{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Getting rid of root at infinity\n",
"**Adapted from**: Section~2.2.1 p. 33 of [D13]\n",
"\n",
"[D13] Dreesen, Philippe.\n",
"*Back to the Roots: Polynomial System Solving Using Linear Algebra*\n",
"Ph.D. thesis (2013)"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using LinearAlgebra\n",
"using TypedPolynomials\n",
"using MacaulayMatrix\n",
"using JuMP\n",
"using MultivariateMoments"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Consider the system given in [D13, (2.3)] which corresponds to `Systems/dreesen2` of [macaulaylab](http://www.macaulaylab.net/):"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "3-element Vector{MultivariatePolynomials.VectorPolynomial{Int64, MultivariatePolynomials.Term{Int64, TypedPolynomials.Monomial{(x, y, z), 3}}}}:\n z - xy + x²\n -3xy + 2y³ - 2xy²\n -2 + z³ - xyz"
},
"metadata": {},
"execution_count": 2
}
],
"cell_type": "code",
"source": [
"@polyvar x y z\n",
"system = [\n",
" x^2 - x*y + z,\n",
" 2y^3 - 2x*y^2 - 3x * y,\n",
" z^3 - x*y*z - 2,\n",
"]"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"We first try to solve the system:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 6 rows to complete columns up to degree 3\n",
"[ Info: Nullspace of dimensions (14, 8) computed from Macaulay matrix of dimension (6, 14) in 8.4166e-5 seconds.\n",
"[ Info: Added 12 rows to complete columns up to degree 4\n",
"[ Info: Nullspace of dimensions (33, 15) computed from Macaulay matrix of dimension (18, 33) in 0.000132997 seconds.\n",
"[ Info: Added 22 rows to complete columns up to degree 5\n",
"[ Info: Nullspace of dimensions (56, 18) computed from Macaulay matrix of dimension (40, 56) in 0.000318782 seconds.\n",
"[ Info: Added 35 rows to complete columns up to degree 6\n",
"[ Info: Nullspace of dimensions (84, 18) computed from Macaulay matrix of dimension (75, 84) in 0.000789476 seconds.\n",
"[ Info: Found 1 real solution\n"
]
}
],
"cell_type": "code",
"source": [
"sols = solve_system(system, column_maxdegree = 6)\n",
"nothing # hide"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"The real solutions are"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "1-element Vector{Vector{Float64}}:\n [3.8420560175113363, 4.99567150625108, 4.432255330406793]"
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"sols"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"## Staicase analysis"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 6 rows to complete columns up to degree 3\n",
"[ Info: Nullspace of dimensions (14, 8) computed from Macaulay matrix of dimension (6, 14) in 4.1076e-5 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"solver = Iterator(system, MacaulayMatrix.Solver())\n",
"step!(solver)"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"We can look at the solver as follows:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "MacaulayMatrix matrix solver. Last iteration considered:\n6×14 Macaulay matrix for polynomials:\n z - x*y + x^2\n -3*x*y + 2*y^3 - 2*x*y^2\n -2 + z^3 - x*y*z\nThe row shifts are:\nMonomialBasis([1, z, y, x])\nThe column basis is:\nMonomialBasis([1, z, z^2, y*z, x*z, x*y, x^2, z^3, y^3, x*y*z, x*y^2, x^2*z, x^2*y, x^3])\nBorderBasis with independent rows and dependent columns in:\nBasisDependence for bases:\n Standard:\n MonomialBasis([1, z, z^2, y*z, x*z, x*y, z^3, y^3])\n Trivial Standard:\n MonomialBasis([y, x, y^2, y*z^2, y^2*z, x*z^2, z^4, y*z^3, y^2*z^2, y^3*z, y^4, x*z^3])\n Corners:\n MonomialBasis([x^2, x*y*z, x*y^2])\n Trivial Independent Border:\n MonomialBasis([x*y*z^2, x*y^2*z, x*y^3, x^2*z^2])\n Dependent Border:\n MonomialBasis([x^2*z, x^2*y])\n\nAnd entries in a 8×5 adjoint(::Matrix{Float64}) with eltype Float64:\n 4.159065386202991e-16 -1.9999999999999998 … -1.9069420129706838e-16\n -1.0 -3.1080979595180984e-16 4.5135339788020976e-17\n 1.1499638451679124e-17 2.176915759031188e-16 -1.2298933558687206e-16\n -1.041204178188655e-16 -3.470680593962184e-16 -1.0\n -7.832624135939215e-17 -2.4017185283265312e-17 -4.699574481563529e-16\n 1.0 -4.3281882871179737e-17 … -1.5000000000000002\n 4.8138576458356415e-17 1.0 -3.677747436866566e-17\n -5.551115123125784e-17 3.8163916471489786e-16 1.0000000000000004\nCurrent status is OPTIMIZE_NOT_CALLED\nHistory of iterations:\n\u001b[1m1×3 DataFrame\n\u001b[1m Row │\u001b[1m nullity \u001b[1m num_rows \u001b[1m num_cols\n │\u001b[90m Int64 \u001b[90m Int64 \u001b[90m Int64\n─────┼─────────────────────────────\n 1 │ 8 6 14"
},
"metadata": {},
"execution_count": 6
}
],
"cell_type": "code",
"source": [
"solver"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"We can see in the border dependence that even if `x^2` is a corner, the multiplication\n",
"matrix for `x` cannot be computed as `y^3` (resp. `x*z^2`, `y*z^2`) is standard but\n",
"`x * y^3` (resp. `x^2 * z^2`, `x * y * z^2`) is indepedent."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=6}",
"image/png": 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]
},
"metadata": {},
"execution_count": 7
}
],
"cell_type": "code",
"source": [
"using Plots\n",
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"Let's do another step:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 12 rows to complete columns up to degree 4\n",
"[ Info: Nullspace of dimensions (33, 15) computed from Macaulay matrix of dimension (18, 33) in 0.000138978 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver)"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"This time, the blocker for computing the multiplication matrix for `x`\n",
"are `z^4` and `y * z^3` among others."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=6}",
"image/png": 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]
},
"metadata": {},
"execution_count": 9
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 9
},
{
"cell_type": "markdown",
"source": [
"Let's do another step:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 22 rows to complete columns up to degree 5\n",
"[ Info: Nullspace of dimensions (56, 18) computed from Macaulay matrix of dimension (40, 56) in 0.000340843 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver)"
],
"metadata": {},
"execution_count": 10
},
{
"cell_type": "markdown",
"source": [
"Now they are `z^5` and `y * z^4` among others."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=7}",
"image/png": 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1GBsb6+jo6OPj079/fxaLhd+Iu7s7vLCwsCgrK4M9ent7w0ITExN7e3t4/fz5c09PT3d399DQ0Hv37uG34OrqCldBeTxeTk4O/l5cRrztgPYIEW0LPp+v/gOiqgBqfwMAMAwTCoVcLhcWamtrtzRRNx1nFyKVKq3bWlNMTKlmFk3pgkKh+Pn5+fn5JSQkPHz4UF9ff/78+SkpKTC1U4cOHfA9VExmYZlEIuELqrLHQ3AdbQDA3Llz58+fP3nyZADAjz/+WHMvFs75oUOHOnToAEvgAxadTod/FLnGa+Ls7Ozs7JyTk5OQkDB37lzZQebm5v7888+pqalQecDCwgIfQM2/Mp1Olz0zhV9HRkauXr161KhRAICIiAi8Bfw2YTwrh8PR19cHLf7glSpoWf8wCIRKgTracH9IY4D6bTAhBpVKxVNEtRztb6I2zXjoiHoqmI6ZoHB8/b1790pKSuB1VlZWYWGhvb19VVWVlpaWoaEhACAxMTEzMxNWMDAwwCsDAOzt7V+8eAEAKCgoqJmzAgJFcAAA5eXlFy5cgIWGhoZlZWXQohAIhMGDB8fFxenr68NdQ2hI+vTpc+rUKXhu8+jRozVb/vLly9u3b+G1UCh89eoV9OEMDAxgQigAQGVlJZVKhRpvV65cKSoqqmcqevfuffv2bbgFePfu3W/fvuG3AOXCi4uLL1++XPONWlpagYGBx44dgyPBcze2HZBHiGgrQB1t2Yd9zUPOTWSz2VKptCVof1vNimK/f8NN/1LzJb3uPmZjwxRu+cWLFyNHjrSysqLT6Z8/f543b15QUBCGYf379+/SpYudnR2BQOjUqROsPG7cuCFDhtjb2wcHBx86dGjt2rWTJ0/u3LkzkUisaz1wyZIlEydO9PLyys/Px+u4u7t37drVxsaGSqWmp6fv2rVrypQpLi4uDg4OWVlZ/fr1++OPP2bOnHnz5k03NzdTU1MXF5eaLVdUVIwePZpMJltaWn79+rVz586rVq0CAIwcOfKvv/6ys7Pr0aPHyZMnfXx8unTp0r59exqN5ujoWM9UdO3aNTo6ukuXLu7u7lKptGPHjrB86dKlI0aM8PT0LCoqwk+0yrF79+6BAwdev369qqqqc+fOTCazYdOvISCtUYTmg8noaDfqjcrSGlUDUCK11pckEgmfz2+69ncTtUYlHHbujq3lCbfA/y/NEUgkk+GjrebMJzbt6UQoFGZnZ4tEIjs7O9m0WRkZGRKJxNnZmcViyQbJwOVxuDBQUVGRn5/fsWNHgUAANbIFAoFYLJZtp6ysrKCgwMXFBZ6uwj8PEomEyWTimRTLy8vz8/OtrKygJwrJzs4mEAg2NjZVVVW15lzMy8srKyuztLQ0NTWVLRcIBDAXJoZhcNezQ4cOTCYTfoy5XC4MqgEy0oD4aEtLS11dXWU/8yUlJcXFxa6urnApmEajiUQiPp8v+5kRi8VpaWlWVlbwlHJLWzhBotsIhOLI6Wg39r0aYAhxMAwTCAQKa38rRXRbWFTIfPtKXFlJNjbW8/IlGxp9/z0IBBLdRiAURnU62q0RAoGAR+vDmVG/9jfF3MJ44FD19IVANBB0WAahsQgEAh6Ph6xgrZBIJDxaXyKRsNnsxoq6KcDDhw+H/TDKwNCUQCCYmLWfEDb5/fv3qusOgWggyCNEaCY8Hg/DMA0Ik1A1+FYT+K+oG5VKVe4y1Jo1MVu3/WbhGmbnv4OqY8Zn5z/5mODj47d7967IyFkKN7tv376nT5/KFfbo0SMqKgpeZ2Zmenl5QT3rWuncuXNsbGxAQECtr965c2flypU1JUwfPHgQGxubl5dnaGjo4+OzcuVKAoHw6NEja2vrWvPXNxwMw4hEYmVlJTws2igWL16so6Ozfv36pgygDYIMIUID4XA4KDm4AsiliILyY0pJEXXmzJnfduzpMui0roEzLKHp2RhY9jC06f/jj7M7depYlx36Ll27doWHUOLi4ggEwrRp0wAAsqbIzMzs4MGD9bSwbds2V1fXRnX64sWLYcOG7dy5Ex7FvHz5slQq1dLS2rx587hx42DQIaIVgQwhQqOAB0RpNFqLVRBtFchpf0MhrqY0+PPKtdbdFuJWEKedhY+l2/SVq9YlPUhQrGV/f39/f38AQFJSEoFAmDBhglAo3Llzp4WFxf79+01NTadPn56TkwMAePjwIZvNHjhwIHwj/mteXl7nzp0BALm5uWfPns3IyDA0NJw6daqTk1Ndnd66dSskJGT69Onw1wEDBgAAnjx5kpGRcf369YKCAm9v7+Dg4EuXLj1+/JjP53t5eYWHh8PjWnFxcT179rx06VJeXl6/fv1w+dDU1NTDhw9LJBLZvBZv3769cuVKQUGBnZ1dZGQkPI+alJQkkUhKSkru3bv3448/Ojs779+//8OHDwEBAejwo2KgPUJEK0ZOWkwqlTKZTF1dXWQFlQiZTIaibgq3kJubm52VbuowqNZXTRwGP3n8QIkqcUKhcPny5dOmTevQoYOLi0tFRcWGDRsAABiGzZkzB9dVWbRoEVS73rVrV3Z2NgDgxYsXRCJx0KBBhoaG/v7+9aiyOTg4PHz48J9//pGVjGnXrp2Ojo6JiYmDg4ORkREA4M6dO15eXn379j127NjixYthtV27do0dO1ZXV7dbt27Tp0+Hgfw5OTkBAQGGhoa+vr4zZ87E27x7966FhcWQIUNKS0t79eoFT/zevn178uTJ9+/fDwoK0tbWnjVr1sWLFwcMGPD8+fM2GAuvFJBHiGjFCIVCfP0TCmSjozEtkMLCQppuOy2ybq2vatPbSyTikpISa2trJXa6ceNG6CnisjIBAQEkEun+/fvBwcEpKSkZGRm4NwYZPXo0AIDH4/Xq1evDhw+XLl2Kjo6utfGwsLCvX79GRUWVlJRAfdExY8Z06tTJwsLCx8dnzJgxsFpsbCyGYVVVVc7Ozn369NmxYwcsj4iImDdvHgAgNTX11q1bvXv33rdv34gRI5YtWwYAMDc3DwwMhDUXLVoEAGCxWL169UpISHjz5g2ULe3QoQMUJi0sLDx9+nRubq6xsfHw4cMblS4YgYM8QoQm0Kp1tDUeBoMhFHAwrPaMiWIhCwDQxPDEmnh4eMiVEAiE8PBwqHZ29OjR8ePH46eEII8ePXJzc/P19R09enRSUlJBQUFdjROJxLVr1+bn53/69Gno0KETJkyomQteIpFERkba2dkNGTJk/vz5paWluOgdrnRjampaXl4OAEhLS/P09ISF+AUA4MiRI3Z2dsHBwWPHjs3Pz8eHhN/d169fraysjI2N4a/du3dv4PwgZEEeIaLVowYdbTxjHDyD09JUrVs4Tk5O2lRtZslbfbNavqarCp/Z2jlBuWclUuvy+JQpU9zd3Xfv3n3y5ElcOBRn3rx5mzZtgm5iRETEd/fbCASCi4vLypUrExMTHzx4gLtxkMuXL79//z4jI4NEIuXl5VlbW+MN1vz86Onp4Z8x/ILD4cyZMyc9PR1Kh3ft2rWmXrbsGwEATCYTN4qIhoP+nxGtG1XraGMYxmQyaTQag8FgMBgUCgVXtW7hyY9aDmQyecbMGXnvdkilIrmXxEJWwce986PnqGcktra23t7es2fP1tPTqykuCjeYAQD5+fkwuW5dJCUlffnyr25qQUFBSkoKPFljZGSEO21MJlNbWxuGoMDEufUQEhJy6tQpmK3ir7/+goU8Hk8qldJoNNjjx48fa77R1dWVRCJdu3YNjgQmPkQ0FmQIEa0YNptNIpHgN4UqkEgkLBaLTqfjEXVQ1ZrBYEDTy2azmUwmjL1T0Rg0gw3r15oZSFMSZrIr0vDC6uI3n++Ed3N3jI6ep7aRTJky5cyZM1OmTKn50qpVq8aOHRsYGDhkyJCgoKB6GsnLywsKCrKxsfHw8OjYseOYMWPGjh0LAJg9e3ZcXJytre2vv/46cuTI6urqzp07e3h44Mme6mLixImdO3d2dnbGM8gDAIyNjSMjI93c3Hr27LlhwwY8X6AsVCr18OHDM2fO7NGjx6BBgxSOQmnjIK1RRKsEhklIJJJahYyVAgwbIJPJsvrLtYKrWgMAmivBRUO0RptIE7VGmUzmosVLjxw+rKtnRtFux+eWigWs+fPnr1sX03IiPqurq8vKyuzs7PDEvHUhlUqLi4v5fL6lpWVd45dIJHl5eXQ6HR4i/S5lZWUSiQRmfcIpLi4WCAQ2Njb1vFEsFufk5Nja2qpIirMlgES3EYj/gOtoczgcFX37Q+1/XV3dRolu46rWGIapOflRyzeEkKqqqmfPnlVVVZmamvr6+n73IQOBgKjUEKKlUUQrQywWs9lsPT091dkYLpcrkUgUsCtQ1ZrBYOjp6cH/WxaLxWazYfgXAgDQrl07Ly+vT58+ISuIaDlorB+N0Eigo6b0o/ayKEuejUQiwadXKFfG5/OBkuTKWjVlZWUBvQMysjIS7yfE30pAthDREkAeIaLVwOPxFHPUGgg8IEqhUJS7ZQXlyuChUy0tLS6Xy2KxOBxOG3QTS0tLA3oHVJCKPTbYpJenBof2kT36rzAYhh07dmzgwIFeXl7Dhg3766+/0IFeRKNAHiGidaBqHW2470in0797SqIpyKlatyk3sbS0NLBPYAWp2C7CmEgiOMw2zvwzPaR/34TbiU18uJk9e/bt27c3btzYpUuXnJycAwcOmJiYDB8+XFkjR2g86LAMoqVTj462sk6IwCy1DAZDzhqpJ0O9SCQSCoVSqRRuMSp2HKCFH5aRs4KwUCqQZv5Z5tDOqSm28OHDhyEhIZ8/f3Z0dMQLuVyujo4On8/ft2/fhw8f7O3to6OjoWJ1XFxcp06d7t+///79+717927dunXmzJm7d+/m8/nTp0/38/ODLbx///7kyZPl5eX9+vUbN24cACAzM/PKlSteXl5HjhwJDg4eMWLEvn373r17p62tHRISAusgVAc6LINou6hBRxvmG2pGeTYYocFgMHR0dMRiMYzWV3WOXHVSqxUEABCpRIfZxplV6SH9+yq8Rnrt2rWgoCBZKwgAgM8uQ4cOffLkydixY8vKynx9fWFWqXPnzk2YMEFLS2vUqFEikWjLli3z588PCgrq1KlTv379SktLAQBJSUnDhg3r2LHjyJEjd+3atX37dgBAbm7u+vXrt27dOnDgQCcnp+XLlz979mzGjBk//PADfBei9YKWRhEtFzXoaKtBnq3hyCU/wnPkamtrq3TBVtVMnT61gPWt41JLAkn+70ikEu1nG39c93HxksX7/9yvQOOFhYW1xti9fPny7du33759o9FogwYN8vT0PHfuXHh4OABgzJgxS5YsAQAwmUwAwNatW2EapvPnzz99+nTYsGFr167duHHjxIkTAQCOjo4hISEwd4RQKDxx4gT0iWNiYoKDgwMDA5HengaA/oSIFooadLShopXq5NmaAu4m0mg0oVCIi7q1RjdxxbIVonJpySNmra8W3a7WJmjPj56vWOMMBgPqVsvx9evXjh074qpD3bt3x0XRoNnDcXb+N0uisbExTGT/6dOnZcuWOTo6Ojo6Dho0qKCgAO7m2tjY4CvDq1at2r9/v62tbURERHJysmKDR7QQkCFEtET4fL5AIFC1jjaJRJLLP9ACIRKJuNIpgUDgcDgsFgtGOjb30BpKr169Eu4kFF9jFt+rlnup4Gol65nwwb0kNzc3xRrv2bPnkydPOByOXHm7du0qKyvxXysrK3ERIrl9ppouXbt27Y4fP56RkZGRkZGZmSmVSuHnRHZ93t/fPz09/datW0ZGRoGBgdBSIlopyBAiWhxq09FuFi20pkChUGCOXCqVKhAIYLR+qwgV8Pf3j7+dUHz9P7aw4Gol86kw6f5Dd3d3hVsePXq0hYXFtGnTqqqqAAAikejgwYP37t3z8/MrKChITEwEAKSlpd25c6d///4Nb3PLli3QuGIY9unTp5p1Pn36hGGYm5vbkiVLWCwW3IBEtFKQIUS0LKCjplIdbSaTKauj3RrBtb9hQHSk0AsAACAASURBVDqHw2Gz2S1c+1vOFirFCgIAKBTKnTt3AACWlpZ2dnYGBgbXrl1zdHQ0MDA4efLk1KlT3d3dAwMDt2/fDldE6XQ6/gBEIBBktWp1dXVhfM7q1avhuqinp6eVldWuXbsAACQSSfbEbExMjLW1ta+vb7du3TZt2qQ6zVuEGkDhE4iWAgyT0NHRabiJamzMgEgk4vF4NcMk6kI94RNKAU6dQCCAS6aq0P5Witboo0eP+g3op22nBYpISfcfym3XNQU+n19WVmZubi73+SkpKTE2NlbgSItEIikuLjY2Nq5rJrlcbmVlpampqeqONCNwkOg2QvORSCRsNpvBYDTqC6tRhlAgEIjF4kZperUuQ4hPBYZhQqFQJBJJpVIlan8rxRACAB49ejRv/twTx04q0QoiNB6VGsJWvDqE0BhgPLtKD4jCLZw2omxJIBCoVCpc5ZNIJDC/KyxsCb5LVx+PmfsmOnd0au6BIBD/ggwhoplRj442mUxudUdjlIKWlhY0/zBFVLOLurGFrJ+uz/hU8v5redrWAfsoWi0lE6FKwTCsqqoK7SO2WNBhGURzogYdbRaL1VzJclsUeIooBoNBIpGaRfsbt4IAgOd5j5beihJKlHDkNS4uLigoyNXVNTAwcN26dfXUfPbs2cuXL5veY0FBwYULFxpen8/nGxoa1nq+9+rVq4MHD3ZxcQkICFi1alVJSUnTh4doLMgQIpoNDodDJBJVtwMHdbR1dXVb9QFRVUAikfBofbg7qwZRN1krCFGKLTx9+nRMTMzatWsTEhI2b95cvwTP+fPnL1++3JTuIKmpqb/88kvT29m5c+fUqVNHjhx59erVbdu2CYXCAwcONL1ZRGNBh2UQzUA9OtqNop7DMnXpaDeKVnpYRjFw7W8ikUilUms+PTTlsExNK4jja91ra3/F10gjIiJ0dXV///13ufKEhIQLFy4UFxd36NBh4cKF5ubmHz9+nDFjBolECgwMdHFxmTZt2ooVK9asWQNjdc6ePWtlZeXv7//06dPs7GyxWHzp0qX58+dbWVnFxcWlpqYaGRlNmzbN399fJBKFh4ffvXt32rRpAIBNmzYRCIS7d++eOXOGw+EMHz58zJgxcAyPHz8+cOCAlpbWnDlzfHx8+Hy+bPqUkpISGxubS5cuDRw4EC8UCARUKlUqle7fvz8pKcnAwCAqKgqeKrp9+7ZIJMrOzk5ISNiwYcOtW7dCQkKOHj1aUFAwbNiwSZMmwRZycnL27NmTm5vr6em5YMECKpXK5/PXrl0bFha2e/duCwuLdevW/fnnn/fv3wcAdO7cec2aNYrNvJpBotsIjUI9Otp8Pr8ZdbRbI7KibsrV/q7HCgIAnn97tPS24n6hm5vb+fPnT506VVhYKFuempo6YMCAJUuWaGtr9+3bVywWm5qa2tra2tvbh4SEdOvWDQCwZcsWXBHm+vXrr169AgC8efMmOjr6xYsXkZGR1tbWGRkZTk5OS5YsCQwMHDFiREpKCpFI7N69O4PBCAkJCQkJAQCcOXNm7ty5gwcPnjZt2qZNmw4ePAgA+PDhw7Bhw/r27RsWFgalSuVITEzU19eXtYIAAGgpFyxYcPLkyYiICDc3t4CAACgOl5SUNG3atJKSkqioKCMjowMHDsycObNnz55hYWELFy6Ehi03N7dHjx4ODg4//vhjWlpaWFgYAEAgEGzZsmXx4sVDhw7t379/XFzciRMnoqOjf/zxxzZyfOy7oCUjhFpRwwFRPp8vlUpbpoJoq0BO+5vD4WAY1pQAjA33ltVlBSHPvz3a9WTTkoC1CjQ+b948DocTExMzceJENze3mJgY6JDNmzePx+N9+/bthx9+OHLkSEpKiru7u62tLcyaVH+b5ubme/bsgdeOjo5isbioqIhCofTt2/fKlSvLli3z9PSEhhDWWbt2bWxsbJ8+fQAAu3fvnj9//syZM2NjY2fOnAllvslkcu/eveV6KSoqsrKyqtk7h8PZt29famqqo6NjcHDwhw8f9u7dC4P6PT09169fj9dcuHAhvNl79+7dv3+/d+/ev/3226RJk6KiogAAPj4+5ubmRUVF0OXdunVr165dAQC3b9+2s7Pz9PTU1dXt2bNno2dcE0GGEKEqJBKJ3IaNUCgUCAQqPSDK5XJVuu/Y1pDNJKxwI3P9ln4u+VjGrfMYiLW+7VTPOYo1TiKRVq5cuXLlyqKioiNHjkyYMMHV1dXd3X3Dhg2HDh1yc3PT1dVls9lFRUUNl7Dp2LEjfp2QkBAZGWljY2NiYvLp0ydTU1O5yiKR6OvXrz/99BOcKLFYXF1dDQDIyMjAlytr7VpfX7+srKxmeW5uLpVKxRNLde3a9dq1azUHBgDo0KEDvDA0NITCqqmpqV++fLl79y4sJ5PJeXl5Tk5Osu+dPXt2eHi4hYVFYGBgZGTk0KFDGzgtGgwyhAhVIRAItLW1cU9C1QmPMAxjs9na2totIVRO82iKR2ijb7d32PG5VybXagut9W33Dj1uomvWhNEBAIC5ufny5cuPHj366tUrIyOjbdu25eXlwacuGxsbfIFXdqWXQqEIhUJ4Da0XRHYjaunSpbt27RoyZAgAYM6cf601gfC/0xVkMllPT+/kSXl9AENDQ5jLAgBQa36MgICA/Pz8jx8/yplJQ0NDHo/H4/GgJ1dWVmZkZIT3JVuz5rKKkZFRVFQUTDKFA28Nv6n27dsnJiaWlZVdunRp4sSJjx496tKlS83htSnQHiFCHahaRxseENXR0UFWsGUCbaGxjrw71XQreOHChffv/113hedcOnfuDFV1YLjCiRMnvn37BiuYmppmZGTgNszFxQXqlCYnJyckJNTaPpTlAwBkZGScPXsWb6eoqAhPeTF+/PiYmBhYTSgUvn37FgAwePDguLg4mPIQLmzK4eTkFB4ePnnyZCjqLRKJLl68eODAATMzM29v7x07dgAASktLjxw50nCnbfz48Xv37s3JyYG/Pn/+vGadDx8+8Pl8Y2Pj8PBwU1NT2RwdbRZkCBEqRw062mw2m06nqy57LZ/PhxkGWrKqdQunpi1Uii9YWVk5evRoPT299u3bjx49+rfffvP29ra1tY2KinJxcXF1db1z505gYCB8Qpo8eXJ5ebmlpeW4ceMAANu3b1+0aJGtre3ixYt/+OEHuC2qra0te4Rk48aNUVFRnTp1CgsLGzt2LPwYu7m5jRo1qlOnToaGhlKpdOvWrcbGxo6Ojq6urnZ2dlevXgUAhIWFBQQEdOjQwdnZ2djYuNZo+v379w8ZMqRPnz7GxsaGhoaxsbE+Pj4AgGPHjl29etXOzs7d3T0sLGz06NFwYLL/RHp6eriTR6PR4EvDhg1bunQpPBZrYWGxcuVKUENb/Pr167a2tu7u7vb29oMHDw4ICGjK/GsGKHwCoSq4XC6VSuVwOI3S0W4ULBZLW1ubz+fT6XRVnL6B4RMAAAKBAEPucFVrCoUiexS+2Wl6+MR3UYrWaG51NlwjVdaKKITP50skErkzkPCPVf+GMVxRr3/q4HqDvr5+/WOA6b3kqsFcyt9Ne1lVVcVgMOSe5Hg8nsI6sXCBpJ5Hw1p7bMkg0W1Eq4TFYonFYn19faUoPtdKaWmpjo6O6o6AS6XSsrKydu3ayQnTyKpaw+y+qrvHBtJaDCEAILcqa3PSmvV9fzPWlV8pRSDqAoluI1ofMExCsfQ3DQTuO6rOCsIHfG1t7ZrybLWqWgPVJD/SAH7duOn589dyhdMPRcn+OnBgyJzZs9U4KATifyBDiFA+UEe7iaou9QMVRNWw74ifKqwLOVVrFouFYZgSkx9pACdO/l0psNE1dK6rQnXxGy7vqooMIYwCrDViD1JYWGhoaFjXQjefz6+qqjI3N2/KGLKzs62srNQm9Zefn29oaKi6/w6FyczMtLOza4H/F8gQIpQMj8fDMIzBYHC5XFW0L5u/t1YV46aDR/03auMAqlrD3SCJRAJ3rVpO8qPmxdi2r4n9gLpezft0DIB3irW8fv36xMREucKQkJDVq1fD69zcXC8vLzySoSahoaGxsbF1nRlJSkpauXKlnFR3Tk5OeHj4gwcPGjjIrl27vnv3zs7OroH1m8jw4cM3bdr0Xd0AOU6dOuXl5eXsLP+88urVqxUrVsBrAwODiRMn/vDDDwqMSiKRODo6VldXqzSSWDGQIUQoEw6HQyKRVHeKBB5baGz+3kYhmxZK4R10LS0teEajhSQ/0mDGjx8Pv/G3b98OAIBiZiYmJniF9u3b3759u54WTpw4gUevNxAOh5OUlIRhmCb9NQ8cOECj0WoawvLy8g8fPty4cUMqlX7+/HnSpElXr16tKZTTqkGGEKEclKWjXQ/qyd8L3VllNSjrJsLxQ1VrCoWC3ESl4OzsDL+7zczMCASCv7+/QCCAImc7duywsrJatmzZ6dOnvb29r127VlpaCpWyAQAXL17k8XgTJ068cuVKWFgYg8FITk7+888/MzIyjIyMZs2aFRgY2JABbN++vWfPnufOnUtNTe3Tp8/ChQvhUcyXL1/+/vvvPB5v/vz5svXPnDlz6dIlqVQ6YcKEkSNHAgDu3r2blZXF4XBu3rzp4uISExMDox3EYvEff/zx4MEDBoMRFRXl5+cHADh27JiZmdmrV68ePnzYrVs3XDQ8IyNj48aNJSUlUNQNJyEh4dixYywWa+DAgREREQQCITk5+dq1ax07djx48KC+vv7q1atdXFwuXrz45cuXP//889atW4MHDx42bJhsIxQKpXv37gAAb2/vkydPvn79GhrClJSUnTt3FhQU+Pn5LV68GH7Oo6KipkyZ8scff9Dp9NjY2AcPHuzbtw/DsAULFuANYhh2+PDhmzdvamlpTZs2rX///gCAq1evstnsgoKC+Pj49evXw0gS9dDi1moRrRH16GjzeDyVWkFVp4VqluRHbRCRSHTgwIFVq1ZNnz597NixTCbzyJEjAABLS8vly5fj+RfXrl0L7c3Zs2ehYHdBQUHv3r23bNkCM0ikpaU1pLurV6/OmjXL399/6dKlBw8ePHnyJAAgJyenf//+oaGhP//882+//YZvE2zdunX37t1z586dN2/e6tWrz507BwBITk5euHBhaWnpxo0bhULh4MGDYeUpU6Y8e/Zs5cqVI0aMGDly5OfPnwEADx48iIyMNDc3j4mJefTo0aZNmwAAHA4Hxg6uW7fu2rVr+MgvXLgwd+7cCRMmLF++/NSpU1u2bAEA5Obmbt68+fbt2ytXrrS2tobG2NfX18LCIjQ0dNasWV5eXnL3KBQKX79+/fr16+PHj79//x664Pn5+T179uzSpUtMTMzr168nTJgAKx88eHDx4sVhYWFTpkxJTk4eOXLkyJEjFy1aFBMTgze4YsWKU6dOLViwYMaMGVFRUXBx+/Xr13PnzuXz+atXr65nT1clYAhE0xCJRNXV1VKpVK6cw+FIJBKldMHlcqH0sxxMJlMp7Uul0urqaqFQKFcukUhq7VeJCIVCNpvNZDJZLJZIJFK4HWVNRT3o6elVV1cr8EbXTh5uwb/3npFa108Hv5/7hg5q4vBmz549Z84cDMNYLBYA4O3bt7A8IyPDwMAAXnt4eFy5cgXDsBcvXpiZmcEJd3Nzg+ucGIbx+fzPnz+/evVq9OjRO3bswDDs9u3bXl5ecn1BLRj4mQ8MDPztt99g+datW2fMmIFh2Jo1a6ZOnQoLv379CgDIysqSSqV6enppaWmw/J9//gkNDcUwbNeuXW5ubrBQKBSampq+evUqIyOjXbt2MAwRw7B169YtWbIEw7Dp06fD28Qw7OLFi0FBQRiGHTt2rFevXrAQHvKKj4/HMKxbt27Xr1+H5R8/frS3t8cw7Pr16xYWFmKxGMMwkUhEoVBKSkowDAsKCrp48WLNib116xaVSg0JCenTp4+dnd2oUaOqqqowDFu/fv3o0aNhnYqKCiqVmp2djWEYmUy+e/cuLJ83b96iRYvg9YsXLwAA1dXVHA6HSqUWFxfD8ri4uPHjx2MYFhMTExISUtffl0QiNeUfpH7Q0iiiSahBR5vD4WhpaanuCBzcd1SpME09yKpaQ68XoN1EZeDi4lKzMDw8/OjRo0OHDj169OiUKVPkjnFeunRpwYIFHh4eRkZG6enpDd84tLe3hxft2rWDwp7Z2dlubm6w0NHREe6aFxYWslgsmBoJACAWi42NjeE1rohNJpM7dOiQlZVVUlIiFAr9/f1huUAgwLflHBwcanaHt6Crq2trawuv09LSli1bBjMOYhimpaWFYRgAwMbGBn7aSSQSg8Gorq6W3VWtiYmJSXx8PGxkypQpCxYsiIuLy8rKwuVVDQwMLC0tMzMzYdf45GdnZw8fPhxed+rUCV5kZmZKJJJBgwbBX0UiEZQFB3X81dQAMoQIxdEAHW3o87WEzIV1JT/S1tZuRfIfLYdaJ23SpElr1qwpKCj4+++/8RQNOD///PORI0egvZkyZUrD+6pV/Lq0tBReV1dXw+PNRkZGRCLx2rVrNYMx8Mrw2tjYmMFg6OnpvXz5siGfTCMjozdv3sBrDMPwpBampqaxsbG9evX67oDrKqxZx9vb+/DhwwAAY2PjkpJ/VdQlEkl5eTluTfHJl50HvDLM4JGUlFRzG0JtESZyoD1ChILAbQ+V6mgzmUyV6miLRCJVn75RDDKZTKfT4W6iUCiEOXLhKllzD611Y2pq2rdv3/DwcHt7+5qpkTAMg2kiPnz4cOnSpaZ09MMPP5w6dSo/Px8AsG3bNvgBo1KpY8aMWbZsGTxFzGQyYSpgAMDjx4+fPn0KAPjnn3/YbLavr2+XLl1MTU03b94MtRoKCgpSU1Pr6m7gwIF37979+PEjAODo0aO4yZk0aVJMTAyU1ebz+Y8fP65nzGZmZp8+fYIKgnJIpdLKysqKiopXr17FxcXBLIbDhw//+++/MzIyAAB79uxp3769q6trzXmIi4srKyvDMAwe6wUAmJqaBgcHL1u2DO7XVlRUvHunYPCMskCGEKEIUEf7uwqKCgPPkujp6alUR1sgEKhalqyJEIlEGo3GYDCgOgGHw2GxWFwut9ZvqzaOoaGhoaEhAIBIJDo4OOAPNyQSSfbkRURERFZW1myZ4H0LCwv4Sd6+fXt0dLSNjc1PP/0UEREBW6PRaDUdODKZbG1tDbuwtLTE5Y309PTMzMwAAEFBQfPnz+/WrZutrS2BQOjSpQv0dWJjYykUioODg7W1dbdu3XA3buDAgWvXrm3fvv3ixYvPnj0LT19fvnz5yZMnVlZW1tbWISEheXl5AAATE5N27drBd9FotPbt2wMA7O3tY2Nj+/fvb21t/eDBg8GDB8OthFWrVkGbamNj4+TkBMNIdHR0LC0t8XuxtbWFz5rLli1LSEhwdnb+/fffZW9WR0dHW1vby8vL29t79uzZAwYM2Lx5MwDA39//119/7dOnj6Wl5d9//33u3Dl4j/b29vi/7fDhw0ePHt2pUyc7OztbW1sHBwcY+HT8+PGKigpbW1tra2s/P7+UlBQAgIGBAZ5wSs0grVFE48Bk4tnrr8nlchUT4RSJRHw+vyEmSmGBTS6XC3W0668GRbdbWppfXPubQCDA3UTQsrVGO7p15RA99Uw96qpQ/u2Bm50g4c71pg1QOYhEImUtQsDTNLU+zMn2snv37pcvXx4/flwsFtf8t8IwTCqVNvCJsNYWgFJvqiY1U3DXrEAkEmtdd2n4wJDWKKKlAB01lcazq3rfEfy/PFvrFQWVjdaHh04xDOPxeLq6ui1QvAoAEBTYK+nhE2lxnctfBhTg7zesrlfVjBINRj1/jlp7qfVbnkAgNHxdpC47odKg1e8Or54KLSSaFhlCREOBGUpVuqMGHTXV7Ts23J1tFchpf0NRN9DytL8NjfQMjb/jfBsYfifJkQYzcOBAGCyPaC404esAoQZkhcdUhKodNTW4s81ITTdRKpW2EO3vS5cvVhgU0W3q3FGuTuNev6W94KcFdVVoyRQVFUGdBIVbwIMHlEtOTo6lpWULcblaOMgQIr4PPCCq0jAJVTtqapBnayHUmiKq2bW/9V11jLrX+fmRiqSgWsGWf/755zt37gAA6HS6g4PDiBEjhg4dqmBbCjF79uwRI0Y0KtwCAHD16tX27dt7enrKlWdkZIwbNw5em5qaDh06dPbs2Yp9aP38/O7evYvHFyLqARlCxHfQMB3tNoVciiiN1P7Oysrq0aPHTz/9VFhY+ObNm8jIyIsXL8JAt5bMmTNnevToUdMQ8ni8N2/efP36VSwWp6enR0RE6OjoNNbKIhoLMoSIOsGQjramoNna3wYGBo6Ojo6Ojr169QoJCenatevUqVODgoIAABcuXDh16hSLxfrhhx+ioqIIBMLz589v3bplZmZ25swZa2vr9evXQ10YqVS6d+/emzdvksnkadOmQT2Uv//+m8PhFBQU3Llzx9nZefPmzVALJi8vb9WqVdnZ2SNGjJA9eP/w4cN9+/aVlpYGBgYuW7aMSqXm5ORs3rx52LBhv//+O5lMXr58ea9evW7evPno0aOUlJSkpKTg4ODZNRIxQu0YZ2fn/v37v3//HhZmZmb+8ssvWVlZXbp0WbNmDYw0mDt37ogRIw4fPlxVVXX9+vXnz59v2bKFzWZHR0fLNnjs2LGLFy8KBIKxY8dC2fGEhIT379+TyeQLFy4sXrxYzW50S0MDN0sQSkENOtoCgaC162i3RjRb+7tTp04+Pj5QxDkuLm7Dhg0LFy7ctm3bhQsXtm3bBgDIy8vbtm0bzLTg5ubWp08fKPuyYMGCO3fubNq0acmSJUuXLoUhd58+fVqyZImJicm+ffuYTOaiRYsAAGKxOCQkxNbW9s8//ywpKcEVau7duzd58uQpU6bs2bMnLS0NmqKqqqqjR4+eO3du69atQ4cOHTFiBJfL7d69e6dOnUJDQ5ctWzZw4MCad/H69evnz5+fOHEiPj4eJv+rrq7u0aOHm5vb3r17pVJpaGgoDLS/cePGkiVLwsPD165dm5eXN2DAgFGjRv3+++/Hjx+HcfQAgO3bt+/fv//nn3/+5ZdfYmNjDx48CADIzMxct25daWnpzp07u3XrpvI/TAtHRRqmiFZNXTrajaJ+0e26dLQbRT1K03XpaDcKNYhuK4smim7j2t9sNrsuaWPFRbc7uzhFWPj96VzXj91Yk779gxUb+fjx41evXi1bMm7cOChL7eTk9ODBA1j4+vVrV1dXDMPOnz+Py21jGNalS5dLly4xmUwKhVJRUQELDx8+DGWgV69ePXLkSFj48uVLR0dHDMPi4+OdnJzgf4dUKrW3tz9y5AiGYQMHDoyLi4OVq6qqtLW1xWLxu3fvqFQql8uF5ba2tm/evMEwLCwsbM+ePTVvB6rDhISEhISEdOvWLSgoKCcnB8OwAwcOBAQEwDoikcjc3Pzhw4cYhtnZ2Z06dQqW//rrrxMnToTXMJ/G58+fMQwzMjL6+PEjLI+Pj+/ZsyeGYfv373d3d1doypsHJLqNUCtq0NFms9l4JLgqaF4d7daIJml/FxQUODk5SSSSzMzM8PBw/DOA6yc4ODjgx7JcXV2zs7OzsrIkEols+iGYfg8AYGNjAy/09PSYTCYAICcnx8nJCU4LgUDAM9mmp6evWrXql19+gb9aWlpCwTYTExO8a319fdhIPRAIBKhwDQCIiYmZNm1aYmJiTk4OLmBGIpGcnJyys7OhiGiHDh1geU5ODj4Yc3NzKEBTWVlZXl4+bNgw/O9oYWEBL/A3IpAhRPwHNehoq3rfseXoaLdG6tH+bu6hNYj09PQXL16sXbtWS0vLxMTk3Llz3t7ecnWKi4vx66KiIlNTU5jU98OHD7hYGk7NT5GJiYlcC/DC3Nx8zpw5eHIJSGFhocIK1wAADw+P/fv3AwBMTU3xzULYLJSuBjLh6rID43K50OLq6+vTaLT4+PiayTTQYyIO2iNE/A816GizWCxV5+9tI2ESakBO+7u5h1MnlZWVmZmZb968OXToUGho6IgRI4KDgwEA06ZNW758OUzFUF1dff/+fVg/Ozv71KlTAIB79+69f/++X79+ZmZm/fr1W7BgATxYm5+f//Lly7q66927d3Z29o0bNwAAly9fhouZsLtff/01OzsbAMDj8eAuY11YWlq+e/eusrISz9krS2ZmZmZm5osXL3bu3AmzYQwbNuzBgwdQNfvIkSNcLhcqX8sycuTIs2fPpqenYxi2ceNGWEgkEsPDwxctWgQTNpWXlz969Kj++WyDIEPYRpFKpXL/gSwWi0wmq1pHm8FgqFRHWygUtvEDoqoAan839yhqx9TU9MaNG/369YuMjIyPj9+6dSs0cgCAtWvX9uzZE+Ze79at2+vXr2G5v7//nTt3LCwsIiMj//77b3gQ9Pjx41Kp1MnJydzcvH///t++fQP/lYEmk8kw2Z6ent6FCxcWLVpkbm5++vTpyZMnw4/ctGnT5syZ079/f3NzcxcXl1u3bgEAKBQKvrgKALCysoIzOW/evIqKip49e65fv172digUir29fWhoaGho6MKFC3v27Ak9Qjs7u9OnT8+aNcvMzGz//v1XrlyBzquNjQ2+xeDp6fnLL78EBwfb2NiQSCRvb28oT7Fjxw5HR8euXbuam5v36NEDZrrH9cERAIlut1mkUilUpwT/v1ypq6urXBMlK7rdcB3tRiGrNM3lcpW+gtcyRbdrpUWLbru7VpuX0O3r/NNUJXO66Hkl3Eps2gAbxIULF/bu3VszGSGihYNEtxFKIyMj49y5c8uXL8dL4I4anU5HOtr1IJFIhEJhS5Ara42E9g1NvH8XlNZZwQQY9B7cR40jQiD+AzKEGgWfzz9y5MiHDx+MjY3DwsJq5snMyspKTEzEDSHuqCEd7XqAs0Sj0VqIXFmrY/fve5p7CP/D19cXroUiEDjIEGoOHHGkHgAAIABJREFUPB4vMDDQyMhoyJAhlZWVHz58qGkIZYFxxKp21Gg0mkodNSaTqeq0UFKpFM4StLUYhgmFQg6HA7PEKZZzEdFcWFlZyebpRSAAMoSaxM6dO3V0dG7evNkQ9w46NzUPiysL6KgZGBiozgqKRCIul2thYaFSdxbDMDl3trUkP0IgEA0EPclqDrdv354wYcKpU6c2bdr09OnTuqrxeLw5c+ZoaWmp7hwgLs+muuVKKCGt0kVdFotFIpHqnyWY/IjBYNDpdAzDoDgLfMhQ0agQCITSQYZQc8jOzt6+ffvz58+JROKIESP++uuvmnVKS0tfvXrVsWNH1fkuYrGYzWbr6empbsGQy+VKJBKVRv0zmcxGLepCN5FOp+vp6VEoFB6Px2KxoFyZigaJQCCUBVoa1Ry0tLR69uy5e/duAICDg8PixYsjIiLk6jAYDA8Pj/nz56vIZVFDwiN1poVSbJbaQvIjBEKTQIZQc7CysnJxcYHXrq6uBQUFMNWObB1tbW3VWSlVJzxSgzybctNCaVjyI0NDQ319/eYeBaKNYmxsrLpFJmQINYeRI0fiWr2PHj3q1KmTOk8zqsdRU6mOtkrdWRKJBHdMoaq1QCDAMKx1uYlZWVnwQiQSSSQSlaqPwlkSi8UYhvH5fGNj49YyS4jWCDKEmsPMmTNPnjwZFBRkYWFx7969s2fPqqffVueo1Yra8vfKyt/Ag68wNlFbW1t1Z4taHWiWEOoEfaQ0Bzqd/vTp04cPHwoEgn379hkaGqqhUzU4ampIC6Vqd7YuNCn5keogk8lwzxXNEkJFIEOoUZBIpD591CdVpYaERxqQFqoh1JP8COXKwUGzhFARyBAiFAQKj6nUUYM62ipNC8Vms5WuNt5EZN1EgUAgFosBABQKhUKhIAcIB80SQokgQ4hQBM3Q0eZwOCoNyW8issmPoKgbhmFaWlpUKrVFWe7mBc0SoukgQ4hoNGrQ0a6srCwqKjI2NsbTcCsXkUhUWlpaVVVlZ2en3CxLGRkZq9ZsktaW3Gz61HH9+4Uq1iz0dQAAEolEIBBIJBICgQD3yZoyWg0DzRJCMZAhRDQOVTtqQqFw1ZoNp05fpBs5iwXV2iTeoQO7fH19lNhFRkbGrDkLMrKKaXrW7MoMf7+usX/8pqyzRWlpac8/sgwdxsmVVxe/sUlMUtgQ4kBRN/D/2t9sNhs6QFDvFAGRmyWkkI6oH2QIEQ1FPQmP5s1fkvRW3KHvOQJRCwDAY30bM2FW4u1zTk5OSumioqJi4OAx9A4L7YO8YUlKzp0Bg0c9f3JXWWukNLoZw9hNrlDIKwPgm1Lah8hpf7PZbBaLBZD2939BCumIhoAejhANAiY8otPpKtXRrqysvHn7voV7NLSCAAAaw9rQ5cdfN+1UShcsFuvq1WtaBgH65t54oZFtv2qB2aNHj5TSRbMAJdSR9nf9IIV0RF0gQ4j4PmKxGIZJqG5ZCX4fFRYW0o1cAfiPZ6Zn2vXtu49NbB/X0X77PoWi30XuVSKjy4cPTe2iJYC0vxsCmiWEHGhpFPEd1KOjTSaTKRSKrq6uVMSWe1UsYtHpTcqbKKujra+nKxGx5GtI2HS6piVrrUv7m0KhoH0yHKSQjgDII0TUD4/HU3XCI9nTN46OjhJ+gZBbKlunMvufMaOGKtyFXFqoH4YN4hZeA+B/xzoxqZhbdCc0NEThLlo4UJmMwWAwGAwSiQQdIA6HgxwgWeRmicvlollqOyBDiKgTDodDJBKVG10gC3TUZPP3EgiEg/t35T6dW557Vyxg8ljfij/9bqj1MWqOfD6pBiIQCHg8nqz2jaen5+BQz9xni9jlKRIRh1nyLvvxnOg5ky0tLZVzVy0bEomkq6vLYDBoNBp+xIbP52NYbQEfbRU0S20NtDSKqAW16WjXjGfv3Tvw2aMbGzb+9urVOUNDw4iZQ6ZN26vYUl5dOtp7dm0dcffe7r1x2cnZrq4uf53+3dPTU/E7+S9EIrHi231MVC5Xzq4u0OoeqKxemk6tqtatN0WUiqhrlqhUKtL+1iTQ3xIhj3p0tOvZd2zfvv2fe3c0sYv6dbSDg/sEB6tElDU4OPjaP4drfcnBwUEVPTYdOe1vtE9WK0ghXYNBhhDxH9Sgow0dNZUK0zSjjjaFQunevbv6+1UKtapao+RHcsjOEozW19HRQeePWjXow434H+pJeASD3lTUvhrc2TaCnKo1fHyhUChIrkwWXNQN0apBhhDxL2pIeMRms7W1tVXnqKnBnW2D1FS1FgqFGIaRyWT0tIHQDJAhRACgeh1tNSQ8UkNaKAR0gEQiEVw8gHJlyE1EtHaQIUSoKeERnU5X3T6KGtJCweOCqmu/dQEFrEEN7W+U/AjRGkGGUHPgcrkpKSn4r7a2tsbGxvW/RT062mrI36vqtFAsFktLS0sqlUJ1LhRggCOnao3cRERrBBlCzSEtLc3f39/d3R3+unLlyhEjRtRTH+poQ+ExFQ0JxiC39vy98PQNnCWU1qceUPIjRCsFGUKNwsLC4tWrVw2pCePZzczMVHeuhMvl0mg0KOSoCqCjZmpqqlJ3lsfjmZiY4LOE0vo0BDRLiNYFekzTKKRS6du3b9PS0sRicV11MAw7f/48j8erqeqiRFgsFolEUl2YBHRnZeXZlA5UG6fT6XXNEkrr0xDQLCFaPsgQahQ8Hi86Orpfv37u7u6fP3+uWYHP5799+/b48eMqDZOACY9U9+yvtrRQDXRnUVqfhiA3S3w+H80SooWAlkY1h06dOhUWFpJIJKlUGh0dPWvWrJrJZlksloGBwcWLF1U0BtmER0KhUBVdqDMtlAJeC0rr0xBkdxPRLCGaHWQINQf8kB6RSIyIiPD19a154t/ExMTe3h4egFT6AOC+oxrk2VQd9U+j0Zq+4gqVyWCMAZwZpGpdEzRLiJYAMoSaSUpKiqmpqTqP6qlHnq0eHe2mA6P+VRHvSCKRoGWFes0CgQAqsyAHSJa6ZgklP0KoGmQINYcdO3aUlpY6OztnZ2fv3r1748aNautaDY5ac6WFUi4orU9DkJslHo9HIBCQ9jdCdaBPlebQt2/fS5cuPX361MjI6Nq1az179lRPvxqgo11/WigVgdL6NAQymQwPnaJZQqgOZAg1Bw8PDw8PD3X2qBk62nw+XyqVqk6Y5rvUmvwIFiK5Mhw0SwjVgQwhQkHUoKOttrRQ8ARjS0Au+RGMB4VS18gBwkGzhFAuyBAiFAE6airdUdOAtFBNoWbyI6RqXRM0SwilgAwhotFogI626txZJpN5+/btWl/y9va2s7NToE08+yuuak0gEOA+WVOGqmGgWUIoDDKEiMahhoRHSUlJW1avzv+WS6JQ+g0e/PO69cq1iCKR6M8//jgdF8flsPXbtZu3bPmYceOU1fjjx4/nb4jSc5U/OsQp4k/oNWXbxm1NaVxO1Vo2+VFTmtUw6polpP2NqAtkCBGNQA0Jj44cOrR//bpFJvr27Y3EGHbj1rWg6zfuv3ypLNMrEonGDhlimP11k5GebjujCpH4z5XLn9y/tzP2T6W0j2GYXgcdw77acuXEZCkGlCZiUDP5EZvNBij50X9B2t+IBoKejxANRQ062pWVldvXr99qZWKvow0AIBEIwwz1BhLFu7ZtVUoXfD4/MTERy0yfY2qgq6UFADAkk362MHpx82Z6erpSulA/0AGi0+nwAQWqWsMIxeYeWgsCaX8j6gEZQsT3UZuOdlFRkQONqqP1n49lkB797q1bTe+Cy+ViGPbk/r0AsvzHvheV+DApqeldNC+yqtZUKhVqf7NYLBWJvrZSkEI6oiZoaRTxHWR1tFXUBa6jLZFISDVOoZIJhHqySjUQPH+vWCQiEeX7IGFAw6yFnPY3i8XCRd3QPhkOUkhHQNC/BKI+xGIxm81WdcIjiUQCtwCdnZ2/sHni/2pLvmCyfXv2Urh9OXfWLzDotVB+Ney1lODr56dwFy0ZqEzGYDD09PTIZDJygGoFnyUGg0EikbhcLovF4nA4aJbaCMgQIupEIBDweDyVqrpwOBwikYjHs1Op1Bnz5v1aUM4US2DJWyb7OEe4aOVKxdqXSqVMJpNOp+MalUOGDs3Wa3e1vBoaWzGGHSut1HPt2K1btybeS8uHRCLp6uoyGAwdHR2JRAIXTvl8PlK1lgWfJRqNJpFI2Gw2miWNBy2NImqnuXS0Fy5fbmljvWTtWqJQKMQwZze3a1f+NDc3V6CLWtNCEYnE6/fur1uxfNqVK9pEggAQJkydum3Fz029HxlY+Vzstbwnwf0mAC3G1MrJlaHkR7WCFNLbDgT0mNOmSEhI2LJlS3x8vFQq5fF4dWVgV0rCIy6XW1fkVkN0tPl8Pv41VBdw87LWl6A8W/2G/LtdSKVSPp/fKAG2wsLCv+L+ktYWKTG4/2BvL++GN9Uo6pmKBgJVreFiYP37ZCKRSCKRfPevoyyafmtKpOGzhGhFoOcaxH9QW8Kj7664NuV7toHurCq+yi0sLNasXKP0ZtVArarWKPmRHLKzhIu66erqoiNIrRr0+Ub8D/UkPFKPjvZ34x3fvXs3dvw0aW0LIosWzJ0ze2bTR7J+w5ZjJ87ULCdpEe7c+sfGxqbpXagIOVVrlPyoVnBRN0RrBxlCxL+oJ+FRy9HRLikpIRv4m7rNlyuvyH+clqac4PoPyakGbmvphq5y5UXvYiorK1uyIcSRVbXG98kkEgnaSkRoEsgQIgBQl442kUhUqY62qt3ZNg7uJgoEAly5BiU/QmgAyBAi1KGjjcezq6h9NbizCBzoJsrtk6HkR4jWCzKEbR016GizWCwdHR3VHbhQgzvL4XCkUilU50KrgrKg5EcIDQAZQk2DzWb37dvX3Nz88uXL362sBkeNy+WqVJ5Nne4sTOsDjSJK6yOHXPIjNEuIVgQyhJrGihUrqFRqfn5+/dWgo2ZsbKxSR00oFOrr66tuuZLH45FIJFW7s0ZGRnCWUFqfhoBmCdHqQE9qGsWTJ0+Sk5NnzvzO0f+Kigomk6mrq6s6KygQCGCYhOqsIIvFakiYhMJIJJJ6Zgml9WkIaJYQrQLkEWoOPB4vMjLy7Nmzr169qqdadna2v7//p0+foNa+KuByuQAANew7NqUROp1e8OUiq/ixXDmfxzL0n4lH/QsEgvrbkXOA4Lc8LDQ20n98ZSmZIm+qWVWFOjobmjL4Vkc9s4T2XBHNDjKEmsPq1avHjx/fsWPHegzht2/fSktLk5OTVaqjDeXZoDlUOspKC+Xv719ZXljrS7jaeGMdF7m0Ptu2bNi2ZQOKQ5cDJT9CtDTQ0qiGkJKScvz4cU9Pz4SEhE+fPjGZzISEhJrf49bW1t7e3lZWVqoYA0x4RKFQVHdiUM1poRQGpfVpCGiWEC0E5BFqCHw+v0uXLjt27AAAFBYWFhcXb9myJSAgQG2n2NUQz47n71VR+0BJauNykEgkuMsI9ZoFAgGeIxc5QDj1zFJzDw2h+SBDqCF069YtPj4eXh8/fnzXrl34r2qggTraTaG50kIpEZTWpyHUnCU2m41mCaFS0AdLA7GwsPDx8VFbd+rR0Va6oyaL+uXZZFWthUIhUrWuFThLUqmURqOhWUKoDmQINZCQkJCQkBD19KUGHW1VO2rNK89Wa/IjWIjkynDQLCFUCjKECMVRg442m83W1f2/9s47IIpr++OzvS9NRAw2iKhYYjSaqEEwoVjAJ3aMGjWJNepLfFHzkvg0eSmmaDBFUWOssWAHKyAWRCO/p9groMYCFsr22TLz++Mmm3V3WZbdmd1h93z+gtnL3MtdmLPn3HO+R9Ko20I5j1XzI6PRiIGqtQ2wSwDlgCEEXESpVDrZ8Mg1kKMmk8kab1sol7FsfgSq1nUBuwRQBRhCoMGgcCWtjpoPtIWiCltVa6RbZnViqlKpMAxjoFH3DKD9DbgDGEKgYSBHTSqV0lfJV11dvXH9uqtnzwUEBw8eObJXr16UT3Hx4sVdW7fev10eFRMzftJbzZo1o3wKkiQnTp5w8dLFY7nHKTG3ZlXrNyaOOX7mKE/wpy+OPGaSJKvv1RYX/d/zzz/v/lyNFyvtb5VKBW4iUC9gCIEGgBw1WsOV586dmzBs6Gt8dg8hX2k0Lty7u+UrvVdu3EjVjCRJZnz7zaYffxgm5vcW8G//73TyihULly5NGzackvubZ3lr6ltFDwq4L2CxCa8ezz1Boa+m0ihDhgtEza0FrLlb2PUKwvkPVqJuyE3EQPsbsAcYQsBZUGIC3Q2Ppo8f/3GQpI34z0qy3kHYkjOnNm/aOGbsOPfvbzKZLly4sOmHZT+0DOOyWBiGdZRJ4oNM7773Xly/14KDg92fAvvLChbeywsZLMIwrJZV1TcxllpbWBcajUahUHC5XGh+ZImtm0gQBAqcwi4BGEisAU6CVJKRRCQdIHm2x48fi7RqsxVEjAyUbFmzxv0pUNp97v79g8UCroV/KeFw4kR8qvQHrKwghmEBXUX4i1V9E2OVSiUlU9QFi4WJxWK5XC4QCLRarVKpVCqVer2e1kkbF8hNlEqlcrmcz+ejXVKpVCDq5ueAIQTqR61W09rwiCAIhUIhlUpra2tDeNYHOU34vMePH7s5BRJ3lsvlTysrg22mCCGJx48euTkF4tq1a7v27gxMfiZHI+AFUSX+YNeunZRMUS9I1Ro1P0JaAdD8yBbzLkkkEpPJBLvkz4AhBByBEkRpPVax1NFu1arVba31KdcttbZtdLQ7U2g0GrOO9vMdY8r0JqsB5WyOm1OY6dChQ+YPKx+uVpt0fz1PSezRLs0/YoeOH/8mJVM4j1nVWi6X83g8cIDsArsEgCEE6gQ5anT370UNj1AuTHBwcNsXu+2rqjUP0JhMK6pUM+d/6PIUyJ01Ny8cMWr0IZ3hnu5vc3tVpblEsl977TWXp7Bi5PCR3y34/uEvapOOQFYwqd2g5ctWUHV/1+ByucgBEovFyAFSKpU6nY4kSe8ujFHALvknkCwD2MdbOtorN2yc+ub4f54921nIU2Oscxrdf77+pkePHi7c3648W2Bg4IZdu6eMfSNCoQ1nY3dMmEoeuP3ANmqVAUYOH0kQxNwv5nCbYAO7DPlxyU8U3hzDMKOOMGqs/VqTwamYnpVcmVn7m8/nQ49cM7BLfgUYQsAOXtTRlkqlG3fsvHPnzoULF4KCgrp16+ZaJ3oHOtovdut26uKl8+fP3717NyoqqnPnzi7+Dg4ZPXI0i4Wdv3T+i0VfUnvn3j37/LHzDyszaCKIEJ4wJCSkQbey0v6GFlF2sdol6CTse7DA5fcr8vLyFi9enJubSxCEVqu1mwWKHDXXzI8lGo3GbhI/hTraqFW97XXkzrpf70gQhE6nc38rPEBdW+ECBoNBr9cTBIEOz2wD4waDwWQymZsl0Q2FvxqF6PV6vV6PqvVFIhFYxEYNeITAM3ggQZTuhkdOurP37t37asmXhL0PgiP/MTI+Pt79lezN2Xsw/6DtdS6bs+jjT4OCgtyfgg6gRZQzWIq6eXstgLuAIQT+hCRJlUrlAR1tWs8dndfRvnLlyp7ft8t6WGfDqu/qePu4lBjCdZvXlrCKBE2s91NZYHxr/NuMNYRm6jonA60yS2A3fAAwhACGeaThEQN1tMWhooAONqLMlJ4VSNsIxRHWU5guN768fEs3UaVS4ThuMBig+RHgG4AhBDyho+2Bhkd01zsCCNT8iM/nC4VCaH4E+AZgCP0dzzhqLBaLvoZHKPtGLBbTV+9oMBhwHDcfCwEIaH4E+AZgCH2Hy5cv//zzz+Xl5Xw+PzExccqUKfUaBp1OZ5ZcoQm6HTWTyaRSqWQyGd3urEQisWzrA6rWllipWqvVaoIgYJeAxgIYQt+hqqoqJiYmLS2ttrb2448/vnfv3pdfOqpg02g0UqmUbh1tqVRKq6NGd/aNRqORSCTInbVs64M+Q2DQ1udZrJofwS4BjQIwhL5DbGxsbGws+rq2tnblypUOBiuVSi6XS1+ZBJKnatKkCa3ybDiOU9U7yS517RK09XEG2CWgsQCG0KcwmUyomdGWLVsGDBhgd4xCoUhKSsrJyaFPU9hcz07f8w4Vt7lz7shisRTXNSzS2pVUPzKwY9nmqn+j0ej4JpYOEOpdgC7yeDwOm60oNOBy6ylqylR+lWnpeJe8vToAAEPoW5SWlr7yyitqtbpbt24zZ860HfDgwYOSkpLt27dzuVyaDCGO43q9Xi6XazQaOu6PYZharebxeHw+350Of7GxsRt++M3uSx06dFAoFOjo1LEhtAS19cEwjCRJ1PXpP/MX3blzh8fjWZk9NpsdExPj8sobNba7hEG1PuBtQGLNB8Fx/P33379y5UpBQYHVS4cPH/7vf/97/PhxBxJr7mApz1aXxJo7oKp/kUiEIq50iG9ZyrO5L7FmNBpxHPeAXrMndcgol1hzvEvMlFgDfAnwCH0QgUAwZcqU7t27oyeL5UtsNpu+1Pa6dLSpApVy01rvaHZnqbohl8tFNhtUrR0AuwR4FzCEvsOtW7ciIyPZbDZBENu2bevUqZPHUhIo1NGuC6p0tB1g2xaKxWKhrB/3H8pIrgx9bSlXJhAI6MsnanTY3SWNRmOOAQAAHcDflu/www8//PbbbxEREZWVlU2aNNmwYYNn5vWMjja1jpotdt1ZFotlPimksCMdqFo7g+UuGY1G2CWAPsAQ+g4ZGRmffPLJ/fv3Q0NDw8PDPfOw8IyONkEQdAvTOHZnaYrdWalaI7kydBHkyszALgF0A4bQp2jSpEmTJk08Np3HdLTp6wjYUHeWvginpQOE47jRaCRJks/ngwNkie0uYX8pvcEuAS4DhhBwEc/oaDO5LRRNEU6kao2+NqtagwNkhd1dAu1vwDXAEAKu4Bkd7cbSFoq+2J2tqjW6CKrWloD2N+AmYAiBBuMBHe3r16+XlZUFBwd37dqVjrioWq0uKSl5+vRpVFRUx44dKbyz2U2sqakpLCzUarUxMTEtW7Z00020lSsjSZLFYv3rwzljR497tc+rlP0CjRm7uwRuIlAvYAiBBuCBhkc1NTXTJrx593xJZyFfhbHOa/GFi78eNmoUhVOcPnVq5qRJLQhDMxZ2myA1AUFrtm6LjIykcIoVPyz76ZtvuktEPIz8r0bXO6n/p998w+Fw3HcTzXJlBEEMHzPsgrI4e9LeNT+s7d6tO1Sdm7ESdQNnGnAMGELAWTzT8GjK+HExpdfmRISiK2qTad4H/2oZGdmjRw9Kprh3797bo0f9t2lAhPBPVZ2rKs3wAf1/v3SZqsPI3Tt37lryXWaLpnw2C8MwEgtYe/zI4k8XfblkKVUPZYIgRo4dccV4NnSwxKAwvTV74o9f/pyQkEAQBJfLheZHltjV/oZdAiyBvwPAKYxGI8oroe/ZodFoqqurS8+fHxQcYL4o4XCmBkt/XPyV+/dHbaH2ZWcni3gRwr8tUAepuBOLsJWjc5llX305OzQAWUEMw1gY9mbToL1ZWahFn1gslslk6HhVpVIplUqNRoNMo5MgK3hJ/39BiUIMw3hyTrNJ4hnzp50pPiOXywUCgVarVSqVSqVSr9dT9Uv5AMhNlEqlsEuAFWAIgfrBcVyr1dJaLIgaHlVUVLQRWztJz0tEN2/ccPP+qC+HVCotu3Y1kmcdmWxDmG5cv+7mFGaePnnSVPDMASobw0IF/KdPn5qvmB/KMplMIBDgOI4eyjiO13v/Rf9dVPzwJLKCCJ6c02yCeOiItKqqKqRqjWwtKg5RKBSo4QNVv6APALsEWAKGEKgHrVZLaxd75KiJRCI+nx8SEvLUYO0bPdEbmoSEuDOFpTsbEtasymaKpyx2aNOm7kxhiUAg1Jqsn6c1ekNdGaq2bqJCoUAVinbHT58yXfBUpryp+/sSiVUd0E2bPs2yOyOLxRIKhTKZTC6X83g85ACpVCr62m81RmCXAAwMIeAYtVpNdz27ZRf7li1bakWSco3OckxWjXrUpEkuT2HlzqaNGJGt0Rstmq5oTKZjWn1iYqLLU1iRNnrUjiqF5ZX/KdSt27Wv90TQydhdWFjYidxC/WH+n7aQxCq2qIf2GvXlp3UGkLlcLnKAxGIxUk9VKpU6nQ6az1gCu+S3QLIMYB+P6WhbRVx/2bp1dMqgJLW2i4ivMJpyNIaIV3qNGTvOtSlsdbTbtm074f05M5d+N1wiiBDwy3T4DrV+0XdLKOx0//78D4cfP7H47u3XhFwRh31GZzjD4u5dt65BN7Hq26dUKs2ibmw2G9nC2MRXlYROfdY08tUxH8392JnbWpY8Uiug6ktYFYbCLvk80I/Qv8jLy1u8eHFubq7jfoSU6Gg77keIFDvtRly1Wu26NWv+d7IwODR08MhRffr0qWsKx53qHLSFunXr1uZ1a8uuXW/XpfObb78THh7uxC/UMA7s35+Xna1WKXu/njBm7FhKCk7MffuQ7/jkyZNefV9JT0//9wcfuRO7Rso4SNTNGWUcyvsROoYh/QgbuktAIwIMoX/hjCFEwmPuNzxyYAgt+/e6Q12PSA+4s94FPZSROA6LxQoJCaHqoWwwGPR6PbK1QqHQrv32T0NoiTO7BDQi4P0DngE5arTqaKtUKlrlr1xwZ7VabXV1dfPmzaldye3bt2/dumV7ncVixcXFufP0RLE7giCuXbum0WgMBgOK3Zm7ZDRp0qRr164u3BlaRDmDeZdQYSibzYaSxEYNGELgb+jW0faAo+aCjrZarY5PjquofJi/ryA6OprCxcz95F/Ff5wSyK216Kovq3J35Xfp0sWdmyOhu6Gj00K6//1+kdifAR78Oll+7TZNLaLcWbaPYa7WBxo1YAiBP0ENj+jT0SYIQqVSMU1HW6PRvDYgXt3hcUgSPzH19QO7DsXExFC1HhNByGN54ghrQ0hqZe4cSVgK3YnloqBBdkRfK0txlOJBSezOqvkRqqhhsVjQ/Aj7BC3XAAAgAElEQVTwDcAQAhjmER1tSs4dHeCCO6vRaPr1j1O2exTwkhDDMOwNbEBaMrW2kHKcFLpjsVjoAJiOFlFcLhcZQmh+BPgGYAj9HQ/oaHumf29D20JpNJq4pL6aTo8DXvwz1icK42Pp2IChyXnZR9q2bUvPSt3CYDA0VOLHky2ioPkR0EgBQ+hTlJSUnDlzhiCI2NhYZ7oLeUZH2wP9e11wZ6uqqh5WPAhNeuapLQjmGrnaGzdvMNAQ4jhuMNQpT+MMNLV3t1K1VqvVSFUVVK2BxgL8mfoOv/76a1paWnFx8fnz5/v06ZOZmel4PPIP6NbRJkmS1v69Znm2hv5sRERE/r6Cp5sM2od/6rYQevLhr5rP5341aOAgqlfqLkgGk6qdRBFOmUyGgtVqtdoF7W9bUHUjEmcRCAQ6nQ5UrYFGAXiEvkNqaur48eNRvCs2NnbevHlTpkypazCO4ziOh4WF0bcelUoll8vpSzJEIljh4eEuG/J27drl7s1PHPx6cDomCOE9XKP+9L3PJ4yfQOkyKUCtVvN4PJpOcF2IcKIxjm9rt/mRWRmH2l8BANwEDKHv0KRJE/PXDtJSjEbj4sWLZ8yYQaujplQqhUIhfdk3SB7M/aBuu3btDu46PGBosomn++rDb8aOGUvVChGqcp1Bae1maZ4anfxxkiRVKhXKT7E7ANfpa6/auW4yNnhbnIxw6nQ6k8lUlyaRLVY9cpFriy76qtwB0OgAQ+iD4Di+cOHCGTNm2L5UW1tbXFzcpUsXsViMMgkpB9Wzy2QynU5X/2iXwHFcr9fL5XKlUun+3WJiYg7uOnyz9ObglMHu382SN9MnNMtvZnud+xq3VatW9f44KjiRSqUOjP3Ut6Y9fvrI9vrz059v0FItsTJdyPJhGCYQCIxGozkf1QWsBFTRXwhU6wNeByTWfA2TyZSeno7j+I4dO2zdiB07dixcuPDixYuOtUZdxuyosVgsx1qjLmMpz8ZA8S2qsNxJb68FwzCMJMmnT58i8RpqI5xmAdW6VK19+F0GGAJ4hD4FQRATJkxQKBR79uyxG0wLCAho1syOj0IJZkeNpvtjDnW0fQm9Xk/3TjYIFOsODAxEf1TURjjNsnCo5BHHcVC1BjwMGELfgSTJ6dOn37lz58CBA543FbYNj6ilLnk2jUbjY9XcOp2OwgRR9zHHus0uIE0RTkv9NsvmR6jMAwDoAwyh77B69erMzMyBAwdOnDgRXdm4cSN96SqW0O2o1aWjLZPJkBuh0WgwnzhtQkJ3zJGvtNsz0gzSb6Oju6FlyaNGo0GHwT7w/gLMBAyh79C3b99t27ZZXvGAn+R1He26eqi6r5zieVCqLXNyKRvUioSmCCd6K1GkgVplHAAwA4bQd2jXrl27du08OaMHdLQb9CymSTnFA3hgJxuKy7HuuiKcAoGAWu3vRvT+AgwHDCHgIszU0UYg5RT0NSqJY7I2NNpJx2USHkatVnM4HPMeugxN3Q0b1/sLMB8whIAreEZHm5K2UAzXhkY7yagyCZVKRXmEFrS/ASYDhhBoMIzV0XYMA7WhUa06c4rkPBOhbVCEU6vVOmmSbUXdwE0EnAQMIdAwXGh41CBIklRUPdUdK3h68xpXFhAU/5okphO1U7BYLFZNde2+vfqKh7znIuTJAzGJFMMwak2vovj32tMnCZ1O+kLXkIT+mI2tRTtJuaaBy3gg1m1FvRFO17KRrZRxkJuIYRifzwc3EbALGEKgAXigf2/tgwcP/z1He7sMXanYsuG5d6aHj5tI4Sy1vxeVfjyX+EsB7tHWTe2+/1nUth2F2tB3lyx+tCsLff14787He3ZGL/2ZbbFvdO9kQ/FArNsxVhFOo9GIrLKbpsuu9jeXy4UWUYAl8KcAOIU7DY+cBB0dabJ3ma0gmvjBLyv0lRWUTUOSd7/7irDQQTUpFXeXfYfcCKlUKpfL+Xy+VqtVKpUqlcpgMDR0BvWVS2YriFBdKHmSveuv+WnfyYai0+lwHGdIhBYFq0mSDA0N5fF4KpWKwhZR6P0VCATo/YUWUQACPEKgfmy1RSjHLM/24GKJ1UukyaS6dCE4jBplOP2Tx/jDB1YX1RfPkwTBokg5RXXB+lfAMEx5/lzTYaM8sJMNhe5Yd0OxLBs1x0WpjXBavb9KpdJc8sic9wXwJGAIgXpwrC1CCUgX5k+PxF5eA8u9+rNnbmU3b4LDsfu7uaicUsev4IGdbCiNJUJLU4TT6v2FFlF+CxhCwBGe19EO6NlLdf6c5QC2UCh74UWqpuMFh4ii2mpLb1pelPd4xTaZxQrnlVPkPV7G2GyMICwvSrr10Gq1TNPRFovFbha5U4gz2ch2uxtiVCQ6Wb2/0CLKr4A4AFAnWq2W1uR+dFpmFekKG/WGvGcv87dsobDVB//mBgZROG+bDxfwQ5uavxW2aNnynx84/+Oo+k0qlcpkMg6Hg5Qw1Wq1WRta1DoyYupMSy82MCFZGv86Qw7hMAwjCEKhUEilUuZYQY1GQ5JkgyK0KMIpk8mkUimKOSsUCrNpdBmzqJvV++vCaTHQWIB+hP5FXl7e4sWLc3Nz6+1H6L6OtuN+hHXpaCMUxb+rr13mygICer/Kbxrm8hrqgtBqqo8V4BUPhC1bB8XGs9yOgyE3Aj0rkRuB/3FXUXya0Ok40e1lnV8wq455HaZ1OsQojdCauxtSG+FE76/RaIQWUT4JUz4PAszBAzra9Z6WyXu8LO/xMk2zYxjGFolD+g+i8oa2yilBweLkQQaDQSqVMufAyQOx7gZBeYSWpginXQFVdMTIHK8acBl4C4FncOyoUUKDdLQbI0g5BYUfeTyeTqfT6XRM0Iamu2dkQ6E1h7autiQUtohCuawosgLppo0aePOAvzGZTCqVSi6X02cFdTqdXq9nzrMYw7AzZ858+emnC+bOzc7OpuqkAO1kQEAAOko0mUyv9O351TdfUlISZ5fjJ463jm516dKlugao1WqmdTpEf2weMCE8Hg+dJopEIpPJhCoIdTqdm283ymVlVDEM4Brw/gF/gj41e6BMglElaxNHj/4kfRRr87rgfbu2zflnbLdujx8/dvO2VjtZW1sbnxyHd6tZsfOn5at+FggEqHZNpVLhOE7F74EVnix8Y3K6ZDA5YFjyxYsXrV61m5TkXZAj5flKEruJMCqVypzoBPgnEBoFMKzR6mi7yc/LlnHPnvm8eQj69lUMO1WjnD7hzax9+12+p9VO1tbWxiX1NfSsDegklHcmf1q/DMOwue/Pw6jThi48WZj+9qimE4T8QC5/rH7g8P77tx/s3LkzetWXOh1SC00tooDGCHiEgCuZ6w2CgaJiiN/WrBkTEmB5pVeg7ObFiy47alY7abaC8k4CDMNYHFb4eMlP25Z9vWQxZiH6hRQ1kZuoVCobNLulFcQwTNiU32Qsf+Dw/sgvRBFa5P249htRDtMitFjd9RJ0RLABZgKG0N9RKpVcLtf9Fqx1YTKZmFayZkajVsu41hYimM+vrq524W62O7k0Y2mVuBJZQQSLwwodLvrss8+sArDm0yZkRFUqlUKhQPkdjied8PabsmQ2soIIYVO+qA85/Z/TPRDrbhAMjNDaYnmaqNfrzR9N6jpNNJlM//rXv7Kysuy+CjQWwBD6DtXV1YmJicHBwSwW6/bt2/WO94yONnoWMzObIDgk+LH+mSppEsMe4XhISEiD7lPXTn704UcdpJ1rjlsIfGuJinXq9b+uDw0NtXurhmpDH9h7UHuIrbn/txOpKtURZ0TrV69njo429lcJv0QiYU4liWNQiyjkJrJYLLVabZvopFar09LSSkpKkpKSvLhUwH2Y+HgCXIPL5U6ePLmwsNCZwSh3jlZHDZWsMapw24ppc/7185NawuLD/o4nNfFJSQ16WDtQaeHxeDk797dURCNbaNISD35R/fDZT2lDhjpzZ2eUU9q2bXt4b54ii0S2UFWq0+7nHtpzuFmzZoxKSqI7G5lW+Hw+imDz+XydTvf555+//PLLH3zwQe/evZs0aXLgwIGAgID67wIwGRLwLVBmZnl5ud1Xc3NzExISzp07V11djUT36VvGkydPTCYTfVNQwuJPF3VtETGjXdR70ZFxbVqPHZqGUjmcxGAw1NbWEgThYIxer09KSWg7IuK5js127dnl5oINBgMKnCI3EV28ceNG6/Yto8Y1i+oYefPmTRTKYwh6vV6hUHh7FVSC4/iqVavkcvnIkSOtXnrjjTfCw8PFYnHHjh03b97sleUBLgCG0NdwbAgPHjzYvHnzl156CX1Ip2kNqDAApRvQNAWFVFRU7Ny587fffrt27VqDflCn0zn5iNfr9SPHjti1110raAmSnFYoFMhNvH79+uv9X7tx44bBYKBwFjdBoV1vr4Ji8vLymjZtunHjRtuXDh8+XFFRodfr9+7dKxAIrl+/7vnlAS4AWqO+hlarFYvF5eXlrVu3tn11/fr18+bNu3HjhkQicaw16hokSapUKpFIxOVyHWuNNnaQ48iQ7EfUvUihUMjlcqFQyJBzONTpkL48LK+wdu3a+fPnb926NS4uzvHIFi1a/PLLL3B82ChgXCIfQCvNmzfv1KmTTCZzU6HfLqhkTSqV+qrxM+OCIvmPy398UmWnVL/Vc60mTpjk5npYLBZJks2bNydJkiEthBhYNuomJEkuWrRow4YNR48ebd++fV3DLl68ePv27cOHD7dq1apeYwkwBDCEADXY7WlgMBiYnCvvAqSriuT/XfyZPMlOqohuHcdNQ2ipo23ZafZP7W+S9LA2NMm8Tofuo9fr33rrrZs3b546dapp06YORubl5R09erSkpGTcuHG+tAO+DbxPPsXatWvVajWGYZs3bw4JCZk0aZJn/hX1er1tTwNzJRaGYch/auyeojsqLQIxP6S7nThq5Un7dRFO4kClxSvKKeYS/sb+XltSXV2dlpYWEhJSUFBQb6T3vffee++991QqVdeuXTt27Jienu6ZRQLu4Dt/rACGYSUlJRcuXJg8efLt27f/97//eeYAGImK2Sbro5I4VImF8s4dl8QxnMar0uIx5RSj0ahWqxlbNuoa5eXlvXv3fuGFF7Kyspw/75RKpR07dnSmnBdgAuAR+hTff/+9h2dUq9VIFcXxMPMY8i+BTYIgkHfSKB6aKBuFOa2jXI7QWrqJOI4jsWlKWkQxrdMhJfz+++9paWkfffTRjBkz6h386NGjkydPvvrqq0Kh8NChQ0eOHPnoo488sEjAfcAQAi6CEkQbmqOI3ER0cIgKAChvJk45HlAkbxCU9IxEyinoa71ej04TXdb+ZoiONrXs3Llz6tSpa9asSUlJcWY8SZIrVqyYNm2awWCIjo7esGFDz5496V4kQAlgCAFXoKSnAVJOwTCMJEkcx825jnw+nzluIqoBYJRKCwo/UnjOhzxC7K9OsyaTicViIX/dmR93IYeW+WRkZHzzzTcHDhzo3r27kz8SFhZ26NAhWlcF0AQYQqDBoGcxhWUSlrmORqMRuYmUNBN3E6bVANAdobWKYKvVaoIgOBxOXfWgLkdomYzJZJo9e/axY8eKiopatmzp7eUAngAMIdAw0LOYPgVRLpfL5XLxhw/U16/qhEJe2/YsPp/6XEeCUF+7glc8FLZoJW4bbfs65TUAOqWuKt/O+k0G22t13MGDEVqrCLZOp0OZNZYfCyiJ0DINtVo9evRonU5XWFgICqL+AxhCoAGgByKtz2KSIP5Y9t3jXVkkQWAYxm8a1ubjTzmduqCeRJS4ifqKh6UL5quvXkbfynu+EvmfL7gWbhZ6xFNbA7Dp1812uzs998/nnPlxL0Zo7SY6sdlso9EYEBDAWEV1F3j48GFqauoLL7ywYsUKX/JxgXoBQwg4C3oWU67KZsXjPTse7dhq/lb/qLL0k7mdt2WjeVFJnJvKKeVfLDRbQQzDFGdO/7Hs2zYff4q+RcoAlLfxS0hIcPlnGRKhNbuJer1eo9HweDyVSsXwRCfnuXTpUkpKyoQJExYuXOjttQCeBgwh4BQeexbXHC+wumKsrVWW/C+wdyz2V0mcO8opxtpaZclZq4vVxwrafERiLBbTagAYqNKCIrSBgYHoW6tEJy+KurlDXl7eG2+8sXTp0jFjxnh7LYAXYMp/F8BYPPwsNmk0thcJtdr2olVJHMrgRw3QHTyLCa0Gs9EZIHAdaTLpDAZG1QAwUKVFo9Gw2WzLCK1VohOFEWyPsWbNmn//+99ZWVl9+/b19loA7wCGEHAEHadljhG3jVZfuWR9Mbqdgx+xWxKHfEfbPA5e0zBuYJCx5pnjOlHk8xocZ1QNAE0RWneoNyqAEp2wvyLYqC0ik91EpKO9cePGY8eOtWvn6G8M8G2Y8kkTYCBGoxE1FvekR9Js7ARuYJDlldDUNGGrNk7+uLmZuFAoxHEcibrhOG4ewGKzI6bOxCyeyywOJ2TC28iVpORXcB/k4DLHCpIkqVAoRCKRk7Fx9CkEvRGWom5IyIYh4Dg+bty4Q4cOFRUVgRX0c8AjBOyDPtF7/rRM0Kx5x3VbK35bp752hSuTBfVLDEns78J9bHMdzcopTQYNFrZs9WjnNn3FQ0FES2nqkOCOnZlTA8A0lRY3I7Re0f6ul6qqqrS0tNDQ0CNHjvhYx0TABcAQAnbw7rOYFxzc4t33qLqbVUkcUk7BWkc+N38Bl8tVq9X01US6ANNUWgwGA1W+qd1Ep7oi2LRSVlY2cODA5OTkpUuXMuf8FfAiYAgBa5COtk9+TLZ0E9VqdU1NjVgs1mq1dSmneBIGqrTQl0NLn/Z3vZw+fXro0KEff/zx9OnTaZ0IaESAIQT+xjUd7cYIOjUMCwvD6lZO8SQMVGnxTFSAWu3vetmxY8e0adN+/fXXQYMGUX5zoPEChhD4EwY+i2nCUqWFwPFH2zbVFB4ncFza+YUmY8brZXJqW0ThD+4/XLtafe0yRyYP7pcQmjaC9ewO06Gj7SZeidC6qf1dLxkZGd9+++3Bgwe7detGyQ0BnwEMIYBhjHwW08QzNQAEcXPOTOX5P+vrtaU3a44XxPz6Gy84xOwmuqmcortz++qUN01/1UGqLpQoL5REffqVeYC3kpLqggkRWgeJTq59SjOZTLNmzTp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]
},
"metadata": {},
"execution_count": 11
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 11
},
{
"cell_type": "markdown",
"source": [
"Let's do a last step:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 35 rows to complete columns up to degree 6\n",
"[ Info: Nullspace of dimensions (84, 18) computed from Macaulay matrix of dimension (75, 84) in 0.000839189 seconds.\n",
"[ Info: Found 1 real solution\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver)"
],
"metadata": {},
"execution_count": 12
},
{
"cell_type": "markdown",
"source": [
"Now we see that the whole border is dependent so the four\n",
"multiplication matrices can be computed."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=6}",
"image/png": 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]
},
"metadata": {},
"execution_count": 13
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 13
},
{
"cell_type": "markdown",
"source": [
"In retrospect, we we probably should have expanded in priority towards larger\n",
"exponents for `z`."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Saturation\n",
"\n",
"Let's start again by starting with the same first stop."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 6 rows to complete columns up to degree 3\n",
"[ Info: Nullspace of dimensions (14, 8) computed from Macaulay matrix of dimension (6, 14) in 5.8619e-5 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"solver = Iterator(system, MacaulayMatrix.Solver())\n",
"step!(solver)"
],
"metadata": {},
"execution_count": 14
},
{
"cell_type": "markdown",
"source": [
"This time, let's focus on saturating the first\n",
"non-saturated standard monomials:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 12 rows to saturate columns `TypedPolynomials.Monomial{(x, y, z), 3}[z, y, x, z², yz, y², xz, xy, z³, yz²]`\n",
"[ Info: Nullspace of dimensions (38, 20) computed from Macaulay matrix of dimension (18, 38) in 0.000134219 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver, FirstStandardNonSaturated(10))"
],
"metadata": {},
"execution_count": 15
},
{
"cell_type": "markdown",
"source": [
"We can see that `z` is now saturated:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=7}",
"image/png": 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",
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]
},
"metadata": {},
"execution_count": 16
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 16
},
{
"cell_type": "markdown",
"source": [
"Let's saturate the next one:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 20 rows to saturate columns `TypedPolynomials.Monomial{(x, y, z), 3}[y²z, y³, xz², z⁴, yz³, y²z², y³z, y⁴, z⁵, yz⁴]`\n",
"[ Info: Nullspace of dimensions (70, 32) computed from Macaulay matrix of dimension (38, 70) in 0.00034996 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver, FirstStandardNonSaturated(10))"
],
"metadata": {},
"execution_count": 17
},
{
"cell_type": "markdown",
"source": [
"We can see that `y` went from trivial to saturated:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=8}",
"image/png": 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]
},
"metadata": {},
"execution_count": 18
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 18
},
{
"cell_type": "markdown",
"source": [
"Let's saturate the next one:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 20 rows to saturate columns `TypedPolynomials.Monomial{(x, y, z), 3}[y⁵, z⁶, yz⁵, y⁶, z⁷, yz⁶, y⁷, z⁸, yz⁷, y⁸]`\n",
"[ Info: Nullspace of dimensions (103, 45) computed from Macaulay matrix of dimension (58, 103) in 0.000688619 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver, FirstStandardNonSaturated(10))"
],
"metadata": {},
"execution_count": 19
},
{
"cell_type": "markdown",
"source": [
"We can see that `x` went from trivial to saturated:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=8}",
"image/png": 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]
},
"metadata": {},
"execution_count": 20
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 20
},
{
"cell_type": "markdown",
"source": [
"Let's saturate the next one:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Added 20 rows to saturate columns `TypedPolynomials.Monomial{(x, y, z), 3}[z⁹, yz⁸, y⁹, z¹⁰, yz⁹, y¹⁰, z¹¹, yz¹⁰, y¹¹, z¹²]`\n",
"[ Info: Nullspace of dimensions (136, 58) computed from Macaulay matrix of dimension (78, 136) in 0.001223162 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"step!(solver, FirstStandardNonSaturated(10))"
],
"metadata": {},
"execution_count": 21
},
{
"cell_type": "markdown",
"source": [
"We can see that `z^2` is now saturated:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=8}",
"image/png": 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]
},
"metadata": {},
"execution_count": 22
}
],
"cell_type": "code",
"source": [
"plot(saturated_dependence(solver))"
],
"metadata": {},
"execution_count": 22
},
{
"cell_type": "markdown",
"source": [
"We can see that this does not seem to work.\n",
"By saturating a monomial,\n",
"we generate all the rows that have a nonzero entry for the corresponding\n",
"column in the MacaulayMatrix matrix.\n",
"If the monomial is standard, it means that the column is a linear combination of other columns\n",
"(which are dependent in the MacaulayMatrix Nullspace)\n",
"of the MacaulayMatrix matrix.\n",
"If we saturate these other columns, the linear combination may not work anymore.\n",
"But we are only saturating the standard monomials, we don't saturate\n",
"the rows that are dependent in the MacaulayMatrix Nullspace which explains\n",
"the result we have seen here."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Moment approach"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"With moment matrix of degree 3:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Nullspace of dimensions (14, 8) computed from Macaulay matrix of dimension (6, 14) in 7.4087e-5 seconds.\n",
"┌ Warning: Missing monomials TypedPolynomials.Monomial{(x, y, z), 3}[y, x, y²] in Macaulay nullspace, leaving them free to take any value in the moment matrix then.\n",
"└ @ MacaulayMatrix ~/.julia/packages/MacaulayMatrix/2RDTD/src/hankel.jl:65\n",
"-------------------------------------------------------------\n",
" Clarabel.jl v0.9.0 - Clever Acronym \n",
" (c) Paul Goulart \n",
" University of Oxford, 2022 \n",
"-------------------------------------------------------------\n",
"\n",
"problem:\n",
" variables = 11\n",
" constraints = 11\n",
" nnz(P) = 0\n",
" nnz(A) = 67\n",
" cones (total) = 2\n",
" : Zero = 1, numel = 1\n",
" : PSDTriangle = 1, numel = 10\n",
"\n",
"settings:\n",
" linear algebra: direct / qdldl, precision: Float64\n",
" max iter = 200, time limit = Inf, max step = 0.990\n",
" tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,\n",
" static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32\n",
" dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07\n",
" iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12, \n",
" max iter = 10, stop ratio = 5.0\n",
" equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04\n",
" max iter = 10\n",
"\n",
"iter pcost dcost gap pres dres k/t μ step \n",
"---------------------------------------------------------------------------------------------\n",
" 0 0.0000e+00 -0.0000e+00 0.00e+00 3.88e-01 6.59e-01 1.00e+00 1.24e+00 ------ \n",
" 1 0.0000e+00 -6.5201e-02 6.52e-02 3.19e-02 7.78e-02 7.16e-03 1.25e-01 9.13e-01 \n",
" 2 0.0000e+00 -5.8123e-04 5.81e-04 3.43e-04 9.79e-04 1.89e-04 1.46e-03 9.89e-01 \n",
" 3 0.0000e+00 -5.8069e-06 5.81e-06 3.43e-06 9.79e-06 1.89e-06 1.46e-05 9.90e-01 \n",
" 4 0.0000e+00 -5.8068e-08 5.81e-08 3.43e-08 9.79e-08 1.89e-08 1.46e-07 9.90e-01 \n",
" 5 0.0000e+00 -5.8068e-10 5.81e-10 3.43e-10 9.79e-10 1.89e-10 1.46e-09 9.90e-01 \n",
"---------------------------------------------------------------------------------------------\n",
"Terminated with status = solved\n",
"solve time = 933μs\n",
"[ Info: Terminated with OPTIMAL (SOLVED) in 0.000933484 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"import Clarabel\n",
"solver = Clarabel.Optimizer\n",
"\n",
"M = moment_matrix(system, solver, 3)\n",
"nothing # hide\n",
"\n",
"atomic_measure(M, 1e-4, ShiftNullspace())"
],
"metadata": {},
"execution_count": 23
},
{
"cell_type": "markdown",
"source": [
"With moment matrix of degree 4:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Nullspace of dimensions (33, 15) computed from Macaulay matrix of dimension (18, 33) in 0.000128759 seconds.\n",
"┌ Warning: Missing monomials TypedPolynomials.Monomial{(x, y, z), 3}[y², y²z²] in Macaulay nullspace, leaving them free to take any value in the moment matrix then.\n",
"└ @ MacaulayMatrix ~/.julia/packages/MacaulayMatrix/2RDTD/src/hankel.jl:65\n",
"-------------------------------------------------------------\n",
" Clarabel.jl v0.9.0 - Clever Acronym \n",
" (c) Paul Goulart \n",
" University of Oxford, 2022 \n",
"-------------------------------------------------------------\n",
"\n",
"problem:\n",
" variables = 17\n",
" constraints = 56\n",
" nnz(P) = 0\n",
" nnz(A) = 784\n",
" cones (total) = 2\n",
" : Zero = 1, numel = 1\n",
" : PSDTriangle = 1, numel = 55\n",
"\n",
"settings:\n",
" linear algebra: direct / qdldl, precision: Float64\n",
" max iter = 200, time limit = Inf, max step = 0.990\n",
" tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,\n",
" static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32\n",
" dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07\n",
" iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12, \n",
" max iter = 10, stop ratio = 5.0\n",
" equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04\n",
" max iter = 10\n",
"\n",
"iter pcost dcost gap pres dres k/t μ step \n",
"---------------------------------------------------------------------------------------------\n",
" 0 0.0000e+00 -0.0000e+00 0.00e+00 7.02e-01 1.07e+00 1.00e+00 4.05e+00 ------ \n",
" 1 0.0000e+00 2.1244e+00 2.12e+00 2.49e-01 2.23e-01 2.83e+00 8.73e-01 8.09e-01 \n",
" 2 0.0000e+00 1.0127e+01 1.01e+01 4.85e-02 4.27e-02 1.08e+01 2.18e-01 8.63e-01 \n",
" 3 0.0000e+00 2.9803e+01 2.98e+01 7.30e-03 7.27e-03 3.02e+01 4.34e-02 8.59e-01 \n",
" 4 0.0000e+00 1.4744e+01 1.47e+01 1.30e-03 1.40e-03 1.49e+01 9.54e-03 8.22e-01 \n",
" 5 0.0000e+00 3.0716e+00 3.07e+00 2.61e-04 3.30e-04 3.11e+00 3.23e-03 8.96e-01 \n",
" 6 0.0000e+00 8.9652e-02 8.97e-02 1.35e-05 1.74e-05 9.14e-02 1.89e-04 9.44e-01 \n",
" 7 0.0000e+00 9.2794e-04 9.28e-04 1.36e-07 1.76e-07 9.46e-04 1.95e-06 9.90e-01 \n",
" 8 0.0000e+00 9.2781e-06 9.28e-06 1.36e-09 1.76e-09 9.46e-06 1.95e-08 9.90e-01 \n",
" 9 0.0000e+00 9.2783e-08 9.28e-08 1.35e-11 1.76e-11 9.46e-08 1.95e-10 9.90e-01 \n",
" 10 0.0000e+00 1.0031e-09 1.00e-09 2.78e-09 1.90e-13 1.02e-09 2.09e-12 9.89e-01 \n",
"---------------------------------------------------------------------------------------------\n",
"Terminated with status = solved\n",
"solve time = 3.27ms\n",
"[ Info: Terminated with OPTIMAL (SOLVED) in 0.0032739120000000003 seconds.\n"
]
}
],
"cell_type": "code",
"source": [
"M = moment_matrix(system, solver, 4)\n",
"nothing # hide\n",
"\n",
"atomic_measure(M, 1e-4, ShiftNullspace())"
],
"metadata": {},
"execution_count": 24
},
{
"cell_type": "markdown",
"source": [
"With moment matrix of degree 5:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ Info: Nullspace of dimensions (56, 18) computed from Macaulay matrix of dimension (40, 56) in 0.000325575 seconds.\n",
"-------------------------------------------------------------\n",
" Clarabel.jl v0.9.0 - Clever Acronym \n",
" (c) Paul Goulart \n",
" University of Oxford, 2022 \n",
"-------------------------------------------------------------\n",
"\n",
"problem:\n",
" variables = 18\n",
" constraints = 56\n",
" nnz(P) = 0\n",
" nnz(A) = 1008\n",
" cones (total) = 2\n",
" : Zero = 1, numel = 1\n",
" : PSDTriangle = 1, numel = 55\n",
"\n",
"settings:\n",
" linear algebra: direct / qdldl, precision: Float64\n",
" max iter = 200, time limit = Inf, max step = 0.990\n",
" tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,\n",
" static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32\n",
" dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07\n",
" iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12, \n",
" max iter = 10, stop ratio = 5.0\n",
" equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04\n",
" max iter = 10\n",
"\n",
"iter pcost dcost gap pres dres k/t μ step \n",
"---------------------------------------------------------------------------------------------\n",
" 0 0.0000e+00 -0.0000e+00 0.00e+00 7.25e-01 1.01e+00 1.00e+00 4.89e+00 ------ \n",
" 1 0.0000e+00 3.7044e+00 3.70e+00 2.92e-01 1.85e-01 4.54e+00 8.83e-01 8.53e-01 \n",
" 2 0.0000e+00 2.4003e+02 2.40e+02 2.57e-02 1.15e-02 2.43e+02 5.85e-02 9.57e-01 \n",
" 3 0.0000e+00 1.4580e+03 1.46e+03 3.15e-03 1.16e-03 1.46e+03 5.54e-03 9.48e-01 \n",
" 4 0.0000e+00 7.8960e+00 7.90e+00 4.79e-04 2.89e-04 8.10e+00 1.88e-03 7.49e-01 \n",
" 5 0.0000e+00 2.2070e-01 2.21e-01 1.50e-05 9.30e-06 2.28e-01 6.24e-05 9.67e-01 \n",
" 6 0.0000e+00 1.5989e-02 1.60e-02 4.61e-07 2.90e-07 1.62e-02 1.98e-06 9.69e-01 \n",
" 7 0.0000e+00 3.2459e-04 3.25e-04 1.08e-08 6.90e-09 3.30e-04 4.76e-08 9.76e-01 \n",
" 8 0.0000e+00 3.2459e-04 3.25e-04 1.08e-08 6.90e-09 3.30e-04 4.76e-08 0.00e+00 \n",
"---------------------------------------------------------------------------------------------\n",
"Terminated with status = numerical error\n",
"solve time = 2.62ms\n",
"[ Info: Terminated with NUMERICAL_ERROR (NUMERICAL_ERROR) in 0.002618824 seconds.\n",
"┌ Warning: * Solver : Clarabel\n",
"│ \n",
"│ * Status\n",
"│ Result count : 1\n",
"│ Termination status : NUMERICAL_ERROR\n",
"│ Message from the solver:\n",
"│ \"NUMERICAL_ERROR\"\n",
"│ \n",
"│ * Candidate solution (result #1)\n",
"│ Primal status : OTHER_RESULT_STATUS\n",
"│ Dual status : OTHER_RESULT_STATUS\n",
"│ Objective value : -0.00000e+00\n",
"│ Dual objective value : -3.24587e-04\n",
"│ \n",
"│ * Work counters\n",
"│ Solve time (sec) : 2.61882e-03\n",
"│ Barrier iterations : 8\n",
"└ @ MacaulayMatrix ~/.julia/packages/MacaulayMatrix/2RDTD/src/hankel.jl:25\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Atomic measure on the variables x, y, z with 1 atoms:\n at [3.84205516042132, 4.99567052245059, 4.432254383584636] with weight 0.9999998706390161"
},
"metadata": {},
"execution_count": 25
}
],
"cell_type": "code",
"source": [
"M = moment_matrix(system, solver, 5)\n",
"nothing # hide\n",
"\n",
"atomic_measure(M, 1e-4, ShiftNullspace())"
],
"metadata": {},
"execution_count": 25
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.0"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.0",
"language": "julia"
}
},
"nbformat": 4
}