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<html><head><meta http-equiv="content-type" content="text/html; charset=UTF-8"> <style>
.KEYW {color: #933;}
.COMM {color: #bbb; font-style: italic;}
.NUMB {color: #393;}
.STRN {color: #393;}
.REGX {color: #339;}
.line {border-right: 1px dotted #666; color: #666; font-style: normal;}
</style></head><body><pre><span class='line'> 1</span> <span class="TOKN"></span><span class="WHIT">
<span class='line'> 2</span> </span><span class="COMM">/**
<span class='line'> 3</span> * @name CeL polynomial function
<span class='line'> 4</span> * @fileoverview
<span class='line'> 5</span> * 本檔案包含了數學多項式的 functions。
<span class='line'> 6</span> * @since
<span class='line'> 7</span> */</span><span class="WHIT">
<span class='line'> 8</span>
<span class='line'> 9</span>
<span class='line'> 10</span> </span><span class="KEYW">if</span><span class="WHIT"> </span><span class="PUNC">(</span><span class="KEYW">typeof</span><span class="WHIT"> </span><span class="NAME">CeL</span><span class="WHIT"> </span><span class="PUNC">===</span><span class="WHIT"> </span><span class="STRN">'function'</span><span class="PUNC">)</span><span class="WHIT">
<span class='line'> 11</span> </span><span class="NAME">CeL.setup_module</span><span class="PUNC">(</span><span class="STRN">'data.math.polynomial'</span><span class="PUNC">,</span><span class="WHIT">
<span class='line'> 12</span> </span><span class="KEYW">function</span><span class="PUNC">(</span><span class="NAME">library_namespace</span><span class="PUNC">,</span><span class="WHIT"> </span><span class="NAME">load_arguments</span><span class="PUNC">)</span><span class="WHIT"> </span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 13</span>
<span class='line'> 14</span> </span><span class="COMM">// no required</span><span class="WHIT">
<span class='line'> 15</span>
<span class='line'> 16</span>
<span class='line'> 17</span> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="WHIT">
<span class='line'> 18</span> </span><span class="COMM">/**
<span class='line'> 19</span> * null module constructor
<span class='line'> 20</span> * @class 數學多項式相關之 function。
<span class='line'> 21</span> * @constructor
<span class='line'> 22</span> */</span><span class="WHIT">
<span class='line'> 23</span> </span><span class="NAME">CeL.data.math.polynomial</span><span class="WHIT">
<span class='line'> 24</span> </span><span class="PUNC">=</span><span class="WHIT"> </span><span class="KEYW">function</span><span class="WHIT"> </span><span class="PUNC">(</span><span class="PUNC">)</span><span class="WHIT"> </span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 25</span> </span><span class="WHIT"> </span><span class="COMM">// null module constructor</span><span class="WHIT">
<span class='line'> 26</span> </span><span class="PUNC">}</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 27</span>
<span class='line'> 28</span> </span><span class="COMM">/**
<span class='line'> 29</span> * for JSDT: 有 prototype 才會將之當作 Class
<span class='line'> 30</span> */</span><span class="WHIT">
<span class='line'> 31</span> </span><span class="NAME">CeL.data.math.polynomial</span><span class="WHIT">
<span class='line'> 32</span> </span><span class="PUNC">.</span><span class="NAME">prototype</span><span class="WHIT"> </span><span class="PUNC">=</span><span class="WHIT"> </span><span class="PUNC">{</span><span class="PUNC">}</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 33</span>
<span class='line'> 34</span>
<span class='line'> 35</span>
<span class='line'> 36</span>
<span class='line'> 37</span>
<span class='line'> 38</span> </span><span class="COMM">// polynomial -----------------------------------</span><span class="WHIT">
<span class='line'> 39</span>
<span class='line'> 40</span> </span><span class="COMM">/*
<span class='line'> 41</span> return [r1,r2,..[,餘式]]
<span class='line'> 42</span> ** 若有無法解的餘式，會附加在最後!
<span class='line'> 43</span>
<span class='line'> 44</span> 高次代數方程數值求根解法: http://www.journals.zju.edu.cn/sci/2003/200303/030305.pdf http://tsg.gxtvu.com.cn/eduwest/web_courseware/maths/0092/2/2-3.htm
<span class='line'> 45</span> 修正牛頓法 1819年霍納法 伯努利法 勞思表格法 http://en.wikipedia.org/wiki/Ruffini%27s_rule
<span class='line'> 46</span> Newton's method牛頓法 x2=x1-f(x1)/f'(x1) http://zh.wikipedia.org/wiki/%E7%89%9B%E9%A1%BF%E6%B3%95
<span class='line'> 47</span> 四次方程Finding roots http://zh.wikipedia.org/wiki/%E5%9B%9B%E6%AC%A1%E6%96%B9%E7%A8%8B
<span class='line'> 48</span> 一元三次方程的公式解 http://en.wikipedia.org/wiki/Cubic_equation http://math.xmu.edu.cn/jszg/ynLin/JX/jiaoxueKJ/5.ppt
<span class='line'> 49</span>
<span class='line'> 50</span> var rootFindingFragment=1e-15; // 因為浮點乘除法而會產生的誤差
<span class='line'> 51</span> */</span><span class="WHIT">
<span class='line'> 52</span> </span><span class="NAME">rootFinding</span><span class="PUNC">[</span><span class="NAME">generateCode.dLK</span><span class="PUNC">]</span><span class="PUNC">=</span><span class="STRN">'rootFindingFragment'</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 53</span> </span><span class="KEYW">function</span><span class="WHIT"> </span><span class="NAME">rootFinding</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 54</span> </span><span class="WHIT"> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="NAME">r</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">,</span><span class="NAME">q</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 55</span>
<span class='line'> 56</span> </span><span class="WHIT"> </span><span class="COMM">//alert(NewtonMethod(polynomial));</span><span class="WHIT">
<span class='line'> 57</span>
<span class='line'> 58</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">polynomial.length</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">></span><span class="NUMB">1</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 59</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">&lt;</span><span class="NUMB">4</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 60</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">==</span><span class="NUMB">2</span><span class="PUNC">)</span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="PUNC">-</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">/</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 61</span> </span><span class="WHIT"> </span><span class="KEYW">else</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 62</span> </span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">-</span><span class="NUMB">4</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">2</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT"> </span><span class="COMM">// b^2-4ac</span><span class="WHIT">
<span class='line'> 63</span> </span><span class="WHIT"> </span><span class="NAME">q</span><span class="PUNC">=</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 64</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">&lt;</span><span class="NUMB">0</span><span class="PUNC">)</span><span class="NAME">a</span><span class="PUNC">=</span><span class="PUNC">(</span><span class="NAME">Math.sqrt</span><span class="PUNC">(</span><span class="PUNC">-</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">/</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="PUNC">+</span><span class="STRN">'i'</span><span class="PUNC">,</span><span class="NAME">q</span><span class="PUNC">=</span><span class="PUNC">-</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">/</span><span class="NAME">q</span><span class="PUNC">,</span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">+</span><span class="STRN">'+'</span><span class="PUNC">+</span><span class="NAME">a</span><span class="PUNC">,</span><span class="NAME">q</span><span class="PUNC">+</span><span class="STRN">'-'</span><span class="PUNC">+</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 65</span> </span><span class="WHIT"> </span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">Math.sqrt</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">/</span><span class="NAME">q</span><span class="PUNC">,</span><span class="NAME">q</span><span class="PUNC">=</span><span class="PUNC">-</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">/</span><span class="NAME">q</span><span class="PUNC">,</span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">+</span><span class="NAME">a</span><span class="PUNC">,</span><span class="NAME">q</span><span class="PUNC">-</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 66</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 67</span> </span><span class="WHIT"> </span><span class="NAME">polynomial</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="KEYW">break</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 68</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="KEYW">else</span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">NewtonMethod</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">></span><span class="NAME">rootFindingFragment</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 69</span> </span><span class="WHIT"> </span><span class="COMM">//alert('rootFinding: NewtonMethod 無法得出根!\n誤差:'+a[1]);</span><span class="WHIT">
<span class='line'> 70</span> </span><span class="WHIT"> </span><span class="KEYW">break</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 71</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 72</span> </span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">qNum</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NUMB">1</span><span class="NAME">e6</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="COMM">//alert(a[0]+'/'+a[1]);</span><span class="WHIT">
<span class='line'> 73</span> </span><span class="WHIT"> </span><span class="NAME">q</span><span class="PUNC">=</span><span class="NAME">pLongDivision</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">,</span><span class="PUNC">[</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="PUNC">-</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 74</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">></span><span class="NAME">pLongDivisionFragment</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="NAME">alert</span><span class="PUNC">(</span><span class="STRN">'rootFinding error!\n誤差:'</span><span class="PUNC">+</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="KEYW">break</span><span class="PUNC">;</span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 75</span> </span><span class="WHIT"> </span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">/</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">polynomial</span><span class="PUNC">=</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 76</span> </span><span class="WHIT"> </span><span class="COMM">//alert('get root: '+a[0]+'\n'+polynomial);</span><span class="WHIT">
<span class='line'> 77</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 78</span>
<span class='line'> 79</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">polynomial.length</span><span class="PUNC">==</span><span class="NUMB">5</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT"> </span><span class="COMM">// 兩對共軛虛根四次方程</span><span class="WHIT">
<span class='line'> 80</span> </span><span class="WHIT"> </span><span class="NAME">q</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">polynomial.length</span><span class="PUNC">,</span><span class="NAME">i</span><span class="PUNC">=</span><span class="NUMB">0</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 81</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">--</span><span class="NAME">a</span><span class="PUNC">)</span><span class="NAME">q.push</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">++</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT"> </span><span class="COMM">// 微分</span><span class="WHIT">
<span class='line'> 82</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">=</span><span class="NAME">rootFinding</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">q.length</span><span class="PUNC">></span><span class="NUMB">1</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 83</span> </span><span class="WHIT"> </span><span class="COMM">//a=0;for(var i=0;i&lt;polynomial.length;i++)a=a*q[0]+polynomial[i];</span><span class="WHIT">
<span class='line'> 84</span> </span><span class="WHIT"> </span><span class="COMM">// 將函數上下移動至原極值有根處，則會有二重根。原函數之根應為(-b +- (b^2-4ac)^.5)/2a，則此二重根即為-b/2a（？）</span><span class="WHIT">
<span class='line'> 85</span> </span><span class="WHIT"> </span><span class="COMM">// 故可將原函數分解為(x^2-2*q[n]*x+&)(?x^2+?x+?)</span><span class="WHIT">
<span class='line'> 86</span> </span><span class="WHIT"> </span><span class="COMM">// 以長除法解之可得&有三解:a*&^2+(-2*q[n]*(b+2*a*q[n])-c)*&+e=0 or ..</span><span class="WHIT">
<span class='line'> 87</span> </span><span class="WHIT"> </span><span class="NAME">q</span><span class="PUNC">=</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NUMB">4</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">+</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 88</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">==</span><span class="NUMB">0</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">rootFinding</span><span class="PUNC">(</span><span class="PUNC">[</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="PUNC">-</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">*</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">+</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">-</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">2</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">4</span><span class="PUNC">]</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">a.length</span><span class="PUNC">&lt;</span><span class="NUMB">2</span><span class="PUNC">)</span><span class="NAME">a</span><span class="PUNC">=</span><span class="KEYW">null</span><span class="PUNC">;</span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 89</span> </span><span class="WHIT"> </span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="PUNC">(</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">2</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">+</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">3</span><span class="PUNC">]</span><span class="PUNC">-</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">*</span><span class="PUNC">(</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">+</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="PUNC">/</span><span class="NAME">a</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 90</span> </span><span class="WHIT"> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="NAME">o</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 91</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">isNaN</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">)</span><span class="PUNC">&&</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">=</span><span class="NAME">pLongDivision</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">,</span><span class="NAME">o</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">,</span><span class="PUNC">-</span><span class="NUMB">2</span><span class="PUNC">*</span><span class="NAME">q</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">&lt;</span><span class="NAME">pLongDivisionFragment</span><span class="PUNC">&&</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">&lt;</span><span class="NAME">pLongDivisionFragment</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="WHIT">
<span class='line'> 92</span> </span><span class="WHIT"> </span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">rootFinding</span><span class="PUNC">(</span><span class="NAME">q</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">=</span><span class="NAME">rootFinding</span><span class="PUNC">(</span><span class="NAME">o</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">a</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">polynomial</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 93</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 94</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'> 95</span>
<span class='line'> 96</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">polynomial.length</span><span class="PUNC">></span><span class="NUMB">1</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'> 97</span> </span><span class="WHIT"> </span><span class="NAME">r.push</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'> 98</span> </span><span class="WHIT"> </span><span class="COMM">//if(polynomial.length%2==1)alert('rootFinding error!');</span><span class="WHIT">
<span class='line'> 99</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>100</span> </span><span class="WHIT"> </span><span class="KEYW">return</span><span class="WHIT"> </span><span class="NAME">r</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>101</span> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>102</span> </span><span class="COMM">//alert(rootFinding(getPbyR([1,4/3,5,2,6])).join('\n'));</span><span class="WHIT">
<span class='line'>103</span> </span><span class="COMM">//alert(NewtonMethod(getPbyR([1,4,5,2,6])).join('\n'));</span><span class="WHIT">
<span class='line'>104</span> </span><span class="COMM">//alert(rootFinding([1,4,11,14,10]).join('\n'));</span><span class="WHIT">
<span class='line'>105</span> </span><span class="COMM">//alert(rootFinding([1,2,3,2,1]).join('\n'));</span><span class="WHIT">
<span class='line'>106</span>
<span class='line'>107</span> </span><span class="COMM">/* 長除法 polynomial long division http://en.wikipedia.org/wiki/Polynomial_long_division 2005/3/4 18:48
<span class='line'>108</span> dividend/divisor=quotient..remainder
<span class='line'>109</span>
<span class='line'>110</span> input (dividend,divisor)
<span class='line'>111</span> return [商,餘式]
<span class='line'>112</span>
<span class='line'>113</span> var pLongDivisionFragment=1e-13; // 因為浮點乘除法而會產生的誤差
<span class='line'>114</span> */</span><span class="WHIT">
<span class='line'>115</span> </span><span class="NAME">pLongDivision</span><span class="PUNC">[</span><span class="NAME">generateCode.dLK</span><span class="PUNC">]</span><span class="PUNC">=</span><span class="STRN">'pLongDivisionFragment'</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>116</span> </span><span class="KEYW">function</span><span class="WHIT"> </span><span class="NAME">pLongDivision</span><span class="PUNC">(</span><span class="NAME">dividend</span><span class="PUNC">,</span><span class="NAME">divisor</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'>117</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="KEYW">typeof</span><span class="WHIT"> </span><span class="NAME">dividend</span><span class="PUNC">!=</span><span class="STRN">'object'</span><span class="PUNC">||</span><span class="KEYW">typeof</span><span class="WHIT"> </span><span class="NAME">divisor</span><span class="PUNC">!=</span><span class="STRN">'object'</span><span class="PUNC">)</span><span class="KEYW">return</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>118</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">dividend</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="NAME">dividend.shift</span><span class="PUNC">(</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">divisor</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="NAME">dividend.shift</span><span class="PUNC">(</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>119</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">dividend.length</span><span class="PUNC">||</span><span class="PUNC">!</span><span class="NAME">divisor.length</span><span class="PUNC">)</span><span class="KEYW">return</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>120</span>
<span class='line'>121</span> </span><span class="WHIT"> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="NAME">quotient</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">remainder</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">r</span><span class="PUNC">,</span><span class="NAME">r0</span><span class="PUNC">=</span><span class="NAME">divisor</span><span class="PUNC">[</span><span class="NUMB">0</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">c</span><span class="PUNC">=</span><span class="PUNC">-</span><span class="NUMB">1</span><span class="PUNC">,</span><span class="NAME">l2</span><span class="PUNC">=</span><span class="NAME">divisor.length</span><span class="PUNC">,</span><span class="NAME">l</span><span class="PUNC">=</span><span class="NAME">dividend.length</span><span class="PUNC">-</span><span class="NAME">l2</span><span class="PUNC">+</span><span class="NUMB">1</span><span class="PUNC">,</span><span class="NAME">i</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>122</span> </span><span class="WHIT"> </span><span class="KEYW">for</span><span class="PUNC">(</span><span class="NAME">i</span><span class="PUNC">=</span><span class="NUMB">0</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">&lt;</span><span class="NAME">dividend.length</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">++</span><span class="PUNC">)</span><span class="NAME">remainder.push</span><span class="PUNC">(</span><span class="NAME">dividend</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>123</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">++</span><span class="NAME">c</span><span class="PUNC">&lt;</span><span class="NAME">l</span><span class="PUNC">)</span><span class="WHIT">
<span class='line'>124</span> </span><span class="WHIT"> </span><span class="KEYW">for</span><span class="PUNC">(</span><span class="NAME">quotient.push</span><span class="PUNC">(</span><span class="NAME">r</span><span class="PUNC">=</span><span class="NAME">remainder</span><span class="PUNC">[</span><span class="NAME">c</span><span class="PUNC">]</span><span class="PUNC">/</span><span class="NAME">r0</span><span class="PUNC">)</span><span class="PUNC">,</span><span class="NAME">i</span><span class="PUNC">=</span><span class="NUMB">1</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">&lt;</span><span class="NAME">l2</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">++</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'>125</span> </span><span class="WHIT"> </span><span class="NAME">remainder</span><span class="PUNC">[</span><span class="NAME">c</span><span class="PUNC">+</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">-</span><span class="PUNC">=</span><span class="NAME">r</span><span class="PUNC">*</span><span class="NAME">divisor</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>126</span> </span><span class="WHIT"> </span><span class="COMM">//if(Math.abs(remainder[c+i])&lt;Math.abs(.00001*divisor[i]*r))remainder[c+i]=0;</span><span class="WHIT">
<span class='line'>127</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>128</span> </span><span class="WHIT"> </span><span class="KEYW">return</span><span class="WHIT"> </span><span class="PUNC">[</span><span class="NAME">quotient</span><span class="PUNC">,</span><span class="NAME">remainder.slice</span><span class="PUNC">(</span><span class="NAME">l</span><span class="PUNC">)</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>129</span> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>130</span> </span><span class="COMM">//alert(pLongDivision([4,-5,3,1/3+2/27-1],[3,-1]).join('\n'));</span><span class="WHIT">
<span class='line'>131</span>
<span class='line'>132</span> </span><span class="COMM">/*
<span class='line'>133</span> // polynomial multiplication乘法
<span class='line'>134</span> function polynomialMultiplication(pol1,pol2){
<span class='line'>135</span> //for()
<span class='line'>136</span> }
<span class='line'>137</span> */</span><span class="WHIT">
<span class='line'>138</span>
<span class='line'>139</span> </span><span class="COMM">/* Newton Iteration Function 2005/2/26 1:4
<span class='line'>140</span> return [root,誤差]
<span class='line'>141</span> */</span><span class="WHIT">
<span class='line'>142</span> </span><span class="KEYW">function</span><span class="WHIT"> </span><span class="NAME">NewtonMethod</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">,</span><span class="NAME">init</span><span class="PUNC">,</span><span class="NAME">diff</span><span class="PUNC">,</span><span class="NAME">count</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'>143</span> </span><span class="WHIT"> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="NAME">x</span><span class="PUNC">=</span><span class="NUMB">0</span><span class="PUNC">,</span><span class="NAME">d</span><span class="PUNC">,</span><span class="NAME">i</span><span class="PUNC">,</span><span class="NAME">t</span><span class="PUNC">,</span><span class="NAME">l</span><span class="PUNC">,</span><span class="NAME">o</span><span class="PUNC">,</span><span class="NAME">dp</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>144</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">polynomial</span><span class="PUNC">||</span><span class="PUNC">!</span><span class="PUNC">(</span><span class="NAME">d</span><span class="PUNC">=</span><span class="NAME">l</span><span class="PUNC">=</span><span class="NAME">polynomial.length</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="KEYW">return</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>145</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">--</span><span class="NAME">d</span><span class="PUNC">)</span><span class="NAME">dp.push</span><span class="PUNC">(</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NAME">x</span><span class="PUNC">++</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">d</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT"> </span><span class="COMM">// dp:微分derivative</span><span class="WHIT">
<span class='line'>146</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">diff</span><span class="PUNC">)</span><span class="NAME">diff</span><span class="PUNC">=</span><span class="NAME">rootFindingFragment</span><span class="PUNC">;</span><span class="NAME">diff</span><span class="PUNC">=</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">diff</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>147</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">count</span><span class="PUNC">)</span><span class="NAME">count</span><span class="PUNC">=</span><span class="NUMB">15</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>148</span> </span><span class="WHIT"> </span><span class="NAME">x</span><span class="PUNC">=</span><span class="NAME">init</span><span class="PUNC">||</span><span class="NUMB">0</span><span class="PUNC">,</span><span class="NAME">o</span><span class="PUNC">=</span><span class="NAME">diff</span><span class="PUNC">+</span><span class="NUMB">1</span><span class="PUNC">,</span><span class="NAME">l</span><span class="PUNC">--</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>149</span> </span><span class="WHIT"> </span><span class="COMM">//alert(polynomial+'\n'+dp+'\n'+diff+',l:'+l);</span><span class="WHIT">
<span class='line'>150</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="NAME">o</span><span class="PUNC">></span><span class="NAME">diff</span><span class="PUNC">&&</span><span class="NAME">count</span><span class="PUNC">--</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'>151</span> </span><span class="WHIT"> </span><span class="COMM">//alert(count+':'+x+','+d);</span><span class="WHIT">
<span class='line'>152</span> </span><span class="WHIT"> </span><span class="KEYW">for</span><span class="PUNC">(</span><span class="NAME">d</span><span class="PUNC">=</span><span class="NAME">t</span><span class="PUNC">=</span><span class="NAME">i</span><span class="PUNC">=</span><span class="NUMB">0</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">&lt;</span><span class="NAME">l</span><span class="PUNC">;</span><span class="NAME">i</span><span class="PUNC">++</span><span class="PUNC">)</span><span class="NAME">d</span><span class="PUNC">=</span><span class="NAME">d</span><span class="PUNC">*</span><span class="NAME">x</span><span class="PUNC">+</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">,</span><span class="NAME">t</span><span class="PUNC">=</span><span class="NAME">t</span><span class="PUNC">*</span><span class="NAME">x</span><span class="PUNC">+</span><span class="NAME">dp</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>153</span> </span><span class="WHIT"> </span><span class="NAME">d</span><span class="PUNC">=</span><span class="NAME">d</span><span class="PUNC">*</span><span class="NAME">x</span><span class="PUNC">+</span><span class="NAME">polynomial</span><span class="PUNC">[</span><span class="NAME">l</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>154</span> </span><span class="WHIT"> </span><span class="COMM">//alert(d+'/'+t);</span><span class="WHIT">
<span class='line'>155</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">t</span><span class="PUNC">)</span><span class="NAME">d</span><span class="PUNC">/</span><span class="PUNC">=</span><span class="NAME">t</span><span class="PUNC">;</span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">d</span><span class="PUNC">=</span><span class="NUMB">1</span><span class="PUNC">;</span><span class="COMM">//alert();</span><span class="WHIT">
<span class='line'>156</span> </span><span class="WHIT"> </span><span class="NAME">t</span><span class="PUNC">=</span><span class="NAME">Math.abs</span><span class="PUNC">(</span><span class="NAME">d</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>157</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">o</span><span class="PUNC">&lt;=</span><span class="NAME">t</span><span class="PUNC">)</span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">o</span><span class="PUNC">&lt;</span><span class="NAME">rootFindingFragment</span><span class="PUNC">)</span><span class="KEYW">break</span><span class="PUNC">;</span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">x</span><span class="PUNC">++</span><span class="PUNC">;</span><span class="WHIT"> </span><span class="COMM">// test</span><span class="WHIT">
<span class='line'>158</span> </span><span class="WHIT"> </span><span class="NAME">o</span><span class="PUNC">=</span><span class="NAME">t</span><span class="PUNC">,</span><span class="NAME">x</span><span class="PUNC">-</span><span class="PUNC">=</span><span class="NAME">d</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>159</span> </span><span class="WHIT"> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>160</span> </span><span class="WHIT"> </span><span class="KEYW">return</span><span class="WHIT"> </span><span class="PUNC">[</span><span class="NAME">x</span><span class="PUNC">,</span><span class="NAME">d</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>161</span> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>162</span>
<span class='line'>163</span> </span><span class="COMM">// 從roots得到多項式 2005/2/26 0:45</span><span class="WHIT">
<span class='line'>164</span> </span><span class="KEYW">function</span><span class="WHIT"> </span><span class="NAME">getPbyR</span><span class="PUNC">(</span><span class="NAME">roots</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="WHIT">
<span class='line'>165</span> </span><span class="WHIT"> </span><span class="KEYW">var</span><span class="WHIT"> </span><span class="NAME">p</span><span class="PUNC">,</span><span class="NAME">r</span><span class="PUNC">,</span><span class="NAME">i</span><span class="PUNC">,</span><span class="NAME">c</span><span class="PUNC">=</span><span class="NUMB">0</span><span class="PUNC">,</span><span class="NAME">l</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>166</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="PUNC">!</span><span class="NAME">roots</span><span class="PUNC">||</span><span class="PUNC">!</span><span class="PUNC">(</span><span class="NAME">l</span><span class="PUNC">=</span><span class="NAME">roots.length</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="KEYW">return</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>167</span> </span><span class="WHIT"> </span><span class="NAME">p</span><span class="PUNC">=</span><span class="PUNC">[</span><span class="NUMB">1</span><span class="PUNC">,</span><span class="PUNC">-</span><span class="NAME">roots.pop</span><span class="PUNC">(</span><span class="PUNC">)</span><span class="PUNC">]</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>168</span> </span><span class="WHIT"> </span><span class="KEYW">while</span><span class="PUNC">(</span><span class="PUNC">++</span><span class="NAME">c</span><span class="PUNC">&lt;</span><span class="NAME">l</span><span class="PUNC">)</span><span class="WHIT">
<span class='line'>169</span> </span><span class="WHIT"> </span><span class="KEYW">if</span><span class="PUNC">(</span><span class="NAME">r</span><span class="PUNC">=</span><span class="NAME">roots.pop</span><span class="PUNC">(</span><span class="PUNC">)</span><span class="PUNC">)</span><span class="PUNC">{</span><span class="NAME">p.push</span><span class="PUNC">(</span><span class="PUNC">-</span><span class="NAME">r</span><span class="PUNC">*</span><span class="NAME">p</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">=</span><span class="NAME">c</span><span class="PUNC">]</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="KEYW">while</span><span class="PUNC">(</span><span class="NAME">i</span><span class="PUNC">)</span><span class="NAME">p</span><span class="PUNC">[</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">-</span><span class="PUNC">=</span><span class="NAME">p</span><span class="PUNC">[</span><span class="PUNC">--</span><span class="NAME">i</span><span class="PUNC">]</span><span class="PUNC">*</span><span class="NAME">r</span><span class="PUNC">;</span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>170</span> </span><span class="WHIT"> </span><span class="KEYW">else</span><span class="WHIT"> </span><span class="NAME">p.push</span><span class="PUNC">(</span><span class="NUMB">0</span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>171</span> </span><span class="WHIT"> </span><span class="KEYW">return</span><span class="WHIT"> </span><span class="NAME">p</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>172</span> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>173</span>
<span class='line'>174</span> </span><span class="COMM">//alert(getPbyR([1,2,3]));</span><span class="WHIT">
<span class='line'>175</span> </span><span class="COMM">//document.write(Newton1(getPbyR([2,32,5,3])));</span><span class="WHIT">
<span class='line'>176</span>
<span class='line'>177</span> </span><span class="COMM">// ↑polynomial -----------------------------------</span><span class="WHIT">
<span class='line'>178</span>
<span class='line'>179</span>
<span class='line'>180</span>
<span class='line'>181</span>
<span class='line'>182</span>
<span class='line'>183</span>
<span class='line'>184</span> </span><span class="KEYW">return</span><span class="WHIT"> </span><span class="PUNC">(</span><span class="WHIT">
<span class='line'>185</span> </span><span class="WHIT"> </span><span class="NAME">CeL.data.math.polynomial</span><span class="WHIT">
<span class='line'>186</span> </span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>187</span> </span><span class="PUNC">}</span><span class="WHIT">
<span class='line'>188</span>
<span class='line'>189</span>
<span class='line'>190</span> </span><span class="PUNC">)</span><span class="PUNC">;</span><span class="WHIT">
<span class='line'>191</span>
<span class='line'>192</span> </span></pre></body></html>
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