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https://gitlab.com/scemama/QCaml.git
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Working on notebook
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56b6bb41a6
commit
e66d790cb7
@ -84,12 +84,15 @@ let annihilation spin h t =
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let single_excitation spin h p t =
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assert (h <> p);
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match spin with
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| Spin.Alfa -> { t with alfa = Spindeterminant.single_excitation h p t.alfa }
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| Spin.Beta -> { t with beta = Spindeterminant.single_excitation h p t.beta }
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let double_excitation spin h p spin' h' p' t =
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assert (h <> p);
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assert (h' <> p');
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match spin, spin' with
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| Spin.(Alfa, Beta) -> { alfa = Spindeterminant.single_excitation h p t.alfa ;
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beta = Spindeterminant.single_excitation h' p' t.beta }
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@ -133,7 +133,7 @@ let pp_s_exc ppf t =
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| Spin.Beta -> "\\beta " )
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t.hole t.particle
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let pp_exc ppf t =
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let pp ppf t =
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let phase, l =
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match t with
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| Identity p -> p, []
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@ -655,18 +655,21 @@
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" let mos_a, mos_b = Determinant.to_lists ki in\n",
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" [ List.map (fun hole -> \n",
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" List.map (fun particle ->\n",
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" Determinant.single_excitation Spin.Alfa hole particle ki\n",
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" if hole = particle then None else\n",
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" Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n",
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" ) mos_abs\n",
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" ) mos_a\n",
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" ;\n",
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" List.map (fun hole -> \n",
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" List.map (fun particle ->\n",
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" Determinant.single_excitation Spin.Beta hole particle ki\n",
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" if hole = particle then None else\n",
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" Some (Determinant.single_excitation Spin.Beta hole particle ki)\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ]\n",
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" |> List.concat\n",
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" |> List.concat\n",
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" |> Util.list_some\n",
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" |> List.filter (fun x -> Determinant.is_none x = false)\n",
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" |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
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" in\n",
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@ -678,6 +681,7 @@
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" List.map (fun particle ->\n",
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" List.map (fun hole' -> \n",
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" List.map (fun particle' ->\n",
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" if hole = particle || hole' = particle' then None else\n",
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" if hole' > hole && particle' < particle then\n",
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" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
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" else None\n",
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@ -1293,7 +1297,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 6. *1 1 21*"
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"# 6. 1 1 21"
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]
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},
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{
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@ -1371,16 +1375,16 @@
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_two i j k a s s ) *.\n",
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" (f_one a j s +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s s) 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s' s) 0. mos_i') ) \n",
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" ) 0. mos_i\n",
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" (List.fold_left (fun accu m -> accu +. f_two m a m j s s) 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. f_two m a m j s' s) 0. mos_i') ) \n",
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" ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_two i j k a s s') *.\n",
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" (f_one a j s' +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s s') 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s' s') 0. mos_i') ) \n",
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" ) 0. mos_i'\n",
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" (List.fold_left (fun accu m -> accu +. f_two m a m j s s') 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. f_two m a m j s' s') 0. mos_i') ) \n",
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" ) 0. mos_j'\n",
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" ) 0. mos_cabs\n",
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" in\n",
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" match phase with\n",
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@ -1388,26 +1392,7 @@
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = check 11 integral_value 1 1 2 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"let ki = det_I.(0)\n",
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"let kj = det_I.(10)\n",
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"\n",
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"\n",
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"let _ =\n",
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" let alphas =\n",
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" generate_alphas ki kj 1 1 2 1\n",
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" in\n",
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" compute_HaaF ki alphas kj\n",
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"\n",
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"let _ = integral_value ki kj"
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"let _ = check 0 integral_value 1 1 2 1"
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]
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},
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{
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@ -1430,7 +1415,239 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 8. 1 2 22 "
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"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
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"\n",
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"$\\sum_{j} \\sum_{a} \\sum_{m} \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} + \n",
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" \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} +\n",
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" \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kj} \n",
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" $\n",
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"\n",
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"$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"$m$ : orbital indices of virtual MOs, unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"\\begin{align}\n",
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" \\sum_{a} \\sum_{j} \\sum_{m}\n",
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" \\langle i j || m a \\rangle \\left[ m a || k j \\right] + \n",
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" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m} \n",
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" \\langle i \\bar{j} | m \\bar{a} \\rangle \\left[ m \\bar{a} | k \\bar{j} \\right] + \\\\\n",
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" \\sum_{a} \\sum_{j} \\sum_{l}\n",
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" \\langle l j || k a \\rangle \\left[ i a || l j \\right] + \n",
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" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l} \n",
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" \\langle l \\bar{j} | k \\bar{a} \\rangle \\left[ i \\bar{a} | l \\bar{j} \\right] + \\\\\n",
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" \\sum_{a} \\sum_{\\bar{j}} \\sum_{\\bar{m}} \n",
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" \\langle i \\bar{j} | a \\bar{m} \\rangle \\left[ a \\bar{m} | k \\bar{j} \\right] \\\\\n",
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"\\end{align}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"let integral_value ki kj = \n",
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" let i, k, s, phase =\n",
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" match Excitation.of_det ki kj with\n",
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" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
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" hole, particle, spin, phase\n",
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" | _ -> assert false\n",
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" in\n",
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" \n",
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" (* mos unoccupied in both I and J *)\n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.init mo_num (fun i -> Some (i+1)) , \n",
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" Array.init mo_num (fun i -> Some (i+1)) \n",
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" in\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
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" \n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.to_list mos_virt_a |> Util.list_some,\n",
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" Array.to_list mos_virt_b |> Util.list_some\n",
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" in\n",
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"\n",
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" let mos_virt =\n",
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" match s with\n",
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" | Spin.Alfa -> mos_virt_a\n",
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" | Spin.Beta -> mos_virt_b\n",
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" in\n",
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" \n",
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" let mos_j, mos_j' =\n",
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" let alfa = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" let beta = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" match s with\n",
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" | Spin.Alfa -> alfa, beta\n",
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" | Spin.Beta -> beta, alfa\n",
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" in\n",
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"\n",
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" let result = \n",
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" let s' = Spin.other s in\n",
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" List.fold_left (fun accu a -> accu +.\n",
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" List.fold_left (fun accu m -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two i j m a s s *. f_two m a k j s s ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two i j m a s s' *. f_two m a k j s s' ) 0. mos_j'\n",
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" ) 0. mos_virt\n",
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" -.\n",
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" List.fold_left (fun accu l -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two l j k a s s *. f_two i a l j s s ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two l j k a s s' *. f_two i a l j s s' ) 0. mos_j'\n",
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" ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu m -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two i j a m s s' *. f_two a m k j s s' ) 0. mos_j'\n",
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" ) 0. mos_virt\n",
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" ) 0. mos_cabs\n",
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" in\n",
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" match phase with\n",
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" | Phase.Pos -> result\n",
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = check 20 integral_value 1 1 2 2\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"let ki = det_I.(0)\n",
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"let kj = det_I.(11)\n",
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"\n",
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"let alpha = \n",
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" generate_alphas ki kj 1 1 2 2\n",
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" |> List.filter (fun alpha -> abs_float (compute_HaaF ki [alpha] kj) < 2.0e-05)\n",
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" |> List.fold_left (fun (a,mx) alpha ->\n",
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" let x = abs_float (compute_HaaF ki [alpha] kj) in\n",
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" if x > mx then (alpha, x) else (a,mx) ) (ki,-1.)\n",
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" |> fst\n",
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" \n",
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"\n",
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"let _ = Determinant.to_lists ki\n",
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"let _ = Determinant.to_lists alpha\n",
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"let _ = Determinant.to_lists kj\n",
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"\n",
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"let _ = \n",
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" Format.printf \"Excitation: %a\\n@.\" Excitation.pp_exc (Excitation.of_det ki alpha);\n",
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" Format.printf \"Excitation: %a\\n@.\" Excitation.pp_exc (Excitation.of_det alpha kj);\n",
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" Format.printf \"Excitation: %a\\n@.\" Excitation.pp_exc (Excitation.of_det ki kj)\n",
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"\n",
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"let integral_value ki kj = \n",
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" let i, k, s, phase =\n",
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" match Excitation.of_det ki kj with\n",
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" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
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" hole, particle, spin, phase\n",
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" | _ -> assert false\n",
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" in\n",
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" \n",
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" (* mos unoccupied in both I and J *)\n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.init mo_num (fun i -> Some (i+1)) , \n",
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" Array.init mo_num (fun i -> Some (i+1)) \n",
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" in\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
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" \n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.to_list mos_virt_a |> Util.list_some,\n",
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" Array.to_list mos_virt_b |> Util.list_some\n",
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" in\n",
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"\n",
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" let mos_virt =\n",
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" match s with\n",
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" | Spin.Alfa -> mos_virt_a\n",
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" | Spin.Beta -> mos_virt_b\n",
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" in\n",
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" \n",
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" let mos_j, mos_j' =\n",
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" let alfa = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" let beta = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" match s with\n",
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" | Spin.Alfa -> alfa, beta\n",
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" | Spin.Beta -> beta, alfa\n",
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" in\n",
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"\n",
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" let result = \n",
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" let s' = Spin.other s in\n",
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" let a = 13 in\n",
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" (*\n",
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" List.fold_left (fun accu m -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two i j m a s s *. f_two m a k j s s ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" h_two i j m a s s' *. f_two m a k j s s' ) 0. mos_j'\n",
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" ) 0. mos_virt\n",
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" +.\n",
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" *)\n",
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" let a = 16\n",
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" and j = 1\n",
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" and m = 7\n",
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" in\n",
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" (*\n",
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" h_two i j a m s s' *. f_two a m k j s s'\n",
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" *)\n",
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" h_two i j m a s s' *. f_two m a k j s s'\n",
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" (*\n",
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" let a = 18\n",
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" and j = 1\n",
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" and l = 2\n",
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" in\n",
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" -. h_two l j k a s s' *. f_two i a l j s s' \n",
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" *)\n",
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"\n",
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" in\n",
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" \n",
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" match phase with\n",
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" | Phase.Pos -> result\n",
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = compute_HaaF ki [alpha] kj\n",
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"let _ = integral_value ki kj\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 8. 1 2 22a"
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]
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},
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{
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@ -1478,6 +1695,8 @@
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" | Spin.Beta -> mos_b ki, mos_a ki\n",
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" in\n",
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" \n",
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" \n",
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"\n",
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" let result = \n",
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" (* Alpha-Beta *)\n",
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" List.fold_left (fun accu j ->\n",
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Reference in New Issue
Block a user