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tomleslie

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15 years, 163 days
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These are answers submitted by tomleslie

This look pretty trivial...

tomleslie 13876
October 10 2022
0 5

See the attached.

Computing the required values is easy, unless one has to cater for weird numerical problems, such as floating point rounding error.

"Tabulating" values - well that depends on how "pretty" you want the result to be. A simple possibility is shown in the attached

> 

  restart;
#
# Define desired expression
#
  expr1:= V__b=V__a*(( C__a/(1+H/K__a)-H+K__w/H)/(C__b/(1+K__w/H/K__b)+H-K__w/H));
#
# Define parameter values
#
  params:=[C__a=1, C__b=2, K__a=3, K__b=4, K__w=5, V__a=6]:
#
# Define a function which will return the value of 'H'
# for the set of parameters above, and a supplied value for
# 'V__b'
#
  getSol:= z-> fsolve( eval( expr1, [params[], V__b=z])):
#
# Apply the above function for a aequence of values for V__b
#
  Matrix( [ [ 'V__b', 'H'],
            seq( [j, getSol(j)], j=1..8)
          ]
        );  

expr1 := V__b = V__a*(C__a/(1+H/K__a)-H+K__w/H)/(C__b/(1+K__w/(H*K__b))+H-K__w/H)

  

Matrix(%id = 36893488148105088524)

 (1)
> 

 

Download doSum1.mw

spacecurve?...

tomleslie 13876
October 10 2022
0 1

sounds like you want the plots:-spacecurve() command. Basic form of this command would be

with(plots):
spacecurve( [x(t), y(t), z(t)] t=0..whatever).

If you want/need 't' on one axis, then it would be

with(plots):
spacecurve( [t, y(t), z(t)] t=0..whatever).

or

with(plots):
spacecurve( [x(t), t, z(t)] t=0..whatever).

You have to be very careful...

tomleslie 13876
October 10 2022
1 0

when using both the geometry{} and plottools() packages, since they share many of the same command names - eg circle(), line(). But, for example the syntax for geometry:-circle() is completely different from plottools:-circle(), and (even if you use the appropriate syntax), they will return very different things.

In the attached the top-level worksheet uses only commands from the plottools() package. I have moved all the code which requires the geometry() package inside the procedure EqBIS() where no commands from the plottools package() are used.

I have also removed some "redundant" code from your original

> 

  restart:
  with(plots):
  with(plottools):
  _EnvHorizontalName:= 'x':
  _EnvVerticalName:= 'y':
  EqBIS:= proc(P, U, V)
               local a, eq, eq1, M1, t, PU, PV, bissec1:
               uses geometry, LinearAlgebra:
               description "P est le sommet de l'angle dont on chercche la bissectrice" :
               a:= (P - U)/Norm(P - U, 2) + (P - V)/Norm(P - V, 2):
               M1:= P + a*t:
               eq1:= op(eliminate({x = M1[1], y = M1[2]}, t)):
               eq:= op(eq1[2]):
               line(bis, eq):
               line(lv, x = 2*sqrt(r1*R)):
               intersection(Omega, bis, lv):
               return coordinates(Omega);
         end proc:
  r1:= 1/2:
  r2:= r1/2:
  R:= r1*(21 - 12*sqrt(3)):
  R:= r1*(21 - 12*sqrt(3)):
  a:= arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6):
  b:= arc([0, 0], r1, Pi/6 .. (5*Pi)/6):
  co:= EqBIS(<sqrt(3)/2, 1/2>, <0, 0>, <0, 1/2>):
  A:=[cos(Pi/6), sin(Pi/6)]:
  B:=[cos(5*Pi/6), sin(5*Pi/6)]:
  Oo:=[0,0]:
  Op:=[0,1/2]:
  poly:=[A,B,Oo]:
  Omega:= [co[1], co[2]]:
  Omega1:= [-co[1], co[2]]:
  r3:= 3/16:
  EF:= sqrt(r3):
  r:= (150 - 72*sqrt(3))/193*1/2:
  alpha:= -5/3*r + 1/2*1/2:
  p:= sqrt(3)/3*1/2 - sqrt(3)/18*r:
  p2:= textplot([[A[], "A"], [B[], "B"], [Oo[], "O"]], align = ["above", "right"]):
  display( [ a,
             b,
             p2,
             polygonplot(poly, thickness = 3, color = blue, transparency = 0.7),
             disk(Omega, R, color = blue),
             disk(Omega1, R, color = blue),
             disk([0, 3/4], 1/4, color = yellow),
             disk([EF, 1/2 + r3], r3, color = green),
             circle([-EF, 1/2 + r3], r3, color = green, thickness = 5),
             circle([p, 3/4 + alpha], r, color = red, thickness = 5),
             circle([-p, 3/4 + alpha], r, color = red, thickness = 5)
          ],
          axes = none,
          scaling = constrained,
          size = [500, 500]
        );

 
> 

 

Download pTools3.mw

 

 

 

maplemint()...

tomleslie 13876
October 10 2022
1 1

being a bit "dim" - and it is not just in the code editor. The same thing happens if you define procedures withing the "normal" Maple GUI

You can suppress these warnings by using uneval quotes (ie '.....') on the options for Maple commands, which is probably "good practice".

See the attached

> 

  restart;
aTest:=proc(m)
> 

 

> 

cTest:= proc(m)
             entries(m, nolist);
        end proc:
dTest:= proc(m)
             entries(m, 'nolist');
        end proc:
> 

maplemint(aTest);
maplemint(bTest);
maplemint(cTest);
maplemint(dTest);

Procedure aTest( m )
  These names were used as global names but were not declared:  nolist
Procedure cTest( m )
  These names were used as global names but were not declared:  nolist

  
> 

 

Download mintTest.mw

Well...

tomleslie 13876
October 09 2022
1 5

there is a lot of stuff in this code which is either redundant or puzzling. The attached does the "same" calculation in a simple, logical manner and produces the same (rather boring!) result .

Why don't you like this result?

> 

restart
> 

U := a[0]+sum(-a[i]*tanh(xi[n])^i, i = 1 .. 1)+sum(-b[i]*tanh(xi[n])^(-i), i = 1 .. 1)

a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n])

 (1)
> 

u(xi[n+1]) := a[0]-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d)); u(xi[n-1]) := a[0]-a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d))

a[0]-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d))

  

a[0]-a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d))

 (2)
> 

eq := c*(diff(U, xi))-(U^2+U*beta+alpha)*(u(xi[n+1])-u(xi[n-1]))

-((a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n]))^2+(a[0]-a[1]*tanh(xi[n])-b[1]/tanh(xi[n]))*beta+alpha)*(-a[1]*(tanh(xi[n])+tanh(d))/(1+tanh(xi[n])*tanh(d))-b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])+tanh(d))+a[1]*(tanh(xi[n])-tanh(d))/(1+tanh(xi[n])*tanh(d))+b[1]*(1+tanh(xi[n])*tanh(d))/(tanh(xi[n])-tanh(d)))

 (3)
> 

> 

fin := simplify(subs(tanh(xi[n]) = Psi, numer(eq)))

2*(Psi^4*a[1]^2-a[1]*(beta+2*a[0])*Psi^3+(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha)*Psi^2-b[1]*(beta+2*a[0])*Psi+b[1]^2)*tanh(d)*((-Psi^2*b[1]-a[1])*tanh(d)^2-2*Psi*tanh(d)*b[1]+a[1]*Psi^2-b[1])

 (4)
> 

Eqs := {seq(simplify(coeff(fin, Psi, i)), i = 0 .. degree(fin, Psi))}
``

{-4*(-(1/2)*(a[1]^2+b[1]^2)*(beta+2*a[0])*tanh(d)+b[1]*(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha))*tanh(d)^2, 2*a[1]^2*tanh(d)*(-b[1]*tanh(d)^2+a[1]), 2*b[1]*tanh(d)*(a[1]*(beta+2*a[0])*tanh(d)^2-2*b[1]^2*tanh(d)+b[1]*(beta+2*a[0])), -2*b[1]^2*tanh(d)*(tanh(d)^2*a[1]+b[1]), -2*(-b[1]*(beta+2*a[0])*tanh(d)^2+2*a[1]*tanh(d)*b[1]+a[1]*(beta+2*a[0]))*tanh(d)*a[1], 2*b[1]^2*tanh(d)*(-b[1]*tanh(d)^2+a[1])+4*b[1]^2*(beta+2*a[0])*tanh(d)^2-2*(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha)*tanh(d)*(tanh(d)^2*a[1]+b[1]), 2*(beta*a[0]+a[0]^2+2*a[1]*b[1]+alpha)*tanh(d)*(-b[1]*tanh(d)^2+a[1])+4*a[1]*(beta+2*a[0])*tanh(d)^2*b[1]-2*a[1]^2*tanh(d)*(tanh(d)^2*a[1]+b[1])}

 (5)
> 

Sol := solve(Eqs, indets(Eqs, name))

{alpha = alpha, beta = beta, d = d, a[0] = a[0], a[1] = 0, b[1] = 0}, {alpha = alpha, beta = beta, d = 0, a[0] = a[0], a[1] = a[1], b[1] = b[1]}``

 (6)

NULL

Download solEq.mw

isolate() !???...

tomleslie 13876
October 09 2022
1 0

as in the attached

> 

  restart;
  eq:=sqrt(exp(y))=tanh(x);
  isolate(eq,y);

(exp(y))^(1/2) = tanh(x)

  

y = 2*ln(tanh(x))

 (1)
> 

 

Download simp.mw

Basically...

tomleslie 13876
October 06 2022
1 2

I agree with Preben.

If you make the assumption that w(x) is constant then your ODE reduces to a quartic in w(x), which (in general) will have four solutions in terms of the parameters 'c' and 'g'. You don't even need a dsolve() command to produce these.

However the dsolve() command will also produce a solution where 'w(x)' actually varies with 'x'. It is trivial to select only this solution (or indeed the four constant solutions) from the output sequence provided by dsolve() - see the attached.

So far as I am aware there is no way to convert a JacobiSN() function to "simple functions". It is possible to convert it to other related Jacobi functions - but that is hardly illuminating!

> 

  restart;
> 

#
# Make the asssumptions c>0, g>0, and suppress
# the assumption-indicator in Maple output
#
  assume(c>0, g>0);
  interface(showassumed=0):
> 

  q := diff(w(x), x)^2/2 + w(x)^4/8 - c*w(x)^2/2 - g = 0;
#
# If one assumes for the moment that w(x)=constant
# then the differential term in q above will be
# identically zero,and one essentially has a quartic
# equation in w(x). In general suxh a quartic equation
# will have four roots, and one can solve for produce
# these roots using a simple solve() command
#
  solve(eval( q, diff(w(x),x)=0), w(x));

(1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

  

(2*c+2*(c^2+2*g)^(1/2))^(1/2), -(2*c+2*(c^2+2*g)^(1/2))^(1/2), I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2), -I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2)

 (1)
> 

#
# The above four "roots" will also be produced by the
# dsolve() command, since they are all valid solutions
# for the ODE
#
  [ dsolve( q ) ];

[w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2), w(x) = I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2), w(x) = 2*JacobiSN((1/2)*(2*(c^2+2*g)^(1/2)-2*c)^(1/2)*x+_C1, I*(-((c^2+2*g)^(1/2)*c-c^2-g)*g)^(1/2)/((c^2+2*g)^(1/2)*c-c^2-g))*g/(g*((c^2+2*g)^(1/2)-c))^(1/2)]

 (2)
> 

#
# One could select the constant solutions provided by
# dsolve, using
#
  select(j->not has(rhs(j), x), [dsolve(q)]);

[w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2), w(x) = I*(2*(c^2+2*g)^(1/2)-2*c)^(1/2)]

 (3)
> 

#
# Alternatively if one wants a solution where w(x)
# actually varies with the independent variable 'x'
# then one coud use
#
  select(j->has(rhs(j), x), [dsolve(q)]);

[w(x) = 2*JacobiSN((1/2)*(2*(c^2+2*g)^(1/2)-2*c)^(1/2)*x+_C1, I*(-((c^2+2*g)^(1/2)*c-c^2-g)*g)^(1/2)/((c^2+2*g)^(1/2)*c-c^2-g))*g/(g*((c^2+2*g)^(1/2)-c))^(1/2)]

 (4)
> 

 

NULL

Download odeProb.mw

 

If you use...

tomleslie 13876
October 05 2022
0 0

maplemint() within the "normal" Maple GUI, rather than the DOS command mint..... then you you just use  Maple's find/replace facility. For your example you woud probably be looking for either "i:=" or "i :=". I don't think this would take me long to find/fix

A guess...

tomleslie 13876
October 05 2022
2 1

Since you do not provide the code which produces the plots (so no-one can here can accurately replicate/fix the issue), the best you are going to get is an educated guess!

The command plot3d() "samples" the data on a grid, for which the default is [49,49]. In your second plot you have extended one plotting range by a factor of 10, but will still be using the same default "grid" so you may be missing some fine detail,

Try setting the plot3d option 'grid' to [490,49] or [49,490] depending on which way round the plot ranges are defined in your plot3d() command.

If this doesn't work then please upload the offending worksheet using the big green op-arrow in the MApleprimes toobar

My $0.02...

tomleslie 13876
October 05 2022
0 0

You have numerous typos in both worksheets. So far as I can tell, the "textbook" is perfectly correct

I have fixed all of these in the attached, which has comments indicating what I have changed. Ihave also included the "textbook" version using 1D-input at the end of the attached.

> 

restart
> 

stelsel := {-x1+7*x2+x3-x5 = -7, 2*x1+3*x2+4*x3-x5 = 10, 5*x1-3*x2+2*x3-x4-2*x5 = 8}

{-x1+7*x2+x3-x5 = -7, 2*x1+3*x2+4*x3-x5 = 10, 5*x1-3*x2+2*x3-x4-2*x5 = 8}

 (1)
> 

solve(stelsel, {x1, x2, x3, x4, x5})

{x1 = 17/3+(4/3)*x2-x3, x2 = x2, x3 = x3, x4 = 53/3-(23/3)*x2-7*x3, x5 = 4/3+(17/3)*x2+2*x3}

 (2)
> 

restart
> 

stelsel := {-x[1]+7*x[2]+x[3]-x[5] = -7, 2*x[1]+3*x[2]+4*x[3]-x[5] = 10, 5*x[1]-3*x[2]+2*x[3]-x[4]-2*x[5] = 8}

{-x[1]+7*x[2]+x[3]-x[5] = -7, 2*x[1]+3*x[2]+4*x[3]-x[5] = 10, 5*x[1]-3*x[2]+2*x[3]-x[4]-2*x[5] = 8}

 (3)
> 

solve(stelsel, {x[1], x[2], x[3], x[4], x[5]})

{x[1] = 17/3+(4/3)*x[2]-x[3], x[2] = x[2], x[3] = x[3], x[4] = 53/3-(23/3)*x[2]-7*x[3], x[5] = 4/3+(17/3)*x[2]+2*x[3]}

 (4)
> 

variab := [x[1], x[2], x[3], x[4], x[5]]

[x[1], x[2], x[3], x[4], x[5]]

 (5)
> 

with(LinearAlgebra)
> 

A, b := GenerateMatrix(stelsel, variab); xopl := LinearSolve(A, b, free = 'alpha')

A, b := Matrix(3, 5, {(1, 1) = -1, (1, 2) = 7, (1, 3) = 1, (1, 4) = 0, (1, 5) = -1, (2, 1) = 2, (2, 2) = 3, (2, 3) = 4, (2, 4) = 0, (2, 5) = -1, (3, 1) = 5, (3, 2) = -3, (3, 3) = 2, (3, 4) = -1, (3, 5) = -2}), Vector(3, {(1) = -7, (2) = 10, (3) = 8})

  

Vector[column](%id = 36893488147959186484)

 (6)
> 

Totmat := GenerateMatrix(stelsel, variab, augmented = true); xopl := LinearSolve(Totmat, free = 'alpha')

Matrix(3, 6, {(1, 1) = -1, (1, 2) = 7, (1, 3) = 1, (1, 4) = 0, (1, 5) = -1, (1, 6) = -7, (2, 1) = 2, (2, 2) = 3, (2, 3) = 4, (2, 4) = 0, (2, 5) = -1, (2, 6) = 10, (3, 1) = 5, (3, 2) = -3, (3, 3) = 2, (3, 4) = -1, (3, 5) = -2, (3, 6) = 8})

  

Vector[column](%id = 36893488147959169260)

 (7)
> 

  restart;
  stelsel:= {  -x[1] + 7*x[2] +   x[3] -          x[5] = -7,
              2*x[1] + 3*x[2] + 4*x[3] -          x[5] = 10,
              5*x[1] - 3*x[2] + 2*x[3] - x[4] - 2*x[5] = 8};
  solve(stelsel, {x[1], x[2], x[3], x[4], x[5]});

{-x[1]+7*x[2]+x[3]-x[5] = -7, 2*x[1]+3*x[2]+4*x[3]-x[5] = 10, 5*x[1]-3*x[2]+2*x[3]-x[4]-2*x[5] = 8}

  

{x[1] = 17/3+(4/3)*x[2]-x[3], x[2] = x[2], x[3] = x[3], x[4] = 53/3-(23/3)*x[2]-7*x[3], x[5] = 4/3+(17/3)*x[2]+2*x[3]}

 (8)
> 

  with(LinearAlgebra):
  variab := [x[1], x[2], x[3], x[4], x5];
  A, b := GenerateMatrix(stelsel, variab);
  xopl := LinearSolve(A, b, free = 'alpha');
  Totmat := GenerateMatrix(stelsel, variab, augmented = true);
  xopl := LinearSolve(Totmat, free = 'alpha');

variab := [x[1], x[2], x[3], x[4], x5]

  

A, b := Matrix(3, 5, {(1, 1) = -1, (1, 2) = 7, (1, 3) = 1, (1, 4) = 0, (1, 5) = 0, (2, 1) = 2, (2, 2) = 3, (2, 3) = 4, (2, 4) = 0, (2, 5) = 0, (3, 1) = 5, (3, 2) = -3, (3, 3) = 2, (3, 4) = -1, (3, 5) = 0}), Vector(3, {(1) = x[5]-7, (2) = x[5]+10, (3) = 2*x[5]+8})

  

Vector(5, {(1) = (25/6)*alpha[2]+19/3-(1/2)*x[5], (2) = alpha[2], (3) = -(17/6)*alpha[2]-2/3+(1/2)*x[5], (4) = (73/6)*alpha[2]+67/3-(7/2)*x[5], (5) = alpha[5]})

  

Matrix(3, 6, {(1, 1) = -1, (1, 2) = 7, (1, 3) = 1, (1, 4) = 0, (1, 5) = 0, (1, 6) = x[5]-7, (2, 1) = 2, (2, 2) = 3, (2, 3) = 4, (2, 4) = 0, (2, 5) = 0, (2, 6) = x[5]+10, (3, 1) = 5, (3, 2) = -3, (3, 3) = 2, (3, 4) = -1, (3, 5) = 0, (3, 6) = 2*x[5]+8})

  

Vector[column](%id = 36893488147935323548)

 (9)
> 

 

> 

NULL

Download linSolve.mw

 

 

I don't think...

tomleslie 13876
October 01 2022
0 0

there is anything particularly difficult with the solution in the attached (although I can think of several other ways to achieve the same thing)

> 

  restart;
  with(plots):
  m:= Matrix( [ [1, 2, 5,  6,  9],
                [3, 4, 5, 13, 14],
                [1, 3, 4, 10, 11]
              ]
            ):
  col:= [red, green, blue, black, orange, brown, cyan]:
  display
  ( [ seq
      ( listplot
        ( m[j,..],
          color=col[j],
          gridlines=true,
          legend=cat(Row, j)
        ),
        j=1..op([1,1],m)
      )
    ]
  );

 
> 

 

 

 
> 

 

Download lplot.mw

Using...

tomleslie 13876
September 30 2022
1 1

a simpliy() on the expresssion to be solved for appears to work - see the attached

restart

U[d] := Zeta[n]*(2^(2/3)*(theta[n]*lambda*A*beta[n])^(2/3)/(4*beta[n])-delta[n]*`&lambda;A`+U[n]+alpha[n])+Zeta[g]*(U[g]-delta[g](1-lambda)*A+tau*A+R+(-2*A*theta[g]*(lambda-1)*beta[g])^(2/3)/(4*beta[g]))+tau*A-A

Zeta[n]*((1/4)*2^(2/3)*(theta[n]*lambda*A*beta[n])^(2/3)/beta[n]-delta[n]*`&lambda;A`+U[n]+alpha[n])+Zeta[g]*(U[g]-delta[g](1-lambda)*A+tau*A+R+(1/4)*(-2*A*theta[g]*(lambda-1)*beta[g])^(2/3)/beta[g])+tau*A-A

 (1)

FOC := diff(U[d], A)``

(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda/(theta[n]*lambda*A*beta[n])^(1/3)+Zeta[g]*(-delta[g](1-lambda)+tau-(1/3)*theta[g]*(lambda-1)/(-2*A*theta[g]*(lambda-1)*beta[g])^(1/3))+tau-1

 (2)

xyz := solve(simplify(FOC) = 0, A, explicit)

(1/54)*(lambda^2*Zeta[g]^3*beta[n]*theta[g]^2+theta[n]^2*lambda^2*Zeta[n]^3*beta[g]+9*2^(1/3)*beta[g]*theta[n]*lambda*Zeta[n]^2*((1/6)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda)-2*lambda*beta[n]*Zeta[g]^3*theta[g]^2+27*2^(2/3)*beta[g]*Zeta[n]*((1/6)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda)^2+beta[n]*Zeta[g]^3*theta[g]^2)/(beta[g]*(delta[g](1-lambda)*Zeta[g]-tau*Zeta[g]-tau+1)^3*beta[n]), (1/54)*(lambda^2*Zeta[g]^3*beta[n]*theta[g]^2+theta[n]^2*lambda^2*Zeta[n]^3*beta[g]+9*2^(1/3)*beta[g]*theta[n]*lambda*Zeta[n]^2*(-(1/12)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda-((1/12)*I)*3^(1/2)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g])-2*lambda*beta[n]*Zeta[g]^3*theta[g]^2+27*2^(2/3)*beta[g]*Zeta[n]*(-(1/12)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda-((1/12)*I)*3^(1/2)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g])^2+beta[n]*Zeta[g]^3*theta[g]^2)/(beta[g]*(delta[g](1-lambda)*Zeta[g]-tau*Zeta[g]-tau+1)^3*beta[n]), (1/54)*(lambda^2*Zeta[g]^3*beta[n]*theta[g]^2+theta[n]^2*lambda^2*Zeta[n]^3*beta[g]+9*2^(1/3)*beta[g]*theta[n]*lambda*Zeta[n]^2*(-(1/12)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda+((1/12)*I)*3^(1/2)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g])-2*lambda*beta[n]*Zeta[g]^3*theta[g]^2+27*2^(2/3)*beta[g]*Zeta[n]*(-(1/12)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g]-(1/6)*Zeta[n]*2^(2/3)*theta[n]*lambda+((1/12)*I)*3^(1/2)*Zeta[g]*(-4*lambda*theta[n]*beta[n]*theta[g]^2*(lambda^2-2*lambda+1)*beta[g]^2)^(1/3)/beta[g])^2+beta[n]*Zeta[g]^3*theta[g]^2)/(beta[g]*(delta[g](1-lambda)*Zeta[g]-tau*Zeta[g]-tau+1)^3*beta[n])

 (3)

``

NULL

Download solEq.mw

This *may* be untrappable...

tomleslie 13876
September 30 2022
1 0

see the excerpt below from the help page fot "try" -emphasis added
 

Some exceptions are untrappable. This means that a catch clause will never match such an exception, even if the catchString is missing. The finalStatSeq is also not executed if an untrappable exceptions occurs. The following exceptions are untrappable:
• Computation timed out (this can only be caught by timelimit, which raises a "time expired" exception, which can be caught).
• Computation interrupted (user pressed Ctrl+C, Break, or equivalent).
• Internal system error (which indicates a bug in Maple itself).
• ASSERT or return type or local variable type assertion failure (assertion failures are not trappable because they indicate a coding error, not an algorithmic failure).
Stack overflow (when that happens, generally stack space is insufficient for doing anything like running cleanup code). This includes the "too many levels of recursion" exception at the Maple language level.

 

Equations...

tomleslie 13876
September 28 2022
1 2

eq1 and eq2 can be considered as "coupled", although "simultaneous" might be a better designation.

eq3 is not "coupled" to either eq1 or eq2 (and pdsolve cannot solve it!)

See further comments in the attached

> 

restart
> 

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

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

 (1)
> 

eq2 := sin(theta)*(r^2+a^2*cos(theta)^2)*(diff(f(r, theta), theta, theta))-cos(theta)*(diff(f(r, theta), theta))*(a^2*cos(theta)^2-2*a^2-r^2)

sin(theta)*(r^2+a^2*cos(theta)^2)*(diff(diff(f(r, theta), theta), theta))-cos(theta)*(diff(f(r, theta), theta))*(a^2*cos(theta)^2-2*a^2-r^2)

 (2)
> 

pdsolve([eq1, eq2])

{f(r, theta) = _F1(r)+(Int((r^2+a^2*cos(theta)^2)/((cos(theta)-1)^(1/2)*(cos(theta)+1)^(1/2)), theta))*_C1/(2*M*r-a^2-r^2)}

 (3)
> 

eq3 := -2*(r^2+a^2*cos(theta)^2)^2*(M*r-(1/2)*a^2-(1/2)*r^2)*sin(theta)*(diff(g(r, theta), r, r))+sin(theta)*(r^2+a^2*cos(theta)^2)^2*(diff(g(r, theta), theta, theta))+(4*(-(1/4)*cos(theta)^4*a^4+a^2*r*(M-(1/2)*r)*cos(theta)^2-M*a^2*r-(1/4)*r^4))*cos(theta)*(diff(g(r, theta), theta))-2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(cos(theta)*a-r)*(cos(theta)*a+r)

-2*(r^2+a^2*cos(theta)^2)^2*(M*r-(1/2)*a^2-(1/2)*r^2)*sin(theta)*(diff(diff(g(r, theta), r), r))+sin(theta)*(r^2+a^2*cos(theta)^2)^2*(diff(diff(g(r, theta), theta), theta))+4*(-(1/4)*cos(theta)^4*a^4+a^2*r*(M-(1/2)*r)*cos(theta)^2-M*a^2*r-(1/4)*r^4)*cos(theta)*(diff(g(r, theta), theta))-2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(cos(theta)*a-r)*(cos(theta)*a+r)

 (4)
> 

pdsolve(eq3); isolate(eq3, diff(g(r, theta), r, r))

diff(diff(g(r, theta), r), r) = -(1/2)*(-sin(theta)*(r^2+a^2*cos(theta)^2)^2*(diff(diff(g(r, theta), theta), theta))-4*(-(1/4)*cos(theta)^4*a^4+a^2*r*(M-(1/2)*r)*cos(theta)^2-M*a^2*r-(1/4)*r^4)*cos(theta)*(diff(g(r, theta), theta))+2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(cos(theta)*a-r)*(cos(theta)*a+r))/((r^2+a^2*cos(theta)^2)^2*(M*r-(1/2)*a^2-(1/2)*r^2)*sin(theta))

 (5)
> 

pdsolve([eq1, eq2, eq3])

[{f(r, theta) = _F1(r)+(Int((r^2+a^2*cos(theta)^2)/((cos(theta)-1)^(1/2)*(cos(theta)+1)^(1/2)), theta))*_C1/(2*M*r-a^2-r^2)}, [diff(diff(g(r, theta), r), r) = (sin(theta)*(sin(theta)^2*a^2-a^2-r^2)^2*(diff(diff(g(r, theta), theta), theta))-4*cos(theta)*((1/4)*a^4*sin(theta)^4+a^2*(-(1/2)*a^2+r*(M-(1/2)*r))*sin(theta)^2+(1/4)*(a^2+r^2)^2)*(diff(g(r, theta), theta))+2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(sin(theta)^2*a^2-a^2+r^2))/(sin(theta)*(sin(theta)^2*a^2-a^2-r^2)^2*(2*M*r-a^2-r^2))]]

 (6)
> 

NULL

Download pdIssue.mw

Not clear what you want!...

tomleslie 13876
September 28 2022
0 0

Maybe just to suppress the trailing ~ on assumed variables as in the attached

> 

restart
> 

A := Omega; assume(Omega > 0); interface(showassumed = 0); B = Omega

B = Omega

 (1)
> 

NULL

Download assTest.mw

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