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07-1 Linear homogeneous ODEs with constant coefficients.ipynb
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| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "# 定数係数線形常微分方程式(斉次)\n\n* Author: 黒木玄\n* Date: 2019-04-23\n* Repository: https://github.com/genkuroki/DifferentialEquations\n$\n\\newcommand\\ds{\\dispplaystyle}\n\\newcommand\\Z{{\\mathbb Z}}\n\\newcommand\\R{{\\mathbb R}}\n\\newcommand\\C{{\\mathbb C}}\n\\newcommand\\eps{\\varepsilon}\n\\newcommand\\QED{\\text{□}}\n\\newcommand\\d{\\partial}\n\\newcommand\\real{\\operatorname{Re}}\n\\newcommand\\imag{\\operatorname{Im}}\n\\newcommand\\tr{\\operatorname{tr}}\n$\n\nこのファイルは [nbviewer](https://nbviewer.jupyter.org/github/genkuroki/DifferentialEquations/blob/master/01-1+Van+der+Pol+oscillator.ipynb) でも閲覧できる.\n\n[Julia言語](https://julialang.org/) と [Jupyter環境](https://jupyter.org/) の簡単な解説については次を参照せよ:\n\n* [JuliaとJupyterのすすめ](https://nbviewer.jupyter.org/github/genkuroki/msfd28/blob/master/msfd28genkuroki.ipynb?flush_cached=true)\n\n[Julia言語](https://julialang.org/) 環境の整備の仕方については次を参照せよ:\n\n* [Julia v1.1.0 の Windows 8.1 へのインストール](https://nbviewer.jupyter.org/github/genkuroki/msfd28/blob/master/install.ipynb)" | |
| }, | |
| { | |
| "metadata": { | |
| "toc": true | |
| }, | |
| "cell_type": "markdown", | |
| "source": "<h1>目次<span class=\"tocSkip\"></span></h1>\n<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#2階単独の定数係数線形常微分方程式\" data-toc-modified-id=\"2階単独の定数係数線形常微分方程式-1\"><span class=\"toc-item-num\">1 </span>2階単独の定数係数線形常微分方程式</a></span><ul class=\"toc-item\"><li><span><a href=\"#2階単独の定数係数線形常微分方程式と定数係数で線形な3項間漸化式の類似性\" data-toc-modified-id=\"2階単独の定数係数線形常微分方程式と定数係数で線形な3項間漸化式の類似性-1.1\"><span class=\"toc-item-num\">1.1 </span>2階単独の定数係数線形常微分方程式と定数係数で線形な3項間漸化式の類似性</a></span></li><li><span><a href=\"#方程式を解くときの考え方\" data-toc-modified-id=\"方程式を解くときの考え方-1.2\"><span class=\"toc-item-num\">1.2 </span>方程式を解くときの考え方</a></span></li><li><span><a href=\"#2階単独の定数係数線形常微分方程式の解全体が2次元のベクトル空間になること\" data-toc-modified-id=\"2階単独の定数係数線形常微分方程式の解全体が2次元のベクトル空間になること-1.3\"><span class=\"toc-item-num\">1.3 </span>2階単独の定数係数線形常微分方程式の解全体が2次元のベクトル空間になること</a></span></li><li><span><a href=\"#解の見付け方(1)\" data-toc-modified-id=\"解の見付け方(1)-1.4\"><span class=\"toc-item-num\">1.4 </span>解の見付け方(1)</a></span></li><li><span><a href=\"#解の見付け方(2)\" data-toc-modified-id=\"解の見付け方(2)-1.5\"><span class=\"toc-item-num\">1.5 </span>解の見付け方(2)</a></span></li><li><span><a href=\"#結果のまとめ\" data-toc-modified-id=\"結果のまとめ-1.6\"><span class=\"toc-item-num\">1.6 </span>結果のまとめ</a></span></li><li><span><a href=\"#一次独立性の証明\" data-toc-modified-id=\"一次独立性の証明-1.7\"><span class=\"toc-item-num\">1.7 </span>一次独立性の証明</a></span><ul class=\"toc-item\"><li><span><a href=\"#$\\alpha\\ne\\beta$-のときの-$e^{\\alpha-t},-e^{\\beta-t}$-の一次独立性の証明\" data-toc-modified-id=\"$\\alpha\\ne\\beta$-のときの-$e^{\\alpha-t},-e^{\\beta-t}$-の一次独立性の証明-1.7.1\"><span class=\"toc-item-num\">1.7.1 </span>$\\alpha\\ne\\beta$ のときの $e^{\\alpha t}, e^{\\beta t}$ の一次独立性の証明</a></span></li><li><span><a href=\"#$e^{\\alpha-t},-te^{\\alpha-t}$-の一次独立性の証明\" data-toc-modified-id=\"$e^{\\alpha-t},-te^{\\alpha-t}$-の一次独立性の証明-1.7.2\"><span class=\"toc-item-num\">1.7.2 </span>$e^{\\alpha t}, te^{\\alpha t}$ の一次独立性の証明</a></span></li></ul></li></ul></li><li><span><a href=\"#高階の場合\" data-toc-modified-id=\"高階の場合-2\"><span class=\"toc-item-num\">2 </span>高階の場合</a></span><ul class=\"toc-item\"><li><span><a href=\"#線形微分作用素\" data-toc-modified-id=\"線形微分作用素-2.1\"><span class=\"toc-item-num\">2.1 </span>線形微分作用素</a></span></li><li><span><a href=\"#定数係数線形常微分方程式の微分作用素を用いた表示\" data-toc-modified-id=\"定数係数線形常微分方程式の微分作用素を用いた表示-2.2\"><span class=\"toc-item-num\">2.2 </span>定数係数線形常微分方程式の微分作用素を用いた表示</a></span></li><li><span><a href=\"#重解がない場合の定数係数線形常微分方程式の解法\" data-toc-modified-id=\"重解がない場合の定数係数線形常微分方程式の解法-2.3\"><span class=\"toc-item-num\">2.3 </span>重解がない場合の定数係数線形常微分方程式の解法</a></span><ul class=\"toc-item\"><li><span><a href=\"#定数係数でない場合の斉次1階の線形常微分方程式の解法\" data-toc-modified-id=\"定数係数でない場合の斉次1階の線形常微分方程式の解法-2.3.1\"><span class=\"toc-item-num\">2.3.1 </span>定数係数でない場合の斉次1階の線形常微分方程式の解法</a></span></li></ul></li><li><span><a href=\"#重解がある場合の定数係数線形常微分方程式の解法の準備\" data-toc-modified-id=\"重解がある場合の定数係数線形常微分方程式の解法の準備-2.4\"><span class=\"toc-item-num\">2.4 </span>重解がある場合の定数係数線形常微分方程式の解法の準備</a></span><ul class=\"toc-item\"><li><span><a href=\"#定数係数でない場合の非斉次1階の線形常微分方程式の解法\" data-toc-modified-id=\"定数係数でない場合の非斉次1階の線形常微分方程式の解法-2.4.1\"><span class=\"toc-item-num\">2.4.1 </span>定数係数でない場合の非斉次1階の線形常微分方程式の解法</a></span></li></ul></li><li><span><a href=\"#重解がある場合の定数係数線形常微分方程式の解法\" data-toc-modified-id=\"重解がある場合の定数係数線形常微分方程式の解法-2.5\"><span class=\"toc-item-num\">2.5 </span>重解がある場合の定数係数線形常微分方程式の解法</a></span></li></ul></li><li><span><a href=\"#一次独立性の証明\" data-toc-modified-id=\"一次独立性の証明-3\"><span class=\"toc-item-num\">3 </span>一次独立性の証明</a></span><ul class=\"toc-item\"><li><span><a href=\"#Wronskian\" data-toc-modified-id=\"Wronskian-3.1\"><span class=\"toc-item-num\">3.1 </span>Wronskian</a></span><ul class=\"toc-item\"><li><span><a href=\"#函数の組の一次独立性の十分条件\" data-toc-modified-id=\"函数の組の一次独立性の十分条件-3.1.1\"><span class=\"toc-item-num\">3.1.1 </span>函数の組の一次独立性の十分条件</a></span></li><li><span><a href=\"#線形常微分方程式の解のWronskian\" data-toc-modified-id=\"線形常微分方程式の解のWronskian-3.1.2\"><span class=\"toc-item-num\">3.1.2 </span>線形常微分方程式の解のWronskian</a></span></li><li><span><a href=\"#行列式の微分\" data-toc-modified-id=\"行列式の微分-3.1.3\"><span class=\"toc-item-num\">3.1.3 </span>行列式の微分</a></span></li></ul></li><li><span><a href=\"#Vandermondeの行列式\" data-toc-modified-id=\"Vandermondeの行列式-3.2\"><span class=\"toc-item-num\">3.2 </span>Vandermondeの行列式</a></span></li><li><span><a href=\"#互いに異なる-$\\alpha_j$-に対する-$e^{\\alpha_j-x}$-達の一次独立性\" data-toc-modified-id=\"互いに異なる-$\\alpha_j$-に対する-$e^{\\alpha_j-x}$-達の一次独立性-3.3\"><span class=\"toc-item-num\">3.3 </span>互いに異なる $\\alpha_j$ に対する $e^{\\alpha_j x}$ 達の一次独立性</a></span></li><li><span><a href=\"#互いに異なる-$\\alpha_j$-に対する(多項式函数)×$e^{\\alpha_j-x}$-達の一次独立性\" data-toc-modified-id=\"互いに異なる-$\\alpha_j$-に対する(多項式函数)×$e^{\\alpha_j-x}$-達の一次独立性-3.4\"><span class=\"toc-item-num\">3.4 </span>互いに異なる $\\alpha_j$ に対する(多項式函数)×$e^{\\alpha_j x}$ 達の一次独立性</a></span></li></ul></li></ul></div>" | |
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| "execution_count": 1, | |
| "outputs": [] | |
| }, | |
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| "source": "showimg(\"image/jpeg\", \"images/generalized-Vandermonde-1.jpg\", scale=\"70%\")", | |
| "execution_count": 2, | |
| "outputs": [ | |
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| "output_type": "display_data", | |
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\" width=\"70%\">" | |
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| "source": "## 2階単独の定数係数線形常微分方程式\n\n複素数値函数 $x=x(t)$ に関する次の線形常微分方程式の解をすべて求めたい:\n\n$$\n\\ddot{x} + p\\dot{x} + qx = 0.\n\\tag{$*$}\n$$\n\nここで $p,q$ は複素定数である(応用上は $p,q$ は実数になることが多い). これを**2階単独の定数係数線形常微分方程式**と呼ぶ." | |
| }, | |
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| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 2階単独の定数係数線形常微分方程式と定数係数で線形な3項間漸化式の類似性\n\n方程式($*$)は高校数学で習う次の**定数係数で線形な3項間漸化式**に似ている:\n\n$$\na_{n+2} + pa_{n+1} + qa_n = 0.\n\\tag{$\\star$}\n$$\n\nこれを満たす数列 $(a_n)_{n\\in\\Z} = (\\ldots,a_{-2},a_{-1},a_0,a_1,a_2,\\ldots)$ をこの漸化式の解と呼ぶ. 漸化式($\\star$)の解をすべて求める問題と方程式($*$)の解をすべて求める問題は「ほぼ同じ問題である」と言ってよいほど似ている. 漸化式($\\star$)の解き方を復習し直せば, 方程式($*$)に関する以下の解説の内容もすんなり理解できるものと思われる. " | |
| }, | |
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| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 方程式を解くときの考え方\n\n方程式は解く手続きは以下の2つに分けられる.\n\n1. どのような手段でもよいので, とにかく, 方程式の解をたくさん見付ける.\n\n2. 見付けた解で方程式の解がすべて尽くされることを確認する.\n\nポイントは解を見付けるための手段は何であっても構わないということである. \n\nとにかくどんな「汚い手」を使っていても, 十分たくさんの解を見付けることができれば「勝ち」になる." | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 2階単独の定数係数線形常微分方程式の解全体が2次元のベクトル空間になること\n\nこのノートでは次の結果を認めて使うことにする.\n\n* 2階単独の定数係数線形常微分方程式($*$)の解全体の集合は2次元のベクトル空間になる.\n\n線形代数の教科書や講義などでベクトル空間の公理的な定義を学んだが, その定義をピンとくるまで理解できなかった人は, 「ベクトル空間になること」は「一次結合で閉じている(空でない)集合になっていること」とほぼ同義であると考えてよい. 実用的にはそれで困らないと思われる. (注意: 「一次独立」の概念はそのように雑な扱いが許されない.)\n\n「ベクトル空間になること」は(認めて使わなくても)容易に確認できる. 実際に確認しておこう. まず, 定数函数 $f(t)=0$ は方程式($*$)の解になっていることがすぐにわかる. これで方程式($*$)の解全体の集合が空集合でないことがわかった. 函数 $f(t)$ と $g(t)$ が方程式\n\n$$\n\\ddot{x} + p\\dot{x} + qx = 0\n\\tag{$*$}\n$$\n\nの解であると仮定する. すなわち\n\n$$\nf''(t)+pf'(t)+qf(t) = 0, \\quad\ng''(t)+pg'(t)+qg(t) = 0\n$$\n\nが成立していると仮定する. このとき, 定数 $a,b$ について,\n\n$$\n\\begin{aligned}\n&\n(af(t)+bg(t))'' + p(af(t)+bg(t))' + q(af(t)+bf(t))\n\\\\ &=\n(af''(t)+bg''(t)) + p(af'(t)+bg'(t)) + q(af(t)+bf(t))\n\\\\ &=\na(f''(t)+pf'(t)+qf(t)) +\nb(g''(t)+pg'(t)+qg(t))\n\\\\ &=\n0.\n\\end{aligned}\n$$\n\nこれで, 方程式($*$)の解全体の集合が一次結合で閉じていることがわかった. これで方程式($*$)の解全体の集合がベクトル空間をなすことがわかったと考えてよい.\n\nそのベクトル空間が2次元になることは以下で認めて使うことにする.\n\nベクトル空間が2次元になることの定義は, そのベクトル空間の2つの要素で一次独立なものが存在し, そのベクトル空間の任意の要素がその2つの一次独立なベクトルの一次結合で表せることである. (再注意: 一次独立性の概念は重要なので正確な意味と直観的な意味を必ず復習しておくこと!)\n\nゆえに, 上の結果を認めると, 方程式($*$)のすべての解を求めるためには, 一次独立な2つの解 $f(t),g(t)$ を見付ければ十分だということがわかる. そのとき, 方程式($*$)の任意の解 $x(t)$ はそれらの一次結合\n\n$$\nx(t) = a f(t) + b g(t)\n$$\n\nの形で一意的に表わされる. 我々はこのような $f(t),g(t)$ を何らかの方法で求めることができればよいということになった." | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 解の見付け方(1)\n\n方程式\n\n$$\n\\ddot{x} + p\\dot{x} + qx = 0\n\\tag{$*$}\n$$\n\nの解で $x(t) = e^{\\lambda t}$ の形のものを見つけてみよう. $x=x(t)=e^{\\lambda t}$ を($*$)に代入すると, \n\n$$\n\\lambda^2 e^{\\lambda t} + p\\lambda e^{\\lambda t} + qe^{\\lambda t} = 0.\n$$\n\nこれと\n\n$$\n\\lambda^2 + p\\lambda + q = 0.\n$$\n\nは同値である. したがって, \n\n$$\n\\lambda^2 + p\\lambda + q = (\\lambda-\\alpha)(\\lambda-\\beta)\n$$\n\nのとき, $f(t) = e^{\\alpha t}$ と $g(t) = e^{\\lambda t}$ は方程式($*$)の解である.\n\nもしも $\\alpha\\ne\\beta$ ならばそれらは異なる解であり, 一次独立であることを示せる(後で証明する). ゆえに $\\alpha\\ne\\beta$ のとき, 方程式($*$)の任意の解は\n\n$$\nx(t) = a e^{\\alpha t} + b e^{\\beta t}\n$$\n\nと一意に表わされる." | |
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| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 解の見付け方(2)\n\n$\\lambda^2+p\\lambda+q=(\\lambda-\\alpha)(\\lambda-\\beta)$ で $\\alpha\\ne\\beta$ の場合には方程式($*$)の2つの異なる解 $e^{\\alpha t}, e^{\\beta t}$ が得られて, それらが一次独立になるので, それですべての解を求める手続きは実質的に終了する. \n\nそれでは $\\alpha=\\beta$ (重解の場合)はどうすればよいのだろうか?\n\n$\\lambda^2+p\\lambda+q=(\\lambda-\\alpha)^2$ の場合には $f(t)=e^{\\alpha t}$ だけではなく, $g(t)=te^{\\alpha t}$ も($*$)の解になることを以下のようにして示せる:\n\n$$\n\\begin{aligned}\n&\ng(t) = t e^{\\alpha t},\n\\\\ &\ng'(t) = e^{\\alpha t}+\\alpha te^{\\alpha t} =\n(\\alpha t+1)e^{\\alpha t},\n\\\\ &\ng''(t) = \\alpha e^{\\alpha t} + \\alpha(1+\\alpha t)e^{\\alpha t} =\n(\\alpha^2 t+2\\alpha)e^{\\alpha t}\n\\end{aligned}\n$$\n\nより, \n\n$$\n\\begin{aligned}\ng''(t)+pg'(t)+qg(t) &= \n(2\\alpha + \\alpha^2 t + p(1+\\alpha t)+qt)e^{\\alpha t}\n\\\\ &=\n(\\alpha^2+p\\alpha+q)t + 2\\alpha + p)e^{\\alpha t}\n\\\\ &=\n0.\n\\end{aligned}\n$$\n\n最後の等号で $\\lambda^2+p\\lambda+q=(\\lambda-\\alpha^2=\\lambda^2-2\\alpha\\lambda+\\alpha^2$ であることを使った. $\\alpha^2+p\\alpha+q=0$ と $p=-2\\alpha$, $q=\\alpha^2$ が成立している. (以上の計算は実は不必要に煩雑になっており, 高階の場合に一般化することが難しくなっている. 後で高階の場合についても通用する楽な考え方を説明する.)\n\nさらに, $f(t)=e^{\\alpha t}$, $g(t)=te^{\\alpha t}$ は一次独立なので(後で証明する), $\\alpha=\\beta$ のとき方程式($*$)の任意の解は\n\n$$\nx(t) = ae^{\\alpha t} + bte^{\\alpha t}\n$$\n\nと一意に表わされる." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "### 結果のまとめ\n\n微分方程式\n\n$$\n\\ddot{x} + p\\dot{x} + qx = 0\n\\tag{$*$}\n$$\n\nの解は以下のようにして求められる. \n\n$\\lambda^2+p\\lambda+q=(\\lambda-\\alpha)(\\lambda-\\beta)$ であるとする.\n\n$\\alpha\\ne\\beta$ のとき, 方程式($*$)の任意の解は次のように一意に表わされる:\n\n$$\nx(t) = ae^{\\alpha t} + be^{\\beta t}.\n$$\n\n$\\alpha=\\beta$ のとき, 方程式($*$)の任意の解は次のように一意に表わされる:\n\n$$\nx(t) = ae^{\\alpha t} + bte^{\\alpha t}.\n$$" | |
| }, | |
| { | |
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| "cell_type": "markdown", | |
| "source": "### 一次独立性の証明\n\n#### $\\alpha\\ne\\beta$ のときの $e^{\\alpha t}, e^{\\beta t}$ の一次独立性の証明\n\n$\\alpha\\ne\\beta$ と仮定し, $a,b\\in\\C$ とし, \n\n$$\na e^{\\alpha t} + b e^{\\beta t} = 0\n$$\n\nであると仮定する. $e^{\\alpha t}, e^{\\beta t}$ の一次独立性を証明するためには $a=b=0$ となることを示せばよい. 上の式の両辺を微分すると,\n\n$$\n\\alpha a e^{\\alpha t} + \\beta b e^{\\beta t} = 0.\n$$\n\nさらに上の2つの公式において $t=0$ とおくと,\n\n$$\na + b = 0, \\quad \\alpha a + \\beta b = 0.\n$$\n\n左の等式の両辺に $\\beta$ をかけたものから, 右の等式を引くと, $(\\beta-\\alpha)a=0$ が得られる. $\\alpha\\ne\\beta$ より, $\\beta-\\alpha\\ne 0$ となるので $a=0$ となる. ゆえに $a+b=0$ より $b=0$ も得られる. 以上によって $e^{\\alpha t}, e^{\\beta t}$ が一次独立であることが示された.\n\n**注意:** $a + b = 0$, $\\alpha a + \\beta b = 0$ は行列を使えば\n\n$$\n\\begin{bmatrix}\n1 & 1 \\\\\n\\alpha & \\beta \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\na \\\\\nb \\\\\n\\end{bmatrix} =\n\\begin{bmatrix}\n0 \\\\\n0 \\\\\n\\end{bmatrix}\n$$\n\nと書き直される. 左辺の行列の行列式は $\\beta-\\alpha$ なので $\\alpha\\ne\\beta$ ならば $0$ にならない. 一般に正方行列について, その行列式が $0$ にならないこととその逆行列が存在することは同値である. ゆえに $\\alpha\\ne\\beta$ のとき, 左辺の行列の逆行列を両辺にかけることによって,\n\n$$\n\\begin{bmatrix}\na \\\\\nb \\\\\n\\end{bmatrix} =\n\\begin{bmatrix}\n0 \\\\\n0 \\\\\n\\end{bmatrix}\n$$\n\nを得ることができる. この筋道であれば高階の場合に一般化しやすい. 高階の場合への一般化では[Vandermondeの行列式](https://www.google.com/search?q=Vandermonde%E3%81%AE%E8%A1%8C%E5%88%97%E5%BC%8F)が出て来る. $\\QED$\n\n**Vandermondeの行列式の様な重要な数学的対象がこのような形で自然に必要になる.** 微分方程式論には数学のあらゆる分野の道具が総動員されることになる. だから, 微分方程式論を詳しく勉強すると, 自然に多くの数学について詳しくなることになる. もちろん, 線形代数についても詳しくなるであろう. 実際には線形代数のような基本的な数学的道具の価値は実際に応用される現場を見て初めて認識できることが多い." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "#### $e^{\\alpha t}, te^{\\alpha t}$ の一次独立性の証明\n\n$a,b\\in\\C$ とし, \n\n$$\na e^{\\alpha t} + b t e^{\\alpha t} = 0\n$$\n\nであると仮定する. $e^{\\alpha t}, t e^{\\alpha t}$ の一次独立性を証明するためには $a=b=0$ となることを示せばよい. 上の式の両辺を微分すると,\n\n$$\n(\\alpha a + b) e^{\\alpha t} + \\beta b t e^{\\alpha t} = 0.\n$$\n\nさらに上の2つの公式において $t=0$ とおくと,\n\n$$\na = 0, \\quad \\alpha a + b = 0.\n$$\n\nこれより, $a=b=0$ となることがわかるので, $e^{\\alpha t}, t e^{\\alpha t}$ が一次独立であることが示された.\n\n**注意:** 横ベクトル値函数 $[e^{\\alpha t}, t e^{\\alpha t}]$ の両辺を $t$ で微分すると, $[e^{\\alpha t}\\alpha, e^{\\alpha t} + t e^{\\alpha t}]$ になるが, これは行列を使って次のように表わされる:\n\n$$\n\\frac{d}{dt}[e^{\\alpha t}, t e^{\\alpha t}] = [e^{\\alpha t}\\alpha, e^{\\alpha t} + t e^{\\alpha t}] =\n[e^{\\alpha t}, t e^{\\alpha t}]\n\\begin{bmatrix}\n\\alpha & 1 \\\\\n0 & \\alpha \\\\\n\\end{bmatrix}.\n$$\n\n再右辺の $2\\times 2$ 行列は基底 $e^{\\alpha t}, te^{\\alpha t}$ で張られる2次元の函数空間に作用する線形変換 $d/dt$ の基底を用いた行列表示である. その行列表示は所謂[Jordan標準形](https://www.google.com/search?q=Jordan%E6%A8%99%E6%BA%96%E5%BD%A2)の形をしている. 高階の場合にも「重解を持つ場合」には同じようにしてJordan標準形の行列が現われる. $\\QED$\n\n**正方行列のJordan標準形の様な重要な数学的対象がこのような形で自然に必要になる.** 微分方程式論には数学のあらゆる分野の道具が総動員されることになる. だから, 微分方程式論を詳しく勉強すると, 自然に多くの数学について詳しくなることになる. もちろん, 線形代数についても詳しくなるであろう. 実際には線形代数のような基本的な数学的道具の価値は実際に応用される現場を見て初めて認識できることが多い." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "## 高階の場合\n\nこの節では $u=u(x)$ に関する次の微分方程式の解をすべて求める:\n\n$$\nu^{(n)} + p_1 u^{(n-1)} + \\cdots + p_{n-1}u' + p_n u = 0.\n\\tag{$*$}\n$$\n\nここで $u^{(k)}$ は $u=u(x)$ の $k$ 階の導函数を表しており, $p_1,\\ldots,p_{n-1},p_n$ は複素数の定数である. この微分方程式は $n$ 階単独の定数係数線形常微分方程式と呼ばれる. (この節では気分を変えて, $t$ ではなく, $x$ の函数を扱う. 読者が記号に頼った悪しき思考に陥らないように, わざとこのようにすることにした.)\n\n方程式($*$)の解全体の空間が $n$ 次元のベクトル空間になることを認めて使うことにする. ゆえに, 方程式($*$)の $n$ 個の解で一次独立になるものを見付けることができれば, 任意の解はそれらの一次結合で一意的に表わされることもわかる. したがって, 以下で方程式($*$)の $n$ 個の解で一次独立になるものを見付けることを目標とする." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "### 線形微分作用素\n\n函数 $f(x)$ をその導函数 $f'(x)$ に対応させる写像は $\\dfrac{d}{dx}$ と書かれる. その写像は線形写像になっており, \n\n$$\n\\frac{d}{dx}f(x) = f'(x)\n$$\n\nの左辺のように書かれる. これを一般化して, 函数をその $k$ 階の導函数に対応させる写像を\n\n$$\n\\left(\\frac{d}{dx}\\right)^k f(x) = f^{(k)}(x)\n$$\n\nと書くことにする. さらに毎回 $\\dfrac{d}{dx}$ と書くのは面倒なので, それを一文字の $\\d$ で表すことにする:\n\n$$\n\\d = \\frac{d}{dx}, \\quad \\d^k = \\left(\\frac{d}{dx}\\right)^k.\n$$\n\n函数を函数に対応させる線形写像 $P,Q$ の和と差と積とスカラー倍と函数 $a(x)$ 倍が\n\n$$\n\\begin{aligned}\n&\n(P\\pm Q)f(x) = Pf(x)\\pm Qf(x),\n\\\\ &\n(PQ)f(x) = P(Qf)(x),\n\\\\ &\n(\\alpha P)f(x) = \\alpha\\cdot Pf(x),\n\\\\ &\n(a(x) P)f(x) = a(x)\\cdot Pf(x)\n\\end{aligned}\n$$\n\nによって定義される. このようにして, 函数を函数に対応させる線形写像(作用素, 演算子, operatorなどと呼ばれる)達はまるで行列のように計算できる. (行列にも和と差と積とスカラー倍が定義されているのであった.) 行列の積が非可換であったのと同じように, 特別な場合を除いて(後でその特別な場合が出て来る!), $PQ=QP$ のような計算を自由にできなくなることに注意せよ. \n\n次の作用素は(線形常)微分作用素と呼ばれる:\n\n$$\nP = a_n(x)\\d^n + \\cdots + a_1(x)\\d + a_0(x).\n$$\n\nこの作用素は函数 $f(x)$ を次に対応させる線形写像になっている:\n\n$$\nPf(x) = a_n(x)f^{(n)}(x) + \\cdots + a_1(x)f'(x) + a_0(x)f(x).\n$$\n\n微分作用素は線形写像の重要な例になっている. \n\n**例:** $\\d=d/dx$ と $a(x)$ をかける操作は非可換である:\n\n$$\n\\begin{aligned}\n&\na(x)\\d f(x) = a(x)f(x), \n\\\\ &\n\\d(a(x)f(x)) = (a(x)f(x))' = a'(x)f(x) + a(x)f'(x)\n\\end{aligned}\n$$\n\nなので\n\n$$\n(\\d a(x) - a(x)\\d)f(x) = \\d(a(x)f(x))-a(x)\\d f(x) = a'(x)f(x).\n$$\n\n以上より, 作用素として, \n\n$$\n\\d a(x) - a(x)\\d = a'(x)\n$$\n\nとなっていることがわかる. $\\QED$" | |
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| "cell_type": "markdown", | |
| "source": "### 定数係数線形常微分方程式の微分作用素を用いた表示\n\n定数係数の線形常微分作用素\n\n$$\n\\d^n + p_1 \\d^{n-1} + \\cdots + p_{n-1}\\d + p_n\n$$\n\nを使うと, 微分方程式\n\n$$\nu^{(n)} + p_1 u^{(n-1)} + \\cdots + p_{n-1}u' + p_n u = 0\n\\tag{$*$}\n$$\n\nは\n\n$$\n(\\d^n + p_1 \\d^{n-1} + \\cdots + p_{n-1}\\d + p_n)u = 0\n$$\n\nと表わされる. " | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "### 重解がない場合の定数係数線形常微分方程式の解法\n\n定数倍と微分する操作は可換なので, 定数係数線形常微分作用素はまるで $\\d$ の(可換な)多項式のように計算できる. ゆえに,\n\n$$\n\\lambda^n + p_1\\lambda^{n-1} + \\cdots + p_{n-1}\\lambda + p_n =\n(\\lambda-\\alpha_1)\\cdots(\\lambda-\\alpha_n)\n$$\n\nのとき,\n\n$$\n\\d^n + p_1\\d^{n-1} + \\cdots + p_{n-1}\\d + p_n =\n(\\d-\\alpha_1)\\cdots(\\d-\\alpha_n)\n$$\n\nも成立している. このとき, 方程式($*$)は次のように書かれる:\n\n$$\n(\\d-\\alpha_1)\\cdots(\\d-\\alpha_n)u = 0.\n$$\n\n$\\d-\\alpha_j$ の積の順序は自由に交換できるので, もしも\n\n$$\n(\\d - \\alpha_j)u = u'-\\alpha_j u = 0\n$$\n\nすなわち\n\n$$\nu' = \\alpha_j u\n$$\n\nが成立しているならば, $(\\d-\\alpha_1)\\cdots(\\d-\\alpha_n)u = 0$ も成立する. そして, \n\n$$\nf_j(x) = e^{\\alpha_j x}\n$$\n\nは微分方程式 $u'=\\alpha u$ の解なので, もしも $n$ 個の $\\alpha_j$ 達が互いに異なるならば, 方程式($*$)の $n$ 個の異なる解が得られたことになる. 実はそれらは一次独立になる(後で証明する). \n\nゆえに, $n$ 個の $\\alpha_j$ が互いに異なるとき, 方程式($*$)の任意の解は次のように一意に表わされる:\n\n$$\nu(x) = a_1 e^{\\alpha_1 x} + \\cdots + a_n e^{\\alpha_n x}.\n$$\n\n**注意:** 以上の議論を見れば, $e^{\\alpha x}$ 型の函数が定数係数線形常微分方程式の解として出て来る理由がわかる. そのような解が出て来る理由は定数係数線形常微分方程式を与える定数係数線形常微分作用素が $(\\d-\\alpha_1)\\cdots(\\d-\\alpha_n)$ と表され, その互いに可換な因子である $\\d-\\alpha_j$ 達を作用させて $0$ になる函数として $e^{\\alpha_j x}$ が取れるからである. $\\QED$" | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "#### 定数係数でない場合の斉次1階の線形常微分方程式の解法\n\n一般に微分方程式 $u'(x) = a(x)u(x)$ の任意の解は\n\n$$\nu(x) = C e^{\\int a(x)\\,dx}\n$$\n\nと表わされる. $C$ は任意定数である. これもよく使われる.\n\n**例:** 作用素として $\\d x = x\\d + 1$ が成立することに注意すれば\n\n$$\n(\\d - x)(\\d + x) = \\d^2 - x\\d + \\d x - x^2 = \\d^2 - x^2 + 1\n$$\n\nが成立することがわかる. ゆえに, 微分方程式\n\n$$\n(\\d + x)u = 0, \\quad\\text{i.e.}\\quad u' = -xu\n$$\n\nの解\n\n$$\nu(x) = e^{\\int (-x)\\,dx} = e^{-x^2/2}\n$$\n\nは微分方程式\n\n$$\n(\\d^2 - x^2 + 1)u = (\\d - x)(\\d + x)u = 0\n$$\n\nの解になっていることがわかる. $e^{-x^2/2}$ は[量子調和振動子](https://www.google.com/search?q=%E9%87%8F%E5%AD%90%E8%AA%BF%E5%92%8C%E6%8C%AF%E5%8B%95%E5%AD%90)の基底状態であり, $0$ 番目の[Hermiteの多項式](https://www.google.com/search?q=Hermite%E3%81%AE%E5%A4%9A%E9%A0%85%E5%BC%8F)の $e^{-x^2/2}$ 倍になっている. $\\QED$\n\nこのように定数係数の場合に限らず, 微分作用素の「因数分解」は数学的に重要なテクニックの一つになっている." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "### 重解がある場合の定数係数線形常微分方程式の解法の準備\n\nそれでは $n$ 個の $\\alpha_j$ 達に重複がある場合にはどのようにして $n$ 個の一次独立な解を見付けたらよいのだろうか?\n\nそのためには作用素として,\n\n$$\ne^{\\alpha x}\\d e^{-\\alpha x} = \\d - \\alpha\n$$\n\nとなっていることが役に立つ. この公式は次のようにして示される:\n\n$$\n\\begin{aligned}\ne^{\\alpha x}\\d(e^{-\\alpha x}f(x)) &= \ne^{\\alpha x}(e^{-\\alpha x}f'(x) - \\alpha e^{-\\alpha x}f(x))\n\\\\ &=\nf'(x) - \\alpha f(x)\n\\\\ &= (\\d - \\alpha)f(x).\n\\end{aligned}\n$$" | |
| }, | |
| { | |
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| "cell_type": "markdown", | |
| "source": "#### 定数係数でない場合の非斉次1階の線形常微分方程式の解法\n\n一般に作用素として, \n\n$$\ne^{\\int a(x)\\,dx}\\d e^{-\\int a(x)\\,dx} = \\d - a(x)\n$$\n\nが成立している. 実際, \n\n$$\n\\begin{aligned}\ne^{\\int a(x)\\,dx}\\d\\left(e^{-\\int a(x)\\,dx}f(x)\\right) &= \ne^{-\\int a(x)\\,dx}\\left(e^{-\\int a(x)\\,dx}f'(x) - a(x) e^{-\\int a(x)\\,dx}f(x)\\right)\n\\\\ &=\nf'(x) - a(x) f(x)\n\\\\ &= (\\d - a(x))f(x).\n\\end{aligned}\n$$\n\nこれもよく使われる.\n\n**例:** 微分方程式 $(\\d - a(x))u = f(x)$ の解\n\n$$\nu(x) = e^{\\int a(x)\\,dx}\\int e^{-\\int a(x)\\,dx}f(x)\\,dx\n$$\n\nは以下のようにして得られる. $\\d - a(x) = e^{\\int a(x)\\,dx}\\d e^{-\\int a(x)\\,dx}$ なので, $(\\d - a(x))u = f(x)$ は\n\n$$\n\\d\\left(e^{-\\int a(x)\\,dx}u(x)\\right) = e^{-\\int a(x)\\,dx}f(x)\n$$\n\nに書き直される. 両辺を $x$ で不定積分すれば,\n\n$$\ne^{-\\int a(x)\\,dx}u(x) = \\int e^{-\\int a(x)\\,dx}f(x)\\,dx\n$$\n\nこれより, 上の解が得られる. $\\QED$\n\n**注意:** 形式的には $\\d^{-1} = \\int dx$ (微分の逆は積分)と書けるので, \n\n$$\n(\\d - \\alpha)^{-1} = \\left(e^{\\int a(x)\\,dx}\\d e^{-\\int a(x)\\,dx}\\right)^{-1} =\ne^{\\int a(x)\\,dx}\\,\\int dx\\; e^{-\\int a(x)\\,dx}\n$$\n\nを $(\\d-\\alpha)u(x)=f(x)$ の両辺に作用させて, 解 $u(x)$ が得られたと考えてもよい. $\\QED$" | |
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| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "### 重解がある場合の定数係数線形常微分方程式の解法\n\n一般に, 中間に挟まった $P^{-1}P$ がことごとく消えて, \n\n$$\n(PAP^{-1})^m = PAP^{-1}PAP^{-1}\\cdots PAP^{-1}PAP^{-1} = PA^m P^{-1}\n$$\n\nとなるので, 作用素としての公式 $e^{\\alpha x}\\d e^{-\\alpha x} = \\d - \\alpha$ より,\n\n$$\n(\\d - \\alpha)^m = e^{\\alpha x}\\d^m e^{-\\alpha x}\n$$\n\nとなる. ゆえに方程式\n\n$$\n(\\d - \\alpha)^m u = 0\n$$\n\nは\n\n$$\ne^{\\alpha x} \\d^m (e^{-\\alpha x} u(x))=0\n$$\n\nに書き直される. これは $e^{-\\alpha x} u(x)$ を $m$ 回微分すると消えることを意味しており, そうなることは, $e^{-\\alpha x} u(x)$ が $x$ に関する $m-1$ 次以下の多項式函数になることと同値である. ゆえに, 解 $u(x)$ は\n\n$$\nu(x) = (a_{m-1}x^{m-1}+\\cdots + a_1 x + a_0)e^{\\alpha x}\n$$\n\nと一意に表わされる. ゆえに方程式 $(\\d - \\alpha)^m u = 0$ の解全体のなすベクトル空間の基底として,\n\n$$\ne^{\\alpha x},\\; x e^{\\alpha x},\\;\\ldots,\\; x^{m-1}e^{\\alpha x}\n$$\n\nが取れる. \n\n以下では\n\n$$\n\\d^n + p_1\\d^{n-1} + \\cdots + p_{n-1}\\d + p_n =\n(\\d-\\alpha_1)^{m_1}\\cdots(\\d-\\alpha_r)^{m_r}\n$$\n\nで $\\alpha_j$ 達が互いに異なると仮定する. \n\n上で注意したことより, 微分方程式\n\n$$\n(\\d^n + p_1\\d^{n-1} + \\cdots + p_{n-1}\\d + p_n)u =\n(\\d-\\alpha_1)^{m_1}\\cdots(\\d-\\alpha_r)^{m_r}u = 0\n$$\n\nの解として, 以下が取れることがわかる:\n\n$$\ne^{\\alpha_j x},\\; x e^{\\alpha_j x},\\;\\ldots,\\; x^{m_j-1}e^{\\alpha_j x}, \\quad j=1,2,\\ldots,r.\n$$\n\n実はこれらが上の微分方程式の解全体のなすベクトル空間の基底になっていることを示せる(一次独立性を後で示す)." | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## 一次独立性の証明\n\nこの節では, 函数達 $f_1(x),\\ldots,f_n(x)$ の一次独立性の証明を扱う." | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "### Wronskian\n\n函数 $f_1(x),\\ldots,f_n(x)$ に対する\n\n$$\nW(f_1,\\ldots,f_n)(x) = \n\\begin{vmatrix}\nf_1(x) & f_2(x) & \\cdots & f_n(x) \\\\ \nf_1'(x) & f_2'(x) & & f_n'(x) \\\\\n\\vdots & \\vdots & \\cdots & \\vdots \\\\\nf_1^{(n-1)} & f_2-^{(n-1)}(x) & \\cdots & f_n^{(n-1)}(x) \\\\\n\\end{vmatrix}\n$$\n\nを $f_1,\\ldots,f_n$ の **Wronskian (ロンスキアン, ロンスキー行列式)** と呼ぶ." | |
| }, | |
| { | |
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| "source": "#### 函数の組の一次独立性の十分条件\n\nもしも, ある $x_0$ で $W(f_1,\\ldots,f_n)(x_0)\\ne 0$ となっていれば $f_1,\\ldots,f_n$ が一次独立である.\n\n**証明:** $W(f_1,\\ldots,f_n)(x_0)\\ne 0$, $a_1f_1+\\cdots+a_nf_n=0$ と仮定する. $a_1=\\cdots~a_n=0$ を示せばよい. $a_1f_1+\\cdots+a_nf_n=0$ の両辺を何度も微分することによって $a_1 f_1^{(k)}+\\cdots+a_n f_n^{(k)}=0$ を得る. ゆえに\n\n$$\n\\begin{bmatrix}\nf_1(x) & f_2(x) & \\cdots & f_n(x) \\\\ \nf_1'(x) & f_2'(x) & & f_n'(x) \\\\\n\\vdots & \\vdots & \\cdots & \\vdots \\\\\nf_1^{(n-1)} & f_2-^{(n-1)}(x) & \\cdots & f_n^{(n-1)}(x) \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\na_1 \\\\\na_2 \\\\\n\\vdots \\\\\na_n \\\\\n\\end{bmatrix} =\n\\begin{bmatrix}\n0 \\\\\n0 \\\\\n\\vdots \\\\\n0 \\\\\n\\end{bmatrix}\n$$\n\nを得る. 左辺の中の行列の行列式は $x=x_0$ で $0$ でないので, その逆行列が存在する. その逆行列を両辺に左からかければ $a_1=\\cdots=a_n=0$ が得られる. $\\QED$\n\n**注意:** $f_1,\\ldots,f_n$ が一次独立であっても, ある $a$ で $W(f_1,\\ldots,f_n)(a)=0$ となるものが存在する場合がある. 例えば, $\\varphi(x)$ を $x\\leqq -2$ で $0$ になり, $x\\geqq -1$ で $1$ となる $C^\\infty$ 函数とすると, $W(f_1,\\ldots,f_n)(0)\\ne 0$ となる $f_1,\\ldots,f_n$ について, $g_j = f_j\\varphi$ とおくと, $W(g_1,\\ldots,g_n)(0)=W(f_1,\\ldots,f_n)(0)\\ne 0$, $W(g_1,\\ldots,g_n)(-3)\\ne 0$ となる. さらに強力な次のような例も存在する. $\\QED$\n\n**例:** $x\\in\\R$ について, $f_1(x)=x^2$, $f_2(x)=|x|x$ のとき, $f_1'(x)=2x$, $f_2'(x)=2|x|$ なので,\n\n$$\nW(f_1,f_2)(x) =\n\\det\n\\begin{bmatrix}\nx^2 & |x|x \\\\\n2x & 2|x| \\\\\n\\end{bmatrix} = \nx^2\\cdot 2|x| - 2x\\cdot|x|x = 0.\n$$\n\nこのように $f_1,f_2$ のWronskianはすべての $x\\in\\R$ について $0$ になる. 一方, $a_1 f_2 + a_2 f_2 = 0$ のとき, $x=\\pm 1$ を代入すると,\n\n$$\na_1 + a_2 = 0, \\quad a_1 - a_2 =0\n$$\n\nとなり, これから $a_1=a_2=0$ が得られるので, $f_1, f_2$ は一次独立であることがわかる. $\\QED$" | |
| }, | |
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| "cell_type": "markdown", | |
| "source": "#### 線形常微分方程式の解のWronskian\n\n$f_1(x),\\ldots,f_n(x)$ は微分方程式\n\n$$\nu^{(n)}(x) = a_1(x)u^{(n-1)}(x) + a_2(x)u^{(n-2)}(x) + \\cdots + a_n(x)u(x)\n$$\n\nの解であると仮定する. このとき, $f_j^{(i-1)}$ を $(i,j)$ 成分とする $n\\times n$ 行列の第 $i$ 行を $f^{(i-1)}$ と書くと, \n\n$$\n\\frac{d f^{(n-1)}(x)}{dx} = a_1(x)f^{(n-1)}(x) + a_2(x)f^{(n-2)}(x) + \\cdots + a_n(x)f^{(0)}(x)\n$$\n\nなので\n\n$$\n\\begin{aligned}\n\\frac{d}{dx}W(f_1,\\ldots,f_n) &=\n\\sum_{i=1}^{n-1}\\det\n\\begin{bmatrix}\nf^{(0)} \\\\\n\\vdots \\\\\ndf^{(i-1)}/dx \\\\\nf^{(i)} \\\\\n\\vdots \\\\\nf^{(n-1)} \\\\\n\\end{bmatrix} +\n\\det\n\\begin{bmatrix}\nf^{(0)} \\\\\nf^{(1)} \\\\\n\\vdots \\\\\nf^{(n-2)}\\\\\ndf^{(n-1)}/dx \\\\\n\\end{bmatrix}\n\\\\ &=\n\\det\n\\begin{bmatrix}\nf^{(0)} \\\\\nf^{(1)} \\\\\n\\vdots \\\\\nf^{(n-2)}\\\\\na_1(x)f^{(n-1)} + a_2(x)f^{(n-2)} + \\cdots + a_n(x)f^{(0)} \\\\\n\\end{bmatrix}\n\\\\ &=\n\\det\n\\begin{bmatrix}\nf^{(0)} \\\\\nf^{(1)} \\\\\n\\vdots \\\\\nf^{(n-2)}\\\\\na_1(x)f^{(n-1)} \\\\\n\\end{bmatrix} =\na_1(x)W(f_1,\\ldots,f_n).\n\\end{aligned}\n$$\n\n3つ目の等号で, 行列式の中で第 $i=1,\\ldots,n-1$ 行 $f^{(i-1)}$ の $a_{n+1-i}(x)$ 倍を第 $n$ 行から引いた. ゆえに\n\n$$\nW(f_1,\\ldots,f_n)(x) = \\exp\\left(\\int_a^x a_1(\\xi)\\,d\\xi\\right)W(f_1,\\ldots,f_n)(a).\n$$\n\n特に, $W(f_1,\\ldots,f_n)(a)\\ne 0$ ならば $W(f_1,\\ldots,f_n)(x)\\ne 0$ となる. すなわち, $n$ 階の線形常微分方程式の $n$ 個の解のWronskianはどこかの $x$ で $0$ にならなければ, 残りの $x$ でも $0$ でなくなる." | |
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| "source": "#### 行列式の微分\n\n一般に函数成分の行列式の微分は以下のようになる.\n\n函数 $a_{ij}(x)$ を成分とする $n\\times n$ 行列を $A(x) = [a_{ij}(x)]$ と書き, その第 $j$ 列を $a_j(x)$ と書き, その $(i,j)$ 余因子を $\\Delta_{ij}(x)$ と書き, $\\Delta_{ij}(x)$ を $(i,j)$ 成分とする $n\\times n$ 行列を $Delta(x) = [Delta_{ij}(x)]$ と書く. $\\det A(x)\\ne 0$ であると仮定する. このとき, 行列 $X$ の転置を $X^T$ と表すと, \n\n$$\n\\Delta(x)^T = \\det(A(x))A(x)^{-1}\n$$\n\nなので, 以下が成立する:\n\n$$\n\\begin{aligned}\n\\frac{d}{dx}\\det A(x) &= \\sum_{j=1}^n \\det[a_1(x),\\ldots,a_j'(x),\\ldots,a_n(x)]\n\\\\ &=\n\\sum_{j=1}^n\\sum_{i=1}^n \\Delta_{ij}(x) a_{ij}'(x) =\n\\tr\\left(\\Delta(x)^T \\frac{d A(x)}{dx}\\right)\n\\\\ &=\n\\tr\\left(A(x)^{-1}\\frac{d A(x)}{dx}\\right)\\,\\det(A(x)).\n\\end{aligned}\n$$" | |
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| "source": "### Vandermondeの行列式\n\n次の公式が成立している:\n\n$$\n\\begin{vmatrix}\n1 & 1 & \\cdots & 1 \\\\\nx_1 & x_2 & \\cdots & x_n \\\\\n\\vdots & \\vdots & & \\vdots \\\\\nx_1^{n-1} & x_2^{n-1} & \\cdots & x_n^{n-1} \\\\\n\\end{vmatrix} =\n\\prod_{1\\leqq i < j \\leqq n} (x_j - x_i).\n$$\n\n左辺をVandermonde(ファンデルモンド, ヴァンデルモンド)の行列式と呼び, 右辺を差積と呼ぶのであった." | |
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| "source": "この公式の証明は $n$ に関する帰納法で以下のように遂行される. $n=1$ の場合には両辺が $1$ になるので成立している. $n$ の場合に成立していると仮定する. このとき,\n\n$$\n\\begin{aligned}\n&\n\\begin{vmatrix}\n1 & 1 & \\cdots & 1 & 1 \\\\\nx_1 & x_2 & \\cdots & x_n & x_{n+1} \\\\\n\\vdots & \\vdots & & \\vdots & \\vdots \\\\\nx_1^{n-1} & x_2^{n-1} & \\cdots & x_n^{n-1} & x_{n+1}^{n-1} \\\\\nx_1^n & x_2^n & \\cdots & x_n^n & x_{n+1}^n \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n\\begin{vmatrix}\n0 & 0 & \\cdots & 0 & 1 \\\\\nx_1 -x_{n+1} & x_2 -x_{n+1} & \\cdots & x_n -x_{n+1} & x_{n+1} \\\\\n\\vdots & \\vdots & & \\vdots & \\vdots \\\\\nx_1^{n-1}-x_{n+1}^{n-1} & x_2^{n-1}-x_{n+1}^{n-1}& \\cdots & x_n^{n-1}-x_{n+1}^{n-1} & x_{n+1}^{n-1} \\\\\nx_1^n -x_{n+1}^n & x_2^n -x_{n+1}^n & \\cdots & x_n^n -x_{n+1}^n & x_{n+1}^n \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n\\begin{vmatrix}\n0 & 0 & \\cdots & 0 & 1 \\\\\nx_1 -x_{n+1} & x_2 -x_{n+1} & \\cdots & x_n -x_{n+1} & 0 \\\\\n\\vdots & \\vdots & & \\vdots & \\vdots \\\\\nx_1^{n-1}-x_{n+1}^{n-1} & x_2^{n-1}-x_{n+1}^{n-1}& \\cdots & x_n^{n-1}-x_{n+1}^{n-1} & 0 \\\\\nx_1^n -x_{n+1}^n & x_2^n -x_{n+1}^n & \\cdots & x_n^n -x_{n+1}^n & 0 \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n(x_1-x_{n+1})(x_2-x_{n+1})\\cdots(x_n-x_{n+1})\n\\\\ \\times\\; &\n\\begin{vmatrix}\n0 & 0 &\n\\cdots & 0 & 1 \\\\\n1 & 1 &\n\\cdots & 1 & 0 \\\\\n\\vdots & \\vdots &\n & \\vdots & \\vdots \\\\\nx_1^{n-2}+\\cdots+x_{n+1}^{n-2} & x_2^{n-2}+\\cdots+x_{n+1}^{n-2} &\n\\cdots & x_2^{n-2}+\\cdots+x_{n+1}^{n-2} & 0 \\\\\nx_1^{n-1}+x_1^{n-2}x_{n+1}+\\cdots+x_{n+1}^{n-1} & x_2^{n-1}+x_2^{n-2}x_{n+1}+\\cdots+x_{n+1}^{n-1} &\n\\cdots & x_2^{n-1}+x_2^{n-2}x_{n+1}+\\cdots+x_{n+1}^{n-1} & 0 \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n(x_1-x_{n+1})(x_2-x_{n+1})\\cdots(x_n-x_{n+1})\n\\begin{vmatrix}\n0 & 0 & \\cdots & 0 & 1 \\\\\n1 & 1 & \\cdots & 1 & 0 \\\\\nx_1 & x_2 & \\cdots & x_n & 0 \\\\\n\\vdots & \\vdots & & \\vdots & \\vdots \\\\\nx_1^{n-1} & x_2^{n-1} & \\cdots & x_n^{n-1} & 0 \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n(x_1-x_{n+1})(x_2-x_{n+1})\\cdots(x_n-x_{n+1})\n(-1)^n\n\\begin{vmatrix}\n1 & 1 & \\cdots & 1 \\\\\nx_1 & x_2 & \\cdots & x_n \\\\\n\\vdots & \\vdots & & \\vdots \\\\\nx_1^{n-1} & x_2^{n-1} & \\cdots & x_n^{n-1} \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n(x_{n+1} - x_1)(x_{n+1}-x_2)\\cdots(x_{n+1}-x_n)\n\\begin{vmatrix}\n1 & 1 & \\cdots & 1 \\\\\nx_1 & x_2 & \\cdots & x_n \\\\\n\\vdots & \\vdots & & \\vdots \\\\\nx_1^{n-1} & x_2^{n-1} & \\cdots & x_n^{n-1} \\\\\n\\end{vmatrix}\n\\\\ =\\; &\n(x_{n+1} - x_1)(x_{n+1}-x_2)\\cdots(x_{n+1}-x_n)\n\\prod_{1\\leqq i<j\\leqq n}(x_j-x_i)\n\\\\ =\\; &\n\\prod_{1\\leqq i<j\\leqq n+1}(x_j-x_i).\n\\end{aligned}\n$$\n\n1つ目の等号では第 $n+1$ 列を他の列から引き, 2つ目の等号では第1行の $x_{n+1}^{i-1}$ 倍を第 $i=2,\\ldots,n+1$ 行から引いた. 3つ目の等号は第 $j=1,\\ldots,n$ 列が $x_j-x_{n+1}$ で割り切れることを使った. 4つ目の等号では, 第 $n$ 行の $x_{n+1}$ 倍を第 $n+1$ から引き, それと同様の操作を下から順番に行った. 残りは易しい計算である." | |
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| "source": "**注意:** 以上では行列式に関する操作による帰納法でVandermondeの行列式が差積に等しくなることを証明したが, 他にも様々な証明がある. 例えば, Vandermondeの行列式が $x_i=x_j$ ($i\\ne j$) のとき0になることから, $x_j-x_i$ ($i<j$) で割り切れることを使う証明も有名である. $\\QED$" | |
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| "source": "### 互いに異なる $\\alpha_j$ に対する $e^{\\alpha_j x}$ 達の一次独立性\n\n$\\alpha_j\\in\\C$ であるとし, $f_j(x)=e^{\\alpha_j x}$ とおく. このとき, $f_1,\\ldots,f_n$ のWronskianは, Vandermondeの行列式が差積に等しくなることより, \n\n$$\n\\begin{aligned}\nW(f_1,\\ldots,f_n) &=\n\\begin{vmatrix}\ne^{\\alpha_1 x} & e^{\\alpha_2 x} & \\cdots & e^{\\alpha_n x} \\\\\n\\alpha_1 e^{\\alpha_1 x} & \\alpha_2 e^{\\alpha_2 x} & \\cdots & \\alpha_n e^{\\alpha_n x} \\\\\n\\vdots & \\vdots & & \\vdots \\\\\n\\alpha_1^{n-1} e^{\\alpha_1 x} & \\alpha_2^{n-1} e^{\\alpha_2 x} & \\cdots & \\alpha_n^{n-1} e^{\\alpha_n x} \\\\\n\\end{vmatrix}\n\\\\ &=\ne^{(\\alpha_1+\\cdots+\\alpha_n)x} \\prod_{1\\leqq i<j\\leqq n}(\\alpha_j - \\alpha_i).\n\\end{aligned}\n$$\n\nとなる. ゆえに, $\\alpha_1,\\ldots,\\alpha_n$ が互いに異なるならば, このWronskianは決して $0$ にならないので, $f_j(x)=e^{\\alpha_j x}$ ($j=1,\\ldots,n$) は一次独立になる." | |
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| "source": "### 互いに異なる $\\alpha_j$ に対する(多項式函数)×$e^{\\alpha_j x}$ 達の一次独立性\n\n$f_1(x),\\ldots,f_r(x)$ は複素係数の多項式函数であるとし, $\\alpha_1,\\ldots,\\alpha_r\\in\\C$ は互いに異なると仮定する. このとき,\n\n$$\nf_1(x)e^{\\alpha_1 x} + \\cdots + f_r(x)e^{\\alpha_r x} = 0 \\quad (x\\in\\R)\n$$\n\nならば $f_1=\\cdots=f_r=0$ となる. このことから, $e^{\\alpha_j x}, x e^{\\alpha_j x}, x^2 e^{\\alpha_j x}, \\ldots$ 達が一次独立であることがわかる.\n\n**証明:** 一致の定理より, すべての実数 $x$ について $f_1(x)e^{\\alpha_1 x} + \\cdots + f_r(x)e^{\\alpha_r x} = 0$ が成立することと, すべての複素数 $x$ についてそれが成立することは同値である. ゆえに $f_1,\\ldots,f_r$ の中に $0$ でないものが存在すると仮定して,\n\n$$\nf_1(z)e^{\\alpha_1 z} + \\cdots + f_r(z)e^{\\alpha_r z} = 0 \\quad (z\\in\\C)\n\\tag{$*$}\n$$\n\nとならないことを示せばよい. $f_1,\\ldots,f_r\\ne 0$ かつ $\\max\\{|\\alpha_1|,\\ldots,|\\alpha_r|\\} = |\\alpha_r|$ と仮定してよい. ($0$ になる $f_j$ が存在するなら除いて考える.) $\\alpha_1,\\ldots,\\alpha_r$ が互いに異なるならば, $\\alpha_r = |\\alpha_r|e^{i\\theta}$, $\\theta\\in\\R$ とおくとき, \n\n$$\n\\real(\\alpha_1 e^{-i\\theta}), \\ldots, \\real(\\alpha_{r-1} e^{-i\\theta}) < \\real(\\alpha_r e^{-i\\theta})\n$$\n\nとなる. これでもしも ($*$) が成立しているならば, 絶対値が十分大きなすべての $z\\in\\C$ について, \n\n$$\n\\frac{f_1(z)}{f_r(z)}e^{(\\alpha_1-\\alpha_r)z} + \\cdots +\n\\frac{f_{r-1}(z)}{f_r(z)}e^{(\\alpha_{r-1}-\\alpha_r)z} + 1 = 0\n$$\n\nとなる. しかし, $z=t e^{-i\\theta}$, $t\\in\\R$ とおいて, $t\\to\\infty$ とすると, $j=1,\\ldots,r-1$ について, \n\n$$\n\\left|\\frac{f_j(z)}{f_r(z)}e^{(\\alpha_j-\\alpha_r)z}\\right| =\n\\left|\\frac{f_j(z)}{f_r(z)}\\right|e^{(\\real(\\alpha_1 e^{-i\\theta})-\\real(\\alpha_r e^{-i\\theta}))t}\\to 0\n$$\n\nとなるので, $1=0$ となって矛盾する. これで($*$)が成立していないことがわかった. $\\QED$" | |
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| "source": "**注意:** ツイッターにおける発言\n\n* https://twitter.com/genkuroki/status/1118680294343659520\n\nにおける注意も参照せよ. 以下の画像中の行列式の公式(の一般の場合)を使っても, 互いに異なる $\\alpha_j$ 達に対する $e^{\\alpha_j x}, x e^{\\alpha_j x}, x^2 e^{\\alpha_j x}, \\ldots$ 達の一次独立性を(より代数的に)証明することができる. $\\QED$" | |
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| "source": "showimg(\"image/jpeg\", \"images/generalized-Vandermonde-1.jpg\", scale=\"70%\")", | |
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WMP1oG3AA4rL0Jg7JnFZBCHGM/jWXzVAxS2xkrpa7S16J0hHXCoR79JoDOQtsMLwu1bdKzLoWrUDRW5CkGnWyHASUwuwrACijUlMoIt64v7X7RmbVb0tfz/kjnCP8LaFUnhoUTmaz+5hsFuvfLKhbU1GN1VpkyI9IPHXUFGXWax0l11YVDqWKkM57QEWDIt0sM2+xvGj/AChLC1lLH5zMQtK9XbYVqj+Mg7f9qKKpa1oL8RqbPThG8Idyok7MAitTol5reJOLYq8BqZ3/AFhMIwxiuXTv0nHfEou7xxEldC9BVqbf9q4lJcLc6Xp3ehG4whKhbwuoaAssVJl4XtqRWXoo/mKyxX2GWl4G6y79HaGSUl5boNe8WSao7GWk/wBvxLXK09dwpwYhcApeqj+yASRfasl3FQzTN0u7/wARw/aeS7Q99UlMg2ZmaHy7rNLKB0NVIqNY5ibVQa3ZlRgup2kQcAVmjVhacgZjQZEtrL/fjsCE29AA93tF/UlHalNfhOmtR1vb5Ht6duT7k9i4e3/lcI3gow9sRre0V1nmbBQKOqvfGIeqfNQsxdE/hf8Aa7mO705cd2Jz20dX8/qWSwxp0+6ffP8A2Vf+j/2E2BQFAdD/ALUGa6FD8Aal1DE8iUy6LTvANlcEGMOlHskNcudAWnYoqg2g5Z/KhbdqzekMaRkQmwxrLpzRGpT1K0yh6lte0VhPia5wnR99CMQBcWulQyZBE0SUB1itw5yya0C7RlX60SjNKoHYINjIoMfRphmEkY2hDNGcRdVB4Rw1FYEsEflGpSmlnXokFBtkBFZd3V//ABGRvq6FJgxldIs7b63BTR0Ypqq3pvgrGGOGX7tJZSs4/EQO6KYwWFYxb+WW935jYIqjAr0HRU950QQ+QMyiEGeCsL7/AJg6Q0YJjV2YKLAO7FZsaL3es6ao3GT41WPMpKCFRSkp7jeuozO5jQOjY0OVMNSGVknD7/8Aa8x3enIbAQEUGgvWc9tHV/P/AH9FkBIhtAshl07wkxAmS+bquiveAUoCAEoLYqoeCZ9C0Db/AIm3VC8FXXvOmj/Ayrf+7d5BVNQSpaQ8BrK+/dn0H/2Af88Yb3j9Fdz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4ldz4m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Leb/lvN/y3m/5bzf8ALeb/AJbzf8t5v+W83/Lf1s/0Zf8AhLIBVot1dgF9pdhNfLRwrHRV7znfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78Tnfic78TlfiVfwxgrVhvcjZrPgtRGk+T/BozBQ86f6IYDPgFbOX+ZyvzBJgWI2JBli+D/f9L2lTSaalIhLMn6NORz/ZLeNjbXFjArQbsLysOUB2QD2ZG+kIEDQEao6DuXDmrlrKpqreqjwIznRmYFlDpLg/Ld0gjRd1BrbkjK7lb6Sp1ZiycjXQ42gIgBlXpAfNT3XjQMFyCkRitMKFuqrQRookQwtVekzmoQizhQlAbHazGsX3VKGC6aABoNMbwzLXsIovgNqDSjOsQhryGkraIUI4zbcJ5oHHEfwDMq64bAw0qnp0aKZbyha1cLuCtyVh450QBFnXQdsjH18D8kr7h+tCpR1M7F7VUUWgVdiKaAKWsZ69KN6/hK2OGsHujir3vFUrqlwSWTB6tEF4NKO7GBNSvQ3zRbFLccMMCyFDTgNKsaVi9qSG8GUOa20Mss6NQ+ZCxGxIragr9w4vpdX0lTNeKEo1q51YOS8YvXb6jVjDLpAkOBfUxpk0dcK7iy1MWoK6wC+9vYj8+ChJ0R0O9QFn0MIGvDd2XgWPJ1nVGwXSqwwK9JQzc3k0lYGp3w1qOXYE2dJS1a4TYSgppferaaQHjTRjvRkYXonWZUjjkruVfXSOhYhQBqrEl+IVr1oOja5UWEmKRRtmxZipRM7jcdxNNF9sNIkj6tSD1Vh8OMCoW+GM1UwG8cfVJEaJ1Oh2ahtfMO462sqdGDsw1woj3IizIWadWhVsii4t5EcZY1YyMGuyCSsBY9yGaGOH1J5biqwZLM6y3WCaUzowoGNR7RIrjhHsgMVeSwyCbNR4MR2YdE63gbjNM8IhFdGKzu9sitsACtFNQe7UAJRDQoddiTJeBYl3FT3ChdDRqsutRzzTkonYCysXkMhjEnGmkLO9JHbhLiN0tik1HW8hKd89ELVONWFapylS2uJBZqZZfi5kjwQLaHsWTCR/ydSXbql5os0dcC5hVHxbyI9TGrGRjtaGgNVXAHeEU5aXGqBwNrlk0fAgUZ0FyUMGvQYBQA5UcX2w3hHpV7Q6qsPhxgVhbxZmVGAO7HrlRYL30Xo2NS/d8ou0psqoxBljAl+KFigosvPakS+JGoDdFnGa1tquGYlgQXqFBM5Qdq+rUnAe5nMcNuTQKCrkSsNdWa5o2/qlioKDW14Vs6VsinRKM8UTSVlWomLk61de0blkCFQFLd3bTOGcmfABm7q7aLq4P2ZQc5DqVprLgRnN0DRWcJ0sioedupUy6CuvtTGd1Q/xK/bjdtQBmry10HrUv0BsuWSlpYsxBDtSXWiuabYq7mUuw15zbTAFZz2mqBDQr8JHJnFmWD67PamUwsLo1u8JLKuDUr8E3XWWMrlkiCW2DT+A609oLQza4tU/mmq1vEGoRJtgsraIHR6wKgFRoA6st0XMFcvhVLyCxZdO7w2DQdCs3jSHQ1jHyFRHcZkmOZvd0ZHTTTFK/wA2BTuGLVBuzK3hCAz8gdeiNyyC2BpdELCHVhXQh/HO69qMga7JvSvpnOQ9jW/yxmNbKTlVWIjdPXaKPO8sAoeoN1/wEC7pzmtbitoCN5jFsyLYKvRe5ENFCy9ACcb3Tl++HiFjQjbehYlgS82stoAs0PSHWPtWmq1y7uYt1kBQLBoyh00ly1TaSpYOnq05HP8AZHvxjSqjQSxBOyTJQns9RLV8roKgiyYbYDoatDm1c5ZVx8JVEGsFkNN2QctgIc7bUu1N6twV6uycrqNl1e19IMk7iZL1tCKaPZGI5YGCrALqa4hI/ZZRFp6XvtcrTGoplRkbCWAOCiusiCVOo0UBvMJ+Fj4oKAzTdHZlbbmq+ECynASgraaIpLcWKM2KXXUqDLNqNZVgdt79qDp4QaiZHoBtLjMRIvIHCI7lB1pDhlCICVGwlHZ3hGAz4/MlZIlmGVG3R0IRgApD8w6yGbZ/Nut6gAhQf1TZcGPKYSUq6rpeuJmiMcRo1iw1NEj07yv810wqa5M6UEspnkBTUTVovFSkWDjJIT0HOzAIAKg0ImZwaWsrPC6zXWa6qBVo2xqCs2uqwu1zcwgipAJpoQjwPOC1XeAsrR2JVX8JKjLqanVZRJ37zYXU2tZMzAVPI16JTXgNU0gKCGlnQVAM0VYx2KRnzWAepu9H8rczM6G5BqFhemTCGEURNIKHV+EGKBYwNebLWqa9ZSQU5GlpsMlOtpqsZVWgu9q91vVR05g7SEXjXhpkxlGo7Qi62rUUcXoAwNoRxZgXsOjNPYljFoRCsGrEEeizAZHOhwl1y3eTNMLusTVsEckcD8JbJXjFAVZpgvYyoQeC1pUNBcAs0wLatG15GmNFEoC/JA2oZq23obCrys5ZX2EARIOkLghXnJfX85osLYFbDXF8seQxbwLZ/KqWvJAJagvC9Kad5oKX6dSpiri0t4JZmqzQLOwuJx5S1VguQtPy1oMdOo+NUNIT4rvGF3WOwaa1S6KsZ0FtCbhAvqb0/JFrSOfKTt0jTqUW0E0uhEZGh0tjZbkwipOA0oaXcRpKwTC2DlbWjYhC/wCVBUlIg2NCN1uoNGgAoRpK3jmUmu6LJuihcijGTl/t7dgNRY9zMEMVy6UCZPQPwlw3+QANcrpbpuoNdCwh5DFvAtnrlVJ95EjIQmuobneI2Bub0QoZaLdc5qQogUqlkUKGKYj7oE66ADfCS7ZRZB38QvLAlqqluH/qSoashXzQI1SYFSVLIG+TLrljHQ4BAzDi2Grlgma3nB0FFqLsOkba/GrukMgVwsJWVg5DvUUI1dIkwEQH9NYSGF6RAwwAV9sUsKu9JZOl1xY6IENWUg9cIAyFpMxYIuwbu5XRtZoNcKO1tQJ9AruzrF4U9ulkr1EHqAgaLoDV/K8eCy4sKmyW4Evjt/pNSmK1i0YYC5oim16DqHe44tgGqSrVoQLsHeLRsalNIF6UvQcJHZq4y8zpeNdmW8SzVcTrHVUuiktgrCxJ93BHGoe8LIikawoQGxYDO8D4iuZB12K6qq82JrvlzMqKqurNYIINOj4B7EvoqoV1KT4EDRowWqrAxXNoD0VqFwNNIvL/ANYIsYg/AnU0LaCh6BGsXE4OrHDwypdLp0FEqQK0TcaaXV1YZSEOw6MN3VlVi8xCuCUmBbAJfQDNOgnFbV0OFl2bQtQBFDXKxRVXpiVO3a665AApvr1iPO9JlEwCitVwXKL52tVfZWCmOsYKxl0Qhgr4X2iliVs+AAvRt8f8DsL6fsxrIKNArTWZpRViOWj1x8ehPje6cv3+h1vCWFKkf8oHTBgimK2jSekohFV0zrXVf0MNORz/AGTJudqtFJ8MdklDBbwwuoRs6TWRAwZraFYdjtmDtCir6tBWM3RBGTfMLb6qubN3m4iAxuACiyFKsUlkao2lDhWhrGKxiby403Qk1MUMxtRQCRShwiYqJ1xWIwRbM0Zo1i6xBpmgkqNDgBzmi7lZksFeglptdbTNcA46rqXq9WZfB+AKAVcVKuh0Zhf+AlRQuZLdOgmcW3ba6Cja7ajrBVyVqqCBqRcBe7aNWMkfXRNTpVPaKcXo2sixacC0txA9TN1ptbHFuLghIDl9aMVE2ygDbVgHlopWBehhshau08wWSvLRtUQDOueKwroFlGhjg7oBa1kZvLoFasG8qW8FhQCE5K1RFHaAOhiFzJbp0xlfEt2LYraq6oYEMQI0QCO26LjdAzayi3OCykog0MWIXHxBkS2aCoqndaqXr67t0pN2uM23ca5txJClbNJsCBloW4KNLSqzQNDYA3CL+kCQCiVRrFBBTrhGEKBd5WshKo42Fdar0Xd5vNBFodlayZWy23gApUoiaGWEGmhQ1k63hWZ8ci7YssrfVnXMtdB6uGRVarllN6DT0GUTIcPo+uMajVqxKOtFSjgzZFF6LVtjTFouGrLX4dFNGUXVnFgZaMGddKgCPgIZqhdGgrAurlxRpfa7cl5GsdK9O6FFUUoWqzrLj1OlFCnMnWoQQaMFIRx0LqKolMBMWWVHULa7aosCiprVyCwUq1k6yuLcWDZGsKaSwZv2om1QpxSgwXM7tb0lC0rg1W5o0+a6ktCezMM+uvPaSl16As3m26pt26A86LFVNsoA3hsIvbBZ2VVDWeq8WnRSVq62QzbqzrmL3wuK0Wrle8GLc8VSDhEaqUBe95l8GzjaJlW2vBKMW02wIDbS9VImQCrwwAtLrrFE9BWKtS4Bk3grQlmeCtFK1BVo04saIFRG+SAwUq1kNZXFJwgmRjYpkjcZxIeALQJTDQwDEIUonfqgLLkLLxAooiAEW6RFsgMGNIjvd9wWyFehXerimCoHRUgUDpW2GCFBRiKVqFWiC63ArrDtLo2nq2ErGHSXEXuAaiXRjFWS2vuqsKcoOgAplOyDXEWVWV1YllRseW4O7QDPaiON1eIMHpWg35uG+kqcj3CkFVrLiCEpKolq40fLkigJHoZKw1Q1ViV9VEISwoguAHpfR7zLWxxfeHO3GjuytagBXKVKvqwIfZIKaNoTCFG0ajw0UpVN7IvCzDjEzkIBaCgzsRuqgaIaARC3IjmJOHRZ0lXpgpYXvL1iO9UJV1BcVZy1ABAVccmlVtAoMBK/MZEJpcRM/UM1e8eaWl+okS0dOBAWHkUjDKib2RbRTGmJlZma0gC3LgNZUVUs0MlXfFzVxvuiEQYwojSAptauAF58TIq5XV9HLFGnoMomQcMZxExgBrYBP/WYDNdMBWFzbw2FxmzEsgBp0ttr/gJwSMI2sTpPv8AcB+FLZfr7cEd6Scb3Tl++CxpAZXC4FEFw2/ogEejHa7aAeyIe+Ok0vdlirlVbquqxtJfE2dsmVdfUqBWjHdM/lh4WgZEpLly5cuXLly5cuX6e09vT2lz2ntPaXPaXPae09pc9p7T2l/p9p7T2ly5cue0uXLntLly57T2ly5cue0uX6e09p7ely5c9pcuXLl+ntLly57T2ly5cue0uXLntPae09pcuXPb0uXLly57S5cv09pcuX6e0uXLntPb0uXLly5cuXLly5cuXLntPae09pTFlTqFH5VIw6as/F/8AAhgGo5RonZJdTKQpb+QPapzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxOZeJzLxKiGBMe5gDvTUEyMLoH+nUkDV1Mn+h0CBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECBAgQIECB/w4ECBAgQIECBAgQIECBX6sWGLdD0x+vEr0aBWgNVlf6CVvPNCaI9Eli0KHpgRykhr+YznD8p+B2+fzKtTdBrSW1iUtYLpYQO8ksstV49oWcMHcWB0TJvsxuEJRSxiERrZKaB6xunUNNO+0ADiLgNXXVLRVi2DJ2sAt1MqabwZ1m94VgTNM43+ITYDiADoTN3szOEfnKDoLHOokP5q9oYXStotWF1EK1emYrXQWGbtcQhzll4ujozoSsX2TczEdYswVrLfK0sOoaam3vCMzjNOa1qDtpca+hXlRlk6A2dJQf0iZrAGlX1pjTPFmKytCPeEcEfztkNmi6auOH9/2nj4EwANVlWIbWrho/lNyTPWXtfhBdRwMxa7aXDqU3rMrRb72B1DC9MtpgbqdYUAjGJaFTRjLA1VknffGYgKyCBQ0BehBdG5Y2FLb6d5i6MamRbN2VW8003h2gZROl0P4lS8CnaIt1uLWvxHYiImRBSWlum0Y0nIlNYTTWJLFyVA2cNVmoD/AIDeoAqDi2Xu2BkF8mqKUabxwXa7tCDqW41+I85jyqoU11ZtIPXytVRc6TWo5rzbgW66wX7xoUTFx0ORaKNdZecNde1Asrr2lsmtH+gbAblXZKf7j7JsGYra65f8IswKGBEpMmQgpoUraAoz+D/Q3NJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJzScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScUnFJxScU/RZAisLOv/AJPvf+JttttttttsM+VGoDMXdFP6T7HH2OPscfY4+xx9jj7HH2OPscfY4+xx9jj7HH2OPscfY4+xx9jj7HH2OPscfY4+xx9jj7HH2OPscJoPQ9Ve72/d3FdmH+I0fmfzv7PRa9LbELg9rRbWxcP+IbRCxPb9D/dECw0DurgDLKsa8HeoahjCDk/QTeLNDdAIEQhEwoAw0nrXxoc/dXARDVQhwLQLQcd/0DqVhOG7FUozmoZItevAdn93cV2Yf4jR+Z/K/s9DPprGBBM5FHuKQ094qf4oauhFhecfpgfjIoFSdUp2sxJGobRI9yW7Dt+gMgVUGgE1O8AIAEAUB6gk3xlZsscOQYR6YABogfoFRs6GVWjLaue7DSKpcaL1QxRVL0v14Ds/u7iuzD/EaPzP5X9nrl0e8qMVeIF1ETOtwCHliIFp3htvrp+jAwnQWeJirBERCJDI5uOeaAUKlNrgD1Wcq1MC7YcX0S56KMe5TQoCh0z6p1KOUmEFJsJ+ZQf3dT2CocIudYergrB6JA2K0gdcS1L1/QZ4Ds/u7iuzD/EaPzP5X9nrl0e//AadGGT1WofoM8B2f3dxXZh/iNH5n8r+z1y6PeM7BVVG+0ti2C0MqEEL4cgywgKZum8X+he+DjRbAEOmUdNIIvelrWoDAGDp+hZxrGh+DKqgBlUDLKfZM3yiF4bVDqHrXZSMHVf/ADVcEIvjyyJQ2bQUrcmg9QQUTSjC3sUAKYNhCcDsoZKrrOhR0/QZ4Ds/u7iuzD/EaPzP5X9nrl0e8sgDkYZYFYRhlxGCmgDCzAE0xp+gUpDkh6MRvWI6UwxChiLA4Wrz+gBpaFqu2DqguTW1S8MEYyBVaKLfTvcOD4r8D3QEupCBTOp0sjenc09FDWIdEt7MPzb9yBRR+gzwHZ/d3FdmH+I0fmfyv7PXLo9/+G2OiTzBBSdnEObU0EqAAABQH5X9BngOz+7uK7MP8Ro/M/lf2euXR7x0l04DCQgrSXoNqtiQ0PRQahtgO43+nQxltBCQlbRMU8lkPRtEy42qrgI3gzEmAEHA1bqoQ5r20XI4CxLGsiPX0WoZd2roWK4Lt/FapBIbNVIZVDUsKMafoM8B2f3dxXZh6KsdwVNkFr1A4sStau2Cmx9j2Xmpphiy3ALTkoUGVIVdUjVgq1lLwLXi8+NdamcoLWgDN6TS/tX9sWKRCsjZjMr5YaBWyihLL0pYeho/M/lf2euVXKBYBoHVNAdVJYQfWlVlMUTAQWMx9syQIKpxppq6UQNPRauU7UvYOHbqWTSh8ho1wBoZyNSBwuifSq6kgVsArF9HMUHtUl5dVi69MCGWujKA44WpXIAxa3x2wJA9SuhBdZU2hfwma2uKi4O3aCga3RxgaAaUvHmVwRzSWMjByYqQwg6BViEKAswB6F/zebRu0brWuuko52y2EEIi53TJrGkbUUNtIKAIACg/QZ4Ds/u7iuzD0DFXutK7Aodaj8CODgaknNEADMSOwkWgw2FUxVMRfe0YujQXYjbi2oyZJ+JcdtMdXRckUy/5bm8GhKZcF1EHA3DHQdLtt5tz6Gj8z+V/Z65bc124hnNlV6XMP6LYwwpGBFDlXgb9Uam9+EELaCiaqdJWyxKJqJLZbazF4msJsUQgsTIzDGbtZUoF5Za0XifxRUAhteQFKgppTTVOj1PnNZHSvQFU0x9sdpgAMzB2+fUoQLMp8UMbCwgAAKA6H6TPAdn93cV2YemCsHa8SgoqOlzJqO95mS8ne8zuB3vM6gvveYqtqru+ho/M/lf2euXR7/8ADeg1RUbuOilAprq/qM8B2f3dxXZh/iNH5n8r+z1ymnvEd4ZhkVl16gIGAhWhp6LQEPNdKH5pGCOkRWtRwS/QoAEbCWipcUsV5ei6nWNTpwrgoFM1Uko1D015foL6Dqyn4gWkUoVuUgaqqqEFr58LDDkrb0WoKiAsJFugBTXABCX59KqWE8UIvUB/QZ4Ds/u7iuzD/EaPzP5X9nrla2cFgO30BL6CsrEXHjiuxsUpaxgaoOYlLrWwLMi02aR0hzEQplYwZYBpqhqotEALR13qov8AMHlDv7YNm3QohSZhkRbUbmtZRehoVNJz/sB3lLd2LRADg7ATnAktAVVoLLHCIQDJQxoYgiog8qyDqRLhulJXJQDidtcgDSFbALwmEztVtVOqVXAW6HpjQXN4ACzKoDmnNOkMXAxDAAoV1BdJUJaCwwVoFSqqs1QepngOz+7uK7MP8Ro/M/lf2euXGFilQEcNMp10jJQMuUDlJu6dgCHollSmaAA1LDjAJAaHBF2vQ9WYD/aL2IdBoAxUWKq8lZXuQpC1ZaNPRLIeWwjPUUbWgyTVBXo5iSXItXbec4rKKMQr6xNTSiujd9SxeyDHGWrF1SMpDT9JngOz+7uK7MP8Ro/M/lf2euXR7+i1+llN/j9Cg1+hQ9QuoGBmgurXS4tSz9BngOz+7uK7MP8AEaPzP5X9nrlNPeLjH9QXCIxIalROlvY0Px6YZZa6sFQoMqoBq5LAdAlxCjPtBSAk6YbVVFrOmhdl3Y6ei4xmLffqORmKYA94LaiwJSWJZh9BVp3z9AAob0ypGoBNz6mjR3zJ/LCQa1sLfzm+76HXVQoAyrBNrLMTTVsKM+WIa3Yk3jAVKCZoNW39BngOz+7uK7MP8Ro/M/lf2euWlhk4RWdRCnWqg8EWurQLJCqKoAxBOh4wn81oXeoYKiCJgtNXYlvfDoHCbaMmgUBT5Cog5TDaGesGrDTSvYIMFVltbhryAPzwEymljUCpogC5PBKBVexFccBTJGr52U0yjtAp1mjExJJt5YjUjtyFBkBopDTc3+TGYFXGm5i2g9DNZN4E7M0gJ1MQOLsGDyXQ0MRfJmbjoCsY17v6DPAdn93cV2Yf4jR+Z/K/s9EYSkhLNQujDepdv8qAuzJkRBEyIM1GeRbDuODAVplsK9RRbBAAyIhkajFKyJtZSJ1ExBDNG4kMnQjEOL0KGzUhaWgrVy+/oLK0nUV3FbX1DN9WdcwJ6JZUGBFBPTe3w1LvMuUgMfy6vn1P3Y/TrnK8GMnBk9FgTO9vysKu/XgOz+7uK7MBlSpUqVKlSpUNT8z+d/Z/xqO3rj14Ds/u4qdCikN+03eTebvLvN3l3m7y7zd5d5u8u83eXebvLvN3l3m7y7zd5N4SFNAM/ucH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8zg/mcH8y3W1sqx+f/pBagXC1cj7KQO1yh3fCP5W17waYFiNidz/AEnZAtahFs3rBuwh0UDAHOsskGGR2l6uTvDIOyDQo7CN10R/0nXG3n6Aj8mvvH0uUWL0v3qBCslYLdL60BpMl528NPyr8f6TNdTzTSOoj0RyMaBHVgG91/Fj2IGY1QJ7G7fwEYqMElWmgHQdD/SlSjt+lJpxbJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CfUJ9Qn1CKNrr3E5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4nJvE5N4/Qtk4EEzSnTELeVXk5odJWMFWwLrPXaH0lYAGrRrEIPFlI70Om8PoZnIAjROsFxkO4JNXd5zKk5HyWgMrTOv8AocmwLVaA7xsGu6PZUq1Y6AGqsVr+uRvpMZNb1lOmpKh7jtYcKM29N6jG/guv5EFYQg+JX4U0mSVZGq92pTet7KlFltxjrAhJkVyt6uim5h0c213/ANDlirAHNEU9wSE2hZ2Wh1FFU/mPfN9eiGlYRblwwdd2AP8AP6XZbFtRSOyQqYvwc7QlHZIHbqPmBXNM0dadfeBVVVenYW6PxFrddkWpVvS6xesoKU2t3q4YsrBFxlFe7/RAWul96lWsA969dv8ACbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsY2MbGNjGxjYxsfRUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlSpUqVKlf5STL2KzQlABoDFTp2l6sLp3/VXl3FojYGEALDBbgvSK3EmXNNgaBUpVZIfq6WwurzXeWOD0KIJYgZo2wQ+ogJEEqAljSa/qZABqrQQRBER/WaEmiNj6jAaAuX9CgA6Bdf3MtdI4aPxCa0HJKjqHX1w6yjSf8AU2jB2KoCAMhGrRtrWNyCba2YZqqn4mrR+Iii51qv4FbDIALO69kWkKCsfatER7xhcwBCykWrLW1RLgZWpVq5yur6StsncPkOppuXAYMgPkjyHZwVaOeiDifgz8H4lX+pAVo9gIkSc8gr5pOq89QaSmxfPKKkres0oRkAlbICoi6YtZS5NrgTE1i6xV1Co64SsuK9ba8HYogWAaEzSodOxtsEra2Ryqn4mrRlWVxYLQLLZeKC9jXNBiEoqzVivwh0gEEYg0JaQqD+dueSsQrS7u3SOViuXoTIBBmqYtl1FKjQABklxXU2Nfgz8H4iXiPUALVegEMLEzpDXCCkWxqm4v8Ase6mx0vPZh1EuPxUFbGOEVW6D0hG2MWYIy+uNC11jOA9h8e2F0neXs/EHOjCqKi1Ido0FB1QQTCMMKtTo0C2hleDttYYnci95eZumsZCqvBjCTVE558uGo6A06N1ZmDsz8H4mUSi0Fr7Sm3EMCtjaxpgN0pGfKXSr/cMVe21/cjBXKMuzn5BGMu0AblmRo0RKrSVmeaRvORMVibqlwIZ0GEwwAt0JUZkjBRjnxLTF8nIcCDYZC4vy1WBgIrtHCZmj5SbpQFgVIUCaFwg6A3vQeIa2EqdLK8xuL8khvuMBLwg6Mu8hvSx6GQNq5x3HlIBUF1ojOl1Kn1C0LGzDVgjWDmi/HBYyxmB13mslxAJLW5wFXRCEtGae6i7A9fSm+XF0P4EWdgY5/F90cVqwhxqgJj8MgVgEtgxmbRgo/nlSzFQzIOiDjULmfgOMqNJ+RIQBwM5GJfYVewfDZIepTKgxlCGH8pGodRdmBzI7NMp1pr2ZQyM8UcCmzEPZjCudCIjJArOdLe8EDUl6imgsbp0onYoaylBrFrDvsTY4TWX9tS2QUgl+oQNCLGrC0XiOwhq2DAArqaSn8Qj05/IDAq5YZeqwoRYf+m0+BmHnL1/hCx2E9I/EVIunTfD+WX1vINywCyC7Le0dkNRbhhWmA7uspz0JgotgNHW6iRMIUUTOKF1GBTeb0BV+CZbVczZd+whOKePQUeqU9mmo/udQ4gLA4ROpNVCDJ0gvQNA6FBADT1QdcxLJDL3A0FMXrWLr1bmsSU6DRTQXNY0lO3q5KlO0Kpp7Cp1RyuhnQAMHoRd0CxHCJ1lb0ZJD0C9A6HQxADT1anhmQKzC005AaxFtVEVDqWU5gldEgCgA0A9EtoVotYhlHcgB+jYgZX3lQKLXNBgNDpHuhuhaiOpAxorxAaZcvv6qM17VWFWPclssGCNyAwABlVtViRxqWnQaC6KZrGkrFS8E0/ZBoW5aq23VZS7r1PqqZgHIWFZKgvMJDXZQBQFaAadpbK9O8tqrlVVVyqr/wDR3//Z\" width=\"70%\">" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "showimg(\"image/jpeg\", \"images/generalized-Vandermonde-2.jpg\", scale=\"70%\")", | |
| "execution_count": 4, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
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width=\"70%\">" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "showimg(\"image/jpeg\", \"images/generalized-Vandermonde-3.jpg\", scale=\"70%\")", | |
| "execution_count": 5, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
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\" width=\"70%\">" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "showimg(\"image/jpeg\", \"images/generalized-Vandermonde-4.jpg\", scale=\"70%\")", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
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\" width=\"70%\">" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "function Pblock(a, n, m)\n P = Array{Sym, 2}(undef, n, m)\n for j in 1:m\n for i in 1:n\n if i < j\n P[i,j] = 0\n elseif i == j\n P[i,j] = 1\n else\n P[i,j] = binomial(i-1, j-1)*a^(i-j)\n end\n end\n end\n P\nend\n\nfunction Pmatrix(as, ms)\n n = sum(ms)\n hcat((Pblock(as[i], n, ms[i]) for i in 1:length(as))...)\nend", | |
| "execution_count": 7, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 7, | |
| "data": { | |
| "text/plain": "Pmatrix (generic function with 1 method)" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@vars a b c d\nV = Pmatrix([a, b, c, d], [1, 1, 1, 1])", | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 8, | |
| "data": { | |
| "text/plain": "4×4 Array{Sym,2}:\n 1 1 1 1\n a b c d\n a^2 b^2 c^2 d^2\n a^3 b^3 c^3 d^3", | |
| "text/latex": "\\[\\left[ \\begin{array}{rrrr}1&1&1&1\\\\a&b&c&d\\\\a^{2}&b^{2}&c^{2}&d^{2}\\\\a^{3}&b^{3}&c^{3}&d^{3}\\end{array}\\right]\\]" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@time V.det().factor()", | |
| "execution_count": 9, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": " 1.058877 seconds (2.25 M allocations: 111.579 MiB, 4.61% gc time)\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 9, | |
| "data": { | |
| "text/plain": "(a - b)*(a - c)*(a - d)*(b - c)*(b - d)*(c - d)", | |
| "text/latex": "\\begin{equation*}\\left(a - b\\right) \\left(a - c\\right) \\left(a - d\\right) \\left(b - c\\right) \\left(b - d\\right) \\left(c - d\\right)\\end{equation*}" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@vars a b c d\nP = Pmatrix([a, b, c, d], [3, 2, 1, 1])", | |
| "execution_count": 10, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 10, | |
| "data": { | |
| "text/plain": "7×7 Array{Sym,2}:\n 1 0 0 1 0 1 1\n a 1 0 b 1 c d\n a^2 2*a 1 b^2 2*b c^2 d^2\n a^3 3*a^2 3*a b^3 3*b^2 c^3 d^3\n a^4 4*a^3 6*a^2 b^4 4*b^3 c^4 d^4\n a^5 5*a^4 10*a^3 b^5 5*b^4 c^5 d^5\n a^6 6*a^5 15*a^4 b^6 6*b^5 c^6 d^6", | |
| "text/latex": "\\[\\left[ \\begin{array}{rrrrrrr}1&0&0&1&0&1&1\\\\a&1&0&b&1&c&d\\\\a^{2}&2 a&1&b^{2}&2 b&c^{2}&d^{2}\\\\a^{3}&3 a^{2}&3 a&b^{3}&3 b^{2}&c^{3}&d^{3}\\\\a^{4}&4 a^{3}&6 a^{2}&b^{4}&4 b^{3}&c^{4}&d^{4}\\\\a^{5}&5 a^{4}&10 a^{3}&b^{5}&5 b^{4}&c^{5}&d^{5}\\\\a^{6}&6 a^{5}&15 a^{4}&b^{6}&6 b^{5}&c^{6}&d^{6}\\end{array}\\right]\\]" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@time P.det().factor()", | |
| "execution_count": 11, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": " 5.802893 seconds (161 allocations: 6.672 KiB)\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 11, | |
| "data": { | |
| "text/plain": " 6 3 3 2 2 \n-(a - b) *(a - c) *(a - d) *(b - c) *(b - d) *(c - d)", | |
| "text/latex": "\\begin{equation*}- \\left(a - b\\right)^{6} \\left(a - c\\right)^{3} \\left(a - d\\right)^{3} \\left(b - c\\right)^{2} \\left(b - d\\right)^{2} \\left(c - d\\right)\\end{equation*}" | |
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| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@vars a b c\nQ = Pmatrix([a, b, c], [4, 2, 1])", | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 12, | |
| "data": { | |
| "text/plain": "7×7 Array{Sym,2}:\n 1 0 0 0 1 0 1\n a 1 0 0 b 1 c\n a^2 2*a 1 0 b^2 2*b c^2\n a^3 3*a^2 3*a 1 b^3 3*b^2 c^3\n a^4 4*a^3 6*a^2 4*a b^4 4*b^3 c^4\n a^5 5*a^4 10*a^3 10*a^2 b^5 5*b^4 c^5\n a^6 6*a^5 15*a^4 20*a^3 b^6 6*b^5 c^6", | |
| "text/latex": "\\[\\left[ \\begin{array}{rrrrrrr}1&0&0&0&1&0&1\\\\a&1&0&0&b&1&c\\\\a^{2}&2 a&1&0&b^{2}&2 b&c^{2}\\\\a^{3}&3 a^{2}&3 a&1&b^{3}&3 b^{2}&c^{3}\\\\a^{4}&4 a^{3}&6 a^{2}&4 a&b^{4}&4 b^{3}&c^{4}\\\\a^{5}&5 a^{4}&10 a^{3}&10 a^{2}&b^{5}&5 b^{4}&c^{5}\\\\a^{6}&6 a^{5}&15 a^{4}&20 a^{3}&b^{6}&6 b^{5}&c^{6}\\end{array}\\right]\\]" | |
| }, | |
| "metadata": {} | |
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| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "@time Q.det().factor()", | |
| "execution_count": 13, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": " 1.124767 seconds (161 allocations: 6.672 KiB)\n", | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 13, | |
| "data": { | |
| "text/plain": " 8 4 2\n(a - b) *(a - c) *(b - c) ", | |
| "text/latex": "\\begin{equation*}\\left(a - b\\right)^{8} \\left(a - c\\right)^{4} \\left(b - c\\right)^{2}\\end{equation*}" | |
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| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "", | |
| "execution_count": null, | |
| "outputs": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "name": "julia-1.1", | |
| "display_name": "Julia 1.1.0", | |
| "language": "julia" | |
| }, | |
| "language_info": { | |
| "file_extension": ".jl", | |
| "name": "julia", | |
| "mimetype": "application/julia", | |
| "version": "1.1.0" | |
| }, | |
| "toc": { | |
| "nav_menu": {}, | |
| "number_sections": true, | |
| "sideBar": true, | |
| "skip_h1_title": true, | |
| "title_cell": "目次", | |
| "title_sidebar": "目次", | |
| "toc_cell": true, | |
| "toc_position": {}, | |
| "toc_section_display": true, | |
| "toc_window_display": false | |
| }, | |
| "gist": { | |
| "id": "", | |
| "data": { | |
| "description": "07-1 Linear homogeneous ODEs with constant coefficients.ipynb", | |
| "public": true | |
| } | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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