diff options
| -rw-r--r-- | 03-brans-dicke-jor.mac | 72 |
1 files changed, 15 insertions, 57 deletions
diff --git a/03-brans-dicke-jor.mac b/03-brans-dicke-jor.mac index 615c024..a5f0a74 100644 --- a/03-brans-dicke-jor.mac +++ b/03-brans-dicke-jor.mac @@ -85,7 +85,7 @@ build_main_ansatz(n) := block([], [ β = H + neg_pow_series(βc, r, 1, n), A = neg_pow_series(Ac, r, 1, n), B = neg_pow_series(Bc, r, -1, n), - λ = neg_pow_series(λc, r, 0, n)])$ + λ = λ_0 + neg_pow_series(λc, r, 1, n)])$ main_ansatz : build_main_ansatz(expansion_order)$ @@ -96,25 +96,15 @@ funcs : [A, B, β, γ, β_expr, γ_expr, λ]; /* Simplify ahead to speed up calculation */ γβ_facts : [H=0, γc[2]=0]; -sim_facts : ev([ - /* From Equation 4 (1/r term) */ - diff(Φc[0],u)=0, - diff(Φc[0],u,2)=0, - /* From Equation 4 (1/r^2 term) */ - diff(Φc[0],θ)=0, - diff(Φc[0],θ, 2)=0, - diff(diff(Φc[0],θ),u)=0, - diff(diff(Φc[0],u),θ)=0], - eval,diff); -coeffs : append(γβ_facts, sim_facts); +coeffs : γβ_facts; /* Equation 1 : determine β */ e_hs_eqs[1] : expand_equation(expand(exp(2*β)*λ^2*hs_eqs[1]), coeffs)$ ce_hs_eqs[1] : coeff_equations(e_hs_eqs[1])$ β_coeffs : block( [vals : []], - for i : 1 thru 5 do ( + for i : 1 thru 4 do ( vals : append(vals, solve(subst(vals, ce_hs_eqs[1][i][2]), βc[i]))), vals)$ @@ -122,8 +112,6 @@ coeffs : append(coeffs, β_coeffs)$ /* Equation 2 : determine A */ e_hs_eqs[2] : expand_equation(expand(exp(2*β)*λ^2*hs_eqs[2]), coeffs)$ -/* BUG: diff(λc[0],θ)=0 does not get substituted */ -e_hs_eqs[2] : subst(coeffs, e_hs_eqs[2])$ ce_hs_eqs[2] : coeff_equations(e_hs_eqs[2])$ A_coeffs : block( @@ -138,13 +126,11 @@ coeffs : append(coeffs, A_coeffs)$ /* Equation 3 : determine B */ print_progress : true; e_hs_eqs[3] : expand_equation(expand(exp(2*β)*λ^2*hs_eqs[3]), coeffs)$ -/* TODO: 17 31 34 slow due to squares? */ -/* BUG: diff(λc[0],θ)=0 does not get substituted; due to missing ev? */ -e_hs_eqs[3] : subst(coeffs, e_hs_eqs[3])$ ce_hs_eqs[3] : coeff_equations(e_hs_eqs[3])$ + B_coeffs : block( [vals : []], - for i : 1 thru expansion_order do ( + for i : 1 thru expansion_order-1 do ( if i=2 then ( vals : append(vals, [Bc[0]=-2*M])) else ( @@ -161,10 +147,11 @@ depends(D, [u, θ]); /* Equation 4 : determine λ */ e_sw_eq : expand_equation(sw_eq, coeffs)$ ce_sw_eq : coeff_equations(e_sw_eq)$ + λu_coeffs : block( - [vals : append(sim_facts, [λc[1]=D])], - for i : 3 thru 6 do ( - vals : append(vals, solve(subst(vals, ce_sw_eq[i][2]), diff(λc[i-1],u)))), + [vals : [λc[1]=D]], + for i : 1 thru 4 do ( + vals : append(vals, solve(subst(vals, ce_sw_eq[i][2]), diff(λc[i+1],u)))), vals)$ coeffs : append(coeffs, λu_coeffs)$ @@ -175,8 +162,6 @@ coeffs : append(coeffs, extra_coeffs)$ /* Equation 5 : determine γ */ e_ev_eqs[2] : expand_equation(expand(exp(2*β)*exp(2*γ)*λ^2*ev_eqs[2]/sin(θ)^2), coeffs)$ -/* BUG: diff(λc[0],θ)=0 does not get substituted; due to missing ev? */ -e_ev_eqs[2] : subst(coeffs, e_ev_eqs[2])$ ce_ev_eqs[2] : coeff_equations(e_ev_eqs[2])$ eq_quad : trigreduce(expand(trigsimp(subst(coeffs, @@ -190,17 +175,19 @@ ce_ev_eqs[2][1]; /* TODO: D_u * c = c_u * D ??? */ /* Supplementary Condition 1 */ e_sc_eqs[1] : expand_equation(expand(λ^2*sc_eqs[1]), coeffs)$ -/* BUG */ -e_sc_eqs[1] : subst(coeffs, e_sc_eqs[1])$ + eq_mono : block( [eq : coeff(e_sc_eqs[1], r, -2)=0], - trigreduce(expand(solve(eq, diff(M,u))))); + eq : solve(eq, diff(M,u))[1], + trigreduce(expand(eq))); /* Supplementary Condition 2 */ e_sc_eqs[2] : expand_equation(sc_eqs[2], coeffs); + eq_dipo : block( [eq : coeff(e_sc_eqs[2], r, -2)=0], - trigreduce(expand(-3*solve(eq, diff(N,u))))); + eq : -3*solve(eq, diff(N,u))[1], + trigreduce(expand(eq))); /* Cache */ @@ -238,32 +225,3 @@ load_cache() := block( for file in cache do load(path(file))); load_cache(); - - -/* Misc. checks */ - -p1 : (4/r + 2*diff(λ,r)/λ)*diff(β,r); -p2 : - diff(λ,r,2)/λ; -p3 : - ω*diff(λ,r)^2/λ^2; -p4 : - sum(sum(sum(sum(uh_AB[A,B]*uh_AB[C,D]*diff(h_AB[A,C],r)*diff(h_AB[B,D],r), A, 3, 4), B, 3, 4), C, 3, 4), D, 3, 4)/4; -eq1 : p1 + p2 + p3 + p4; - -expand(λ^2 * (p1 + p2 + p3 + p4)) - -expand(λ^2 * (p1)) - -expand(exp(2*β)*λ*hs_eqs[1]) - -expand(λ^2 * (p4)) - -uE_ab[1,2]=0; - -tmp : subst([diff(diff(λc[0], u), θ)=0, diff(λc[0], u, 2)=0],eq_mono) - -tmp : trigreduce(expand(trigsimp(tmp))) - -λu_coeffs[5] - -subst(diff(λu_coeffs[5], u), ev(tmp, eval)) - -/* define eth and compare with paper */ |