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When i am running a code in maple worksheet , one error is shown by maple. My code and error (in bold) is below

Instructional workheet for the FracSym package
G. F. Jefferson and J. Carminati

Read in accompanying packages: ASP, DESOLVII and initialise using the with command:

read `ASP v4.6.3.txt`:

DESOLVII_V5R5 (March 2011)(c), by Dr. K. T. Vu, Dr. J. Carminati and Miss G. 


 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing the article:
  K.T. Vu, G.F. Jefferson, J. Carminati, Finding generalised symmetries of 

     differential equations
using the MAPLE package DESOLVII,Comput. Phys. Commun. 183 (2012) 1044-1054.

       ASP (November 2011), by Miss G. Jefferson and Dr. J. Carminati

 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing the article:
    G.F. Jefferson, J. Carminati, ASP: Automated Symbolic Computation of 

       Approximate Symmetries
    of Differential Equations, Comput. Phys. Comm. 184 (2013) 1045-1063.

              [ApproximateSymmetry, applygenerator, commutator]
[classify, comtab, defeqn, deteq_split, extgenerator, gendef, genvec, 

  icde_cons, liesolve, mod_eq, originalVar, pdesolv, reduceVar, reduceVargen, 

  symmetry, varchange]

Read in FracSym and initialise using the with command:
read `FracSym.v1.16.txt`;
       FracSym (April 2013), by Miss G. Jefferson and Dr. J. Carminati

 The authors kindly request that this software be referenced, if it is used 

    in work eventuating in a publication, by citing:
G.F. Jefferson, J. Carminati, FracSym: Automated symbolic computation of Lie 

of fractional differential equations, Comput. Phys. Comm. Submitted May 2013.

 [Rfracdiff, TotalD, applyFracgen, evalTotalD, expandsum, fracDet, fracGen, 



The Riemann-Liouville fractional derivatives is expressed in "inert" form using the FracSym routine Rfracdiff.
The explicit formula for the form of these fractional derivatives may be found in I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications, San Diego, 1999.)

Rfracdiff(u(x, t),t,alpha);
                             D[t     ](u(x, t))

If the fractional derivative is taken for a product, the generalised Leibnitz rule is used to express the result (the product operator used is &* and is non-commutative). 
Rfracdiff(u(x, t)&*v(x,t),t,alpha);
        )                          (alpha - n)              n          
       /     binomial(alpha, n) D[t           ](u(x, t)) D[t ](v(x, t))
      n = 0                                                            
Rfracdiff(v(x, t)&*u(x,t),t,alpha);
        )                          (alpha - n)              n          
       /     binomial(alpha, n) D[t           ](v(x, t)) D[t ](u(x, t))
      n = 0                                                            

Fractional derivatives of integer order revert to the MAPLE diff routine.

Rfracdiff(u(x, t)&*v(x,t),t,2);
         / d  / d         \\             / d         \ / d         \
         |--- |--- u(x, t)|| v(x, t) + 2 |--- u(x, t)| |--- v(x, t)|
         \ dt \ dt        //             \ dt        / \ dt        /

                      / d  / d         \\
            + u(x, t) |--- |--- v(x, t)||
                      \ dt \ dt        //

The FracSym rouine TotalD may also be used to find total derivatives. evalTotalD is then used to evaluate the result (in jet notation). For example, 

TotalD(xi[x](x, y),x,2);
                             D[x ](xi[x](x, y))
        [     / d             \      2 / d  / d             \\
        [y_xx |--- xi[x](x, y)| + y_x  |--- |--- xi[x](x, y)||
        [     \ dy            /        \ dy \ dy            //

               / d  / d             \\       / d  / d             \\]
           + 2 |--- |--- xi[x](x, y)|| y_x + |--- |--- xi[x](x, y)||]
               \ dy \ dx            //       \ dx \ dx            //]


Consider the fractional PDE from: R. Sahadevan, T. Bakkyaraj, Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations, J. Math. Anal. Appl. 393 (2012) 341-347.

We use the Rfracdiff routine to express the 
 fractional derivative with respect to t:
fde1:=Rfracdiff(u(x, t),t,alpha) = (diff(u(x, t), x,x))+n*(u(x, t))^p*(diff(u(x, t),  x));
        alpha             / d  / d         \\            p / d         \
     D[t     ](u(x, t)) = |--- |--- u(x, t)|| + n u(x, t)  |--- u(x, t)|
                          \ dx \ dx        //              \ dx        /

sys1:=[Rfracdiff(u(x, t),t,alpha) = (diff(v(x, t), x)), Rfracdiff(v(x, t),t,alpha) = -u(x, t)*diff(u(x, t),x)];
[   alpha              d              alpha                      / d         \]
[D[t     ](u(x, t)) = --- v(x, t), D[t     ](v(x, t)) = -u(x, t) |--- u(x, t)|]
[                      dx                                        \ dx        /]

We use the the FracSym routine fracDet to find the determining equations for the symmetry for fde1. 
NOTE: The fourth argument (some integer at least 1) corresponds to the number of terms to be "peeled off" from the sums which occur in the extended infintesimal function for the fractional derivative. A value of 2 provides a good balance between information for solution of determining equations and speed.

deteqs:=fracDet([sys1], [u, v],[x, t], 2, alpha=(0.1)..1);
Error, (in desolv/PickLHSDerivative) Cannot pick out the left hand side derivatives

Please suggest what problem it may be?

would like to point to graph then it highlight graph with virtical line

and mark 1 in one of row in one of column in table like data 

just like define feature manually for machine learning but using graph

why pdsolve does not work?

Q and alpha are constant. I want to find f(x,y).


"restart: w(x,y) :=Q*sin^(2)(Pi*x)*sin^(2)(Pi*y)"

proc (x, y) options operator, arrow, function_assign; Q*sin(Pi*x)^2*sin(Pi*y)^2 end proc


PDE := diff(f(x, y), x, x, x, x)+2*(diff(f(x, y), x, x, y, y))/alpha^2+(diff(f(x, y), y, y, y, y))/alpha^4+((diff(w(x, y), y, y))*(diff(w(x, y), x, x))-(diff(w(x, y), x, y))^2)/alpha^2

diff(diff(diff(diff(f(x, y), x), x), x), x)+2*(diff(diff(diff(diff(f(x, y), x), x), y), y))/alpha^2+(diff(diff(diff(diff(f(x, y), y), y), y), y))/alpha^4+((2*Q*sin(Pi*x)^2*Pi^2*cos(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)*(2*Q*Pi^2*cos(Pi*x)^2*sin(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)-16*Q^2*sin(Pi*x)^2*sin(Pi*y)^2*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2)/alpha^2





Download PLATE.mw






no matter what e is , expect to output the same 0.733333



I have a set of nonlinear equations (transcendental) containing variables and one free parameter. I want to solve this system for variables while varying parameter's value. I have tried with fsolve and solve commands keeping fixed the parameter value, but they are not solving yet. Is there any way to solve this system for a range of parameter's value.
The systmem is like this, x,y,z are the variables and 'a' is the parameter:

Many thanks in advance.


I submit you this strange result:
for somenumerical  values of a, b, c  (a, b, c real and b > a), Maple 2018 is not able to compute the mean of
c*U where U is a Uniform random variable with support [a, b].





`Standard Worksheet Interface, Maple 2018.0, Windows 7, March 10 2018 Build ID 1298750`


z := .4070716688*RandomVariable(Uniform(0.12-0.02*0.12, 0.12+0.02*0.12));



Error, (in Statistics:-Mean) the expression does not have a taylor expansion at t = 0


z := .4070716688*RandomVariable(Uniform(a, b));
subs({a=0.12-0.02*0.12, b=0.12+0.02*0.12}, %);









Download Mean.mw

PLEASE: Maple still fails if I replace  a = 0.12 -0.02*0.12 by its value 0.1174
                                                                       and b = 0.12+0.02*0.12 by its value 0.1224

This is incomprehensible and could hide a more profound problem.

Hello everyone, i've a problem working with Maple because i have a really big system of equations and for everything that i have to do with them, for example, collect terms, coefficients, take a lot of time from me. The problem it is when, for example, i wait 30 minutes to take the coefficients from a equation and in the next command Maple might stop, then i have to close and start all over again... My question it is if have anyway to save my file in a way that if i close and re open i dont have to compile all again. Maybe this is pretty obvious but i really dont know how to do it, because if i close my work and open again, i have to compile everything again.

I have a eigenvalue problem like:

[FF1]* {w}=N^2 *[FF2] *{w}

[FF1] and [FF2] are a*b matrices (non square matrix) , {w} are vectors(eigenvectors) and the values of N are eigenvalues.

I want to obtain eigenvalues and eigenvectors by computing Moore-Penrose pseudo-inverse of [FF2] and do the procedures below :

[FF2]^-1 * [FF1] *{w} =N^2 *{w}            ,        (assume  [FF2]^-1   is Moore-Penrose pseudo-inverse of [FF2]   )

[FF2]^-1 * [FF1] = [FF3]  ,  ( [FF3] is a b*b matrix- squre matrix) 

so  [FF3] *{w}=N^2 *{w}

then I can use LinearAlgebra[Eigenvectors](FF3) to get eigenvalues and eigenvectors. 

I know that Moore-Penrose pseudo-inverse of [FF2] * [FF1] isn't equal to Identity matrix. [FF2]^-1 * [FF1] <> [ I ] . But assume it can be. ( I have a solution for this problem) . 

My biggest problem is [FF2] and [FF1] are large-scale sparse matrix and it takes hours or several days that maple can compute Moore-Penrose pseudo-inverse of [FF2]  and also LinearAlgebra[Eigenvectors](FF3). 

Main question : can I compute Moore-Penrose pseudo-inverse and LinearAlgebra[Eigenvectors]  by using Parallel Programming?  if the answer is yes , how? give me an example please.

if the answer is No , is there any way (any algorithm) to find the inverse of a large non-sqaure matrix or eigenvalues of a large matrix faster?

please introduce some books for parallel programming in maple or general.




From the attached code, you can see that I have a Matrix, A, that I am trying to output into Fortran code so that I can simply copy and paste this long matrix into fortran. The output does not look correct. Doesa anyone have an idea on how to put this matrix A into a form that can be easily copy and pasted into Fortran? You can see that I tried to do each line individually in the attatched code but I am really looking for a way to do the entire Matrix. Thanks for any help or suggestions.



I'm trying to solve an ODE system from an IVP problem, but the error occurs: "Error, (in ...) cannot evaluate the solution further left of ..., maxfun limit exceeded (see ?dsolve,maxfun for details)"

I've already tried modifying the maxfun value but this did not work. I would like some suggestion.

Thank you



 I created my own costum package and I want to edit this package: insert procedures or modules. Is there a way?

Thank you.

What's going on here? Am I missing something, or is it a bug? If it's a bug, then it's by far the deepest and most profound bug that I've ever found or seen in Maple (and I've seen thousands over the decades). And since that surprises me, my guess is that I'm missing something obvious.

Op:= (R,F)-> F(['R()'$2]):
Op(rand(1..9), [f,f]);
                     [f([7, 6]), f([2, 4])]

The expected output is [f([7,6]), f([7,6])]. The same thing happens if I replace with seq, or if I replace -> with proc.

pls help me cirrect this. i am trying to use finite element method to siolve a fluid equation. The code is give below

> pde := alpha^2*(diff(u(t, r), t))+2*(-1/2)^(1/n)*(diff(u(t, r), r))/r-(-1/2)^((1-n)/n)*(diff(u(t, r), `$`(r, 2)))*(diff(u(t, r), r))^(1/n-1)/n+2*theta/r-4*(1+e)+4*B*cos(.2) = 0; /1\ |-| \n/ /-1\ / d \ 2 |--| |--- u(t, r)| 2 / d \ \2 / \ dr / alpha |--- u(t, r)| + ----------------------- \ dt / r /1 - n\ /1 \ |-----| |- - 1| \ n / \n / /-1\ / d / d \\ / d \ |--| |--- |--- u(t, r)|| |--- u(t, r)| \2 / \ dr \ dr // \ dr / 2 theta - ---------------------------------------------------- + ------- - 4 - 4 e n r + 3.920266311 B = 0 > tmax := 0.5e-1; > rmin := 0; > rmax := 10; > N := 6; > bc1 := diff(u(t, r = rmin), r) = 1/mu; > bc2 := u(t, r = rmax) = 0; > ic1 := u(0, r) = 0; > PDE*Boundary*condition*colllection; > bcs := {u(0, r) = rhs(ic1), D[1](diff(u(t, r = rmin), r)) = rhs(bc1), (D[1](u))(t, r = rmax) = rhs(bc2)}; / / d \ 1 \ { u(0, r) = 0, D[1]|--- u(t, r = 0)| = --, D[1](u)(t, r = 10) = 0 } \ \ dr / mu / > > Collocation*method; > Typesetting[delayDotProduct](Define*a*simple*function*with*known*solution.one, can, true)*choose*either*a*trigonometric*function, othorgonal*polynomia, (Typesetting[delayDotProduct](legendre*polynomia*etc.we, want, true)*will*choose*a*simple*polynomia*which*will)*make*our*work*easier; > basis := r^i; > uhat := sum(A[i](t)*basis, i = 0 .. N-1); > Alist := indets(uhat, function(identical(t))); > Here, we*will*determine*the^2*two*unknowns*(A1, A2)*using*boundary*conditions; > duhat := diff(uhat, r); > knownAs := solve({subs(r = rmin, duhat) = rhs(bc1), subs(A[1](t) = 0, r = rmax, duhat) = rhs(bc2)}, {A[1](t), A[2](t)}); > unknownAs := `minus`(Alist, {seq(lhs(knownAs[i]), i = 1 .. nops(knownAs))}); > `and`(uhat*after*substituting*A1, A2); > uhat := subs(knownAs, uhat); > uhat := collect(uhat, Alist); > Residual*function*is*obtai*ned*after*substituting*uhat*into*the*original*pde; > residual := eval(subs(u(t, r) = uhat, pde)); > residual := collect(residual, r); > `and`(Typesetting[delayDotProduct](Now*we*choose*points*where*exact*solution*must*be*matched.since, we, true)*have*point*A[1], A[2]), we*will*only*need*N-2*points; > odes := {seq(subs(r = i*rmax/N, residual), i = 1 .. nops(unknownAs))}; > Find*ICs*of*unknown*A(t)*s; > iceqs := {seq(subs(t = 0, r = i*rmax/N, uhat) = rhs(bc2), i = 1 .. nops(unknownAs))}; > ics := solve(iceqs, subs(t = 0, unknownAs)); > > sols := dsolve(`union`(odes, ics)); Warning, computation interrupted > Approximate*solution; > uhat := subs(sols, uhat); Error, invalid input: subs received sols, which is not valid for its 1st argument > uhat := collect(uhat, r); > Plot*solution; > plot3d(uhat, r = 0 .. rmax, t = 0 .. tmax, axes = boxed, lightmodel = light4, orientation = [-120, 40], shading = zhue, transparency = .3); Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct > >

The question is all in the title really. I am struggling to make a subsection on my macbook, using 2018 Maple software. The cmd + shift + . will only make sections, regardless of where i place my cursor.

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