Advanced Search

Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024
View unanswered posts
Maple 2024 Questions and Posts Feed

Can anyone generate this series ? ...

Asked by: salim-barzani 925
combinatorics summation index
February 08 2025
0  13

the series is so complicated but have a strange pattern if you watch the index of parameter  they are not repeated 

 

 

String and parse on decimal number...

Asked by: nm 10973
string decimal
February 08 2025
1  1

Do you think the result of String(0.016)  should be "0.016"  instead of ".16e-1" ?

Any reason why it gives the second form and not the first?  Now have to keep using sprintf to force formating as decimal point. Is this documented somewhere? quick search did not find anything do far.

Maple 2024.2 on windows.

> 

s:="0.016";

"0.016"

> 

z:= :-parse(s);

0.16e-1

> 

String(z);

".16e-1"

> 

sprintf("%0.3f",z);

"0.016"

 

 

Download string_of_decimal_number.mw

Grid problem when using module. Does not see local...

Asked by: nm 10973
module grid local
February 07 2025
2  7

I am calling a proc inside a module, where this module had local module variable initialized to false;

This works fine when calling the proc normally.

When calling it from Grid:-Run() it says it is not seeing the module local variable at all.

Why does this happen and is there a workaround this? Here a simple worksheet showing this.

I hope there is a way to make the proc inside the module see the local module variables when using it from Grid node. Otherwise, this whole thing will not work for me, as I have few variables initialized at modules level in number of places.

> 

restart;
> 

A := module()
  local DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",DEBUG_MSG);
  end proc;
end module;
> 

 

_m1690230418240

> 

#THis works as expected
A:-work_proc(0)

"My flag is ", false

> 

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.
> 

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"My flag is ", DEBUG_MSG

 

 

Download grid_with_module_local_variable_feb_7_2025.mw


Update 2/7/2025

I tried to change the access to the module local variables from the module local procs, by adding explicit A:- to each variable name where A here is the module name.

This works for normal calls, but not when using Grid to call the proc.

This workaround fail, it gives error that module does not export `%1`

May be I have to redo all my code not to use local module variables. But in some places I have to do this, in order to detect if something has happened before or not. I use module local variables to store state the presist after call is completed.

It looks like Grid is not meant to be used for calling proc() that uses/lives inside modules. But this makes Grid not very useful then for large application.

> 

restart;
> 

A := module()
  local DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",A:-DEBUG_MSG);
  end proc;
end module;
> 

 

_m1690230418240

> 

#THis works as expected
A:-work_proc(0)

"My flag is ", false

> 

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.
> 

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) module does not export `%1`

 

 

Download grid_with_module_local_variable_feb_7_2025_V2.mw

I also tried to make the module variable as export instead of local, and that also did not work. I am starting to run out of ideas what else to try...

> 

restart;
> 

A := module()
  export DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",A:-DEBUG_MSG);
  end proc;
end module;
> 

 

_m1690230418208

> 

#THis works as expected
A:-work_proc(0)

"My flag is ", false

> 

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.
> 

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) `%1` does not evaluate to a module

 

 

Download grid_with_module_local_variable_feb_7_2025_V3.mw

Update

I think now that using module level local variables will not work with parallel processing anyway. It is like using global variable in parallel processing. Does not work without synchorization of access to this shared variable. 

So this means I have to change my code and not use any module local variables, and pass any information between functions via arguments only.

Using module local variable is more convenient, but I now realize this design is not good for parallel processing.  This means some code changes I have to do. 

On the positive side, I find using Grid can really speed things up. On some tests, up to 10 times faster. The larger the number of problems to process, the more speed up is gained.

So I think it is worth to rewrite my code and remove any use of local level module variables.

Update Feb 11, 2024

Found the solution!  With grid, one must pass in all variables that to be used on a node. So the above now becomes this

> 

restart;
> 

A := module()
  export DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",DEBUG_MSG);
  end proc;
end module;
 

_m1739526597408

> 

#THis works as expected
A:-work_proc(0)

"My flag is ", false

> 

#this does not work. Because we did not pass all variables to be used at node
Grid:-Set(0,A:-work_proc);
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"My flag is ", DEBUG_MSG

> 

#this now worksheetdir
Grid:-Set(0,A:-work_proc,'A:-DEBUG_MSG');
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"My flag is ", false

 

 

Download grid_with_module_V4_feb_11_2025.mw

Actually the above could be done easier this way. By passing in the name of the whole module A, now nodes are able to see all module A local vaiables. Like this

> 

restart;
> 

A := module()
  export DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",A:-DEBUG_MSG);
  end proc;
end module;
 

_m1739526597408

> 

#THis works as expected
A:-work_proc(0)

"My flag is ", false

> 

#this does not work. Because we did not pass the name of the A
Grid:-Set(0,A:-work_proc);
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) `%1` does not evaluate to a module

> 

#this now works, becuase we pass the module A
Grid:-Set(0,'A:-work_proc','A');
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"My flag is ", false

 

 

Download grid_with_module_V6_feb_11_2025.mw

And to be able to access global variables in another module from inside the worker module, we must pass the other module name. Here is an example

> 

restart;
> 

B := module()
  export some_value::integer:=10;
end module;

A := module()
  export work_proc:=proc(n::integer)
     print("the value is ",B:-some_value);
  end proc;
end module;
 

_m1739526597280

_m1739594742272

> 

#THis works as expected
A:-work_proc(0)

"the value is ", 10

> 

#this does not work. Because we did not pass the name of the other module B in this case
Grid:-Set(0,A:-work_proc);
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) `%1` does not evaluate to a module

> 

#this now works, becuase we pass the module name B to the node, so it sees it
Grid:-Set(0,'A:-work_proc','B');
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"the value is ", 10

 

 

Download grid_with_module_V5_feb_11_2025.mw

The main point, if one is using modules with Grid, names of all modules to be accessed from a node need to be passed in in the Set call. Otherwise the node will not see them.

Update For the above method to work, all module variables to be accessed at node, have to export and not local.

Update 2/11/2025  4 AM

I think I'll give up on Grid. It is completely useless. I found out that I have to make all my modules proc's export now, even though they are only used in that one module, just in order to call them from same module when running in Grid node.

Otherwise, I have to list each proc name in each module and sub module in the Set command. This is ridiculous design. I have 5,000 proc's. I am not going to list them all each time.

Here is an example where a boo() is local proc to a module. But it is not called, because the proc is local.

> 

restart;
> 

A := module()

  export foo:=proc()
       print("entering A:-foo(), before calling local proc boo()");
       boo(); #this call will not work in Grid setting
  end proc;

  local boo:=proc()
     print("inside local A:-foo()");
  end proc;
end module:
> 

A:-foo();

"entering A:-foo(), before calling local proc boo()"

"inside local A:-foo()"

> 

Grid:-Set(0,A:-foo,'A');
Grid:-Run(0,A:-foo,[0]);
Grid:-Wait();

"entering A:-foo(), before calling local proc boo()"

> 

 


 

Download calling_proc_in_module_V1.mw

To make it work, I have to make all my local proc export, and not only that, I have to call it using A:-boo() as well. So the above becomes


 

> 

restart;
> 

A := module()

  export foo:=proc()
       print("entering A:-foo(), before calling local proc boo()");
       A:-boo(); #this call will not work in Grid setting
  end proc;

  export boo:=proc()
     print("inside local A:-foo()");
  end proc;
end module:
> 

A:-foo();

"entering A:-foo(), before calling local proc boo()"

"inside local A:-foo()"

> 

Grid:-Set(0,A:-foo,'A');
Grid:-Run(0,A:-foo,[0]);
Grid:-Wait();

"entering A:-foo(), before calling local proc boo()"

"inside local A:-foo()"

> 

 

 

Download calling_proc_in_module_V2.mw

I am not going to edit 100,000 lines of Maple code and change all the procs to export and make sure each call have the fully qualified module name attched to it even though it is local to the module.

I will not use Grid. It simply does not work with modules. Maplesoft should fix Grid so code works as with minimal changes.

How find generate series solution from known serie...

Asked by: salim-barzani 925
pde series differential-equations
February 07 2025
0  8

How i can get FN from N-soliton to FN for M-lump by applying long wave method and using limit How we can get the series of lump , there is some example for nowing how lump work like f[2] for 1 lump and f[4] for two lump and f[6] for 3 lump i, and also in last of work i showed the series of for n soliton which we can change it to m-lump  but i don't know how work and a[12] will change to b[12] by applying long wave method

m-lump.mw

Inconsistent Convert Output Units behavior between...

by: Geoff 10 Maple 2024 , Maple Flow 2024
February 05 2025
0  1

Referring to the screenshots, "J" can be converted to "N m" in MF2024.1, but not in M2024.2.
Is this some sort of bug in M2024.2?

 

 

How to select files in directory with different ex...

Asked by: nm 10973
filetools listdirectory
February 04 2025
1  5

To select all pdf files in folder the command is

L1:=FileTools:-ListDirectory(currentdir(),'all','select'="*.pdf");

And to select all dvi files the command is 

 L2:=FileTools:-ListDirectory(currentdir(),'all','select'="*.dvi");

Is there a syntax to select both in one command? THis does not work as input to select must be string. It can not be list nor set.

  FileTools:-ListDirectory(currentdir(),'all','select'=["*.dvi","*.pdf"]);

So I end up doing

L1:=FileTools:-ListDirectory(currentdir(),'all','select'="*.pdf");
L2:=FileTools:-ListDirectory(currentdir(),'all','select'="*.dvi");
the_list := [ op(L1), op(L2) ];

If will be nice if Maple allows one to select based on different extensions in one command.  Imagine you have 5 different extensions to select. Now one has to issue 5 different commands, then collect all the 5 lists into one.

why am I getting "insufficient initial/boundary va...

Asked by: Tom GIV 25
ode syntax dsolve
February 04 2025
1  4

I'm trying to solve a system of two differential equations numerically
 

> 

restart
> 

eq1 := diff(A(t), t) = c1*(A__T-A(t))-c2*A(t)*R(t)

diff(A(t), t) = c1*(A__T-A(t))-c2*A(t)*R(t)

 (1)
> 

NULL
> 

eq2 := diff(R(t), t) = (c3+c1)*(R__T-R(t))-c2*Ab(t)*R(t)

diff(R(t), t) = (c3+c1)*(R__T-R(t))-c2*Ab(t)*R(t)

 (2)
 

 
> 

sys1 := [eq1, eq2]

[diff(A(t), t) = c1*(A__T-A(t))-c2*A(t)*R(t), diff(R(t), t) = (c3+c1)*(R__T-R(t))-c2*Ab(t)*R(t)]

 (3)
> 

A__T := 100

100

 (4)
> 

R__T := 100

100

 (5)
> 

c2 := 1000

1000

 (6)
> 

c1 := 0.2e-4

0.2e-4

 (7)
> 

c3 := 2000

2000

 (8)
> 

``
> 

InitCond := A(0) = A__T, R(0) = R__T

A(0) = 100, R(0) = 100

 (9)
> 

nsol := dsolve(sys1, InitCond, type = numeric)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

  

 

It seems to me this problem should be solvable for the initial conditions given.  Am I entering them wrong somehow?

 

NULL

Download dsolve_problem.mw

How to get solution Soll11 for the reduced Liouvil...

Asked by: janhardo 540
pde dsolve pdsolve
February 02 2025
0  5

The modified Liouville equation

> 

> 

How to solve this pde for a general solution ?

The general solution in this form exist.

> 

restart;
> 

with(PDEtools): declare(u(x,t)); U:=diff_table(u(x,t));
PDE1:=U[t,t]=a^2*U[x,x]+b*exp(beta*U[]);
Sol11:=u(x,t)=1/beta*ln(2*(B^2-a^2*A^2)/(b*beta*(A*x+B*t+C)^2));
Sol12:=S->u(x,t)=1/beta*ln(8*a^2*C/(b*beta))
-2/beta*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C);
Test11:=pdetest(Sol11,PDE1);
Test12:=pdetest(Sol12(1),PDE1);
Test13:=pdetest(Sol12(-1),PDE1);

u(x, t)*`will now be displayed as`*u

  

table( [( ) = u(x, t) ] )

  

diff(diff(u(x, t), t), t) = a^2*(diff(diff(u(x, t), x), x))+b*exp(beta*u(x, t))

  

u(x, t) = ln(2*(-A^2*a^2+B^2)/(b*beta*(A*x+B*t+C)^2))/beta

  

proc (S) options operator, arrow; u(x, t) = ln(8*a^2*C/(b*beta))/beta-2*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C)/beta end proc

  

0

  

0

  

0

 (1)

The Soll11 can be plotted with a Explore plot in this form of soll11 with th eparameters , but suppose i try to get the general solution in Maple ?

> 

infolevel[pdsolve] := 3
> 

pdsolve(PDE1, generalsolution)
> 

ans := pdsolve(PDE1);

What solvin gstrategy to follow ? : the pde is a non-linear wave eqation  with a exponentiel sourceterm
It seems that the pde can reduced to a ode? :

> 

 

> 

with(PDEtools):
declare(u(x,t));

# Stap 1: Definieer de PDE
PDE := diff(u(x,t), t,t) = a^2 * diff(u(x,t), x,x) + b * exp(beta * u(x,t));

# Stap 2: Definieer de transformatie naar karakteristieke variabelen
# Nieuw: x en t uitgedrukt in ξ en η
tr := {
    x = (xi + eta)/2,
    t = (eta - xi)/(2*a)
};

# Pas de transformatie toe op de PDE
simplified_PDE := dchange(tr, PDE, [xi, eta], params = [a, b, beta], simplify);

# Stap 3: Definieer de algemene oplossing
solution := u(x,t) = (1/beta) * ln(
    (-8*a^2/(b*beta)) *
    diff(_F1(x - a*t), x) * diff(_F2(x + a*t), x) /
    (_F1(x - a*t) + _F2(x + a*t))^2
);

# Stap 4: Controleer de oplossing (optioneel)
pdetest(solution, PDE);  # Moet 0 teruggeven als correct

u(x, t)*`will now be displayed as`*u

  

diff(diff(u(x, t), t), t) = a^2*(diff(diff(u(x, t), x), x))+b*exp(beta*u(x, t))

  

{t = (1/2)*(eta-xi)/a, x = (1/2)*xi+(1/2)*eta}

  

a^2*(diff(diff(u(xi, eta), xi), xi)-2*(diff(diff(u(xi, eta), eta), xi))+diff(diff(u(xi, eta), eta), eta)) = a^2*(diff(diff(u(xi, eta), xi), xi))+2*a^2*(diff(diff(u(xi, eta), eta), xi))+a^2*(diff(diff(u(xi, eta), eta), eta))+b*exp(beta*u(xi, eta))

  

u(x, t) = ln(-8*a^2*(D(_F1))(-a*t+x)*(D(_F2))(a*t+x)/(b*beta*(_F1(-a*t+x)+_F2(a*t+x))^2))/beta

  

0

 (2)

missing some steps here : solution u  without  the pde reduced ?
there is a ode ?

> 

# Definieer de ODE # vorige stappen ontbreken van de reduktie
ode := (v^2 - a^2) * diff(f(xi), xi, xi) = b * exp(beta * f(xi));

# Algemene oplossing zoeken
sol := dsolve(ode, f(xi));

(-a^2+v^2)*(diff(diff(f(xi), xi), xi)) = b*exp(beta*f(xi))

  

f(xi) = ln((1/2)*c__1*(tan((1/2)*(-c__1*a^2*beta+c__1*beta*v^2)^(1/2)*(c__2+xi)/(a^2-v^2))^2+1)/b)/beta

 (3)
> 

 

> 

, ,

Question : how do i arrive on Soll11   in Maple  ?

 

Download liouville_reduced_2-2-2025_mprimes_vraag.mw

Where to set stack size and heap limit...

Asked by: segfault 140
heap stack incomplete-question
February 01 2025
1  11

I read the install.html that is installed with Maple2024 and the instructions to increase stack and heap limits are definately outdated.

None of the files they list there for Linux even exists after the Maple2024 installation.

So where exactly can I set the stack and heap size limits on Linux,  as Maple give me stack and heap errors.

How find phase shift parameter in solution of PDE ...

Asked by: salim-barzani 925
solve parameters substitution
January 30 2025
0  16

It been a while i try to figure out How they find dispersion parameter and phase shift i figure out how find dispersion in some of pde but some of them is not give me even dispresion parameter i don't know they wrong or i am , but for finding phase shift there is three cenarios, when we change pde to bilinear form we have linear term in bilinear form so after substitute in linear term f bilinear form we can get dispersion parameter which is a parameter beside (t) also we can generalized for all of solution by changing the number of parameter as mention in the paper, but for phase shift parameter i don't know how find it i must substitute our solution in linear term or whole  bilinear form of in first pde linear term i try all  but i don't know what is i did mistake the paper say put in pde but i think he mention the the bilinear form i did all part for one soliton is w[1] for 2soliton is w[2] file i just want find parameter a[12] in paper for 2-soliton eq(19)  then i will find for other just i need to find one of them, thanks for any help  in this topic .

 

How to show symbolically that eigenvalues are the ...

Asked by: dharr 7720
complex sort eigenvalues
January 29 2025
3  6

I am trying to show that the eigenvalues of a matrix are described by my proposed formula. I managed to show this numerically, but I would like to show this symbolically. There are two issues here - the orders of the two lists are different, and the forms are different (sums of complex exponentials vs RootOfs). Any suggestions?

> 

restart;
> 

with(LinearAlgebra): with(GraphTheory): with(plots):
> 

L:=9;

9

Generate a matrix and its eigenvalues

> 

C := AdjacencyMatrix(CycleGraph(L, directed)):
Id := IdentityMatrix(L):
A := KroneckerProduct(C, Id) + KroneckerProduct(Id, C) + KroneckerProduct(C, C):
evs := Eigenvalues(A, output = list):
plotevs := complexplot(evs, style = point, color = blue, scaling = constrained):

My guess as to their values

> 

evstheory:=[seq(seq(exp((2*Pi)*I*k/L) + exp((2*Pi)*I*m/L) + exp((2*Pi)*I*(m + k)/L), k = 0 .. L - 1), m = 0 .. L - 1)]:
plotevstheory:=complexplot(evstheory, style = point, color = red, scaling = constrained):

They look to be the same

> 

display(Array([plotevs,plotevstheory]));

 

 
 

 

 

Even showing they are the same numerically is nontrivial because the sorting is not consistent

> 

fnormal(sort(evalf(evs))-sort(evalf(evstheory)));

[0., 0., 0., 0.*I, 0.*I, 0.*I, 0.*I, 0.+0.*I, 0.+0.*I, 0.-1.285575219*I, 0.-1.285575219*I, 0.-.9216049846*I, 0.-.9216049846*I, 0.-1.732050808*I, 0.-1.732050808*I, 0.+1.732050808*I, 0.+1.732050808*I, 0.+.9216049846*I, 0.+.9216049846*I, 0.+1.285575219*I, 0.+1.285575219*I, 0.+0.*I, 0.+0.*I, 0.-0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+.6840402864*I, 0.+.6840402864*I, 0.-.6840402858*I, 0.-.6840402858*I, 0.+0.*I, 0.+0.*I, 0.-3.701666314*I, 0.-3.701666314*I, 0.-.6840402857*I, 0.-.6840402857*I, 0.-.6840402863*I, 0.-.6840402863*I, 0.+.6840402868*I, 0.+.6840402868*I, 0.+.6840402862*I, 0.+.6840402862*I, -0.+3.701666314*I, -0.+3.701666314*I, 0.-4.623271298*I, 0.-.6840402860*I, 0.-.6840402860*I, 0.+.6840402865*I, 0.+.6840402865*I, -0.+4.623271298*I, 0.-4.987241533*I, 0.-4.987241533*I, 0.-.6840402866*I, 0.-.6840402866*I, 0.-1.732050808*I, 0.-1.732050808*I, 0.+1.732050808*I, 0.+1.732050808*I, 0.+.6840402863*I, 0.+.6840402863*I, -0.+4.987241532*I, -0.+4.987241532*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.-4.540765944*I, 0.-0.*I, 0.-0.*I, 0.-0.*I, 0.-0.*I, -0.+4.540765944*I, 0.-1.285575219*I, 0.-1.285575219*I, 0.-1.285575219*I, 0.-1.285575219*I, -0.+2.571150438*I, -0.+2.571150438*I]

This succeeds, so they are the same

> 

fnormal(sort(evalf[20](evs),key=evalf)-sort(evalf[20](evstheory),key=evalf));

[0., 0., 0., 0.*I, 0.*I, 0.*I, 0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.+0.*I, 0.-0.*I, 0.-0.*I, 0.+0.*I, 0.+0.*I]

What about symbolically? [Edit - only part of output shown]

> 

ans1:=simplify(sort(evs,key=evalf)-sort(evstheory,key=evalf));

> 

NULL

Download verification.mw

How find true parameter which satisfy pde?...

Asked by: salim-barzani 925
solve parameters substitution
January 28 2025
0  2
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

 (2)
> 

pde := diff(u(x, y, z, t), `$`(t, 2))+diff(u(x, y, z, t), `$`(x, 2))-(diff(u(x, y, z, t)^2, `$`(x, 2)))-(diff(u(x, y, z, t), `$`(x, 4)))+diff(diff(u(x, y, z, t), y)+diff(u(x, y, z, t), z)+diff(u(x, y, z, t), t), x)+2*(diff(u(x, y, z, t), y, t))+diff(u(x, y, z, t), `$`(y, 2)) = 0

diff(diff(u(x, y, z, t), t), t)+diff(diff(u(x, y, z, t), x), x)-2*(diff(u(x, y, z, t), x))^2-2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))-(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))+diff(diff(u(x, y, z, t), x), y)+diff(diff(u(x, y, z, t), x), z)+diff(diff(u(x, y, z, t), t), x)+2*(diff(diff(u(x, y, z, t), t), y))+diff(diff(u(x, y, z, t), y), y) = 0

 (3)
> 

declare(v(t))

v(t)*`will now be displayed as`*v

 (4)
> 

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

 (5)
> 

Q := u(x, y, z, t) = 6*(diff(ln(f(x, y, z, t)), `$`(x, 2)))
> 

LL := diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

 (6)
> 

S22 := f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)

f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)

 (7)
> 

NULL
> 

R11 := eval(LL, S22)

k[1]^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*(k[1]+k[2])^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))^2*k[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*(k[1]+k[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-2*(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*s[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(s[1]+s[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]*l[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]*l[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])*(l[1]+l[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t) = 0

 (8)
> 

L4 := collect(%, [x, y, t], 'distributed')

k[1]^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*(k[1]+k[2])^5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^3*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))^2*k[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))^2*(k[1]+k[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*k[1]*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-2*(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*k[2]*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-2*B[1]*(-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*(k[1]+k[2])*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*l[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*l[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(l[1]+l[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]^2*s[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])^2*(s[1]+s[2])*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[1]*l[1]^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)-k[2]*l[2]^2*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-B[1]*(k[1]+k[2])*(l[1]+l[2])^2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t) = 0

 (9)
> 

indets(%)

{t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2), (4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2), exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)}

 (10)
> 

eq2 := algsubs(exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z) = X, L4)

-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])*k[2]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^2*s[1]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^2*s[2]+5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^4*k[2]+10*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^3*k[2]^2+10*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*k[2]^3+5*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]^4-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*s[1]-exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^2*s[2]-(9/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[2]^2*k[1]-(9/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[1]^2*k[2]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])*k[1]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])*k[2]-(1/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])*k[1]+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]^5+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[2]^5-(3/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[1]^3-(3/4)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*k[2]^3-(1/4)*k[1]*X*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])-(1/4)*k[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])-k[1]^2*s[1]*X-(3/4)*k[2]^3*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+k[2]^5*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)-k[2]^2*s[2]*exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+k[1]^5*X-(3/4)*k[1]^3*X-2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]*s[1]-2*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*B[1]*k[1]*k[2]*s[2]-(1/2)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2)*k[1]-(1/2)*B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2)*k[2] = 0

 (11)
> 

eq3 := simplify(eq2)

-(1/2)*(k[1]+k[2])*B[1]*((k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-8*k[1]*k[2]^3-12*k[2]^2*k[1]^2+(-8*k[1]^3+3*k[1]+2*s[1])*k[2]+2*s[2]*k[1])*exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = 0

 (12)
> 

indets(eq3)

{t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2), exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2]))}

 (13)
> 

eq4 := algsubs(exp((1/2)*t*sqrt(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))+(1/2)*t*sqrt(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = V, eq3)

-(1/2)*(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])*V = 0

 (14)
> 

indets(eq4)

{V, B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

 (15)
> 

eqs := {coeffs(collect(numer(normal(lhs(eq4))), {V}, 'distributed'), {V})}; nops(%); indets(eqs)

{-(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])}

  

1

  

{B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

 (16)
> 

vars := indets(eqs); ans := solve(eqs, vars)

{B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

  

Warning, solving for expressions other than names or functions is not recommended.

  

{B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = 0, k[1] = k[1], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = B[1], k[1] = k[1], k[2] = k[2], s[1] = (1/2)*(8*k[2]*k[1]^3+12*k[2]^2*k[1]^2+8*k[1]*k[2]^3-3*k[1]*k[2]-2*s[2]*k[1]-(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))/k[2], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

 (17)
> 

case2 := ans[1]

{B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}

 (18)
> 

FF := subs(case2, S22)
> 

NULL
> 

F11 := eval(Q, FF)
> 

pdetest(F11, pde)

-6*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(B[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+56*k[2]^4*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-6*k[2]^2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+B[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-24*B[1]*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+4*k[2]*s[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-4*k[2]*s[2]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*k[2]*s[2]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-224*k[2]^4*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-4*k[2]*s[2]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*k[2]*s[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+6*B[1]*k[2]^2*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-8*B[1]*k[2]^4*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+3*B[1]*k[2]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-28*B[1]*k[2]^4*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-28*B[1]*k[2]^4*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+24*k[2]^2*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+16*B[1]*k[2]*s[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-16*B[1]*k[2]*s[2]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+8*B[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-4*B[1]*k[2]*s[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]*k[2]*s[2]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*exp(-t*k[2]+2*t*l[1]+4*k[2]*x+2*l[2]*y+2*s[2]*z+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-2*B[1]*k[2]*s[1]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*B[1]*k[2]*s[2]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*k[2]*s[1]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[2]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*k[2]*s[1]*B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[2]*B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*k[2]*s[2]*B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*k[2]*s[1]*B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-4*B[1]*k[2]*s[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*B[1]*k[2]*s[2]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-2*B[1]*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-2*B[1]*k[2]*s[2]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+32*B[1]*k[2]^4*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+2*k[2]*s[2]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-2*k[2]*s[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[1]*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+3*k[2]^2*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+3*k[2]^2*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-28*k[2]^4*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-28*k[2]^4*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+3*B[1]*k[2]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-3*B[1]*k[2]^2*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]*k[2]^4*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+2*B[1]*k[2]*s[1]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-2*B[1]*k[2]*s[2]*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+B[1]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+B[1]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-B[1]*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-B[1]*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+4*B[1]*k[2]^4*exp(-(1/2)*t*k[2]+2*t*l[1]+t*l[2]+3*k[2]*x+l[2]*y+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+4*B[1]^2*k[2]^4*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+16*k[2]*s[2]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-16*k[2]*s[1]*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-8*exp(t*l[1]+t*l[2]+2*k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-6*k[2]^2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+56*k[2]^4*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+6*B[1]*k[2]^2*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-8*B[1]*k[2]^4*exp(t*k[2]+2*t*l[2]+2*l[1]*y+2*s[1]*z+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-3*B[1]*k[2]^2*exp((1/2)*t*k[2]+t*l[1]+2*t*l[2]+k[2]*x+l[1]*y+s[1]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))-3*B[1]^2*k[2]^2*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))-3*B[1]^2*k[2]^2*exp(t*l[1]+3*k[2]*x+l[1]*y+2*l[2]*y+s[1]*z+2*s[2]*z-(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+4*B[1]^2*k[2]^4*exp(t*l[2]+k[2]*x+2*l[1]*y+l[2]*y+2*s[1]*z+s[2]*z+(1/2)*t*k[2]+t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)))/(B[1]*exp(k[2]*x+l[1]*y+l[2]*y+s[1]*z+s[2]*z+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+exp(t*l[1]+2*k[2]*x+l[2]*y+s[2]*z-(1/2)*t*k[2]+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))+exp(t*l[2]+l[1]*y+s[1]*z+(1/2)*t*k[2]+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]+4*s[1]))^(1/2))+exp(t*l[1]+t*l[2]+x*k[2]))^4

 (19)
 

NULL

Download hard_parameters.mw

Grid with numnodes option does not create files...

Asked by: nm 10973
grid parallelization
January 28 2025
1  5

I've been evaluating Grid but I found some problems with SQLite DB when not using numnodes.

So I am now using numnodes option to setup explicitly number of nodes to use with Grid.

But the problem is now print() do not show on the screen from node code. So hard to debug. So I changed code to send debug messages to print files.

But now I find that the files do even get created when using numnodes. 

When removing numnodes option, the text file gets created. 

I am using FileTools:-Text:-WriteString() and FileTools:-Text:-Close() in the node code.
I also tried using fopen(). Both do not work. 

Same code works OK if I do not use numnodes. 

Any idea why the file do not get created when using numnodes? Worksheet to produce this is below.

I use C:\\tmp folder for testing. Feel free to change this. When I run the code and look in the folder, I do not see the text file there when using numnodes. 

It is possible the file is created but saved somewhere else on the system even though the full file name is given?

It seems to me now that when using numnodes option, there are some things that work and some things that do not work. I do not know if this is by design or a bug. Any one knows?

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1843 and is the same as the version installed in this computer, created 2025, January 25, 22:5 hours Pacific Time.`

Why task running on node do not create text file?

 
> 

restart;

> 

currentdir("C:\\TMP"): #change as needed

> 

foo:=proc(n::integer)   
   local file_name::string;
   currentdir("C:\\TMP"): #change as needed
   file_name:=cat(currentdir(),"\\",n,"_file.txt");
   FileTools:-Text:-WriteString(file_name,cat("processing at node =",n));
   FileTools:-Text:-Close(file_name);
end proc:

> 

Grid:-Set(foo):
Grid:-Setup("local",numnodes=1);
Grid:-Run(0,foo,[0]):
Grid:-Wait();

> 

#No file "0_file.txt" is created in my C:\\TMP\ folder

> 

 

> 

 

> 

 

Another version using fopen instead of FileTools. This also do not work

 
> 

restart;

> 

currentdir("C:\\TMP"): #change as needed

> 

foo:=proc(n::integer)   
   local file_name::string, fileID;
   currentdir("C:\\TMP"): #change as needed
   file_name:=cat(currentdir(),"\\",n,"_file.txt");
   try
        fileID := fopen(file_name,WRITE);
    catch:
        error StringTools:-FormatMessage(lastexception[2..-1]);
    end try;   

   fprintf(fileID,"%s",cat("processing at node =",n));
   fclose(fileID);        
end proc:

> 

Grid:-Set(foo):
Grid:-Setup("local",numnodes=1);
Grid:-Run(0,foo,[0]):
Grid:-Wait();


Download grid_question_jan_29_2025.mw

To see the file 0_file.txt get created in the folder, simply remove the numnodes option.

single PDE solver error ...

Asked by: sarah_r21 5
homework pde dsolve
January 26 2025
1  2

Dear all,

I'm a new maple user trying to solve a single PDE in maple using finite volume.

For simplicity I'm using three volumes. When I'm trying to apply a simple flux limiter, up-wind scheme, (relation between the wall and the node values u[j+0.5](t)=u[j](t)), I'm solver works well and produces accurate results.

However, when I try to a more complicated flux limiter, the solver doesn't initialize and I'm getting an error:
"Error, (in dsolve/numeric/DAE/make_proc) specified dependent variables [u[0](t), u[.5](t), u[1](t), u[1.5](t), u[2](t), u[2.5](t), u[3](t), u[3.5](t), u[4](t)] do not agree with input system {u[0], u[1], u[2], u[3], u[4], u[1/2], u[1.5], u[2.5], u[3.5]}, differences: {u[1/2]}, {u[.5]}".

I would greatly appreciate it if somebody helps me on in this issue.

error.mw

How can fix `[Length of output exceeds limit of 10...

Asked by: salim-barzani 925
January 26 2025
1  4

in a lot of my equation i have such problem and really i don't know how fix this also i try to put : in end and sometime is work and i keep contionues  but sometime not there is any way for solve this problem?

limit.mw

5 6 7 8 9 10 11 Last Page 7 of 38