Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Here's something neat to be done in Maple. 
This anaglyph or stereo image uses the red green glasses to make the model appear more 3 dimensional.  The static-non-stereo image of the animated plot below is done in maple by plot3d(sin(x*y)^2,x=-2..2,y=-2..2,scaling=constrained)

Anyone?

 

hi

how i can pdsolve these partial differentialequations?

thanks

10.mw
 

restart; R := 1; UB := 1; lambda := 1; pe1 := 1; pe2 := 1; L := 1; Gr := 1; Br := 1; p := 1; LinearAlgebra:-HermitianTranspose(L) := 1; Nb := 1; Nt := 1; a := lambda*pe1*u(r, z)*(diff(sigma(r, z), z))-(diff(r*(diff(sigma(r, z), r)), r))/r-lambda^2*(diff(sigma(r, z), z, z))-Nt*((diff(r*(diff(theta(r, z), r)), r))/r+lambda^2*(diff(theta(r, z), z, z)))/Nb

u(r, z)*(diff(sigma(r, z), z))-(diff(sigma(r, z), r)+r*(diff(diff(sigma(r, z), r), r)))/r-(diff(diff(sigma(r, z), z), z))-(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r-(diff(diff(theta(r, z), z), z))

(1)

b := lambda*pe2*u(r, z)*(diff(theta(r, z), z))-(diff(r*(diff(theta(r, z), r)), r))/r-lambda^2*(diff(theta(r, z), z, z))-Nb*((diff(sigma(r, z), r))*(diff(theta(r, z), r))+(diff(sigma(r, z), z))*(diff(theta(r, z), z))*lambda^2)-Nt*((diff(theta(r, z), r))^2+lambda^2*(diff(theta(r, z), z))^2)

u(r, z)*(diff(theta(r, z), z))-(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r-(diff(diff(theta(r, z), z), z))-(diff(sigma(r, z), r))*(diff(theta(r, z), r))-(diff(sigma(r, z), z))*(diff(theta(r, z), z))-(diff(theta(r, z), r))^2-(diff(theta(r, z), z))^2

(2)

c := -p+(diff(r*(diff(u(r, z), r)), r))/r-L^2*(diff(r*(diff((diff(r*(diff(u(r, z), r)), r))/r, r)), r))/r+Gr*theta(r, z)+Br*sigma(r, z)

-1+(diff(u(r, z), r)+r*(diff(diff(u(r, z), r), r)))/r-(-(diff(u(r, z), r)+r*(diff(diff(u(r, z), r), r)))/r^2+(2*(diff(diff(u(r, z), r), r))+r*(diff(diff(diff(u(r, z), r), r), r)))/r+r*(2*(diff(u(r, z), r)+r*(diff(diff(u(r, z), r), r)))/r^3-2*(2*(diff(diff(u(r, z), r), r))+r*(diff(diff(diff(u(r, z), r), r), r)))/r^2+(3*(diff(diff(diff(u(r, z), r), r), r))+r*(diff(diff(diff(diff(u(r, z), r), r), r), r)))/r))/r+theta(r, z)+sigma(r, z)

(3)

bc := {sigma(R, z) = 0, sigma(r, 0) = 1, theta(R, z) = 0, theta(r, 0) = 1, u(R, z) = UB, (D[1](sigma))(0, z) = 0, (D[1](sigma))(r, LinearAlgebra:-HermitianTranspose(L)) = 0, (D[1](theta))(0, z) = 0, (D[1](theta))(r, LinearAlgebra:-HermitianTranspose(L)) = 0, (D[1](u))(0, z) = 0, (D[2](u))(R, z) = 0}

{sigma(1, z) = 0, sigma(r, 0) = 1, theta(1, z) = 0, theta(r, 0) = 1, u(1, z) = 1, (D[1](sigma))(0, z) = 0, (D[1](sigma))(r, 1) = 0, (D[1](theta))(0, z) = 0, (D[1](theta))(r, 1) = 0, (D[1](u))(0, z) = 0, (D[2](u))(1, z) = 0}

(4)

``


 

Download 10.mw

 

Dear Maple  users,

I am facing the memory allocation problem while calculating the inverse Laplace transformation of a big expression. I have many such terms (401) and I am importing them from a text file.

For an individual term itself, Maple consumes huge memory but at the end, it is able to calculate it in about an hour. I want to automate the process of reading and writing the terms one by one from the different text files. While doing so, maple eats a lot of memory and I see the error msg

"Error, (in expand/bigprod) Maple was unable to allocate enough memory to complete this computation.
Please see ?alloc "

Is there a way to do so? The maple file is attached.

InvLaplace_ex.mw

Thanks,

I´m new to Maple and I´m trying to find the minimum distance of an ECC from its parity check matrix or the generator matrix. Is this possible?

A fact that seems to be not documented. Probably it should be obvious.

 

Digits := d0
evalf[d](expr);

 

The toplevel float sub-expressions in expr  are computed with Digits=d0 but in procedures Digits is set to d.
Notice that the actual float parameters of the toplevel procedures are evalf-ed with Digits=d0.

 

restart;

g:=proc() convert(1/3., string) end:
h:=proc() 1/3. end:

Digits:=3;
evalf[10]([
  1/3. = h(),
  convert(1/3.,string) = g(),  
  fsolve(3*x=1) = add([1/3]),
  fsolve(x/3=1/9.) # 1/9. being at top level is evalf-ed with Digits=3
])

3

 

[.333 = .3333333333, ".333" = ".3333333333", .3333333333 = .3333333333, .3330000000]

(1)

 

k:=proc(x) convert(x,string) end:

kernelopts(floatPi);

true

(2)

4.+Pi;

7.14

(3)

evalf(k(1/3.+Pi));
# floatPi seems to be ignored inside actual parameters

".333+Pi"

(4)

evalf(k(4+evalf(Pi)));

"7.14"

(5)

evalf(k(4+Pi));
# 4 not being float (or "infected" by a float) is not evalf-ed

"4+Pi"

(6)

 

### (this is documented)

`evalf/h` := proc() 7.777 end:

evalf(h(1/3));

.333

(7)

evalf('h'(1/3));

7.777

(8)

 

 

Download digits.mw

(edited)

After waiting about six hours for the worksheet to be executed, I finally lost hope and stopped it. (My CPU usage was stuck on 100% the whole time and I almost ran out of memory) Is this evaluation time normal and should I have waited longer, or is there a problem with my worksheet? (I'm uploading it here) Or is it possible that the equation cannot be solved by Maple at all?

parasitic.mw

help me on thispde_solutionalpha.mw
 

restart

M := 1; S := .78; K := .5; Sh := .2; alpha := .7; R := .3; N := .6; k := .5

pde1 := diff(u(y, t), t)+S.(diff(u(y, t), y))-2*k^2*u(y, t) = diff(u(y, t), y, y)+theta(y, t)+N.C(y, t)+M.u(y, t)+u(y, t)/K

                pde2 := theta(y, t)+t*(diff(theta(y, t), t))+S*(diff(theta(y, t), y)) = (diff(theta(y, t), y, y))/Pr-alpha.theta(y, t)

pde3 := C(y, t)+t*(diff(C(y, t), t))+S*(diff(C(y, t), y)) = (diff(C(y, t), y, y))/Sh-R.C(y, t)

PDE := unapply({pde || (1 .. 3)}, Pr)

proc (Pr) options operator, arrow; {C(y, t)+t*(diff(C(y, t), t))+.78*(diff(C(y, t), y)) = 5.000000000*(diff(diff(C(y, t), y), y))-.3*C(y, t), diff(u(y, t), t)+.78*(diff(u(y, t), y))-.50*u(y, t) = diff(diff(u(y, t), y), y)+theta(y, t)+.6*C(y, t)+3.000000000*u(y, t), theta(y, t)+t*(diff(theta(y, t), t))+.78*(diff(theta(y, t), y)) = (diff(diff(theta(y, t), y), y))/Pr-.7*theta(y, t)} end proc

(1)

IBC := {C(0, t) = 1, C(1, t) = 0, C(y, 0) = 0, theta(0, t) = 1, theta(1, t) = 0, theta(y, 0) = 0, u(0, t) = 0, u(1, t) = 0, u(y, 0) = 0}

``

PrList := [.71, 7, 10, 100]; Colours := table(`~`[`=`](PrList, ["blue", "red", "green", "cyan"])); for Pr in PrList do pds := pdsolve(PDE(Pr), IBC, numeric); Plots[Pr] := pds:-plot[display](u(y, t), t = .5, linestyle = "solid", colour = Colours[Pr], legend = sprintf("Pr=%2.2f", Pr), title = "Velocity Profile", labels = ["y", "theta"]) end do; plots:-display([seq(Plots[Pr], `in`(Pr, PrList))])

 

NULL


 

Download pde_solutionalpha.mw

 

How can i export a plot using open maple in java?

engine.evaluate("Export(\"D:\\MyGraph.jpeg\", plot(sin(x)));");

and 

engine.evaluate("exportplot(\"D:\\MyGraph.jpeg\", plot(sin(x)));");

doesn't work,

exception - com.maplesoft.externalcall.MapleException: Error, (in Export) exported file D:MyGraph.jpeg could not be createdError, plotting was not implemented by the application

 

Thanks.

How do i find the distance between the quasi cyclic codes in maple ?

how do i solve a system of PDE's with variable coeffiecients in Maple?

what package I need to add in order to use commands named "Drawmatrix, Translatemat and Transform" ? I add package named Lamp but it is not working. I have maple 15. Please try to respond as soon as possible because its urgent.

 

Thank you

Hi everyone

I have a problem with differentiating an equation. I have the following code:


(sum((x(i)-M)^3, i = 1 .. n))/(n*((sum((x(i)-M)^2, i = 1 .. n))/(n-1))^(3/2));


The values of x(i) is available in Excel and I want to import that. For this case, I copy the column and paste in maple and it seems work fine. But, I want to calculate the differentiate of the summation with respect to x(i) and M and find the answer. I don't know how to write the code appropriately.

In other words, how could I differetiate the following function with respect to x(i) and put the values from excel into it.

(sum((x(i)-M)^3, i = 1 .. n))/(n*((sum((x(i)-M)^2, i = 1 .. n))/(n-1))^(3/2));

 

Thank you so much for your kind attentions  in advance

 

Dear all

Hope everything is fine with everything. I want to draw the graph of the u(x,0.5) and T(x,0.5) for different values of alpha like alpha =0.4,0.6,0.8 while keeping Gr, R and Pr are fixed. Please solve the following problem I shall be vary thankful to you. Thanks in advance

with the following BCs

I have a polynomial of 4th order and I wanted to use allvalues on the RootOf expression. It then says:
 

Error, (in evala/Normal/preproc) reducible RootOf detected.  Substitutions are {RootOf(4678560000000000000000000000000000000000+(16573041*CO^2+70122975000000000000*CO-623180900000000000000000000000000)*_Z^4+(-19887649200*CO^2-82987335000000000000000*CO+745755960000000000000000000000000000)*_Z^3+(5966294760000*CO^2+23851989000000000000000000*CO-221858784000000000000000000000000000000)*_Z^2+(417684600000000000000000000*CO-757598400000000000000000000000000000000)*_Z) = 600, RootOf(4678560000000000000000000000000000000000+(16573041*CO^2+70122975000000000000*CO-623180900000000000000000000000000)*_Z^4+(-19887649200*CO^2-82987335000000000000000*CO+...
Error, (in allvalues) numeric exception: division by zero

So apparently the expression is reducible but how do I do that?

 I have in my Maple documents many good quality plots resulting from simulations. I need to export (or paste) them to templates of transactions in Word without loosing quality, and beeing flexible to some degree to fit the dimension.

Until now when I paste such plots the quality is lost and especially on descripltion on axes (vertical).

What I have to do? Do I need to go throuhg pdf format ? 

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