MaplePrimes Questions

Hi,

Does anyone know how the command PLOT(POLYGONS(...)) fills  polygons?
I'm interested in polygons that are not simple, that is polygons for which 2 different sides without common vertex do not intersect.

Thanks in advance

Hi,

Is it possible to change programmatically the permissions of a file without using ssystem?
Such as in ssystem("chmod +x MyFile") for instance

TIA

I'm using dsolve command to solve a differential equation. Using infolevel to 3 will tell me the classification of said DE. However, how can I see the step by step solution? I'm using Maple as a study tool so I do solve manually a DE then I'd like to compare my answer with Maple's. How can I acomplish this? Thanks in advance. 

How do I write plot ceil(x) mod 2 properly?

If I write: 

plot(ceil(x) mod 2, x = 0 .. 4)

it produces a step pattern and not a square wave. (Only 0 and 1 should be plotted.) 

Can i use the file tools package to change the file extension of a file or open up a powershell terminal to do so from within the maple interface via command line?

I need to solve a system of differential equations, which have been obtained from the method of multiple scales. However, for some reason Maple returns an error and will not give a solution. Could someone help me find a solution? The associated filed is attached.

File.mw

So, basically i plan to define procedures based on if conditions that will assume arbitarily large float approximations as being infinity, as with the example i have uploaded, but i feel that i need some people from here that are smarter than me to tell me why this is going to be terrible or what i need to consider. 

I am willing to consider my current view naive and or inept, however i feel as if computer algebra systems will eventually develop means of reducing the need for floating point results by making concise implicit steps of manipulation on floating point computations, naturally i feel as if these routines are evidence that maybe some of the maple programmers have such an objective, but i do tend to misinterpret everything all the time.

 


 

convert(evalf[100](1/RootOf(floor(_Z))), 'rational', 'exact')

infinity

(1)

``


 

Download primes_Question_Algebra.mw

Please may I know if you can offer ma student's discount ob the seleted version.

Thank you.

Fred.

How can I apply differential transformation method in differential equations with maple commands .DE is y'''(x)+xy''(x)-y(x)=0;

I solve a boundary value problem for a linear system of first order PDEs
in the unknowns u(x, t) and "v(x,t)."  Ultimately, I am interested in the graph
of the function v(0, t) but numerical artifacts distort that graph badly by
imposing spurious oscillation.

Is there a way to maneuver the calculations to obtain the graph of v(0, t)
without the oscillation?

restart;

pde1 := diff(u(x,t),t)=diff(v(x,t),x);

diff(u(x, t), t) = diff(v(x, t), x)

pde2 := diff(u(x,t),x)=v(x,t);

diff(u(x, t), x) = v(x, t)

ibc := u(x,0)=1, u(0,t)=0, u(1,t)=0;

u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0

dsol := pdsolve({pde1,pde2}, {ibc}, numeric, spacestep=0.01, timestep=0.01);

_m139872446597344

dsol:-value(output=listprocedure):
my_u := eval(u(x,t), %):
my_v := eval(v(x,t), %%):

plot3d(my_u(x,t), x=0..1, t=0..0.5);

plot3d(my_v(x,t), x=0..1, t=0..0.5);

The oscillations are numerical artifacts.  Can they be avoided?

plot(my_v(0,t), t=0..0.5);

A side comment: By eliminating vbetween the two PDEs we see that u
satisfies the standard heat equation, thus vis the flux.  The expression
v(0, t) expresses the heat flux at the boundary, and that's what I am after.
 


 

Download calculating-flux-in-the-heat-equation.mw

I open a completely new document, type in a few simple expressions and get this weird complex number out. Can someone pleas help me fix this?

In this question at here https://tex.stackexchange.com/questions/503745/how-can-i-get-correct-the-point-a-and-b-automatically-in-this-picture/503838?noredirect=1#comment1272706_503838
The points A and B lie on the circle is intersection of the sphere x^2 + y^2 + (z-3)^2 = 25 and the plane z = 0. 
How can I find coordinates of the points A and B by Maple?

 

searchtext and SearchText do not work well with non-ASCII characters.
Strangely, StringTools:-Search is OK.

restart;
m:=convert([77,97,116,104,195,169,109,97,116,105,113,117,101], bytes);
                      m := "Mathématique"
seq(searchtext(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 1
seq(SearchText(m[i..7], m), i=1..7);
                      1, 0, 0, 4, 0, 0, 7
seq(StringTools:-Search(m[i..7], m), i=1..7);
                      1, 2, 3, 4, 5, 6, 7

 

I'm a Maple novice.  I have two questions.  (1) I'm trying to use Maple to confirm some Fourier transforms of selected probability density functions.  In general I've succeeded, but Maple fails to find the Fourier transform of the pdf of a logistic random variable with mean 0.  Please explain how I can get Maple to carry out this request.  I've attached a Maple file with my work to this question.  (2) At several points in my computations, I wish to substitute 2*Pi*xi for omega.  I have an expression containing two omegas.  If I use algsubs(), only one of the two omegas is replaced.  I have to use subs() to replace both omegas.  Why is this?
 

Use Maple to confirm selected Fourier transform of logistic random variable

with(inttrans)

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

(1)

assume(a > 0)

NULL

"f(x):=((e)^(x/(a)))/(a*(1+(e)^(x/(a)))^(2))"

proc (x) options operator, arrow, function_assign; exp(x/a)/(a*(1+exp(x/a))^2) end proc

(2)

int(f(x), x = -infinity .. infinity)

1

(3)

fourier(f(x), x, omega)

fourier(exp(x/a)/(1+exp(x/a))^2, x, omega)/a

(4)

"f(x) := 1/(4*a*(cosh(x/(2*a)))^(2))"

proc (x) options operator, arrow, function_assign; (1/4)/(a*cosh((1/2)*x/a)^2) end proc

(5)

int(f(x), x = -infinity .. infinity)

1

(6)

fourier(f(x), x, omega)

fourier(1/(exp((1/2)*x/a)+exp(-(1/2)*x/a))^2, x, omega)/a

(7)

Wikipedia's article on "Logistic distribution" gives a characteristic function that implies that the Fourier transform of this pdf should equal Pi*a*omega/sinh(Pi*a*omega).

Unit rectangular function

rect := proc (x) options operator, arrow; Heaviside(x+1/2)-Heaviside(x-1/2) end proc

proc (x) options operator, arrow; Heaviside(x+1/2)-Heaviside(x-1/2) end proc

(8)

fourier(rect(a*x), x, omega)

2*sin((1/2)*omega/a)/omega

(9)

algsubs(omega = 2*Pi*xi, 2*sin((1/2)*omega/a)/omega)

2*sin(Pi*xi/a)/omega

(10)

subs(omega = 2*Pi*xi, 2*sin(Pi*xi/a)/omega)

sin(Pi*xi/a)/(Pi*xi)

(11)

``

NULL


 

Download Logistic_pdf.mw

 

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