Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

most people who post here seem to use .mw written in 2D, which I do not like to use.

Is there a tool to convert such a file to 1D worksheet that one can use from the command line before opening the document itself in Maple?

The reason I ask, sometimes opening the original file and trying to do this from inside Maple by selecting the code using the mouse, then  Format->ConvertTo->1D   does not work, and gives an error.

Also, sometimes, when I try to first create an empty worksheet document, and then try to copy/paste the code from the other document over, it also does not work. This happens when there are syntax errors in the original document. The error that comes up is

        Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

As an example, please see the attached file in the following question

https://www.mapleprimes.com/questions/227506--I-Need-Help-Trying-To-Write-A-Code

It will good to have a tool that converts such documents to 1D worksheet or even plain Maple code (.mpl) but I did not see such option under SAVE AS either. Also, when I tried to export it as .mpl file, I get the same error as above in the file. So I gave up.

 

Hello Anybody can help me to write codes for PDE to solve by Galerkin finite element method or any other methods can be able to gain results? parameter omega is unknown and should be determined.

I attached a pdf file for more .

Thanks so much

fem2
 

"restart:  rho:=7850:  E:=0.193e12:  n:=1:  AD:=10:  upsilon:=0.291:   mu:=E/(2*(1+upsilon)):  l:=0:  lambda:=E*upsilon/((1+upsilon)*(1-2*upsilon)):  R:=2.5:  ii:=2:  J:=2:       m:=1:       `u__theta`(r,theta,phi):= ( V(r,theta))*cos(m*phi):  `u__r`(r,theta,phi):= ( U(r,theta))*cos(m*phi): `u__phi`(r,theta,phi):= ( W(r,theta))*sin(m*phi):  :        eq1:=(r (R+r cos(theta))^2 (mu+lambda) (((∂)^2)/(∂r∂theta) `u__theta`(r,theta,phi))+2 r^2 (mu+lambda/2) (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__r`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂r) `u__phi`(r,theta,phi))+mu (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__r`(r,theta,phi))+(((∂)^2)/(∂phi^2) `u__r`(r,theta,phi)) mu r^2-3 (R+r cos(theta))^2 (mu+lambda/3) ((∂)/(∂theta) `u__theta`(r,theta,phi))+2 r (mu+lambda/2) (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__r`(r,theta,phi))-r^2 sin(theta) (mu+lambda) (R+r cos(theta)) ((∂)/(∂r) `u__theta`(r,theta,phi))-3 r^2 cos(theta) (mu+lambda/3) ((∂)/(∂phi) `u__phi`(r,theta,phi))-r mu sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__r`(r,theta,phi))-2 (mu+lambda/2) (2 (cos(theta))^2 r^2+2 cos(theta) R r+R^2) `u__r`(r,theta,phi)+r `u__theta`(r,theta,phi) sin(theta) (3 r (mu+lambda/3) cos(theta)+R mu))/(r^2 (R+r cos(theta))^2):  eq2:=(2 (mu+lambda/2) (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__theta`(r,theta,phi))+r (R+r cos(theta))^2 (mu+lambda) (((∂)^2)/(∂r∂theta) `u__r`(r,theta,phi))+r (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂theta) `u__phi`(r,theta,phi))+r^2 mu (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__theta`(r,theta,phi))+(((∂)^2)/(∂phi^2) `u__theta`(r,theta,phi)) mu r^2+3 (R+r cos(theta)) ((4 r (mu+lambda/2) cos(theta))/3+R (mu+lambda/3)) ((∂)/(∂theta) `u__r`(r,theta,phi))-2 r (mu+lambda/2) sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__theta`(r,theta,phi))+r mu (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__theta`(r,theta,phi))+3 r^2 sin(theta) (mu+lambda/3) ((∂)/(∂phi) `u__phi`(r,theta,phi))+(-3 r R (mu+lambda/3) cos(theta)+(-lambda-2 mu) r^2-R^2 mu) `u__theta`(r,theta,phi)-2 r (mu+lambda/2) sin(theta) R `u__r`(r,theta,phi))/(r^2 (R+r cos(theta))^2):  eq3:=(r (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂theta) `u__theta`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂r) `u__r`(r,theta,phi))+mu (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__phi`(r,theta,phi))+r (r mu (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__phi`(r,theta,phi))+2 r (mu+lambda/2) (((∂)^2)/(∂phi^2) `u__phi`(r,theta,phi))+(4 r (mu+lambda/2) cos(theta)+R (mu+lambda)) ((∂)/(∂phi) `u__r`(r,theta,phi))+mu (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__phi`(r,theta,phi))-mu sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__phi`(r,theta,phi))-r (3 sin(theta) (mu+lambda/3) ((∂)/(∂phi) `u__theta`(r,theta,phi))+`u__phi`(r,theta,phi) mu)))/(r^2 (R+r cos(theta))^2):  "

EQ1 := collect(eq1, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ2 := collect(eq2, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ3 := collect(eq3, sin(m*phi))/sin(m*phi)+rho*omega^2

(0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), theta))+0.2535718390e12*r^2*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), r))+0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(W(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), theta), theta))-0.7474825716e11*U(r, theta)*r^2-0.3283200960e12*(2.5+r*cos(theta))^2*(diff(V(r, theta), theta))+0.2535718390e12*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(U(r, theta), r))-0.1788235818e12*r^2*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), r))-0.3283200960e12*r^2*cos(theta)*W(r, theta)-0.7474825716e11*r*sin(theta)*(2.5+r*cos(theta))*(diff(U(r, theta), theta))-0.2535718390e12*(2.*cos(theta)^2*r^2+5.0*r*cos(theta)+6.25)*U(r, theta)+r*V(r, theta)*sin(theta)*(0.3283200960e12*r*cos(theta)+0.1868706429e12))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

 

(0.2535718390e12*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), theta), theta))+0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), theta))+0.1788235818e12*r*(2.5+r*cos(theta))*(diff(W(r, theta), theta))+0.7474825716e11*r^2*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), r))-0.7474825716e11*V(r, theta)*r^2+3.*(2.5+r*cos(theta))*(0.1690478927e12*r*cos(theta)+0.2736000800e12)*(diff(U(r, theta), theta))-0.2535718390e12*r*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), theta))+0.7474825716e11*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(V(r, theta), r))+0.3283200960e12*r^2*sin(theta)*W(r, theta)+(-0.8208002400e12*r*cos(theta)-0.2535718389e12*r^2-0.4671766072e12)*V(r, theta)-0.6339295976e12*r*sin(theta)*U(r, theta))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

 

(-0.1788235818e12*r*(2.5+r*cos(theta))*(diff(V(r, theta), theta))-0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(U(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), theta), theta))+r*(0.7474825716e11*r*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), r), r))-0.2535718390e12*r*W(r, theta)-1.*(0.5071436780e12*r*cos(theta)+0.4470589545e12)*U(r, theta)+0.7474825716e11*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(W(r, theta), r))-0.7474825716e11*sin(theta)*(2.5+r*cos(theta))*(diff(W(r, theta), theta))-1.*r*(-0.3283200960e12*sin(theta)*V(r, theta)+0.7474825716e11*W(r, theta))))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

(1)

#BCs can be from following
``
U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0

U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0

(2)

NULL
V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0
NULL
W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0
``

V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0

 

W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0

(3)

``


 

Download fem2

buchanan2005.pdf

 

 

I wanted to remove entry from a list that contain y=y or x=x in it. Here is an example

f:= (x-1)*y^4/(x^2*(2*y^2-1));
S:=[singular(f)]

Where I wanted to remove those entries highlighted above to obtain

This is below how I ended up doing it. I'd like to ask if there is a better or more elegent way. I had to use map, since could not get remove() to work on the original list in one shot. 

foo:= z->remove(has,z,{y = y,x = x});
map(foo,[singular(f)])

Which gives the output above.

Is there a better way to do this? I always learn when I find how to do something better.

Maple 2019.1

 

 

is the reason for Image result?


 

R+r__i*cos(`θ__j`)

R+(1.-0.750482401378084e-231*I)*r__i

(1)

``


 

Download cos

 

Are there commands in Maple to find the order and degree of an ODE?  Searching help I could not find anything so far.

For an example, given 

restart;
ode:=(1+diff(y(x),x)^2)^(3/2)=diff(y(x),x$2)

I want the command to return 2 for the order of the ODE and degree is also 2 in this case.

I looked at DEtools package and googled. I am sure Maple have build in commands to do this without me having to parse the ODE myself to find out.

so i just went from a really old version of maple to a the newest one maple 2019 and at first glance it doesn't seem to work correctly please take a look at the picture maybe there is a toggle i missed or something of the sorts thanks you for your time 

I have a tough integral I'm trying to solve (see attatched code). Maple seems to be able to compute it if I instruct it to integrate by parts, however the solutions don't make sense. For example, if I differentiate the result I expect to get my original integrand, but I do not. Furthermore, depending on which function you choose as 'u' and which as 'dv' when integrating by parts yields different results.

071319_Integral.mw

The attatched code has four examples:

1) Definite integration by parts

2) Indefinite integration by parts

3) Indefinite integration by parts, alternate choice of 'u'

4) Definite integration by parts, alternate choice of 'u'

and after each indefinite integration, I differentiate the result to compare with the orginal integrand.

What is going on here?

Hi,
I would like to trace periodic functions. I saw that this was possible with the old 'FourierSeries' package with the "Rept" command. How to reproduce the same thing in the Maple 19 environment? Thank you

fs_examples.mw

fyi, there seems to be a problem here. Maple 2019, Physics version 395 on windows 10.

The solution given to this wave PDE by Maple as sum that starts from zero, has "n" in the denominator. When n=0, this gives division by zero.  Is this a bug?

restart;
L:=3: c:=4: h:=1/10: b:=Pi*c/L:
f:=piecewise(0<=x and x<=L/3,3*h/L*x,L/3<x and x<=L,h):
pde := diff(u(x,t),t$2) + b*diff(u(x,t),t) = c^2*diff(u(x,t),x$2):
bc  := u(0,t)=0,D[1](u)(L,t)=0:
ic  := D[2](u)(x,0)=0,u(x,0)=f:
sol:=pdsolve([pde,bc,ic],u(x,t));
subs(n=0,sol)

u(x, t) = Sum(-((3/10)*I)*sin((1/6)*(1+2*n)*Pi*x)*(3^(1/2)*sin((1/3)*Pi*n)+cos((1/3)*Pi*n))*((2*I)*exp((4/3)*t*(I*n^(1/2)*(n+1)^(1/2)-1/2)*Pi)*n^(1/2)*(n+1)^(1/2)+(2*I)*exp(-(4/3)*(I*n^(1/2)*(n+1)^(1/2)+1/2)*t*Pi)*n^(1/2)*(n+1)^(1/2)+exp((4/3)*t*(I*n^(1/2)*(n+1)^(1/2)-1/2)*Pi)-exp(-(4/3)*(I*n^(1/2)*(n+1)^(1/2)+1/2)*t*Pi))/(n^(1/2)*(n+1)^(1/2)*Pi^2*(1+2*n)^2), n = 0 .. infinity)

Error, numeric exception: division by zero

 


 

Download bug_july_11_2019.mw

 

 I'm confused as to why Maple can't perform a certain integral for me. Please see my attached code - it get's stuck on the last step.

 

070919_ThetaIntegral.mw

Does anyone know how collect zero epsilon coefficient from follow expression?

coeff_test.mw

Is it possible?

Thank you!

I am able to generate random polynomials with non-zero coefficents, and define sets of all the positive divisors of the leading coefficient and the constant terms. My question is this, how may I apply the rational zeros theorem to generate the set of all possible rational zeros of the polynomial. I basically need to form all the possible quotients (positive and negative) with numerator in one set and denominator in the other set, ignoring duplicates. The attached worksheet has what I've done so far.rational_zeros.mw
 

attempt := 1; while attempt > 0 do q := randpoly(x, coeffs = rand(-9 .. 9), degree = 3, dense); if nops(q) = 4 then attempt := -2 end if; attempt := attempt+1 end do; q

5*x^3+3*x^2-4*x-8

(1)

NumberTheory[Divisors](coeff(q, x, 3))

{1, 5}

(2)

NumberTheory[Divisors](coeff(q, x, 0))

{1, 2, 4, 8}

(3)

``


 

Download rational_zeros.mw

 

The command eval allows to simplify a complicated expression

in a more compact form for a later output in LATEX

In the example which follows I was able to insert A and B but non C in the expression.

There is already a post on this kind of topic but I failed to understand the details.

Perhaps a Maple worksheet of answer on this topic  would be useful !

bye Lorenzo
 

restart;

expression:=exp(-b*x^c/2)*((x^(-(3*c)/2 + a/2 + 1/2)*(c + a + 1)*b^(-(3*c + a + 1)/(2*c)) + c*x^(a/2 + 1/2 - c/2)*b^(-(c + a + 1)/(2*c)))*c*WhittakerM((-c + a + 1)/(2*c), (2*c + a + 1)/(2*c), b*x^c) + b^(-(3*c + a + 1)/(2*c))*x^(-(3*c)/2 + a/2 + 1/2)*WhittakerM((c + a + 1)/(2*c), (2*c + a + 1)/(2*c), b*x^c)*(c + a + 1)^2)/((a + 1)*(c + a + 1)*(2*c + a + 1));

exp(-(1/2)*b*x^c)*((x^(-(3/2)*c+(1/2)*a+1/2)*(c+a+1)*b^(-(1/2)*(3*c+a+1)/c)+c*x^((1/2)*a+1/2-(1/2)*c)*b^(-(1/2)*(c+a+1)/c))*c*WhittakerM((1/2)*(-c+a+1)/c, (1/2)*(2*c+a+1)/c, b*x^c)+b^(-(1/2)*(3*c+a+1)/c)*x^(-(3/2)*c+(1/2)*a+1/2)*WhittakerM((1/2)*(c+a+1)/c, (1/2)*(2*c+a+1)/c, b*x^c)*(c+a+1)^2)/((a+1)*(c+a+1)*(2*c+a+1))

(1)

``

(2)

expression_ABC:=eval(expression,[x^(-(3*c)/2 + a/2 + 1/2)*(c + a + 1)*b^(-(3*c + a + 1)/(2*c))=A,c*x^(a/2 + 1/2 - c/2)*b^(-(c + a + 1)/(2*c))=B,((a + 1)*(c + a + 1)*(2*c + a + 1))=C]);

exp(-(1/2)*b*x^c)*((A+B)*c*WhittakerM((1/2)*(-c+a+1)/c, (1/2)*(2*c+a+1)/c, b*x^c)+b^(-(1/2)*(3*c+a+1)/c)*x^(-(3/2)*c+(1/2)*a+1/2)*WhittakerM((1/2)*(c+a+1)/c, (1/2)*(2*c+a+1)/c, b*x^c)*(c+a+1)^2)/((a+1)*(c+a+1)*(2*c+a+1))

(3)

 

 

 

 


 

Download maple_primes_eval.mw

 

Hi

 

I've just installed Maple latest + MapleSim with the license provided by my university (I use VPN with a secure key to remotely access server license. Everything works fine, except for the context menu. It seems that the context menu module is missing! I tried uninstalling and reinstalling, but did not help.

 

I went back to the campus and checked Maple installation on computers there, and this problem is absent (context menu is working fine).

 

I can only use the context menu toolbar on the right... but this is not very convenient. 

What could be the problem? See the attached image.

 

Thanks

---------------------

 

Hi!

How to calculate  a value in MAPLE:

My code:

evalf(eval(diff(n*Zeta(n, 3), n), n = 3)); give me:

#-0.3740436824 + 3.*eval(diff(Zeta(n, 3), n), {n = 3}) ,it should be only:-0.3740436824

OR:

fdiff(n*Zeta(n, 3), [n], n = 3);

#fdiff(n -> n*Zeta(n, 3), [1], [3]) ???

It's a Bug  or (As Designed / Not a Bug) ?

Thanks in advance.

 

Mathematica code:

D[n*Derivative[n][Zeta][3], n] /. n -> 3 // N;

(* -0.374044*)

 

 

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