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maple2024 worksheet suddenly outputs typesetting...

Asked by: segfault 145
worksheet gui prettyprint
April 25 2025
0  5

This never happened to me before.

Without any changes made in the worksheet, and just executing it again, suddenly Maple 24 gives me all output that starts with

typesetting:-mprintslash

etc

What the heck is this ? and where has the normal output suddenly gone to ?

Before this change Maple did not want to stop an execution on a limit. I had to kill the mserver which then allowed me to save the docuemnt. After that the document has all this unusable typeset nonsense as output.

I opened a new page and pasted the commands into that document. Problem remains the same, so it seems to be something in the system wide config that was changed.

Here is what is causing the problem:

What I noticed  is that my output is now "Line Printer" as default. How did that happen ? I never did that. It must be a consequence of the infinite limit calculation that could not be interrupted (whish Maple will fix their break and interrupt commands).

So how do I set all output to Maple Output. I see no such ability in config. It states there that "Output Display" is set to "Maple Output" , but every new document has line printer as output !!!

Totally unusable now.

No way to configure default Font and color....

Asked by: segfault 145
April 22 2025
0  7

The Maple 2024 default Document is largely unreadable to me. the multiplication sign is a minute dot that I miss most of the time on very high resolution monitors.

What really works well for me is Maple Input as was used in Maple 9.5. A Pleasure to work with. Using Maple 2024 it is a real pain to "go figure" all the time.

I tried the Global Config, but there is no way to set the default font and the defualt color so I can get the exact same text and color as Maple 9.5.
After I set the colors to bright red, and change to Monospace 12 font and use mapleinput, all is well.
However there is no way to save this setup as the configuration has no way to set font and color. It does set mapleinput at least.

So how do I fix this GLOBALLY so I dont have to run into Maple2024's microscopic math.

The Old Simplification problem....

Asked by: segfault 145
radical simplification trig
April 19 2025
1  7

I am just wondering why something that has been bothering me since Maple V up to including Maple 2024 has never been resolved properly.

Why is it so difficult for maple to solve a dead obvious and simple expression e.g.

sqrt(cos(gamma)^(5/3)/sin(2*gamma)^(5/3));

You can use algsubs to tell maple to use an elementary identity to substitute the double angle away, but even then it refuses to simplify the remaining fraction which is elementary at most.

So, when will e.g. this simple multiple generational issue be addressed  so maple can do the obvious simplifications.

There are much more severe examples concerning trigonometric functions under square roots, which was left out in this case to show just one issue.

How i can find the parameter in PDE ?...

Asked by: salim-barzani 1410
parameters substitution pde
April 19 2025
3  6

How i can get this special parameter i try to do substitution in another mw file but stilli can't reach this parameter and without this parameter my PDE is not give me zero so i have to find this r[i] parameter, some letter of my mw file are not similar to paper but r[i]=l[i] as mention is paper al clear and i found all structure just this remain, i am looking for equation (14), thanks for any help 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

NULL
> 

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

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

 (1)
> 

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

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

 (2)
> 

pde1 := a*(diff(u(x, y, z, t), x, t))-((a^4-6*a^2*b^2+b^4)*(1/16))*(diff(u(x, y, z, t), `$`(x, 4)))-(1/4)*(3*(-a^2+b^2))*(diff(u(x, y, z, t)^2, `$`(x, 2)))+alpha*(diff(u(x, y, z, t), `$`(x, 2)))+beta*(diff(u(x, y, z, t), x, y))+delta*(diff(u(x, y, z, t), x, z))+lambda*(diff(u(x, y, z, t), `$`(z, 2)))+mu*(diff(u(x, y, z, t), y, z))+mu^2*(diff(u(x, y, z, t), `$`(y, 2)))/(4*lambda)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+mu*(diff(diff(u(x, y, z, t), y), z))+(1/4)*mu^2*(diff(diff(u(x, y, z, t), y), y))/lambda

 (3)
> 

Tr := {beta = alpha, delta = alpha, mu = 2*lambda}

{beta = alpha, delta = alpha, mu = 2*lambda}

 (4)
> 

pde := subs(Tr, pde1)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y))

 (5)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, t) = T*u(x, y, z, t)))/T, T) end proc, expand(pde))

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^4+(3/8)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^2*b^2-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*b^4+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y)), (3/2)*(diff(u(x, y, z, t), x))^2*a^2-(3/2)*(diff(u(x, y, z, t), x))^2*b^2+(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*a^2-(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*b^2

 (6)
> 

NULL
> 

eq17 := u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2)/(2*a^2-2*b^2)
> 

``NULL
> 

betai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

 (7)
> 

W := w[i] = ((a^4-6*a^2*b^2+b^4)*k[i]^2-16*lambda*l[i]^2+(-32*lambda*r[i]-16*alpha)*l[i]-16*lambda*r[i]^2-16*alpha*r[i]-16*alpha)/(16*a)
> 

AA := A[12] = (16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]-k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))/(16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]+k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))
> 

F2 := 1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

 (8)
> 

NULL
> 

F22 := f(x, y, z, t) = 1+exp((a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/(16*a))+exp((a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/(16*a))
> 

eq := eval(eq17, F22)

u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((k[1]^2*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]^2*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))-(k[1]*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2)/(2*a^2-2*b^2)

 (9)
> 

pdetest(eq, pde)

Download fusion-undon.mw

How can I declare a local variable in an anonymous...

Asked by: Hsingyu Yen 5
procedure incomplete-question
April 18 2025
1  4

I encountered this issue while writing some code. Here is my code:

numArray := [17, 18, 19];
symArray := [x, y, z];
kronArray := map(i -> local j; symArray[i] = symArray[1]^mul(numArray[j], j = 1 .. i - 1), [$ (1 .. 3)]);

When I run it, I get the following warning:

Warning, (in anonymous procedure created in Typesetting:-FI) `j` is implicitly declared local;

After clicking the LINK  to Maple's help, I saw a similar issue in Example 3. However, Example 3 didn't resolve the problem. How can I declare a variable as local within an anonymous function?

How apply substitution and apply limit For get ex...

Asked by: salim-barzani 1410
solve parameters substitution
April 16 2025
2  50

As shown in the paper, and in many similar ones, the authors use a particular method that I believe is related to the long wave limit. I’m familiar with other approaches, but the traditional methods haven’t been successful in this case. This author, along with a few others, has tried applying this long wave limit approach, though many papers don’t explicitly mention the substitutions they use to arrive at the lump solution.

I’ve been able to separately find the lump series, but for some of the other solutions, we first need to figure out how to derive this key result. Once that part is clear, the rest should be easier to handle. I've been working through everything step by step and have managed to reproduce many of the solutions from the paper.

Also i don't know how finding (eq17) in paper, which they found by apply long wave limit to (eq7) in paper

additionaly How finding line which i think they found by finding velocity?

Please, if you have any information or insight into how we can obtain this more difficult result, I would really appreciate your help.

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)
> 

NULL
> 

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

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

 (1)
> 

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

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

 (2)
> 

alpha := 1; beta := 1; delta := 1; lambda := 1

1

  

1

  

1

  

1

 (3)
> 

pde := diff(diff(u(x, y, z, t), t)+6*u(x, y, z, t)*(diff(u(x, y, z, t), x))+diff(u(x, y, z, t), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+delta*(diff(u(x, y, z, t), z)), x)

diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*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), y), y))+diff(diff(u(x, y, z, t), x), x)+diff(diff(u(x, y, z, t), x), y)+diff(diff(u(x, y, z, t), x), z)

 (4)
> 

thetai := t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]
> 

eq15 := w[i] = -(k[i]^4+k[i]^2+k[i]*l[i]+k[i]*r[i]-l[i]^2)/k[i]
> 

eq17 := u(x, y, z, t) = 2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2
> 

A[sj] := (3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)
> 

F2 := 1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])

 (5)
> 

F22 := 1+exp(eta[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(eta[1]+eta[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(eta[2])

1+exp(eta[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(eta[1]+eta[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(eta[2])

 (6)
> 

NULL
> 

NULL
> 

F222 := exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])

exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])

 (7)
> 

indets(F222)

{t, x, y, eta[1], eta[2], k[1], k[2], l[1], l[2], r[1], r[2], exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]), exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2]), exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])}

 (8)
> 

eq1 := eval(F222, {eta[1] = -1, eta[2] = -1, k[1] = K[1]*epsilon, l[1] = L[1]*epsilon, r[1] = R[1]*epsilon})

exp(-(epsilon^4*t*K[1]^4+epsilon^2*t*K[1]^2+epsilon^2*t*K[1]*L[1]+epsilon^2*t*K[1]*R[1]-epsilon^2*t*L[1]^2-epsilon^2*x*K[1]^2-epsilon^2*y*K[1]*L[1]+epsilon*K[1])/(K[1]*epsilon))+(3*K[1]^4*epsilon^4*k[2]^2-6*K[1]^3*epsilon^3*k[2]^3+(3*k[2]^4+l[2]^2)*K[1]^2*epsilon^2-2*K[1]*epsilon^2*k[2]*L[1]*l[2]+k[2]^2*L[1]^2*epsilon^2)*exp(-(epsilon^4*t*K[1]^4+epsilon^2*t*K[1]^2+epsilon^2*t*K[1]*L[1]+epsilon^2*t*K[1]*R[1]-epsilon^2*t*L[1]^2-epsilon^2*x*K[1]^2-epsilon^2*y*K[1]*L[1]+epsilon*K[1])/(K[1]*epsilon)-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]+k[2])/k[2])/(3*K[1]^4*epsilon^4*k[2]^2+6*K[1]^3*epsilon^3*k[2]^3+(3*k[2]^4+l[2]^2)*K[1]^2*epsilon^2-2*K[1]*epsilon^2*k[2]*L[1]*l[2]+k[2]^2*L[1]^2*epsilon^2)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]+k[2])/k[2])

 (9)
> 

G := limit(eq1, epsilon = 0)

exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]+2*k[2])/k[2])+exp(-1)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]+k[2])/k[2])

 (10)

Download LWL.mw

generate the systems with curly braces ?...

Asked by: jalal 435
solve typesetting piecewise
April 12 2025
0  6

Hi,

I'm experimenting with building random series on different topics, inspired by several of your comments, using a table-style layout. For this example, I'm testing systems of linear equations with two unknowns, but I can't manage to generate the systems with curly braces. I hope the purpose of my question is clear. Any ideas? Thanks

Systmes_Idea.mw

How finding parameter, in somewhere i did mistake ...

Asked by: salim-barzani 1410
syntax pde differential-equations
April 10 2025
2  4

This is first type of solving parameter but  i solved some semilar but the shape of them are so different and solving them different too i did my trail but i can't reach out solution also the author solve by another way which i did too but i have to solve in this way too thanks  for any help !

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

``

`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)
> 

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

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

 (3)
> 

pde := 9*(diff(u(x, y, z, t), t, x))+diff(u(x, y, z, t), `$`(x, 6))-5*(diff(u(x, y, z, t), `$`(x, 3), y)+diff(u(x, y, z, t), `$`(y, 2)))+15*((diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), `$`(x, 3)))+(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), `$`(x, 4)))-(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, y))-(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), y)))+45*(diff(u(x, y, z, t), x))^2*(diff(u(x, y, z, t), `$`(x, 2)))+alpha*(diff(u(x, y, z, t), `$`(x, 2)))+beta*(diff(u(x, y, z, t), x, y))+delta*(diff(u(x, y, z, t), x, z))

9*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), y))-5*(diff(diff(u(x, y, z, t), y), y))+15*(diff(diff(u(x, y, z, t), x), x))*(diff(diff(diff(u(x, y, z, t), x), x), x))+15*(diff(u(x, y, z, t), x))*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-15*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), y))-15*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), y))+45*(diff(u(x, y, z, t), x))^2*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))

 (4)
> 

``
> 

oppde := [op(expand(pde))]; u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

9*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), y))-5*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))

  

15*(diff(diff(u(x, y, z, t), x), x))*(diff(diff(diff(u(x, y, z, t), x), x), x))+15*(diff(u(x, y, z, t), x))*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-15*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), y))-15*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), y))+45*(diff(u(x, y, z, t), x))^2*(diff(diff(u(x, y, z, t), x), x))

 (5)
> 

H := u(x, y, z, t) = 2*(diff(ln(f(x, y, z, t)), x))

u(x, y, z, t) = 2*(diff(f(x, y, z, t), x))/f(x, y, z, t)

 (6)
> 

L := eval(pde_linear, H) = 0

2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t) = 0

 (7)
> 

numer(lhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))*denom(rhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0)) = numer(rhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))*denom(lhs(-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^4+alpha*(2*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)-6*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^3)+beta*(2*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3)+delta*(2*(diff(diff(diff(f(x, y, z, t), x), x), z))/f(x, y, z, t)-2*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2-4*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)^2+4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))/f(x, y, z, t)^3)+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))/f(x, y, z, t)-10*(diff(diff(diff(f(x, y, z, t), x), y), y))/f(x, y, z, t)+1440*(diff(f(x, y, z, t), x))^7/f(x, y, z, t)^7+18*(diff(diff(diff(f(x, y, z, t), t), x), x))/f(x, y, z, t)+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))/f(x, y, z, t)^3-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5/f(x, y, z, t)^6+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^5-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))/f(x, y, z, t)^4-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^3+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2/f(x, y, z, t)^3+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))/f(x, y, z, t)^3-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))/f(x, y, z, t)^2-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))/f(x, y, z, t)^5+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)^2 = 0))

420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-6*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*alpha-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))*beta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*beta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*beta-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))*delta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))*delta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))*delta-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))*f(x, y, z, t)^6-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))*f(x, y, z, t)^6-10*(diff(diff(diff(f(x, y, z, t), x), y), y))*f(x, y, z, t)^6+18*(diff(diff(diff(f(x, y, z, t), t), x), x))*f(x, y, z, t)^6-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^5-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))*f(x, y, z, t)^5+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^5-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))*f(x, y, z, t)^5-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5*f(x, y, z, t)+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)^2+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2*f(x, y, z, t)^4+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^5+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), x))*alpha+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^3*alpha+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), y))*beta+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), z))*delta+1440*(diff(f(x, y, z, t), x))^7 = 0

 (8)
> 

F1 := %

420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4-2520*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-6*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*alpha-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), y))*beta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*beta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*beta-2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), z))*delta-4*f(x, y, z, t)^5*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), z))*delta+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), z))*delta-80*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3-240*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+2*(diff(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x), x))*f(x, y, z, t)^6-10*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), y))*f(x, y, z, t)^6-10*(diff(diff(diff(f(x, y, z, t), x), y), y))*f(x, y, z, t)^6+18*(diff(diff(diff(f(x, y, z, t), t), x), x))*f(x, y, z, t)^6-14*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-42*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^5-70*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))*f(x, y, z, t)^5+10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+40*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5+40*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^5-120*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), y))*f(x, y, z, t)^5-60*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+240*(diff(f(x, y, z, t), x))^3*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^4*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2+20*(diff(diff(f(x, y, z, t), x), y))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+280*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-5040*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^5*f(x, y, z, t)+5040*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2-1260*(diff(diff(f(x, y, z, t), x), x))^3*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3-20*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+84*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^4-420*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^3+1680*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)^2+420*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(diff(f(x, y, z, t), x), x))^2*f(x, y, z, t)^4+36*(diff(f(x, y, z, t), x))^2*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-36*(diff(diff(f(x, y, z, t), t), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^5-18*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^5+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), x))*alpha+4*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^3*alpha+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), y))*beta+2*f(x, y, z, t)^6*(diff(diff(diff(f(x, y, z, t), x), x), z))*delta+1440*(diff(f(x, y, z, t), x))^7 = 0

 (9)
> 

NULL
> 

S := f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])

f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])

 (10)
> 

A := eval(F1, S)

600*a[1]^4*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3+1204*a[1]^3*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4-4200*a[1]^4*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3-500*a[1]^3*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+30*a[1]^2*k[1]*p[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-54*a[1]^2*w[1]*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*alpha-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*beta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*beta-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*r[1]*delta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*r[1]*delta+18*a[1]*w[1]*k[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]*p[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6+2*a[1]*k[1]^7*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]^4*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*beta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*r[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*delta+1440*a[1]^7*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^7-5040*a[1]^6*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))+6720*a[1]^5*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-20*a[1]^3*k[1]*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+36*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*w[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^3*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*alpha+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*alpha-126*a[1]^2*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5+150*a[1]^2*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-240*a[1]^5*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2 = 0

 (11)
> 

simplify(1440*a[1]^7*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^7+6720*a[1]^5*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-126*a[1]^2*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5+1204*a[1]^3*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4-4200*a[1]^4*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3+2*a[1]*k[1]^7*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-5040*a[1]^6*k[1]^7*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))+600*a[1]^4*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3-500*a[1]^3*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+30*a[1]^2*k[1]*p[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-54*a[1]^2*w[1]*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*alpha+18*a[1]*w[1]*k[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]*p[1]^2*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-10*a[1]*k[1]^4*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6-20*a[1]^3*k[1]*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]^2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+36*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*w[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^3*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*alpha+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^3*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*alpha+150*a[1]^2*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5-240*a[1]^5*k[1]^4*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*p[1]*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*p[1]*beta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*p[1]*beta-6*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^5*a[1]^2*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^2*r[1]*delta+4*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^4*a[1]^3*k[1]^2*(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^3*r[1]*delta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*p[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*beta+2*(a[0]+a[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]))^6*a[1]*k[1]^2*r[1]*exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*delta = 0)

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1])+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1])-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1])+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1])+(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*a[0]^5-exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])*a[1]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (12)
> 

E := %

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1])+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1])-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1])+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1])+(exp(t*w[1]+x*k[1]+y*p[1]+z*r[1])*a[0]^5-exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])*a[1]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (13)
> 

indets(E)

{alpha, beta, delta, t, x, y, z, a[0], a[1], k[1], p[1], r[1], w[1], exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]), exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1]), exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1]), exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1]), exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1]), exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1])}

 (14)
> 

E1 := subs({exp(t*w[1]+x*k[1]+y*p[1]+z*r[1]) = eX, exp(2*t*w[1]+2*x*k[1]+2*y*p[1]+2*z*r[1]) = eY, exp(3*t*w[1]+3*x*k[1]+3*y*p[1]+3*z*r[1]) = eZ, exp(4*t*w[1]+4*x*k[1]+4*y*p[1]+4*z*r[1]) = eW, exp(5*t*w[1]+5*x*k[1]+5*y*p[1]+5*z*r[1]) = eV, exp(6*t*w[1]+6*x*k[1]+6*y*p[1]+6*z*r[1]) = eB}, E)

2*a[0]*k[1]*(-57*a[0]^4*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]*eY+302*a[0]^3*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^2*eZ-302*a[0]^2*(k[1]^6+(25/151)*k[1]^3*p[1]+(1/151)*k[1]^2*alpha+(1/151)*(beta*p[1]+delta*r[1]+9*w[1])*k[1]-(5/151)*p[1]^2)*a[1]^3*eW+57*a[0]*(k[1]^6-(15/19)*k[1]^3*p[1]-(1/19)*k[1]^2*alpha+(1/19)*(-beta*p[1]-delta*r[1]-9*w[1])*k[1]+(5/19)*p[1]^2)*a[1]^4*eV+(-eB*a[1]^5+eX*a[0]^5)*(k[1]^6-5*k[1]^3*p[1]+k[1]^2*alpha+(beta*p[1]+delta*r[1]+9*w[1])*k[1]-5*p[1]^2))*a[1] = 0

 (15)
> 

indets(E1)

{alpha, beta, delta, eB, eV, eW, eX, eY, eZ, a[0], a[1], k[1], p[1], r[1], w[1]}

 (16)
> 

p2c := normal(E1)

-2*a[0]*k[1]*(eB*a[1]^5*k[1]^6-57*eV*a[0]*a[1]^4*k[1]^6+302*eW*a[0]^2*a[1]^3*k[1]^6-eX*a[0]^5*k[1]^6+57*eY*a[0]^4*a[1]*k[1]^6-302*eZ*a[0]^3*a[1]^2*k[1]^6-5*eB*a[1]^5*k[1]^3*p[1]+45*eV*a[0]*a[1]^4*k[1]^3*p[1]+50*eW*a[0]^2*a[1]^3*k[1]^3*p[1]+5*eX*a[0]^5*k[1]^3*p[1]-45*eY*a[0]^4*a[1]*k[1]^3*p[1]-50*eZ*a[0]^3*a[1]^2*k[1]^3*p[1]+alpha*eB*a[1]^5*k[1]^2+3*alpha*eV*a[0]*a[1]^4*k[1]^2+2*alpha*eW*a[0]^2*a[1]^3*k[1]^2-alpha*eX*a[0]^5*k[1]^2-3*alpha*eY*a[0]^4*a[1]*k[1]^2-2*alpha*eZ*a[0]^3*a[1]^2*k[1]^2+beta*eB*a[1]^5*k[1]*p[1]+3*beta*eV*a[0]*a[1]^4*k[1]*p[1]+2*beta*eW*a[0]^2*a[1]^3*k[1]*p[1]-beta*eX*a[0]^5*k[1]*p[1]-3*beta*eY*a[0]^4*a[1]*k[1]*p[1]-2*beta*eZ*a[0]^3*a[1]^2*k[1]*p[1]+delta*eB*a[1]^5*k[1]*r[1]+3*delta*eV*a[0]*a[1]^4*k[1]*r[1]+2*delta*eW*a[0]^2*a[1]^3*k[1]*r[1]-delta*eX*a[0]^5*k[1]*r[1]-3*delta*eY*a[0]^4*a[1]*k[1]*r[1]-2*delta*eZ*a[0]^3*a[1]^2*k[1]*r[1]+9*eB*a[1]^5*k[1]*w[1]-5*eB*a[1]^5*p[1]^2+27*eV*a[0]*a[1]^4*k[1]*w[1]-15*eV*a[0]*a[1]^4*p[1]^2+18*eW*a[0]^2*a[1]^3*k[1]*w[1]-10*eW*a[0]^2*a[1]^3*p[1]^2-9*eX*a[0]^5*k[1]*w[1]+5*eX*a[0]^5*p[1]^2-27*eY*a[0]^4*a[1]*k[1]*w[1]+15*eY*a[0]^4*a[1]*p[1]^2-18*eZ*a[0]^3*a[1]^2*k[1]*w[1]+10*eZ*a[0]^3*a[1]^2*p[1]^2)*a[1] = 0

 (17)
> 

indets(p2c)

{alpha, beta, delta, eB, eV, eW, eX, eY, eZ, a[0], a[1], k[1], p[1], r[1], w[1]}

 (18)
> 

eqns := {coeffs(collect(p2c, {eB, eV, eW, eX, eY, eZ}, distributed), {eB, eV, eW, eX, eY, eZ})}; nops(%)

Error, invalid arguments to coeffs

  

1

 (19)
> 

NULL
> 

Co := solve(E1, {a[0], a[1], k[1], n[1], p[1], r[1], w[1]}, explicit)

{a[0] = a[0], a[1] = a[1], k[1] = 0, n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = a[0], a[1] = 0, k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = 0, a[1] = a[1], k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}, {a[0] = a[0], a[1] = a[1], k[1] = k[1], n[1] = n[1], p[1] = p[1], r[1] = -(eB*a[1]^5*k[1]^6-57*eV*a[0]*a[1]^4*k[1]^6+302*eW*a[0]^2*a[1]^3*k[1]^6-eX*a[0]^5*k[1]^6+57*eY*a[0]^4*a[1]*k[1]^6-302*eZ*a[0]^3*a[1]^2*k[1]^6-5*eB*a[1]^5*k[1]^3*p[1]+45*eV*a[0]*a[1]^4*k[1]^3*p[1]+50*eW*a[0]^2*a[1]^3*k[1]^3*p[1]+5*eX*a[0]^5*k[1]^3*p[1]-45*eY*a[0]^4*a[1]*k[1]^3*p[1]-50*eZ*a[0]^3*a[1]^2*k[1]^3*p[1]+alpha*eB*a[1]^5*k[1]^2+3*alpha*eV*a[0]*a[1]^4*k[1]^2+2*alpha*eW*a[0]^2*a[1]^3*k[1]^2-alpha*eX*a[0]^5*k[1]^2-3*alpha*eY*a[0]^4*a[1]*k[1]^2-2*alpha*eZ*a[0]^3*a[1]^2*k[1]^2+beta*eB*a[1]^5*k[1]*p[1]+3*beta*eV*a[0]*a[1]^4*k[1]*p[1]+2*beta*eW*a[0]^2*a[1]^3*k[1]*p[1]-beta*eX*a[0]^5*k[1]*p[1]-3*beta*eY*a[0]^4*a[1]*k[1]*p[1]-2*beta*eZ*a[0]^3*a[1]^2*k[1]*p[1]+9*eB*a[1]^5*k[1]*w[1]-5*eB*a[1]^5*p[1]^2+27*eV*a[0]*a[1]^4*k[1]*w[1]-15*eV*a[0]*a[1]^4*p[1]^2+18*eW*a[0]^2*a[1]^3*k[1]*w[1]-10*eW*a[0]^2*a[1]^3*p[1]^2-9*eX*a[0]^5*k[1]*w[1]+5*eX*a[0]^5*p[1]^2-27*eY*a[0]^4*a[1]*k[1]*w[1]+15*eY*a[0]^4*a[1]*p[1]^2-18*eZ*a[0]^3*a[1]^2*k[1]*w[1]+10*eZ*a[0]^3*a[1]^2*p[1]^2)/(delta*k[1]*(eB*a[1]^5+3*eV*a[0]*a[1]^4+2*eW*a[0]^2*a[1]^3-eX*a[0]^5-3*eY*a[0]^4*a[1]-2*eZ*a[0]^3*a[1]^2)), w[1] = w[1]}

 (20)
> 

NULL
> 

case1 := Co[1]

{a[0] = a[0], a[1] = a[1], k[1] = 0, n[1] = n[1], p[1] = p[1], r[1] = r[1], w[1] = w[1]}

 (21)
> 

F := subs(case1, S)

f(x, y, z, t) = a[0]+a[1]*exp(t*w[1]+y*p[1]+z*r[1])

 (22)
> 

F1 := eval(H, F)

u(x, y, z, t) = 0

 (23)
> 

NULL
> 

pdetest(F1, pde)

0

 (24)

Download F-P-O-W.mw

How seperate Linear and nonlinear term in equation...

Asked by: salim-barzani 1410
pde differential-equations duplicate-question
April 09 2025
3  3

sometime this code i use make a problem for me and sometime they work very good how i can get something general for use in all equation 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

``

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

 (1)
> 

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

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

 (2)
> 

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

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

 (3)
> 

pde := 4*(diff(u(x, y, z, w, t), x, t))-(diff(u(x, y, z, w, t), `$`(x, 3), y))+diff(u(x, y, z, w, t), x, `$`(y, 3))+12*(diff(u(x, y, z, w, t), x))*(diff(u(x, y, z, w, t), y))+12*u(x, y, z, w, t)*(diff(u(x, y, z, w, t), x, y))-6*(diff(u(x, y, z, w, t), z, w)) = 0

4*(diff(diff(u(x, y, z, w, t), t), x))-(diff(diff(diff(diff(u(x, y, z, w, t), x), x), x), y))+diff(diff(diff(diff(u(x, y, z, w, t), x), y), y), y)+12*(diff(u(x, y, z, w, t), x))*(diff(u(x, y, z, w, t), y))+12*u(x, y, z, w, t)*(diff(diff(u(x, y, z, w, t), x), y))-6*(diff(diff(u(x, y, z, w, t), w), z)) = 0

 (4)
> 

oppde := [op(expand(pde))]; u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

0

  

4*(diff(diff(u(x, y, z, w, t), t), x))-(diff(diff(diff(diff(u(x, y, z, w, t), x), x), x), y))+diff(diff(diff(diff(u(x, y, z, w, t), x), y), y), y)+12*(diff(u(x, y, z, w, t), x))*(diff(u(x, y, z, w, t), y))+12*u(x, y, z, w, t)*(diff(diff(u(x, y, z, w, t), x), y))-6*(diff(diff(u(x, y, z, w, t), w), z)) = 0

 (5)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, w, t) = a*u(x, y, z, w, t)))/a, a) end proc, expand(pde))

() = 0, 4*(diff(diff(u(x, y, z, w, t), t), x))-(diff(diff(diff(diff(u(x, y, z, w, t), x), x), x), y))+diff(diff(diff(diff(u(x, y, z, w, t), x), y), y), y)+12*(diff(u(x, y, z, w, t), x))*(diff(u(x, y, z, w, t), y))+12*u(x, y, z, w, t)*(diff(diff(u(x, y, z, w, t), x), y))-6*(diff(diff(u(x, y, z, w, t), w), z)) = ()

 (6)
 

NULL

Download seperate_L-NL.mw

How determine the ode type ? my answer and real an...

Asked by: Arya-S-AA 165
ode differential-equations duplicate-account
April 08 2025
1  2

my answer is so different but  and i want remove this lambert in my test? can we do something for giving question exactly solve the question by model i have a book of ode which a lot of time i do some trail but have a problem? how i can remove this issue specially for bernoli and  other type?

> 

restart
> 

with(DEtools, odeadvisor)
> 

ode := diff(y(x), x)+x/y(x)+2 = 0

diff(y(x), x)+x/y(x)+2 = 0

 (1)
> 

Student:-ODEs:-Type(ode)

{}

 (2)
> 

odeadvisor(ode)

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

 (3)
> 

Student:-ODEs:-Type(ode); W := dsolve(ode); odetest(W, ode)

{}

  

y(x) = -x*(LambertW(-c__1*x)+1)/LambertW(-c__1*x)

  

0

 (4)

Download test.mw

Why the code is not apply when i try to finding p...

Asked by: salim-barzani 1410
solve parameters
April 05 2025
3  0

A lot of time i finded but i have a dubt about this why this is happen each time number of equation for finding parameter a_12 is 4 but this time is 28 which i thoght some thing must be mistake also the author of paper use  u=2(ln(f))_xx which is wronge and not satisfy but i try to find R which is strange again is not number contain parameter but is satisfy also in equation 14 i don't know each i is 2 or 1 or it can be i remain itself?

thanks for any help ?

t1.mw

How get piecewise function by substitution? ...

Asked by: salim-barzani 1410
substitution piecewise limit
April 02 2025
3  2

In this example by applying the substitution i can get half of paicewise function but how get another  half ? i am looking for B_rs as Piecewise function ?

> 

restart
> 

eij := ((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-(2*(-3*k[j]*(k[i]-k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-(2*(3*k[j]*(k[i]+k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)

((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-2*(-(3/2)*k[j]*(k[i]-k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-2*((3/2)*k[j]*(k[i]+k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

 (1)
> 

eval(eij, k[j] = b*k[i]); series(%, k[i], 3); convert(%, polynom); eval(%, b = k[j]/k[i]); Bij := (%-1)/(k[i]*k[j])

((-3*k[i]*(-b*k[i]+k[i])*l[j]+beta)*l[i]^2-2*(-(3/2)*b*k[i]*(-b*k[i]+k[i])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(b*k[i]+k[i])*l[j]+beta)*l[i]^2-2*((3/2)*b*k[i]*(b*k[i]+k[i])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

  

series(1+((-3*(-b+1)*l[j]*l[i]^2+3*b*(-b+1)*l[j]^2*l[i]+3*(b+1)*l[j]*l[i]^2+3*b*(b+1)*l[j]^2*l[i])/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2))*k[i]^2+O(k[i]^4),k[i],4)

  

1+(-3*(-b+1)*l[j]*l[i]^2+3*b*(-b+1)*l[j]^2*l[i]+3*(b+1)*l[j]*l[i]^2+3*b*(b+1)*l[j]^2*l[i])*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

  

1+(-3*(-k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(-k[j]/k[i]+1)*l[j]^2*l[i]/k[i]+3*(k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(k[j]/k[i]+1)*l[j]^2*l[i]/k[i])*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

  

(-3*(-k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(-k[j]/k[i]+1)*l[j]^2*l[i]/k[i]+3*(k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(k[j]/k[i]+1)*l[j]^2*l[i]/k[i])*k[i]/((beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)*k[j])

 (2)
> 

simplify((-3*(-k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(-k[j]/k[i]+1)*l[j]^2*l[i]/k[i]+3*(k[j]/k[i]+1)*l[j]*l[i]^2+3*k[j]*(k[j]/k[i]+1)*l[j]^2*l[i]/k[i])*k[i]/((beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)*k[j]))

6*l[j]*l[i]*(l[i]+l[j])/((l[i]-l[j])^2*beta)

 (3)


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How plot complex function including two complex f...

Asked by: salim-barzani 1410
contourplot substitution plotting
March 29 2025
4  7

why i get error in end and how i can fix this error?

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet); declare(u(x, y, t), quiet); declare(f(x, y, t), quiet)
> 

theta := i -> t*w[i]+y*l[i]+x:
> 

eqf := f(x, y, t) = theta(1)*theta(2)+Bij(1, 2):
> 

eqfcomplex := eval(eqf, l[2] = conjugate(l[1])):
> 

eq17 := u(x, y, t) =2*diff(f(x, y, t), x)/f(x, y, t):
> 

equ := eval(eq17, eqfcomplex):
> 

sys := map(normal, {diff(rhs(equ), x), diff(rhs(equ), y)}):
> 

nsys  := map(numer, sys):
nroot := solve(nsys, {x, y}, explicit):
> 

dsys  := map(denom, sys):
droot := solve(dsys, {x, y}, explicit):
> 

{nroot} intersect {droot}

{}

 (1)
> 

compact_ans1 := nroot[1]:
> 

__w := seq(w[i] = (-beta*l[i]^2 - b*l[i] - a), i=1..2):
> 

__Bij := (i,j) -> 12*alpha/(beta*(l[i] - l[j])^2):
> 

eval(eval(compact_ans1, {__w, Bij(1, 2) = __Bij(1, 2)}), l[1]=lambda[1]+I*lambda[2])
assuming lambda[1]::real, lambda[2]::real:
 
> 

ans1 := map(simplify, %, size): # it's up to you to use another simplification strategy
> 

eqp1 := eval(eval(ans1, l[2] = conjugate(l[1])), l[1] = lambda[1]+I*lambda[2])
> 

NULL
> 

# Do the same for the other nroot solutions
> 

eqp := {x = xp+((1/2)*beta*lambda[2]^3+I*(-beta*lambda[1]-b)*lambda[2]^2*(1/2)-((1/2)*beta*conjugate(lambda[1]+I*lambda[2])^2-(1/2)*beta*lambda[1]^2+(1/2)*b*conjugate(lambda[1]+I*lambda[2])+a)*lambda[2]+I*lambda[1]*(conjugate(lambda[1]+I*lambda[2])-lambda[1])*(beta*conjugate(lambda[1]+I*lambda[2])+beta*lambda[1]+b)*(1/2))*t/lambda[2], y = yp-(I*beta*lambda[2]^2+(2*beta*lambda[1]+b)*lambda[2]+I*((conjugate(lambda[1]+I*lambda[2])+lambda[1])*beta+b)*(conjugate(lambda[1]+I*lambda[2])-lambda[1]))*t/(2*lambda[2])}
> 

NULL
> 

vx, vy := diff(eval(x, eqp), t), diff(eval(y, eqp), t); dydx := simplify(vy/vx)
> 

eqfp := dchange(eqp, eqfcomplex, [xp, yp], params = [a, b, alpha, beta, `λ__1`, `λ__2`], simplify); eq17p := dchange(eqp, eq17, [xp, yp], params = [a, b, alpha, beta, `λ__1`, `λ__2`], simplify); eqt := simplify(eval(eq17p, eqfp))
> 

eqt1 := eval(subs({xp = x, yp = y}, eqt), l[1] = lambda[1]+I*lambda[2])
> 

with(plots); lambda[1] := .14; lambda[2] := .68; alpha := -.46; beta := 1.83; a := 1.56; b := -.19; eq := y = (-beta*conjugate(lambda[1]+I*lambda[2])^2-b*conjugate(lambda[1]+I*lambda[2])-beta*lambda[2]^2+I*(2*beta*lambda[1]+b)*lambda[2]+lambda[1]*(beta*lambda[1]+b))*(x+(2*I)*sqrt(3)*lambda[1]*sqrt(alpha/(beta*(lambda[1]+I*lambda[2]-conjugate(lambda[1]+I*lambda[2]))^2))/lambda[2])/((lambda[1]+I*lambda[2])*beta*conjugate(lambda[1]+I*lambda[2])^2+(lambda[1]+I*lambda[2])*b*conjugate(lambda[1]+I*lambda[2])-I*beta*lambda[2]^3+(-beta*lambda[1]-b)*lambda[2]^2+I*(-beta*lambda[1]^2+2*a)*lambda[2]-beta*lambda[1]^3-b*lambda[1]^2); U := proc (x, y, a, b, alpha, beta, `λ__1`, `λ__2`) options operator, arrow; rhs(eqt1) end proc; contour1 := contourplot(eval(U(x, y, a, b, alpha, beta, `λ__1`, `λ__2`), t = -50), x = -200 .. 200, y = -100 .. 100, contours = 30, color = red, grid = [100, 100], transparency = .1); contour2 := contourplot(eval(U(x, y, a, b, alpha, beta, `λ__1`, `λ__2`), t = 0), x = -200 .. 200, y = -100 .. 100, contours = 30, color = green, grid = [100, 100], transparency = .1); contour3 := contourplot(eval(U(x, y, a, b, alpha, beta, `λ__1`, `λ__2`), t = 50), x = -200 .. 200, y = -100 .. 100, contours = 30, color = blue, grid = [100, 100], transparency = .1); trajectory_plot := implicitplot(eq, x = -200 .. 200, y = -200 .. 200, color = black, thickness = 1); T := textplot([[100, 45, "t=50", color = blue], [45, -10, "t=0", color = green], [-100, -45, "t=-50", color = red]], font = [Times, Roman, 16]); display(contour1, contour2, contour3, trajectory_plot, T, labels = ["x", "y"], scaling = constrained, size = [1200, 800])

.14

  

.68

  

-.46

  

1.83

  

1.56

  

-.19

  

y = (.4755583090+0.*I)*(x+(-0.+.1517971372*I)*3^(1/2))

  

proc (x, y, a, b, alpha, beta, lambda__1, lambda__2) options operator, arrow; rhs(eqt1) end proc

  

Error, (in plot/iplot2d) invalid input: Plot:-ColorBar expects its 2nd argument, ymin, to be of type numeric, but received infinity

  

Error, (in plot/iplot2d) invalid input: Plot:-ColorBar expects its 2nd argument, ymin, to be of type numeric, but received infinity

  

Error, (in plot/iplot2d) invalid input: Plot:-ColorBar expects its 2nd argument, ymin, to be of type numeric, but received infinity

  

Error, (in plots:-display) expecting plot structure but received: contour1

  
8

Download line-plot.mw

How do I change the legend position so it doesn't ...

Asked by: nmacsai 260
label axis legend
March 29 2025
2  1

How do I change the legend position so it doesn't cover the plot label?

Before entertaining non-standard solutions to this problem such as building my own from scratch, is the a standard method for changing the position of the default legend generated along with a standard plot? I couldn't find anything about custom legend positions in the help sheets.

I can't help but wonder why this observed behaviour occurs by default? In what kind of plot would I prefer the plot labels to be obscured by the plot legend?



legend_covers_plot_labels.mw

Can I open Maple 2025 files in Maple 2024, if the ...

Asked by: nmacsai 260
March 27 2025
0  4

Can I open Maple 2025 files in Maple 2024? Further, what if the files don't use Maple 2025 features/packages? Does that change the outcome?

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