Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

how i can write these boundary conditions for dsolve?

(diff(u(r), r))^(n-1)*(diff(r*(diff(u(r), r)), r))/r    be [finite] at r =0

and  u(0) = finite?

Thanks..

 

Hello!

I can't seem to figure out how to use the Physics package within a procedure. In particular, I can't get tensors to be recognized within the body of the proc.

As an example, here's a short program that works correctly when not in a procedure:

with(Physics):
Coordinates(X,quiet):
d_[mu](X[~mu]);
# Returns 4; Correct

However, placing this code inside a proc causes the tensor X to not be recognized as a tensor:

Test := proc()
  uses Physics:

  Coordinates(X,quiet):
  d_[mu](X[~mu]);
end proc:
Test();
# Returns 0; Wrong

Apparently, Physics:-Coordinates still defines the tensor X (as can be checked by calling Physics:-Define()). However, the derivative d_[mu] (X[~mu]) seems to be treating X as a standard symbol. Any idea how I would go about correcting this?

Thanks!


I have a procedure which works. ⊕(a,b) gives annwer.   a ⊕ b also gives answer. That was a surprise, discovered from a typing mistake. If b is negative is needs to be enclosed in delay evulation quotes.

2  questions 

Can anyoone expllain this useful property? Any way around having to use delay evaluation quotes for negative numbers?

restart

NULL

``

NULL

`⊕` := proc (a, b) (a+b)/(1-a*b) end proc

proc (a, b) (a+b)/(1-a*b) end proc

(1)

`⊕`(1, 2)

-3

(2)

`⊕`(1, 2)

-3

(3)

`⊕`(`⊕`(`⊕`(1, 2), '-5'), 4)

-32/9

(4)

``

`⊕`(1, 1/2)

3

(5)

`⊕`(1/2, '-1')

-1/3

(6)

"(=)"

-1/3

(7)

`⊕`(0, h)

h

(8)

`⊕`(h, 0)

h

(9)

`⊕`(1/h, '-h')

(1/2)/h-(1/2)*h

(10)

`⊕`(1/h, -h)

(1/2)/h-(1/2)*h

(11)

-`⊕`(h, 1/h^2)

-(h+1/h^2)/(1-1/h)

(12)

"(=)"

(-h^3-1)/(h*(h-1))

(13)

NULL


 

Download Circle_Sum.mw

On the maple cloud, I see that current version is 38 for Physics 

After I installed, I typed

Physics:-Version();

It gives 
  "......\maple\toolbox\2018\Physics Updates\lib\Physics Updates.maple", 2018, May 8, 17:49 hours

I was expecting to see "38".  Why does Physics:-Version(); does not give the version number as shown on Maple cloud? Using only a date for a version number is not a good idea. There should be a number there. (date can also be included, but a number should be the official version number).

Is there another command to use to obtain Version number "38"?

Does each package shown on cloud support packageName:-Version()? I tried this command on another package I have, but I got an error saying it does not Version() 

OrthogonalExpansions:-Version();
Error, Version is not a command in the OrthogonalExpansions package
 

Yet, on cloud, it says the version number is "1" for the above package. What does the version number shown on the cloud then really mean?

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

 

It's a bug, design or  something else ?

 

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
moadele_asli2.mw

solve does not show result!!

dtm.mw

fsolve does not any answer!!!!

please help me.

 

fsolve.mw

Dear friends,

maybe, somebody knows how to remove annoying text of the first line of a Code Edit Region when a Region is collapsed.

Here, Region in expanded state:

But after collapsing the first line still remains:

when I  have transformed symbol expression  from matlab 2017b to  maple 2018 , maple took a mistake that  "maple kernel connection not available", What  is the  reason?Can anyone help me?Thank you!

How to explain the difference in the outputs of

restart; ans1 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), {x, y});
ns1 := {x = 3-sqrt(-y^2-4*y+77), -11 <= y, y < 13/25},
 {-11 < y, x < -5+sqrt(-y^2+8*y+273), y < 13/25, 3-sqrt(-y^2-4*y+77) < x}, 
{x = -5+sqrt(-y^2+8*y+273), -11 < y, y < 13/25}, {y = 13/25, -141/25 <= x, x <= 291/25},
 {x = 3-sqrt(-y^2-4*y+77), y <= 7, 13/25 < y}, 
{13/25 < y, x < 3+sqrt(-y^2-4*y+77), y < 7, 3-sqrt(-y^2-4*y+77) < x}, 
{x = 3+sqrt(-y^2-4*y+77), 13/25 < y, y < 7}

and

restart; ans2 := solve(eval({-4*a^2+x^2+y^2 <= 8*y-10*x+4*a-40, -a^2+x^2+y^2 <= 6*x-4*y-13}, a = -9), [x, y]);
ans2 := [[x < 3, -6 <= x, y = -2-sqrt(-x^2+6*x+72)], 
[x < 3, -6 < x, y < -2+sqrt(-x^2+6*x+72), -2-sqrt(-x^2+6*x+72) < y], 
[x < 3, -6 < x, y = -2+sqrt(-x^2+6*x+72)], [x = 3, y <= 7, -11 <= y],
 [x <= 291/25, 3 < x, y = 4-sqrt(-x^2-10*x+264)],
 [x < 291/25, 3 < x, y < -2+sqrt(-x^2+6*x+72), 4-sqrt(-x^2-10*x+264) < y],
 [x < 291/25, 3 < x, y = -2+sqrt(-x^2+6*x+72)]]

?

In the former x is expressed through y and in the latter y is expressed through x. I find explanation  in neither ?solve nor ?solve,details.

I do not know what I am doing wrong. I am trying to plot each of the solutions to an ODE. One of the solutions Maple gives is  LegendreQ((1/2)*sqrt(5)-1/2, x) and the other is LegendreP((1/2)*sqrt(5)-1/2, x)

Maple can plot the  LegendreP, but gives an error plotting LegendreQ((1/2)*sqrt(5)-1/2, x)

ode:=(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+y(x)=0:
sol:=dsolve(ode,y(x));

sol := y(x) = _C1*LegendreP((1/2)*sqrt(5)-1/2, x)+_C2*LegendreQ((1/2)*sqrt(5)-1/2, x)

Now when I do 

plot(LegendreQ((1/2)*sqrt(5)-1/2, x),x=-1..1);

Maple says

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
 

Why is that? I tried x=-0.5..1 and x=0.5..1 and keep getting same error message. It works ok for 

plot(LegendreP((1/2)*sqrt(5)-1/2, x),x=-1..1);

Mathematica can plot both with no problem.

int(exp(-sec(t))*cos(t)/(-1/4+sin(t)^2), t = 0 .. (1/2)*Pi, CauchyPrincipalValue = true, numeric = true);

Returns unevaluated for me.

I tried all the methods in HELP documentation and I failed.
Integral is singular at point 1/4.

Thank you.

Hello my friends

I have a problem with initial condition for below system of differential equation

sys := {6*(diff(a(t), t))^2+12*a(t)*(diff(a(t), t$2))-3*a(t)^2*phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2), 2*c*a(t)^3*phi(t)^(-2*c-1)*sqrt(1-alpha*(diff(phi(t), t))^2)-3*alpha*a(t)^2*phi(t)^(-2*c)*(diff(a(t), t))*(diff(phi(t), t))/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t$2))/sqrt(1-alpha*(diff(phi(t), t))^2)+2*c*alpha*a(t)^3*phi(t)^(-2*c-1)*(diff(phi(t), t))^2/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha^2*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t))^2*(diff(phi(t), t$2))/(1-alpha*(diff(phi(t), t))^2)^(3/2), R(t) = 6*((diff(a(t), t))^2/a(t)^2+(diff(a(t), t$2))/a(t)), W(t) = -phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2)/(1/a(t)^3+a(t)^3+phi(t)^(-2*c)/sqrt(1-alpha*(diff(phi(t), t))^2))}

I set {c,alpha}={1,1} but initial conditon is problem ... since I got the following message from maple to illustrate diagrams of W(t), a(t) and even phi(t)

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up
 

please help me.

 

with the best regard

 

Hi,

I would like to control the extents of my 3D parametric plot. Increasing the grid creates too many gridlines and I just get a black plot  (and I still don't get the extent in the y-coordinate that I want).

Any suggestions how I might be able to get this plot from -360 to 0 and -20 to 60 completely filled in? (see attached workbook).

Any suggestions on how to control the gridlines?

An idea of what I am trying to do...I want to plot argument(z/(1+z)) vs. argument(z)*180/pi vs. 20*log10(abs(z)) with contours of argument(z/(1+z)) and 20*log10(abs(z/(1+z))
This is a 3D plot of the output phase of a Nichol's Chart (with the output contours of the Nichol's chart).

Thanks.

phaseplot.mw

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