Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

When printing a Maple Worksheet  often I go in the PrintPrewiev of the Mac and then select some sides to print.

This is not working anymore since I have updated from Maple 2021 to Maple 2023.

Is this known ?

Any help for his ?

For the following Equation:

Equation := int(diff(u(x), x)*v(x), x) = int(u(x)^(1/2)*v(x), x)^(-2/3);
Maplesoft finds the following solution:

Solution1:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Intat(1/(sqrt(u(x))*Int(v(_b), _b))^(5/3), _b = x) + _C1 = 0

or , which I believe as an alternative, can be written as

Solution2:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Int(1/(sqrt(u(x))*Int(v(x),x))^(5/3) +_C1=0

My question is how did Maple arrive at 'Solution1' from 'Equation'? In other words, can someone fill

in the steps between 'Equation'  and 'Solution1'? Or even, prove that Solution 1 is a valid solution to Equation.

Plugging the Solution1 into Equation, did not clearly demonstate the validity of the solution (to me at least)

Unfortunately, I am still unable to post the corresponding Maplesoft worksheet onto this post.

Invoked by the OEIS superseeker, Maple "gfun" package "listtoalgeq" identified possible lgdegf for https://oeis.org/A035001

1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232, 256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048, 2329, 3104, 3328, 4096, 4864, 6266, 6802, 7168, 8192, 11952, 15360, 16384, 16428, 19149, 28928, 32768, 37120, 42168 

as follows:

1024-5120*a(n)+11520*a(n)^2-15360*a(n)^3+13440*a(n)^4-8064*a(n)^5+3360*a(n)^6-960*a(n)^7+180*a(n)^8-20*a(n)^9+a(n)^{10}

The coefficients of above polynomial are:

{1, -20, 180, -960, 3360, -8064,13440, -15360, 11520, -5120, 1024,...}

It is interesting that the absolute values of above polynomial coefficients satisfy a(n) of

https://oeis.org/A013609

for n=55...65,

which is the 11th row in the triangle presentation of A013609, so in other words the absolute values of above polynomial coefficients are T={11, k} for k=1...11

Dear Users!

I hope you are doing well. I have the following discretized form

for n>=1 and j=0..M. We obtained the following matrix equation for any "n" and j=0..M as:

I want matrix proc of any useful way to define A^n, u^n, and b^n. I am waiting for your positive response. Thanks in advancs

Dear all 

I have a function defined on many sub-intervals, how can I simplify this the funciton obtained at each iteration. I hope obatin B_{i,1}, B_{i,2}, and B_{i,3} 

B_Spline.mw

Thank you 

  I am unable to draw both 3d plots sowing error please help me to solve

restart:NULLNULL

p1 := 0.1e-1; p2 := 0.2e-1; p3 := 0.1e-1; Px := p1+p2+p3

rf := 1050; kf := .52; cpf := 3617; sigmaf := .8

sigma1 := 25000; rs1 := 5200; ks1 := 6; cps1 := 670

sigma2 := 59.7*10^6; rs2 := 8933; ks2 := 400; cps2 := 385

sigma3 := 2380000; rs3 := 4250; ks3 := 8.9538; cps3 := 686.2

NULL

B1 := 1+2.5*Px+6.2*Px^2; B2 := 1+13.5*Px+904.4*Px^2; B3 := 1+37.1*Px+612.6*Px^2; B4 := (ks1+2*kf-2*Px*(kf-ks1))/(ks1+2*kf+Px*(kf-ks1)); B5 := (ks2+3.9*kf-3.9*Px*(kf-ks2))/(ks2+3.9*kf+Px*(kf-ks2)); B6 := (ks3+4.7*kf-4.7*Px*(kf-ks3))/(ks3+4.7*kf+Px*(kf-ks3))

a2 := B1*p1+B2*p2+B3*p3

a1 := 1-p1-p2-p3+p1*rs1/rf+p2*rs2/rf+p3*rs3/rf

a3 := 1-p1-p2-p3+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf)+p3*rs3*cps3/(rf*cpf)

a4 := B4*p1+B5*p2+B6*p3

NULL

a5 := 1+3*((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3)/(2+(p1*sigma1+p2*sigma2+p3*sigma3)/((p1+p2+p3)*sigmaf)-((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3))

``

``



NULL

ODE:=[(a2+K)*(diff(U0(eta), eta, eta))/a1-Ra*(diff(U0(eta), eta))+lambda0/a1-a5*M1^2*U0(eta)/a1+K*(diff(N0(eta), eta))/a1+la*Ra*Theta0(eta)*(1+Qc*Theta0(eta)), (a2+K)*(diff(U1(eta), eta, eta))/a1-H^2*l1*U1(eta)-Ra*(diff(U1(eta), eta))+lambda1/a1-a5*M1^2*U1(eta)/a1+K*(diff(N1(eta), eta))/a1+la*Ra*(Theta1(eta))(1+2*Qc*Theta0(eta)), diff(N0(eta), eta, eta)-Ra*a1*Pj*(diff(N0(eta), eta))-2*n1*N0(eta)-n1*(diff(U0(eta), eta)), diff(N1(eta), eta, eta)-Ra*a1*Pj*(diff(N1(eta), eta))-2*n1*N1(eta)-n1*(diff(U1(eta), eta))-H^2*a1*Pj*l1*N1(eta), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta0(eta), eta, eta))-Ra*(diff(Theta0(eta), eta))+a5*Ec*M1^2*U0(eta)^2/a3+(a2+K)*Ec*(diff(U0(eta), eta))^2/a1+Q*Theta0(eta)/a3+4*(diff(Theta0(eta), eta))^2*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta1(eta), eta, eta))-(H^2*l1+2*Ra*delta*l1+Ra)*(diff(Theta1(eta), eta))+(Q/a3-delta*H^2*l1^2)*Theta1(eta)+2*(a2+K)*Ec*(diff(U0(eta), eta))*(diff(U1(eta), eta))/a1+2*a5*Ec*M^2*U0(eta)*U1(eta)/a3+4*(diff(Theta0(eta), eta, eta))*Theta1(eta)*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr)+4*Rd*(diff(Theta0(eta), eta))^2*(6*(Tp-1)^2*Theta1(eta)+6*(Tp-1)^3*Theta0(eta)*Theta1(eta))/(3*a3*Pr)+4*Rd*(diff(Theta1(eta), eta))*(diff(Theta0(eta), eta))*(6*(Tp-1)+6*(Tp-1)^3*Theta0(eta)^2+12*(Tp-1)^2*Theta0(eta))/(3*a3*Pr)]:


(LB,UB):= (0,1):


BCs:= [
  
  U0(0) = 0, U1(0) = 0, N0(0) = 0, N1(0) = 0, Theta0(0) = 0, Theta1(0) = 0, U0(1) = 0, U1(1) = 0, N0(1) = 0, N1(1) = 0, Theta0(1) = 1, Theta1(1) = 0
]:

NULL


Params:= Record(
   
   M1=  1.2, Rd=0.8,la=0.8,n1=1.2,Q=0.2,Pj=0.001,Ra=0.8,Ec=1,    Pr= 21,   delta= 0.2,    t1= (1/4)*Pi, lambda0=2,lambda1=3,   Qc= 0.1,    l1= 1,K=0.4,H=3 ,deltat=0.05  ):
   

NBVs:= [   
 
a1**D(U0)(0) = `C*__f` , # Skin friction coefficient
 (a4+(4*Rd*(1/3))*(1+(Tp-1)*(Theta0(0)+0.1e-2*exp(l1*t1)*Theta1(0)))^3)*((D(Theta0))(0)+0.1e-2*exp(l1*t1)*(D(Theta1))(0)) = `Nu*`    # Nusselt number     
]:
Nu:= `Nu*`:
Cf:= `C*__f`:

 

Solve:= module()
local
   nbvs_rhs:= rhs~(:-NBVs), #just the names
   Sol, #numeric dsolve BVP solution of any 'output' form
   ModuleApply:= subs(
      _Sys= {:-ODEs[], :-BCs[], :-NBVs[]},
      proc({
          M1::realcons:=  Params:-M1,
         Pr::realcons:= Params:-Pr,
         Rd::realcons:= Params:-Rd,
         la::realcons:= Params:-la,
         Tp::realcons:= Params:-Tp,
         n1::realcons:= Params:-n1,
         Q::realcons:= Params:-Q,
         Pj::realcons:= Params:-Pj,
         Ra::realcons:= Params:-Ra,
         Ec::realcons:= Params:-Ec,
         t1::realcons:=  Params:-t1,
         delta::realcons:= Params:-delta,
         lambda0::realcons:= Params:-lambda0,
         lambda1::realcons:= Params:-lambda1,
         Qc::realcons:= Params:-Qc,
         K::realcons:= Params:-K,
         l1::realcons:= Params:-l1,
         H::realcons:= Params:-H
      })
         Sol:= dsolve(_Sys, _rest, numeric);
         AccumData(Sol, {_options});
         Sol
      end proc
   ),
   AccumData:= proc(
      Sol::{Matrix, procedure, list({name, function}= procedure)},
      params::set(name= realcons)
   )
   local n, nbvs;
      if Sol::Matrix then
         nbvs:= seq(n = Sol[2,1][1,Pos(n)], n= nbvs_rhs)
      else
         nbvs:= (nbvs_rhs =~ eval(nbvs_rhs, Sol(:-LB)))[]
      fi;
      SavedData[params]:= Record[packed](params[], nbvs)
   end proc,
   ModuleLoad:= eval(Init);
export
   SavedData, #table of Records
   Pos, #Matrix column indices of nbvs
   Init:= proc()
      Pos:= proc(n::name) option remember; local p; member(n, Sol[1,1], 'p'); p end proc;
      SavedData:= table();
      return
   end proc ;
   ModuleLoad()
end module:
 


 

 

#procedure that generates 3-D plots (dropped-shadow contour + surface) of an expression


ParamPlot3d:= proc(
   Z::{procedure, `module`}, #procedure that extracts z-value from Solve's dsolve solution
   X::name= range(realcons), #x-axis-parameter range
   Y::name= range(realcons), #y-axis-parameter range
   FP::list(name= realcons), #fixed values of other parameters
   {
      #fraction of empty space above and below plot (larger "below"
      #value improves view of dropped-shadow contourplot):
      zmargin::[realcons,realcons]:= [.05,0.15],
      eta::realcons:= :-LB, #independent variable value
      dsolveopts::list({name, name= anything}):= [],
      contouropts::list({name, name= anything}):= [],
      surfaceopts::list({name, name= anything}):=[]    
   }
)
local
   LX:= lhs(X), RX:= rhs(X), LY:= lhs(Y), RY:= rhs(Y),
   Zremember:= proc(x,y)
   option remember; #Used because 'grid' should be the same for both plots.
      Z(
         Solve(
            LX= x, LY= y, FP[],
            #Default dsolve options can be changed by setting 'dsolveopts':
            'abserr'= 0.5e-7, 'interpolant'= false, 'output'= Array([eta]),  
            dsolveopts[]
         )
      )
   end proc,
   plotspec:= (Zremember, RX, RY),
   C:= plots:-contourplot(
      plotspec,
      #These default plot options can be changed by setting 'contouropts':
      'grid'= [25,25], 'contours'= 5, 'filled',
      'coloring'= ['yellow', 'orange'], 'color'= 'green',
      contouropts[]
   ),
   P:= plot3d(
      plotspec,
      #These default plot options can be changed by setting 'surfaceopts':
      'grid'= [25,25], 'style'= 'surfacecontour', 'contours'= 6,
      surfaceopts[]
   ),
   U, L #z-axis endpoints after margin adjustment
;
   #Stretch z-axis to include margins:
   (U,L):= ((Um,Lm,M,m)-> (M*(Lm-1)+m*Um, M*Lm+m*(Um-1)) /~ (Um+Lm-1))(
      zmargin[],
      (max,min)(op(3, indets(P, 'specfunc'('GRID'))[])) #actual z-axis range
   );
   plots:-display(
      [
         plots:-spacecurve(
            {
               [[lhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),L]], #yz backwall
               [[rhs(RX),rhs(RY),U],[rhs(RX),lhs(RY),U],[rhs(RX),lhs(RY),L]]  #xz backwall
            },
            'color'= 'grey', 'thickness'= 0
         ),
         plottools:-transform((x,y)-> [x,y,L])(C), #dropped-shadow contours
         P
      ],
      #These default plot options can be changed simply by putting the option in the
      #ParamPlot3d call:
      'view'= ['DEFAULT', 'DEFAULT', L..U], 'orientation'= [-135, 75], 'axes'= 'frame',
      'labels'= [lhs(X), lhs(Y), Z], 'labelfont'= ['TIMES', 'BOLDOBLIQUE', 16],
      'caption'= nprintf(cat("%a = %4.2f, "$nops(FP)-1, "%a = %4.2f"), (lhs,rhs)~(FP)[]),
      'captionfont'= ['TIMES', 14],
      'projection'= 2/3,   
      _rest
   )
end proc:

NULL

NULL

GetNu := proc (Sol::Matrix) options operator, arrow; Sol[2, 1][1, Solve:-Pos(:-Nu)] end proc

ParamPlot3d(
   GetNu,Q= 0..5, Rd= 0..5, [
   
   Pr= 21   ],
   labels= [Q, gamma, Nu]
);

Error, (in plot/iplot2d/levelcurve) could not evaluate expression

 

``

Download P6_3D_plots.mw

Dear all

I would like to get the solution of a system : pde with boundary and initial condition. Everything well coded, but the code does not return the solution 

sol_heat.mw

Thanks for your help 

Hi, I'm looking to create a discovery activity to introduce the cosine . Any ideas for using Maple components with a slider to vary the position of a point on a line while displaying distances and their ratios? Thank you

Doc2.pdf

Can anyone assist with this error please?

#Clear memory and load package.
restart;  
with(LinearAlgebra):

#Initialise variables,matrices and vectors.
b:=<<18>,<-2>>:
c:=<<1>,<1>>:
i:=0:
P:=<1.08,1.37,1.56,1.61>;
t:=<5,10,15,20>;
tol:=1e-6:

#Initialise Gauss-Newton matrices.
n:=Dimension(t):
f:=Matrix(n,1):
J:=Matrix(n,2):

#Display initial parameter values.
printf("Gauss-Newton Method\n");
printf("-------------------\n");
printf("Before iterations,A = %f and B = %f\n",b(1),b(2));

#Perform the Gauss-Newton method.
while max(abs(evalf(c)))>tol do
  i:=i+1;
  for r from 1 to n do
     f(r,1):=evalf((In(b(1)+t[r])+b(2))-P[r]);
     J(r,1):=evalf(1/b(1)+t[r]);
     J(r,2):=evalf(1);
end do;
c:=Multiply(MatrixInverse(Multiply(Transpose(J),J)),Multiply(Transpose(J),f));
b:=b-c;
printf("After iterations %d, A = %f and B = %f\n",i,b(1),b(2));
end do:

Vector(4, {(1) = 1.08, (2) = 1.37, (3) = 1.56, (4) = 1.61})

 

Vector[column](%id = 36893488152076174028)

 

Gauss-Newton Method
-------------------
Before iterations,A = 18.000000 and B = -2.000000
After iterations 1, A =

 

Error, (in fprintf) number expected for floating point format

 

NULL

Download Asst_3_Q4b.mw

can you do groupwork on a single documet 

Dear Colleagues,

I wish to use plot3d to the attached code but always encoutered error. However, pointplot3d runs perfectly. Please I need your assistance in this regards.

Thank you all and best regards.K2_Problem_2_two_body_kepler_e=0.mw

I have been having problem in solving this question because of the 'Whittaker'.

Can anyone please asist me how to integrate below problem with the 'Whitaker?

f := exp(-1.5*t)*(GAMMA(2)*t^(2-alpha)/GAMMA(3-alpha)-t^(1-alpha)/GAMMA(2-alpha)+t^2-t);
               /   (2 - alpha)        (1 - alpha)           \
               |  t                  t                 2    |
   exp(-1.5 t) |---------------- - ---------------- + t  - t|
               \GAMMA(3 - alpha)   GAMMA(2 - alpha)         /
int(f, t);
 

2.^(3.-1.*alpha)*3.^(alpha-3.)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(alpha-3.)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(1.500000000*t-1.*alpha+2.)*(alpha-3.)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(3.-1.*alpha))/GAMMA(3.-1.*alpha)-1.*2.^(2.-1.*alpha)*3.^(-2.+alpha)*(t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha, -.5000000000*alpha+.5000000000, 1.500000000*t)+t^(-.5000000000*alpha)*3.^(-.5000000000*alpha)*2.^(.5000000000*alpha)*(-2.+alpha)*exp(-.7500000000*t)*WhittakerM(-.5000000000*alpha+1., -.5000000000*alpha+.5000000000, 1.500000000*t)/(2.-1.*alpha))/GAMMA(2.-1.*alpha)+.1481481481+(0.9876543210e-1*(-6.750000000*t^2-9.*t-6.))*exp(-1.500000000*t)-(.2222222222*(-2.-3.*t))*exp(-1.500000000*t)

I can import maple, but I get an error when importing namespace/symbols:

import maple.namespace as mpl

Hi!

I'm having problems with my maple not saving. I get no error message and no windows pop up.
The error occurred after the summer holidays in Maple 2022. I use Windows 11, everything is up to date. Have no Anti-virus programs.

  I have tried the following after I discovered the error:
- To install Maple 2023
- Uninstall and delete all maple folders, then reinstall Maple 2023
- Pressed Ctrl + s
- Press "Save as..."
- Pressed on the floppy disk/save icon
- Restarted computer and updated windows
- Run Maple as administrator

The only thing I can be allowed to do is:
- Ctrl + p
- Print to PDF/printer

Really hope you can help!

I don't know where my last exchange with @mz6687  has been moved (not to the initial question  https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs for what I see).
Nevertheless here is the reply I was sending to @mz6687  which ended with the message "Page not found".
Are_you_ok_with_that.mw

Could the one who moved the question meanwhile be so kind as to attach this reply?
TIA

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