Maple Questions and Posts

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Hi. what is reason maple unable to integral in answer of dsolve? when I try to use dsolve for solve my equation in answer of maple there are expressions of integral that isnot calculated

∫(-625 R^2 ro (-2 cp3 x1 lambdaopt+sin((pi t)/10) cp2+(16 cp2)/5) (-cos((pi t)/10)+cos(2 pi)+((-t/5+4) x1+(8 t)/25-32/5) pi) lambdaopt pi b11 (e)^(-((16+5 sin((pi t)/10)) cp1)/(10 lambdaopt x1))+625 (-R^2 k11 (cos((pi t)/10))^3+k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) (cos((pi t)/10))^2+((32 sin((pi t)/10) R^2 k11)/5+(281 R^2 k11)/25+4 lambdaopt^2 (a11 x1+a13 x3)) cos((pi t)/10)-(32 k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) sin((pi t)/10))/5+(281 (x1-8/5) (R^2 k11+(100 lambdaopt^2 (a11 x1+a13 x3))/281) pi t)/125) x1^2)ⅆt

I am using code given in https://www.mapleprimes.com/questions/227270-Is-It-Possible-To-Tell-Maple-NOT-To  which is meant to check if the solution returned by pdsolve is trivial or not.

The code works well for many cases, but I just found few cases (10 cases so far) where it gives 1/0 and not able to figure why

running in the debugger shows it gives this error in the "depvars" function.

Since this is a useful function and I need to use it, is there a way to fix this problem? I am posting this as new question instead of a follow up to original old question as I thought this will make it easier for everyone.

Maple 2019.1

 


 

restart;

depvars:= (pde::{algebraic, `=`(algebraic), {set,list}(algebraic, `=`(algebraic))})->
   indets(
      indets(convert(pde, diff), specfunc(diff)),
      And(typefunc(name, name), Not(typefunc({mathfunc, identical(diff)})))
   ):

is_solution_trivial:= (pde, sol::{`=`, set(`=`),`function`})->
   evalb(eval(`if`(sol::set, sol, {sol}), depvars(pde)=~ 0) = {0=0}):

pde := diff(w(x,y),x)-( diff(f(x),x)*y^2 -f(x)*g(x)*y+ g(x))*diff(w(x,y),y) = 0;

diff(w(x, y), x)-((diff(f(x), x))*y^2-f(x)*g(x)*y+g(x))*(diff(w(x, y), y)) = 0

sol:=pdsolve(pde,w(x,y));

w(x, y) = _F1((y*f(x)*(Int((diff(f(x), x))*exp(Int(f(x)*g(x), x))/f(x)^2, x))-f(x)*exp(Int((f(x)^2*g(x)-2*(diff(f(x), x)))/f(x), x))-(Int((diff(f(x), x))*exp(Int(f(x)*g(x), x))/f(x)^2, x)))/(y*f(x)-1))

is_solution_trivial(pde,sol)

 

Error, (in eval/Int) numeric exception: division by zero

 


 

Download bug_june_25_2019_4.mw

 

I was trying the command sol:=subs(AllSolutions=(), sol):  given in

https://www.mapleprimes.com/questions/227232-A-New-Problem-In-Latex-Command

On a PDE output and I find the result very surprising:


 

restart;

pde:= diff(u(x,t),t)= u(x,t)*(1-u(x,t))+ diff(u(x,t),x$2):
sol:=PDEtools:-TWSolutions(pde,u(x,t));

{u(x, t) = 1}, {u(x, t) = (1/4)*tanh(-(5/12)*t+(1/12)*6^(1/2)*x+_C1)^2-(1/2)*tanh(-(5/12)*t+(1/12)*6^(1/2)*x+_C1)+1/4}, {u(x, t) = (1/4)*tanh((5/12)*t-(1/12)*6^(1/2)*x+_C1)^2+(1/2)*tanh((5/12)*t-(1/12)*6^(1/2)*x+_C1)+1/4}, {u(x, t) = (1/4)*tanh(-(5/12)*t-(1/12)*6^(1/2)*x+_C1)^2-(1/2)*tanh(-(5/12)*t-(1/12)*6^(1/2)*x+_C1)+1/4}, {u(x, t) = (1/4)*tanh((5/12)*t+(1/12)*6^(1/2)*x+_C1)^2+(1/2)*tanh((5/12)*t+(1/12)*6^(1/2)*x+_C1)+1/4}, {u(x, t) = -(1/4)*tanh(-(5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)^2-(1/2)*tanh(-(5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)+3/4}, {u(x, t) = -(1/4)*tanh((5/12)*t-((1/12)*I)*6^(1/2)*x+_C1)^2+(1/2)*tanh((5/12)*t-((1/12)*I)*6^(1/2)*x+_C1)+3/4}, {u(x, t) = -(1/4)*tanh(-(5/12)*t-((1/12)*I)*6^(1/2)*x+_C1)^2-(1/2)*tanh(-(5/12)*t-((1/12)*I)*6^(1/2)*x+_C1)+3/4}, {u(x, t) = -(1/4)*tanh((5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)^2+(1/2)*tanh((5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)+3/4}

sol:=subs(AllSolutions=(), sol):
sol;

{1 = -(1/4)*tanh((5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)^2+(1/2)*tanh((5/12)*t+((1/12)*I)*6^(1/2)*x+_C1)+3/4}

 


What happened to the sol ?  why it says 1=...

Note that Maple returns the solution as expression sequence.  If instead the call was like this

sol:=subs(AllSolutions=(), [sol]):

Then the problem goes away!  and sol remains the same as expected.

Maple 2019.1

 

How could this be explained>?

 

Download bug_june_25_2019_3.mw

Hi all

trying to find analytically sin(erf(t)) and cos(erf (t)) rather than numerically

 

1/0;
Error, numeric exception: division by zero
lastexception;
            0, "numeric exception: division by zero"
lastexception; # ???
            Typesetting:-Typeset, "invalid input: %1 expects %2 arguments, but received %3", type, 2, 3

 

So, printing lastexception produces a new error!
When typesetting=standard, it's OK.

 

Hi, I have a procedure named f1. In it, it calls another procedure f couple of times. procedure f does not have recursive calls implemented.

I have no idea what caused the error. Could anyone give a hint?

Thanks a million in advance,

Best,

Jie

I like Maple the most for calculation of difficult parts. But when it comes to display, I am ignorant and do not know how to command the maple for showing me what is visible in the document.

I attach herewith my document which shows in print view only top half of the sketch. What should I do to show all three figures in the portrait page.
(Here below, after uploading it is shown alright, but in the print preview it is not showing!!).

I want to convert the doc to pdf. Therefore, in the doc preview itself it should be complete.

Thanks for help.

Ramakrishnan V
 

NULL

 

NULL

 

 

 

NULL

 

 

``

NULL


 

Download sketchesNotComing_in_full.mw

So, I am trying to write a method for array interpolation. I have a Matrix that is X by 3, where each column holds specific data (column 1 holds independent data 1, column 2 holds independent data 2, column 3 holds dependent data).

This data comes from a function with 2 independent variables, and I am creating a graph of this function, basically, with both independent variables going from 0 to 1 (approximately 300 values per variable, giving me a matrix with 90k values already). My goal is to use interpolation to get a lot of values in between the points I already calculated.

That being said, I don't know how to use the ArrayInterpolation command to achieve this. I will post my code below if anyone can help me out!

Code:

Interpolate := proc(M::Matrix)
  local i; local j;
  local M1 := Matrix(RowDimension(M),1);
  local M2 := Matrix(RowDimension(M),1);
  local M3 := Matrix(RowDimension(M),1);
  for i from 1 to RowDimension(M) do
    M1(i) := M(i,1);
    M2(i) := M(i,2);
    M3(i) := M(i,3);
  end do;
  print(M1,M2,M3);
  local M4 := Matrix(1000,1);
  local M5 := Matrix(1000,1);
  for j from 1 to 1000 do
    M4(j,1) := 0.001*j;
    M5(j,1) := 0.001*j;
  end do;
  ArrayInterpolation([M1,M2],M3,[M4,M5]);
end proc;

How I can replace  u__0r, theta, t) with f1, 1(r, theta) in attached file.

I want in I have only f1,1] function.

Thanks 


 

````

"f[1, 1](r, theta):=`u__0`(r, theta,t)  "

proc (r, theta) options operator, arrow, function_assign; u__0(r, theta, t) end proc

(1)
``````````

"L[1, 1](r, theta):=-`A__0`*(∂)/(∂r) (F*(∂)/(∂r)`u__0`(r,theta))-1/(2)*`A__0`*(∂)/(∂r) (`K__1`*`u__0`(r,theta))+1/(2)*`A__0`*`K__1`*(∂)/(∂r)`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`H__1`*`u__0`(r,theta))+1/(2)*`A__0`*`H__1`*(∂)/(∂r)`u__0`(r,theta)+`K__3`*`A__0`*`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`K__4`*`u__0`(r,theta))+1/(2)*`A__0`*`K__4`*(∂)/(∂r)`u__0`(r,theta)+`A__0`*`K__5`*`u__0`(r,theta)-2*`A__0`*(∂)/(∂ theta) ((`H__2`)/(r)*(∂)/(∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂ r ∂ theta)(mu*((∂)^(2))/(∂r ∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂theta^(2))(mu*((∂)^(2))/(∂ theta^(2))`u__0`(r,theta))+rho*`A__0`*`K__16`*((∂)^(2))/(∂t^(2))`u__0`(r,theta);"

proc (r, theta) options operator, arrow, function_assign; -A__0*(diff(F*(diff(u__0(r, theta), r)), r))-(1/2)*A__0*(diff(K__1*u__0(r, theta), r))+(1/2)*A__0*K__1*(diff(u__0(r, theta), r))-(1/2)*A__0*(diff(H__1*u__0(r, theta), r))+(1/2)*A__0*H__1*(diff(u__0(r, theta), r))+K__3*A__0*u__0(r, theta)-(1/2)*A__0*(diff(K__4*u__0(r, theta), r))+(1/2)*A__0*K__4*(diff(u__0(r, theta), r))+A__0*K__5*u__0(r, theta)-2*A__0*(diff(H__2*(diff(u__0(r, theta), theta))/r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), r, theta)), r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), theta, theta)), theta, theta))+rho*A__0*K__16*(diff(u__0(r, theta), t, t)) end proc

(2)

``


 

Download replace

 

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Thanks a million in advance,

Best,

Jie

 

 

How 2 solve summation when M,  Z,  X are given with mixed conditions?

restart;

##########  omega and theta are variables,where J[3],F[2],H[2],etc are constants.

#### I tried with "evlf" and "evlc" command but maple was not ready to provide the solution,please help me to solve this

t1:=-1/(-16.*omega^2+exp(-4*omega)+exp(4*omega)-2.)*(-(0.5817764173e-1*I)*exp((2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]-(.6981317009*I)*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*G[3]-.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*H[2]+.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*F[2]+.9308422676*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*H[3]-.1034269187*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*G[2]-0.7757018900e-1*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^2*G[2]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*J[3]-0.9696273622e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*J[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*J[3]-.2714956613*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*H[3]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*G[3]+0.8726646261e-1*exp((2/9)*omega*cos(theta))*omega^3*J[3])*cos((2/9)*omega*sin(theta));

t2:=int(int(t1,omega=0..infinity),theta=0..2*Pi);

 

 

Problem copying a document to Maple Cloud (Public domain)

• Reset password

• Verified email is correct

• Chose File → Save to Cloud... (or clicked Send Document to Cloud on Maple Cloud palette) either way opend Login dialog

• Entered  Account = Maplesoft account, my Email and password then clicked Log in.  The following message appears: "The account type or email address or password is incorrect"

I've saved .mw files to Maple Cloud before with no problems.  Any help appreciated.

Thanks, Les

I have the equation (𝑑π‘₯/𝑑𝑑)^2=π‘Žπ‘₯^3+𝑏π‘₯^2+𝑐π‘₯+𝑑.

How do I plot π‘‘π‘₯/𝑑𝑑 against x? (as the coefficients a, b, c and d vary)

I expect it looks like the following graph:

Thank you for your help.

Hello,

I'm confused about Maple's adjoint function (in the DEtools package). When I take the adjoint of the derivative operator:

DEtools:-adjoint(Dx, [Dx, x])

 

I get back simply "Dx". However, doing the calculation by hand and integrating by parts seems to indicate that this should return the negative of Dx. The inner product I'm using is int(f(x)*conjugate(g(x)), x=0..1). Is Maple perhaps using a different inner product? Or is this a generalization that I'm unaware of? Or is it perhaps just a bug?

 

Thanks!

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