Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

I experience Maple 2024 not beeing responsive.

It happens often that nothing is happening for 10 to 15 seconds after placing the cursor in an input line.

When the cursor is back, typing is normal for a little while and then again Maple is not reacting to user input.

The worksheets I am working with are between 50 and 100 Mb large in file size (containing plot3d structures, approx 1000 frames distributed across several plots:-display statements). It looks to me that the GUI has to do some house keeping from time to time which keeps it buisy with all the plot structures.

I could delete (plot) output, but this would require execution of the worksheet (before deleting the output) each time I want to continue working normally. This takes several minutes to be ready to work.

Anything else that I can do?

I am learning patten matching in Maple. 

Any one could explain why patmatch(1, (x::anything)^(n::'nonunit'(anything)))   gives true but patmatch(2, (x::anything)^n::'nonunit'(anything)); gives false?

interface(version);

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

restart;

patmatch(1, (x::anything)^(n::'nonunit'(anything)))

true

patmatch(2, (x::anything)^n::'nonunit'(anything));

false

Download patmatch_question_nov_16_2024.mw

I was expecting result similar to using this other software

I do not understand Maple's result. How could I change the patmatch so it does not match 1 to the pattern x::anything^n::anything where n is not 1 ?

Update

To give context, I was trying to write this example from the other software  in Maple:

But when I wrote this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
       f(eval(n,la));
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

Maple gave 

So I modified the code now to check for explicit 1,  to avoid this bad match, like this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
        if eval(y,la)=1 then #bug in maple?
           X;
        else
           f(eval(n,la));
        fi;
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

And now it gives expected result

A farmer has exactly 100m of wire mesh fence available to enclose a pasture. The fence must begin and end at his large oak tree. To do this, imagine the usual "north-south/west-east" cross of the cardinal directions in the drawing plane. The oak tree is at the center of this.

1. All land that lies west of the imaginary axis is not worth a cent.

2. All land that lies east of the oak tree becomes continuously more expensive the further it is from the north-south axis. The property value is based on the function y = k · x, where y represents the price per square meter and x represents the distance in meters to the north-south axis. k is a proportionality factor, which for the task is k = 1 euro/m^3.

a) On which curve must the fence run so that the enclosed pasture area has the greatest possible value?

b) On which curve must the fence run if instead of the distance x from the north-south axis the distance r from the oak tree is decisive with the same factor k?

I was watching Maple's video for conference 2024. In one of the presentation, this example is given

But in my Mapple 2024.2 I get an error typing the same command:

interface(version);

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

restart;

my_ode:={diff(x(t),t$2)-t^2*x(t)=0, x(0)=1,D(x)(0)=1}:
MultivariatePowerSeries:-PowerSeries(my_ode,t,x);

Error, invalid input: too many and/or wrong type of arguments passed to MultivariatePowerSeries:-PowerSeries; first unused argument is t

 

 

Download powerSeries_nov_14_2024.mw

Link to the video is here  it is around 39:00 in time. 

Any one knows why I get an error using same command shown in the video?

I tried connecting Maple to Jupyter Notebook, but it seems that it is not keen on outputting everything within the for loop; it only outputs the last item.

for i from 1 to 24 do
    print(i);
end do;

I've noticed that the Maple interface is always white, and after a long time, it causes eye strain. I wonder if it's possible to adjust the interface color, similar to Mathematica. My system is Windows 11.

Currently, I often use VSCode as an alternative, but some mathematical symbols don't display very clearly.

I have noticed similar discussions, such as this one, but I don’t know how to do it

I have been working on solving a system of PDEs and plotting the results. However I've been encountered issues with setting the spacestep and timestep parameters.

First of all, i attempted to plot graphs t=0..2 using the animate command,

with spacestep = 5*10-4 x 1/151,          timestep=1/1000

However, as shown in the image, an error ocurred indicating that calculations could not proceed after 1.57 sec.

Secondly, i kept the same spacestep but changed the timestep to 1/100 for plotting graphs 
t=0..2. This time, the graphs were plotted without any issues.

I initially beleved that larger spacesteps or timesteps would produce more accurate data. However, in my case, simply increasing these parameters did not work.

I would greatly appreciate if you could provide guidance on what factors should be considered when setting timestep and spacestep parameters, or any experiences in resolving similar issues.

In the publication
https://www.scirp.org/pdf/apm_2021062513594181.pdf
I read that Maple18 contains the "Adomian Decomposition". In "Help" of "Maple2024" I found no direct reference to this method. I would like to ask you to provide references in the help text to this method for solving differential equations.

The other night, first time using Maple in more than 20 years, I asked for the solution to this, looking for u1 in terms of u2:

equ := u2 - u1/(-u1^2 + 1)

solve(equ, [u1])

==> u1 = (-1 + sqrt(4*u2^2 + 1))/(2*u2)

But this is sheer nonsense. The correct solution should be:

u1 = (-1 + sqrt(u2^2 + 1))/u2   ;; note the lack of 4x scaling inside the Sqrt, nor the 2x in the denominator.

What the heck??

there is four formula for calculate them which i know them by name of author the first one is adomian second one is (BiazarShafiofAdomian) which one member of mableprimes write code for me,but i don't know how use for all kind function maybe in future i upload this program for fix this issue, the third one is by zhao which is i think i easy for calculate just  i need someone one to wite the program and do some test for some example i  upload some picture in case for getting algorithm to writting and have some example for testing  so  lets see who can do this algorithm is very usfule when we solve ODE or PDE by LDM, also last method is by taking integral have a good method, in this question this algorithm is zhao which is usfull one

[moderator: The Physics update Library fixes this bug with the same error generated and reported by the same Mapleprimes member on another ODESteps example.]

I have removed Physics update from libname path. 

Now I find I get error calling latex command. When Physics update is on libname, no error.

The error is 

         Error, (in Typesetting:-Parse) too many levels of recursion

I am using worksheet with typesetting extended. But also when I change it to typesetting standard, same error. 

Does this mean one must keep Physics update on libname path for Maple to work OK?

Is this error expected if Physics update is not on libname?

Worksheet below that shows this problem

restart;

interface(version);

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

CASE 1. With Physics update in libname path, no error

 

restart;

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

ode:=[diff(x__1(t),t)=2*x__1(t)+x__2(t),diff(x__2(t),t)=2*x__1(t)+3*x__2(t)];

[diff(x__1(t), t) = 2*x__1(t)+x__2(t), diff(x__2(t), t) = 2*x__1(t)+3*x__2(t)]

the_output:=Student:-ODEs:-ODESteps(ode,output=typeset):

latex(the_output,'output'=string):

 

CASE 2.  Removing Physics from libname path, gives internal error

 

restart;

libname:=libname[2];

"C:\Program Files\Maple 2024\lib"

ode:=[diff(x__1(t),t)=2*x__1(t)+x__2(t),diff(x__2(t),t)=2*x__1(t)+3*x__2(t)];

[diff(x__1(t), t) = 2*x__1(t)+x__2(t), diff(x__2(t), t) = 2*x__1(t)+3*x__2(t)]

the_output:=Student:-ODEs:-ODESteps(ode,output=typeset):

latex(the_output,'output'=string):

Error, (in Typesetting:-Parse) too many levels of recursion

 

 

 

Download internal_error_from_latex_when_libname_changed_nov_2_2024.mw

I think I just found one of the most serious problems in Maple I've seen (other than timelimit hanging).

This is using Maple 2024.2 on windows 10.

I'll explain in words the problem, then give worksheet below to reproduce this. I can reproduce this all the time.

I have implicit solution in y(x) to an ode.

If I first solve for y(x) from the solution, so solution is now explicit, then call odetest to check if this explicit solution is correct, and if I use assumptions on the odetest call, and then after that call odetest on the original implicit solution, then odetest fails to verify the implicit solution.

But, if I change the order, and first call odetest to verify the implicit solution first, it verifies it OK !  

So the problem ONLY happens if I change the order of calling odetest and if I use assumptions on the odetest call that was used before on the explicit solution.

This tells me that Maple remembers something from earlier call. Does it remember the assumptions used? If so, this is very risky. As some part of program might call odetest with some assumptions, and another part of the program can use no assumptions.  I thought assuming is only applied to the call it is used at only and will not affect future calls.

Is there a way then to clear all assumptions used on earlier call to Maple command before using the command again? Or to tell Maple not to remember assumptions used on a call?

This is a big problem. It took me 14 hrs of debuging to find it. Order of calls to odetest should not make it behave different.

I hope someone could find solution to this, since now I have no idea what to do as I need to use odetest on explicit and implicit solutions and I do not want the order of calling Maple command to make difference in results.

This worksheet shows the problem. 3 cases are given. Notice that when using assumptions on earlier call to odetest, how it fails to verify the implicit solution in later call.

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 1824 and is the same as the version installed in this computer, created 2024, October 31, 14:22 hours Pacific Time.`

kernelopts('assertlevel'=2):

CASE 1. Calling odetest on explicit first with assumptions, make odetest hang when calling on implicit after

 

restart;

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

#NOw check the explicit solution. Using assumptions to see the problem
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr) time expired

#Now odetest hangs on the implicit solution

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

Error, (in is/internal/rename) time expired

 

 

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

y(x)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

CASE 2. Calling odetest on implicit solution first, then it DOES NOT hang !!

 

restart;

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

#notice, no hang now, since called before
timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

#NOw check the explicit solution. This will timeout which is OK
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in type/complex) time expired

#check again that odetest still verifies the implicit solution OK

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

 

CASE 3. Calling odetest with no assumptions on explicit solution, then it also does not hang

 

restart;

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

#Now check the explicit solution. but DO NOT use assumptions
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):
timelimit(30, odetest(y(x)=EXPLICIT_SOL,[ode,IC]));

Error, (in factor/remember) time expired

#check again that odetest still verifies the implicit solution OK

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

 


 

Download order_of_ode_test_makes_difference_oct_31_2024.mw

 

update NOV 2, 2024 6 AM

I found the cause.

Removing PHYSICS from libname, then the problem goes away !

So this is caused by PHYSICS package. For some reason, having Physics package in the libname causes odetest to hang/fail compared to when the physics package is not in the libname path. Worksheet below.

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 1824 and is the same as the version installed in this computer, created 2024, October 31, 14:22 hours Pacific Time.`

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

CASE 1. without PHYSICS on libname, it works !!

 

restart;

kernelopts('assertlevel'=2):

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

libname:=libname[2]; #remove PHYSICS

"C:\Program Files\Maple 2024\lib"

libname;

"C:\Program Files\Maple 2024\lib"

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

#NOw check the explicit solution. Using assumptions to see the problem
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr/ln) time expired

#Now try odetest  on the implicit solution

infolevel[odetest]:=5;

5

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

odetest: Performing an implicit solution test

odetest: Performing an explicit (try soft) solution test

odetest: Performing an implicit solution (II) test

[0, 0]

 

 

CASE 2. With Physics on libname, it fails !

 

restart;

kernelopts('assertlevel'=2):

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr/shake) time expired

#Now try odetest  on the implicit solution

infolevel[odetest]:=5;

5

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

odetest: Performing an implicit solution test

odetest: Performing an explicit (try soft) solution test

odetest: Performing an implicit solution (II) test

Error, (in is/internal/rename) time expired

 

 

Download order_of_ode_test_makes_difference_NOV_2_2024.mw

my question is: Is it safe to permanently remove Physics package from libname? Why is having physics package in libname (which is by default) causes this problem?

I do not use Physics package explicitly in my code. i.e. I do not do Physics:- calls. 

Any one knows what effect not having Physics on libname cause? Will Maple still work OK for everything if one is not calling Physics package explicitly?

Here are two systems over the reals:

sys__1:=And(r*(387*r+52)+2<r*(226*q+121*s)+9*q*(q*(2*q-5)-3*s+2)+6*s,4*q^3+r*(27*r+4)+s^2=q*(q+18*r),q>=0,r>=0):
sys__2:=And((392-1739*q)*r+4*(2-9*q)**2+2151*r**2<75*r*s,4*q**3+r*(27*r+4)+s**2=q*(q+18*r),q>=0,r>=0):

The following results indicate that both and are satisfiable 

QuantifierElimination:-QuantifierEliminate(exists([s,q,r],sys__1));
                              true
QuantifierElimination:-QuantifierEliminate(exists([s,q,r],sys__1));
                              true

but RealDomain:-solve simply returns an empty list (that is, no solution exists) in both cases

RealDomain:-solve(sys__1,[q,s,r]); # ⟹ sys1 cannot be satisfied
                               []
RealDomain:-solve(sys__2,[q,s,r]); # ⟹ sys2 cannot be satisfied
                               []

As discussed in the previous problem, in contrast to using QuantifierElimination:-QuantifierEliminate, the use of RealDomain:-solve is unsafe. Nevertheless, the above output suggests that even the much-more-sophisticated QuantifierElimination:-QuantifierEliminate is still not always reliable (since the correct returnedvalue appears to be in lieu of ). So, what is the right command to handle polynomial systems over real domains in Maple? 

I have this problem:

(x'+x''+epsilon/x)(x'-(x')^3/3!)(x''-(x'')^3/3!)(epsilon/x -(epsilon/x)^3/3!)=1

x(0)=epsilon , x'(epsilon)=epsilon+epsilon^{-1}

0<epsilon<<1

Now I want to try the ansatz: x(epsilon,t)=x_{-1}(t)/epsilon+x_0(t)+x_1(t)epsilon.

Can you suggest me a way to implement this ansatz (i.e finding x_{-1}(t),x_0(t),x_1(t)).

Appreciate your time!

every time i have a small problem 2  why not cancel number 2 in denominator , i don't want see a number with fraction like 1/3  3/4 how i fix this

restart

K := (1/2)*sqrt(2*sqrt(2)*sqrt(lambda*a[5]/a[4])+2*sqrt(-2*a[5]/a[4])*(B[1]*sqrt(-lambda)*sinh(sigma)+B[2]*sqrt(-lambda)*cosh(sigma))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda)+2*sqrt(-(2*(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5]))/(lambda*a[4]))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda))*e^(i*psi(x, t))

Warning, if e is meant to be the exponential e, use command/symbol completion or palettes to enter this special symbol, or use the exp function

 

(1/2)*(2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*(B[1]*(-lambda)^(1/2)*sinh(sigma)+B[2]*(-lambda)^(1/2)*cosh(sigma))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda))^(1/2)*e^(i*psi(x, t))

(1)

B[1] := 0; mu := 0

0

 

0

(2)

simplify(eval(K))

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

(3)

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)), 'trig')

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

(4)

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)))

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

(5)

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)), 'constant')

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

(6)
 

 

 

NULL

Download cancelation.mw

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