Maple 2024 Questions and Posts

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

In this work, I do not intend to expand all the variables across the monomials. Instead, I want to restrict the distribution to only the variables x,y,z,tx, y, z, tx,y,z,t, possibly raising them to appropriate powers as needed, until I obtain the desired solution and satisfy the conditions of my PDE tests. However, I am uncertain whether "monomial" is the correct term to use here.

S1.mw

trail-1.mw

I have a list of candidate solutions. Some of them satisfy my PDE test (i.e., they make the PDE equal to zero), while others do not. How can I separate the solutions that satisfy the PDE from those that do not?

Trail-pdetest.mw

How to modify the ND procedure to handle derivatives with respect to more than three independent variables for higher-dimensional PDEs, it is work for [x,t] i want  it work for [x,y,z,t] , 

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

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

(1)

alias(F=F(x, t), G=G(x, t))

F, G

(2)

with(PDEtools):
undeclare(prime):

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

(3)

ND := proc(F, G, U)
  local v, w, f, g, a:
  v := op(F):
  if v[1] in U then w := -v[1] else w := v[1] end if:
  if v[2] in U then w := w, -v[2] else w := w, v[2] end if:
  f := op(0, F):
  g := op(0, G):
  a := diff(f(w)*g(v), U);
  convert(subs([w]=~[v], a), diff)
end proc:

ND(F, G, [x]);
ND(F, G, [t]);

-(diff(F, x))*G+F*(diff(G, x))

 

-(diff(F, t))*G+F*(diff(G, t))

(4)

ND(F, F, [x]);
ND(F, F, [x, x]);

0

 

2*F*(diff(diff(F, x), x))-2*(diff(F, x))^2

(5)

ND(F, G, [x$3]);

-(diff(diff(diff(F, x), x), x))*G+3*(diff(diff(F, x), x))*(diff(G, x))-3*(diff(F, x))*(diff(diff(G, x), x))+F*(diff(diff(diff(G, x), x), x))

(6)

ND(F, F, [x$3, t]);

2*F*(diff(diff(diff(diff(F, t), x), x), x))-2*(diff(diff(diff(F, x), x), x))*(diff(F, t))-6*(diff(diff(diff(F, t), x), x))*(diff(F, x))+6*(diff(diff(F, x), x))*(diff(diff(F, t), x))

(7)

NULL

NULL

#if i collect P1+P1+...+P7 it must get equation 26 in paper so i want define the up proc to open but is not for (3+1) dimesnion,

P1 := 9*ND(F, F, [x, t])

18*F*(diff(diff(F, t), x))-18*(diff(F, x))*(diff(F, t))

(8)

NULL

P2 := -5*ND(F, F, [`$`(x, 3), y])

0

(9)

P3 := ND(F, F, [`$`(x, 6)])

2*F*(diff(diff(diff(diff(diff(diff(F, x), x), x), x), x), x))-12*(diff(diff(diff(diff(diff(F, x), x), x), x), x))*(diff(F, x))+30*(diff(diff(diff(diff(F, x), x), x), x))*(diff(diff(F, x), x))-20*(diff(diff(diff(F, x), x), x))^2

(10)

P4 := -5*ND(F, F, [`$`(y, 2)])

0

(11)

P5 := alpha*ND(F, F, [`$`(x, 2)])

alpha*(2*F*(diff(diff(F, x), x))-2*(diff(F, x))^2)

(12)

P6 := beta*ND(F, F, [x, y])

0

(13)

P7 := gamma*ND(F, F, [x, z])

0

(14)

Download define.mw

I try to construct a system of coefficient but  i don't know why distribute of them is not working, beside this there is any other way for build this kind of systems 

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

_local(gamma)

``

`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)

H1 := int(pde_linear, x)

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

(7)

L := eval(H1, H) = 0

-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+240*(diff(diff(diff(f(x, y, z, t), 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+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(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(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(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)+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t) = 0

(8)

numer(lhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(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) = 0))*denom(rhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(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) = 0)) = numer(rhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(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) = 0))*denom(lhs(240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^3-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))/f(x, y, z, t)^2-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)^2+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))/f(x, y, z, t)^2+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^2-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)^3+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))/f(x, y, z, t)^4+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^3-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3/f(x, y, z, t)^4+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4/f(x, y, z, t)^5-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^4+beta*(2*(diff(diff(f(x, y, z, t), x), y))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))/f(x, y, z, t)^2)-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2/f(x, y, z, t)^2+60*(diff(diff(f(x, y, z, t), x), x))^3/f(x, y, z, t)^3-240*(diff(f(x, y, z, t), x))^6/f(x, y, z, t)^6-10*(diff(diff(f(x, y, z, t), y), y))/f(x, y, z, t)+10*(diff(f(x, y, z, t), y))^2/f(x, y, z, t)^2+18*(diff(diff(f(x, y, z, t), t), x))/f(x, y, z, t)+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))/f(x, y, z, t)-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))/f(x, y, z, t)+(2*(diff(diff(f(x, y, z, t), x), z))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), z))/f(x, y, z, t)^2)*delta+alpha*(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) = 0))

2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*alpha+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y))*beta+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-240*(diff(f(x, y, z, t), x))^6-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), y))*beta-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), z))*delta+240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3+2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

(9)

simplify(2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y))*beta+720*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+60*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-60*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2-18*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), t))*f(x, y, z, t)^4-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4-30*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(f(x, y, z, t), x), y))*f(x, y, z, t)^4+10*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^4+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4+2*f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x))*alpha-240*(diff(f(x, y, z, t), x))^6-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), y))*beta-2*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4*(diff(f(x, y, z, t), z))*delta+240*(diff(diff(diff(f(x, y, z, t), x), x), x))*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*f(x, y, z, t)^3-60*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3 = 0)

2*(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-12*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), x)))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-10*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-20*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+10*(-24*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+24*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3*(diff(diff(f(x, y, z, t), x), x))+(diff(f(x, y, z, t), y))*f(x, y, z, t)^4)*(diff(diff(diff(f(x, y, z, t), x), x), x))+30*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+60*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3-540*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2+2*(alpha*f(x, y, z, t)^5+360*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-30*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3*(diff(f(x, y, z, t), x))+15*f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), y)))*(diff(diff(f(x, y, z, t), x), x))+2*(beta*f(x, y, z, t)^5-30*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3)*(diff(diff(f(x, y, z, t), x), y))+18*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5+2*(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5-10*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5-240*(diff(f(x, y, z, t), x))^6+60*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-2*(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-2*f(x, y, z, t)^4*(beta*(diff(f(x, y, z, t), y))+(diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+10*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

(10)

F1 := %*(1/2)

(diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x))*f(x, y, z, t)^5-6*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+15*(2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3-f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), x)))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-5*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))*f(x, y, z, t)^5-10*(diff(diff(diff(f(x, y, z, t), x), x), x))^2*f(x, y, z, t)^4+5*(-24*(diff(f(x, y, z, t), x))^3*f(x, y, z, t)^2+24*(diff(f(x, y, z, t), x))*f(x, y, z, t)^3*(diff(diff(f(x, y, z, t), x), x))+(diff(f(x, y, z, t), y))*f(x, y, z, t)^4)*(diff(diff(diff(f(x, y, z, t), x), x), x))+15*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))*f(x, y, z, t)^4+30*(diff(diff(f(x, y, z, t), x), x))^3*f(x, y, z, t)^3-270*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^2+(alpha*f(x, y, z, t)^5+360*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-30*(diff(f(x, y, z, t), y))*f(x, y, z, t)^3*(diff(f(x, y, z, t), x))+15*f(x, y, z, t)^4*(diff(diff(f(x, y, z, t), x), y)))*(diff(diff(f(x, y, z, t), x), x))+(beta*f(x, y, z, t)^5-30*(diff(f(x, y, z, t), x))^2*f(x, y, z, t)^3)*(diff(diff(f(x, y, z, t), x), y))+9*(diff(diff(f(x, y, z, t), t), x))*f(x, y, z, t)^5+(diff(diff(f(x, y, z, t), x), z))*delta*f(x, y, z, t)^5-5*(diff(diff(f(x, y, z, t), y), y))*f(x, y, z, t)^5-120*(diff(f(x, y, z, t), x))^6+30*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))*f(x, y, z, t)^2-(diff(f(x, y, z, t), x))^2*alpha*f(x, y, z, t)^4-f(x, y, z, t)^4*(beta*(diff(f(x, y, z, t), y))+(diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+5*(diff(f(x, y, z, t), y))^2*f(x, y, z, t)^4 = 0

(11)

collect(F1, {alpha, beta, f(x, y, z, t)})

(-f(x, y, z, t)^4*(diff(f(x, y, z, t), x))^2+f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), x)))*alpha+(-(diff(f(x, y, z, t), y))*f(x, y, z, t)^4*(diff(f(x, y, z, t), x))+f(x, y, z, t)^5*(diff(diff(f(x, y, z, t), x), y)))*beta+((diff(diff(f(x, y, z, t), x), z))*delta+diff(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x), x)-5*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), y))+9*(diff(diff(f(x, y, z, t), t), x))-5*(diff(diff(f(x, y, z, t), y), y)))*f(x, y, z, t)^5+(-6*(diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x))*(diff(f(x, y, z, t), x))-15*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-10*(diff(diff(diff(f(x, y, z, t), x), x), x))^2+5*(diff(f(x, y, z, t), y))*(diff(diff(diff(f(x, y, z, t), x), x), x))+15*(diff(diff(diff(f(x, y, z, t), x), x), y))*(diff(f(x, y, z, t), x))+15*(diff(diff(f(x, y, z, t), x), y))*(diff(diff(f(x, y, z, t), x), x))-((diff(f(x, y, z, t), z))*delta+9*(diff(f(x, y, z, t), t)))*(diff(f(x, y, z, t), x))+5*(diff(f(x, y, z, t), y))^2)*f(x, y, z, t)^4+(30*(diff(f(x, y, z, t), x))^2*(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x))-30*(diff(f(x, y, z, t), x))^2*(diff(diff(f(x, y, z, t), x), y))+120*(diff(f(x, y, z, t), x))*(diff(diff(f(x, y, z, t), x), x))*(diff(diff(diff(f(x, y, z, t), x), x), x))-30*(diff(f(x, y, z, t), x))*(diff(f(x, y, z, t), y))*(diff(diff(f(x, y, z, t), x), x))+30*(diff(diff(f(x, y, z, t), x), x))^3)*f(x, y, z, t)^3+(-120*(diff(f(x, y, z, t), x))^3*(diff(diff(diff(f(x, y, z, t), x), x), x))+30*(diff(f(x, y, z, t), x))^3*(diff(f(x, y, z, t), y))-270*(diff(diff(f(x, y, z, t), x), x))^2*(diff(f(x, y, z, t), x))^2)*f(x, y, z, t)^2+360*(diff(diff(f(x, y, z, t), x), x))*(diff(f(x, y, z, t), x))^4*f(x, y, z, t)-120*(diff(f(x, y, z, t), x))^6 = 0

(12)

NULL

T := f(x, y, z, t) = g(x, y, z, t)^2+h(x, y, z, t)^2+a[11]

T1 := g(x, y, z, t) = t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5]

T2 := h(x, y, z, t) = t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10]

L2 := subs({T1, T2}, T)

f(x, y, z, t) = (t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11]

(13)

L3 := eval(F1, L2)

30*(2*a[1]^2+2*a[6]^2)^3*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3-270*(2*a[1]^2+2*a[6]^2)^2*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^2+(alpha*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5+360*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^4*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])-30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])+15*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4*(2*a[1]*a[2]+2*a[6]*a[7]))*(2*a[1]^2+2*a[6]^2)+(beta*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^3)*(2*a[1]*a[2]+2*a[6]*a[7])+9*(2*a[1]*a[4]+2*a[6]*a[9])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5+(2*a[1]*a[3]+2*a[6]*a[8])*delta*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-5*(2*a[2]^2+2*a[7]^2)*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^5-120*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^6+30*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^3*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^2-(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])^2*alpha*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4-((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4*(beta*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])+(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[3]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[8])*delta+18*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[4]+18*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[9])*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[1]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[6])+5*(2*(t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])*a[2]+2*(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])*a[7])^2*((t*a[4]+x*a[1]+y*a[2]+z*a[3]+a[5])^2+(t*a[9]+x*a[6]+y*a[7]+z*a[8]+a[10])^2+a[11])^4 = 0

(14)

L4 := collect(L3, [x, y, z, t], 'distributed')

Warning,  computation interrupted

 

` `

(15)

Download systems.mw

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.

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.

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 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

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?

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

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

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

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

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

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

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