of the convolution product can be obtained for a sum of 2 abstract URVs, but not for a sum of a larger number of abstract URVs.

Thus the second workaround which consists in using direct and inverse Fourier transform.

The question is :
obviously, the PDF f(t ; a1...aN, b1...bN) of  U1 + ... + UN is a continuous function of t: why does discont(f(t ; ...), t) returns the non empty set of the values where the Heaviside functions are undefined ?

Here is a very simple result

u1 := RandomVariable(Uniform(-1, 1)): 
u2 := RandomVariable(Uniform(-1, 1)):
p := PDF(u1+u2, t):
discont(p, t);

print("-------------------------------------");

f1 := convert(PDF(u1, t), Heaviside):
f2 := convert(PDF(u2, t), Heaviside):
g1 := fourier(f1, t, xi):
g2 := fourier(f2, t, xi):
g  := g1*g2:
f  := invfourier(g, xi, t):
discont(f, t);

                               {}
            "-------------------------------------"
                           {-2, 0, 2}

The problem is (IMO) that discont(f, t) should return { }, but that some function (does it exists) should say that d is undefined at points t=-2, t=0, t=2.
The output of discont(f, t) doesn't seem consistent with the definition of the continuity

limit(f, t=-2, left);
limit(f, t=-2, right);
eval(f, t=-2)
                               0
                               0
                           undefined

restart:

with(inttrans);
with(Statistics):

[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, invfourier, invhilbert, invlaplace, invmellin, laplace, mellin, savetable]

(1)

N := 3:
for n from 1 to N do
  U||n := RandomVariable(Uniform(a__||n, b__||n)):
end do;

_R

 

_R0

 

_R1

(2)

# Maple fails to compute the PDF of a sum of abstract (meaning with symbolic support) uniform RVS
# PDF(U1+U2, t)

# For N <=3 the computation of the convolution product is possible.
#
# For N > 4 (Maple 2015) it seems this is no longer the case. The trick used here is based on
# the fact that Fourier(Conv(f, g)) : Fourier(f)*Fourier(g)
# Thus PDF(U1+U2) = conv(PDF(U1), PDF(U2)) = invFourier(Fourier(PDF(U1)).Fourier(PDF(U1)))


for n from 1 to N do
  f||n := convert(PDF(U||n, t), Heaviside):
end do:

for n from 1 to N do
  g||n := fourier(f||n, t, xi):
end do:
g := mul(g||n, n=1..N):

hyp := seq(b__||n > a__||n, n=1..N);
f   := invfourier(g, xi, t) assuming hyp;

a__1 < b__1, a__2 < b__2, a__3 < b__3

 

((1/2)*(t-a__1-a__2-a__3)^2*Heaviside(-t+a__1+a__2+a__3)-(1/2)*(t-a__1-a__2-b__3)^2*Heaviside(-t+a__1+a__2+b__3)-(1/2)*(t-a__1-a__3-b__2)^2*Heaviside(-t+a__1+a__3+b__2)+(1/2)*(t-a__1-b__2-b__3)^2*Heaviside(-t+a__1+b__2+b__3)-(1/2)*(t-a__2-a__3-b__1)^2*Heaviside(-t+a__2+a__3+b__1)+(1/2)*(t-a__2-b__1-b__3)^2*Heaviside(-t+a__2+b__1+b__3)+(1/2)*(t-b__1-a__3-b__2)^2*Heaviside(-t+b__1+a__3+b__2)-(1/2)*(t-b__1-b__2-b__3)^2*Heaviside(-t+b__1+b__2+b__3))/((-b__1+a__1)*(-b__2+a__2)*(-b__3+a__3))

(3)

# f is obviously a continuous function of t, but I get this strange result

discont(f, t);

{a__1+a__2+a__3, a__1+a__2+b__3, a__1+a__3+b__2, a__1+b__2+b__3, a__2+a__3+b__1, a__2+b__1+b__3, b__1+a__3+b__2, b__1+b__2+b__3}

(4)

# note that this "error" also appears if the a__n's and b__n's are numeric

r := rand(0. .. 1.):
P := convert(indets(g, name) minus{xi}, list):
E := NULL:
for n from 1 to N do
  a := r():
  b := a + r():
  E := E, a__||n = a, b__||n = b
end do:
E := [E];

G := eval(g, E):
f := invfourier(G, xi, t);
discont(f, t);

[a__1 = .3055679837, b__1 = .7906643786, a__2 = .8311025583, b__2 = .9857257095, a__3 = .4223879539, b__3 = .7034757826]

 

0.1333206533e-8*(-0.1000000000e11*t+0.1136670542e11)*Heaviside(-t+1.136670542)+0.1333206533e-8*(0.1000000000e11*t-0.1291293693e11)*Heaviside(-t+1.291293693)+0.1333206533e-8*(0.1000000000e11*t-0.1621766937e11)*Heaviside(-t+1.621766937)+0.1333206533e-8*(-0.1000000000e11*t+0.1776390088e11)*Heaviside(-t+1.776390088)

 

{1.136670542, 1.291293693, 1.621766937, 1.776390088}

(5)

u1 := RandomVariable(Uniform(-1, 1)):
u2 := RandomVariable(Uniform(-1, 1)):
p := PDF(u1+u2, t):
discont(p, t);

print("-------------------------------------");

f1 := convert(PDF(u1, t), Heaviside):
f2 := convert(PDF(u2, t), Heaviside):
g1 := fourier(f1, t, xi):
g2 := fourier(f2, t, xi):
g  := g1*g2:
f  := invfourier(g, xi, t):
discont(f, t);
 

{}

 

"-------------------------------------"

 

{-2, 0, 2}

(6)

limit(f, t=-2, left);
limit(f, t=-2, right);
eval(f, t=-2);

print("-------------------------------------");

limit(f, t=0, left);
limit(f, t=0, right);
eval(f, t=0)

0

 

0

 

undefined

 

"-------------------------------------"

 

1/2

 

1/2

 

undefined

(7)

 

Download Sum_of_Uniform_RVs.mw

Hello im an amateur using maple for my hidraulics machines course at engineering school. Does anyone know how to use the degrees package on maple 2022, i called it out by using the short form. with(Degrees): and then try to use sind but it doesnt recognice the command.

Also when using RPMs the units that should be giving me m/s appear as m2/m*s(radious). I know that the software recognice it as angular speed but is there anyway to eliminate the (radious) so i can work with the speed as lineal?

Please show me how to enter "positive infinity" value in the dialog box of "Maple Tutors". Thanks!i

Hi.  I am using the linux version of Maple.  I seem to experience more bombs in Maple/Linux vs MathCad/Windows.  The program just froze as I was entering text.  Just text.  It is not a disaster since I make very frequent saves.  But it is very annoying.  I was a heavy user of MathCad from about 2005 to 2019.  In the early days, it bombed a lot.  But I do not recall that it ever bombed when I was entering text.  Any suggestions?  Would there be a limition on the number of text characters?  Is it Linux?  Other than this problem, it is a great program.

I made an error by trying to multiply two nonconformable matrices. I think, I should receive an error message. But in this example this did not occur.

Strange.mw

restart; with(LinearAlgebra); alias(`&bigotimes;` = LinearAlgebra:-KroneckerProduct); interface(rtablesize = 16); kernelopts(version); interface(version)

`&bigotimes;`

[10, 10]

`Maple 2021.2, X86 64 LINUX, Nov 23 2021, Build ID 1576349`

`Standard Worksheet Interface, Maple 2021.2, Linux, November 23 2021 Build ID 1576349`

Matrices nonconformable, Maple should give error message:

`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)); Dimension(%); M := Matrix(4, 4, shape = symmetric, symbol = m); Dimension(%)

Matrix([[1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]])

4, 16

M := Matrix(4, 4, {(1, 1) = m[1, 1], (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 4) = m[4, 4]}, storage = triangular[upper], shape = [symmetric])

4, 4

MatrixMatrixMultiply(`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)), DiagonalMatrix(Diagonal(M)))

Matrix([[m[1, 1], 0, 0, 0], [0, m[2, 2], 0, 0], [0, 0, m[3, 3], 0], [0, 0, 0, m[4, 4]]])

`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)).DiagonalMatrix(Diagonal(M))

Matrix([[m[1, 1], 0, 0, 0], [0, m[2, 2], 0, 0], [0, 0, m[3, 3], 0], [0, 0, 0, m[4, 4]]])

KroneckerProduct(Matrix(1, 4, 1), IdentityMatrix(4)).DiagonalMatrix(Diagonal(M))

Matrix([[m[1, 1], 0, 0, 0], [0, m[2, 2], 0, 0], [0, 0, m[3, 3], 0], [0, 0, 0, m[4, 4]]])

(Matrix(4, 16, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 1, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 1, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 1, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 1, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 1, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 1, (2, 15) = 0, (2, 16) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 1, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 1, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 1, (3, 16) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 1, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 1, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 1})).DiagonalMatrix(Diagonal(M))

Matrix([[m[1, 1], 0, 0, 0], [0, m[2, 2], 0, 0], [0, 0, m[3, 3], 0], [0, 0, 0, m[4, 4]]])

`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)).Matrix(4, 4, shape = diagonal, symbol = m)

Matrix([[m[1, 1], 0, 0, 0], [0, m[2, 2], 0, 0], [0, 0, m[3, 3], 0], [0, 0, 0, m[4, 4]]])

whattype(`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4))); Dimension(`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)))

Matrix

4, 16

whattype(DiagonalMatrix(Diagonal(M))); Dimension(M)

Matrix

4, 4

hereafter results are correct: Matrices

nonconformable, therefore error messages appear.

`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)).M

Error, (in LinearAlgebra:-Multiply) first matrix column dimension (16) <> second matrix row dimension (4)

`&bigotimes;`(Matrix(1, 4, 1), IdentityMatrix(4)).Matrix(4, 4, shape = symmetric, symbol = m)

Error, (in LinearAlgebra:-Multiply) first matrix column dimension (16) <> second matrix row dimension (4)

Download Strange.mw

Hi! This is probably simple, but
I would like to know if there's an specific algorithm to do this:

let B = {x[i], i=1..n} in such a way that:

f( B ) = Sum(a[i]*b[i], i=1..N); a_i in R; b_i in B; N>n.

so Linearcomb: f->V(R).

Linearcomb( f ) =

 (Sum(a[j],j in J))*x[1]+(Sum(a[k],k in K))*x[2] + ... +(Sum(a[z],z in Z))*x[n].

with V(R) a vector space; R the Real numbers, and B the base. Neither the "factorize", nor the "simplify" are proving useful to this. Is there something i'm missng?

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