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What does this error mean in pdsolve?...

RK1 160 Maple 2018
pde pdsolve differential-equations
August 31 2022
2 5
> 

eq1 := f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/(sqrt(-g(t, phi, r)^2*f(r)^2+1)*sqrt(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2)))

f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/((-g(t, phi, r)^2*f(r)^2+1)^(1/2)*(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2))^(1/2))

 (1)
> 

eq2 := (((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(g(t, phi, r), phi, t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(g(t, phi, r), phi, phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

(((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(diff(g(t, phi, r), phi), t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(diff(g(t, phi, r), phi), phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

 (2)
> 

pdsolve([eq1, eq2])

Error, (in pdsolve/sys) found the element '_F4' repeated in the indication of blocks variables

  
> 

``

Download problemfile.mw

I am trying to solve these two coupled PDE and am getting this error. Does anyone know what this mean?

permute into a list of sums...

RK1 160 Maple
combinatorics permutation
August 27 2022
1 0

I was wondering if there was a way to permute a list to get a list of sums of permutations.
for example,

list:=[a,b,c]
permute(list,2) gives me ([a,b] [b,c] [c,a])

I would like to get this instead: ([a+b],[b+c],[c+d])

supress expression....

RK1 160 Maple
substitution simplification alias
August 24 2022
1 2

I have defined several expressions that keep coming up in my calculations. 
Like :

Delta := -2*M*r+a^2+r^2;
Sigma := (a^2+r^2)^2-Delta*a^2*sin(theta)^2;

Is it possible to make maple recognize these objects whenever they appear in the result of a calculation?

Calculating Exterior Derivative in Diffe...

RK1 160 Maple
grtensorii differentialgeometry tensor
May 24 2022
1 1

I am having trouble calculating exterior derivatives for one forms, maple does not seem to recognize them as one forms.

 
> 

Delta := -2*M*R+R^2+a^2
> 

Sigma2 := (R^2+a^2)^2-Delta*a^2*sin(Theta)^2
> 

rho2 := R^2+a^2*cos(Theta)^2
> 

z := 2*M*R/rho2
> 

interface(typesetting = extended)
> 

with(DifferentialGeometry); with(Tensor)
> 

DGsetup([T, R, Theta, Phi], BlackHole, verbose)

`The following coordinates have been protected:`

  

[T, R, Theta, Phi]

  

`The following vector fields have been defined and protected:`

  

[_DG([["vector", BlackHole, []], [[[1], 1]]]), _DG([["vector", BlackHole, []], [[[2], 1]]]), _DG([["vector", BlackHole, []], [[[3], 1]]]), _DG([["vector", BlackHole, []], [[[4], 1]]])]

  

`The following differential 1-forms have been defined and protected:`

  

[_DG([["form", BlackHole, 1], [[[1], 1]]]), _DG([["form", BlackHole, 1], [[[2], 1]]]), _DG([["form", BlackHole, 1], [[[3], 1]]]), _DG([["form", BlackHole, 1], [[[4], 1]]])]

 (1)
BlackHole > 

g := evalDG((-1+z)*`&t`(dT, dT)+`&t`(dT, dR)+`&t`(dR, dT)+rho2*`&t`(dTheta, dTheta)-z*a*sin(Theta)^2*(`&t`(dPhi, dT)+`&t`(dT, dPhi))-a*sin(Theta)^2*(`&t`(dR, dPhi)+`&t`(dPhi, dR))+Sigma2*sin(Theta)^2*`&t`(dPhi, dPhi)/rho2)
BlackHole > 

ON := evalDG(DGGramSchmidt([D_T, D_R, D_Theta, D_Phi], g, signature = [-1, 1, 1, 1]))

[_DG([["vector", BlackHole, []], [[[1], 1/(-(-a^2*cos(Theta)^2+2*M*R-R^2)/(R^2+a^2*cos(Theta)^2))^(1/2)]]]), _DG([["vector", BlackHole, []], [[[1], -(R^2+a^2*cos(Theta)^2)/((-(R^2+a^2*cos(Theta)^2)/(-a^2*cos(Theta)^2+2*M*R-R^2))^(1/2)*(-a^2*cos(Theta)^2+2*M*R-R^2))], [[2], 1/(-(R^2+a^2*cos(Theta)^2)/(-a^2*cos(Theta)^2+2*M*R-R^2))^(1/2)]]]), _DG([["vector", BlackHole, []], [[[3], 1/(R^2+a^2*cos(Theta)^2)^(1/2)]]]), _DG([["vector", BlackHole, []], [[[1], a*sin(Theta)^2/((R^2+a^2*cos(Theta)^2)*sin(Theta)^2)^(1/2)], [[2], a*sin(Theta)^2/((R^2+a^2*cos(Theta)^2)*sin(Theta)^2)^(1/2)], [[4], 1/((R^2+a^2*cos(Theta)^2)*sin(Theta)^2)^(1/2)]]])]

 (2)
BlackHole > 

Oneform := RaiseLowerIndices(g, ON[1], [1])

_DG([["tensor", BlackHole, [["cov_bas"], []]], [[[1], (-a^2*cos(Theta)^2+2*M*R-R^2)/((R^2+a^2*cos(Theta)^2)*(-(-a^2*cos(Theta)^2+2*M*R-R^2)/(R^2+a^2*cos(Theta)^2))^(1/2))], [[2], 1/(-(-a^2*cos(Theta)^2+2*M*R-R^2)/(R^2+a^2*cos(Theta)^2))^(1/2)], [[4], -2*M*R*a*sin(Theta)^2/((R^2+a^2*cos(Theta)^2)*(-(-a^2*cos(Theta)^2+2*M*R-R^2)/(R^2+a^2*cos(Theta)^2))^(1/2))]]])

 (3)
BlackHole > 

ExteriorDerivative(Oneform)

Error, (in DifferentialGeometry:-ExteriorDerivative) expected 1st argument to be a differential form. Received: _DG([["tensor", BlackHole, [["cov_bas"], []]], [`...`]])

  
BlackHole > 

``

Download teste.mw

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