Thanks pagan, I'll keep a record of these!

From the Help menu

The simplify/radical command has three phases.  In the first phase, it tries to simplify each radical individually.  In the second phase, it looks at the set of all the radicals that appear in the expression and tries to eliminate radicals by writing one radical in terms of others.  Finally, the expression as a whole is normalized as a rational expression.

It seems that an intermediate phase is "missing":

In the third phase, it looks at the set of all the radicals that appear in the expression and tries to eliminate radicals by normalizing all possible combinations of expressions involving radicals.

... or something like that

From the Help menu

The simplify/radical command has three phases.  In the first phase, it tries to simplify each radical individually.  In the second phase, it looks at the set of all the radicals that appear in the expression and tries to eliminate radicals by writing one radical in terms of others.  Finally, the expression as a whole is normalized as a rational expression.

It seems that an intermediate phase is "missing":

In the third phase, it looks at the set of all the radicals that appear in the expression and tries to eliminate radicals by normalizing all possible combinations of expressions involving radicals.

... or something like that

very elegant use of square brackets, thanks Georgios!

I knew about the "radical" option, but couldn't make it to work until your suggestion:

> simplify(Q,radical);

                               2500 x
                     ---------------------------
                             1/2 2     1/2     2
                     (2 + 3 6   )  (3 6    - 2)

> simplify(Q,[radical]);

                                  x

very elegant use of square brackets, thanks Georgios!

I knew about the "radical" option, but couldn't make it to work until your suggestion:

> simplify(Q,radical);

                               2500 x
                     ---------------------------
                             1/2 2     1/2     2
                     (2 + 3 6   )  (3 6    - 2)

> simplify(Q,[radical]);

                                  x

thanks Joe!

thanks Joe!

http://physics.about.com/od/glossary/g/velocity.htm

Definition: Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time.

I stand corrected, magnitude would seem to be more appropriate than velocity (if I understand correctly the above definitions, speed would have been quite appropriate too). I am also reminded of the difference between velocity and speed. Thanks to both of you.

http://physics.about.com/od/glossary/g/velocity.htm

Definition: Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time.

I stand corrected, magnitude would seem to be more appropriate than velocity (if I understand correctly the above definitions, speed would have been quite appropriate too). I am also reminded of the difference between velocity and speed. Thanks to both of you.

>  restart;
>  E := 1.0*10^12; upsilon := .27; sigma := .34*10^(-9); rho[C] := 2.0; epsilon := (2.967*1.6)*10^(-13); h := 8.0*10^(-10); r := 2.2*10^(-9); R := 3.0*10^(-9); K := (1-sigma^2)/(E*h); alpha := h^2/(12*R^2); rho[f] := 1.0;
>  L := (20*2)*R; C[f] := 340; C[l] := 1437; V := 0.5e-1*C[f]; g := 1.736;
>  K[ij] := proc (r, R) options operator, arrow; 4*r*R/(r+R)^2 end proc; K[12] := K[ij](2.2*10^(-9), 3.0*10^(-9));
>  H[m] := proc (r, R, m) options operator, arrow; (r+R)^(-m)*(int(1/(1-K[12]*cos(theta)^2)^((1/2)*m), theta = 0 .. (1/2)*Pi)) end proc;
>  H[7] := H[m](2.2*10^(-9), 3.0*10^(-9), 7); H[13] := H[m](2.2*10^(-9), 3.0*10^(-9), 13);
>  cc := Pi*epsilon*r*sigma^6*((1001*sigma^6*(1/3))*H[13]-(1120*sigma^6*(1/9))*H[7])/alpha^4; cc := evalf(%);
>  cccc := Pi*epsilon*R*sigma^6*((1001*sigma^6*(1/3))*H[13]-(1120*sigma^6*(1/9))*H[7])/alpha^4; cccc := evalf(%);
> w := proc (x, theta, t) options operator, arrow; bb*cos(n*theta)*exp(I*omega*t-I*g*x) end proc; u := proc (x, theta, t) options operator, arrow; bbbb*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
> BesselJ(v, x); plot(BesselJ(1, x), x); plot(BesselJ(2, x), x); plot(BesselI(1, x), x); plot(BesselI(2, x), x);
>  E := 1.0*10^12; upsilon := .27; sigma := .34*10^(-9); rho[C] := 2.0; epsilon := (2.967*1.6)*10^(-13); h := 8.0*10^(-10); r := 2.2*10^(-9); R := 3.0*10^(-9); K := (1-sigma^2)/(E*h); alpha := h^2/(12*R^2); rho[f] := 1.0; L := (20*2)*R; m := 1; n := 1; C[f] := 340; C[l] := 1437; V := 0.5e-1*C[f]; g := 1.736; H := proc (omega) options operator, arrow; sqrt(abs((omega*sqrt((1-upsilon^2)*rho[C]/E)*C[l]/C[f]-V*g*R/C[f])^2-g^2*R^2))/R end proc;
>  plot(H(omega), omega);
> NULL;
>  y := proc (x) options operator, arrow; BesselJ(2, x) end proc; www := proc (x) options operator, arrow; (D(y))(x) end proc;
>  p := proc (x, theta, t) options operator, arrow; K*rho[f]*(omega^2+V^2*g^2-2*omega*V*g)*bb*BesselJ(1, x)*cos(n*theta)*exp(I*omega*t-I*g*x)/(H(omega)*www(x))+cccc*(bbbb-bb)*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
> q := proc (x, theta, t) options operator, arrow; K*cc*(bb-bbbb)*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
>
> l[1] := (D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[1] := simplify(l[1]/exp((2*I)*omega-1.736*I)); s[1] := (D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[1] := simplify(s[1]/exp((2*I)*omega-1.736*I)); l[11] := (D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[11] := simplify(l[11]/exp((2*I)*omega-1.736*I)); s[11] := (D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[11] := simplify(s[11]/exp((2*I)*omega-1.736*I));
> l[2] := (1+sigma)*(D[1, 2](w))(1, (1/3)*Pi, 2)/(2*R); L[2] := simplify(l[2]/exp((2*I)*omega-1.736*I)); s[2] := (1+sigma)*(D[1, 2](u))(1, (1/3)*Pi, 2)/(2*R); S[2] := simplify(s[2]/exp((2*I)*omega-1.736*I)); l[22] := (1+sigma)*(D[1, 2](p))(1, (1/3)*Pi, 2)/(2*R); L[22] := simplify(l[22]/exp((2*I)*omega-1.736*I)); s[22] := (1+sigma)*(D[1, 2](q))(1, (1/3)*Pi, 2)/(2*R); S[22] := simplify(s[22]/exp((2*I)*omega-1.736*I));
> l[3] := -sigma*(D[1](w))(1, (1/3)*Pi, 2)/R; L[3] := simplify(l[3]/exp((2*I)*omega-1.736*I)); s[3] := -sigma*(D[1](u))(1, (1/3)*Pi, 2)/R; S[3] := simplify(s[3]/exp((2*I)*omega-1.736*I)); l[33] := -sigma*(D[1](p))(1, (1/3)*Pi, 2)/R; L[33] := simplify(l[33]/exp((2*I)*omega-1.736*I)); s[33] := -sigma*(D[1](q))(1, (1/3)*Pi, 2)/R; S[33] := simplify(s[33]/exp((2*I)*omega-1.736*I));
> l[4] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[4] := simplify(l[4]/exp((2*I)*omega-1.736*I)); s[4] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[4] := simplify(s[4]/exp((2*I)*omega-1.736*I)); l[44] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[44] := simplify(l[44]/exp((2*I)*omega-1.736*I)); s[44] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[44] := simplify(s[44]/exp((2*I)*omega-1.736*I));
> l[5] := (D[2](w))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](w))(1, (1/3)*Pi, 2)/R^2); L[5] := simplify(l[5]/exp((2*I)*omega-1.736*I)); s[5] := (D[2](u))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](u))(1, (1/3)*Pi, 2)/R^2); S[5] := simplify(s[5]/exp((2*I)*omega-1.736*I)); l[55] := (D[2](p))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](p))(1, (1/3)*Pi, 2)/R^2); L[55] := simplify(l[55]/exp((2*I)*omega-1.736*I)); s[55] := (D[2](q))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](q))(1, (1/3)*Pi, 2)/R^2); S[55] := simplify(s[55]/exp((2*I)*omega-1.736*I));
> l[6] := -w(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](w))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](w))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[6] := simplify(l[6]/exp((2*I)*omega-1.736*I)); s[6] := -u(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](u))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](u))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[6] := simplify(s[6]/exp((2*I)*omega-1.736*I)); l[66] := -p(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](p))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](p))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[66] := simplify(l[66]/exp((2*I)*omega-1.736*I)); s[66] := -q(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](q))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](q))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[66] := simplify(s[66]/exp((2*I)*omega-1.736*I));
> l[a] := L[5]*(L[2]*L[3]-L[1]*L[5])+L[6]*(L[2]*L[2]-L[1]*L[4])+L[3]*(L[5]*L[2]-L[3]*L[4]); L[a] := normal(l[a], expanded); L[A] := collect(L[a], bb); s[a] := S[5]*(S[2]*S[3]-S[1]*S[5])+S[6]*(S[2]*S[2]-S[1]*S[4])+S[3]*(S[5]*S[2]-S[3]*S[4]); S[a] := normal(s[a], expanded); S[A] := collect(S[a], bbbb);
>  L[A] := collect((1.388888889*10^(-7)*omega^4+3.429355280*10^50-1.000000000*10^(-36)*omega^6-1.543209877*10^22*omega^2)*bb^3+(-1.000000000*10^(-12)*omega^2*(-5.702224882*10^14*bb)^2+6.584362140*10^(-10)*bb^2*omega^4-1.646090536*10^20*bb^2*omega^2+4.064421073*10^48*bb^2+2.777777776*10^16*(-3.292181070*10^14*bb)^2+2.777777776*10^16*(-5.702224882*10^14*bb)^2-1.000000000*10^(-12)*omega^2*(-3.292181070*10^14*bb)^2)*bb, bb);
> S[A] := collect((1.388888889*10^(-7)*omega^4+3.429355280*10^50-1.000000000*10^(-36)*omega^6-1.543209877*10^22*omega^2)*bbbb^3+(-1.000000000*10^(-12)*omega^2*(-5.702224882*10^14*bbbb)^2+6.584362140*10^(-10)*omega^4*bbbb^2-1.646090536*10^20*bbbb^2*omega^2+4.064421073*10^48*bbbb^2+2.777777776*10^16*(-3.292181070*10^14*bbbb)^2+2.777777776*10^16*(-5.702224882*10^14*bbbb)^2-1.000000000*10^(-12)*omega(-3.292181070*10^14*bbbb)^4)*bbbb, bbbb);
>  l[ee] := L[22]*L[22]; collect(l[ee], bb);
>  l[ff] := L[11]*L[44]; collect(l[ff], bb);
>  l[dd] := L[22]*L[22]-L[11]*L[44]; L[dd] := normal(l[dd], expanded); L[DD] := collect(L[dd], bb); s[dd] := S[22]*S[22]-S[11]*S[44]; S[dd] := normal(s[dd], expanded); S[DD] := collect(L[dd], omega);
>  eliminate({L[A]+L[DD], S[A]+S[DD]}, {omega});
>  solve(L[A]*S[DD]-S[A]*L[DD] = 0, omega);
>
 

>  restart;
>  E := 1.0*10^12; upsilon := .27; sigma := .34*10^(-9); rho[C] := 2.0; epsilon := (2.967*1.6)*10^(-13); h := 8.0*10^(-10); r := 2.2*10^(-9); R := 3.0*10^(-9); K := (1-sigma^2)/(E*h); alpha := h^2/(12*R^2); rho[f] := 1.0;
>  L := (20*2)*R; C[f] := 340; C[l] := 1437; V := 0.5e-1*C[f]; g := 1.736;
>  K[ij] := proc (r, R) options operator, arrow; 4*r*R/(r+R)^2 end proc; K[12] := K[ij](2.2*10^(-9), 3.0*10^(-9));
>  H[m] := proc (r, R, m) options operator, arrow; (r+R)^(-m)*(int(1/(1-K[12]*cos(theta)^2)^((1/2)*m), theta = 0 .. (1/2)*Pi)) end proc;
>  H[7] := H[m](2.2*10^(-9), 3.0*10^(-9), 7); H[13] := H[m](2.2*10^(-9), 3.0*10^(-9), 13);
>  cc := Pi*epsilon*r*sigma^6*((1001*sigma^6*(1/3))*H[13]-(1120*sigma^6*(1/9))*H[7])/alpha^4; cc := evalf(%);
>  cccc := Pi*epsilon*R*sigma^6*((1001*sigma^6*(1/3))*H[13]-(1120*sigma^6*(1/9))*H[7])/alpha^4; cccc := evalf(%);
> w := proc (x, theta, t) options operator, arrow; bb*cos(n*theta)*exp(I*omega*t-I*g*x) end proc; u := proc (x, theta, t) options operator, arrow; bbbb*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
> BesselJ(v, x); plot(BesselJ(1, x), x); plot(BesselJ(2, x), x); plot(BesselI(1, x), x); plot(BesselI(2, x), x);
>  E := 1.0*10^12; upsilon := .27; sigma := .34*10^(-9); rho[C] := 2.0; epsilon := (2.967*1.6)*10^(-13); h := 8.0*10^(-10); r := 2.2*10^(-9); R := 3.0*10^(-9); K := (1-sigma^2)/(E*h); alpha := h^2/(12*R^2); rho[f] := 1.0; L := (20*2)*R; m := 1; n := 1; C[f] := 340; C[l] := 1437; V := 0.5e-1*C[f]; g := 1.736; H := proc (omega) options operator, arrow; sqrt(abs((omega*sqrt((1-upsilon^2)*rho[C]/E)*C[l]/C[f]-V*g*R/C[f])^2-g^2*R^2))/R end proc;
>  plot(H(omega), omega);
> NULL;
>  y := proc (x) options operator, arrow; BesselJ(2, x) end proc; www := proc (x) options operator, arrow; (D(y))(x) end proc;
>  p := proc (x, theta, t) options operator, arrow; K*rho[f]*(omega^2+V^2*g^2-2*omega*V*g)*bb*BesselJ(1, x)*cos(n*theta)*exp(I*omega*t-I*g*x)/(H(omega)*www(x))+cccc*(bbbb-bb)*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
> q := proc (x, theta, t) options operator, arrow; K*cc*(bb-bbbb)*cos(n*theta)*exp(I*omega*t-I*g*x) end proc;
>
> l[1] := (D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[1] := simplify(l[1]/exp((2*I)*omega-1.736*I)); s[1] := (D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[1] := simplify(s[1]/exp((2*I)*omega-1.736*I)); l[11] := (D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[11] := simplify(l[11]/exp((2*I)*omega-1.736*I)); s[11] := (D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(1-sigma)*(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/(2*R^2)-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[11] := simplify(s[11]/exp((2*I)*omega-1.736*I));
> l[2] := (1+sigma)*(D[1, 2](w))(1, (1/3)*Pi, 2)/(2*R); L[2] := simplify(l[2]/exp((2*I)*omega-1.736*I)); s[2] := (1+sigma)*(D[1, 2](u))(1, (1/3)*Pi, 2)/(2*R); S[2] := simplify(s[2]/exp((2*I)*omega-1.736*I)); l[22] := (1+sigma)*(D[1, 2](p))(1, (1/3)*Pi, 2)/(2*R); L[22] := simplify(l[22]/exp((2*I)*omega-1.736*I)); s[22] := (1+sigma)*(D[1, 2](q))(1, (1/3)*Pi, 2)/(2*R); S[22] := simplify(s[22]/exp((2*I)*omega-1.736*I));
> l[3] := -sigma*(D[1](w))(1, (1/3)*Pi, 2)/R; L[3] := simplify(l[3]/exp((2*I)*omega-1.736*I)); s[3] := -sigma*(D[1](u))(1, (1/3)*Pi, 2)/R; S[3] := simplify(s[3]/exp((2*I)*omega-1.736*I)); l[33] := -sigma*(D[1](p))(1, (1/3)*Pi, 2)/R; L[33] := simplify(l[33]/exp((2*I)*omega-1.736*I)); s[33] := -sigma*(D[1](q))(1, (1/3)*Pi, 2)/R; S[33] := simplify(s[33]/exp((2*I)*omega-1.736*I));
> l[4] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](w))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[4] := simplify(l[4]/exp((2*I)*omega-1.736*I)); s[4] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](u))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[4] := simplify(s[4]/exp((2*I)*omega-1.736*I)); l[44] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](p))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[44] := simplify(l[44]/exp((2*I)*omega-1.736*I)); s[44] := ((1-sigma)*(1/2))*(D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/R^2+alpha*((2*(1-sigma))*(D[`$`(1, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 2)](q))(1, (1/3)*Pi, 2)/R^2)-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[44] := simplify(s[44]/exp((2*I)*omega-1.736*I));
> l[5] := (D[2](w))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](w))(1, (1/3)*Pi, 2)/R^2); L[5] := simplify(l[5]/exp((2*I)*omega-1.736*I)); s[5] := (D[2](u))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](u))(1, (1/3)*Pi, 2)/R^2); S[5] := simplify(s[5]/exp((2*I)*omega-1.736*I)); l[55] := (D[2](p))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](p))(1, (1/3)*Pi, 2)/R^2); L[55] := simplify(l[55]/exp((2*I)*omega-1.736*I)); s[55] := (D[2](q))(1, (1/3)*Pi, 2)/R^2-alpha*((2-sigma)*(D[`$`(1, 2), 2](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 3)](q))(1, (1/3)*Pi, 2)/R^2); S[55] := simplify(s[55]/exp((2*I)*omega-1.736*I));
> l[6] := -w(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](w))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](w))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](w))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](w))(1, (1/3)*Pi, 2); L[6] := simplify(l[6]/exp((2*I)*omega-1.736*I)); s[6] := -u(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](u))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](u))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](u))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](u))(1, (1/3)*Pi, 2); S[6] := simplify(s[6]/exp((2*I)*omega-1.736*I)); l[66] := -p(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](p))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](p))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](p))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](p))(1, (1/3)*Pi, 2); L[66] := simplify(l[66]/exp((2*I)*omega-1.736*I)); s[66] := -q(1, (1/3)*Pi, 2)/R^2-alpha*[R^2*(D[`$`(1, 4)](q))(1, (1/3)*Pi, 2)+2*(D[`$`(1, 2), `$`(2, 2)](q))(1, (1/3)*Pi, 2)+(D[`$`(2, 4)](q))(1, (1/3)*Pi, 2)/R^2]-K*rho[C]*h*(D[`$`(3, 2)](q))(1, (1/3)*Pi, 2); S[66] := simplify(s[66]/exp((2*I)*omega-1.736*I));
> l[a] := L[5]*(L[2]*L[3]-L[1]*L[5])+L[6]*(L[2]*L[2]-L[1]*L[4])+L[3]*(L[5]*L[2]-L[3]*L[4]); L[a] := normal(l[a], expanded); L[A] := collect(L[a], bb); s[a] := S[5]*(S[2]*S[3]-S[1]*S[5])+S[6]*(S[2]*S[2]-S[1]*S[4])+S[3]*(S[5]*S[2]-S[3]*S[4]); S[a] := normal(s[a], expanded); S[A] := collect(S[a], bbbb);
>  L[A] := collect((1.388888889*10^(-7)*omega^4+3.429355280*10^50-1.000000000*10^(-36)*omega^6-1.543209877*10^22*omega^2)*bb^3+(-1.000000000*10^(-12)*omega^2*(-5.702224882*10^14*bb)^2+6.584362140*10^(-10)*bb^2*omega^4-1.646090536*10^20*bb^2*omega^2+4.064421073*10^48*bb^2+2.777777776*10^16*(-3.292181070*10^14*bb)^2+2.777777776*10^16*(-5.702224882*10^14*bb)^2-1.000000000*10^(-12)*omega^2*(-3.292181070*10^14*bb)^2)*bb, bb);
> S[A] := collect((1.388888889*10^(-7)*omega^4+3.429355280*10^50-1.000000000*10^(-36)*omega^6-1.543209877*10^22*omega^2)*bbbb^3+(-1.000000000*10^(-12)*omega^2*(-5.702224882*10^14*bbbb)^2+6.584362140*10^(-10)*omega^4*bbbb^2-1.646090536*10^20*bbbb^2*omega^2+4.064421073*10^48*bbbb^2+2.777777776*10^16*(-3.292181070*10^14*bbbb)^2+2.777777776*10^16*(-5.702224882*10^14*bbbb)^2-1.000000000*10^(-12)*omega(-3.292181070*10^14*bbbb)^4)*bbbb, bbbb);
>  l[ee] := L[22]*L[22]; collect(l[ee], bb);
>  l[ff] := L[11]*L[44]; collect(l[ff], bb);
>  l[dd] := L[22]*L[22]-L[11]*L[44]; L[dd] := normal(l[dd], expanded); L[DD] := collect(L[dd], bb); s[dd] := S[22]*S[22]-S[11]*S[44]; S[dd] := normal(s[dd], expanded); S[DD] := collect(L[dd], omega);
>  eliminate({L[A]+L[DD], S[A]+S[DD]}, {omega});
>  solve(L[A]*S[DD]-S[A]*L[DD] = 0, omega);
>
 

square brackets in cc

square brackets in cc

you've got square brackets in your expression for ldd... can you show more code?

you've got square brackets in your expression for ldd... can you show more code?