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Rev | Author | Line No. | Line |
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2071 | zjchen | 1 | !set methtit=变量的逆替换 |
2 | !set methenv=ZZ QQ RR |
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3 | !set methparmtype=parm function integrate, function, function |
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4 | !set methhelp=本方法对不定积分应用变量逆替换. |
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5 | |||
6 | !if $wims_read_parm iswordof form check |
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7 | !goto $wims_read_parm |
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8 | !endif |
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9 | |||
10 | !exit |
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11 | :form |
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12 | !set N=!linecnt $mtobj1 |
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13 | !if $N>1 and $methsubstep=1 |
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14 | :first |
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15 | !set methsubstep=2 |
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16 | 施行变量逆替换: <p> |
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17 | !read deduc/methparm.phtml 1 |
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18 | !else |
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19 | !bound methparm1 between integer 0 and $N default 1 |
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20 | !if $methparm1=0 or $error!=$empty |
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21 | !goto first |
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22 | !endif |
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23 | <input type=hidden name=methparm1 value=$methparm1> |
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24 | !set methsubstep=1 |
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25 | !set l=!line $methparm1 of $mtobj1 |
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26 | !set l=!item 2 to -1 of $l |
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27 | !set k=!mathsubst integrate= in $l |
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28 | !set k=!declosing $k |
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29 | !set v=!item 2 of $k |
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30 | !set nvar=!item 1 of $newvariables |
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31 | 对 \($l) 作变量逆替换: 令 <br> |
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32 | \($nvar = h($v) = ) |
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33 | !read deduc/methparm.phtml 2,18 |
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34 | , 可得 |
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35 | <p><center> |
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36 | \($l = integrate(f(h($v))h'($v)d$v) = integrate(f($nvar)d$nvar)) , |
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37 | </center> <p> |
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38 | 其中 |
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39 | \(f($nvar) = ) |
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40 | !read deduc/methparm.phtml 3,36 |
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41 | . |
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42 | !endif |
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43 | !exit |
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44 | :check |
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45 | ker=!item 2 of $methparmobj1 |
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46 | ker=!mathsubst integrate= in $ker |
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47 | ker=!trim $ker |
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48 | ker=!declosing $ker |
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49 | !distribute items $ker into iker,ivar |
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50 | vartest=!varlist $ivar |
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51 | !if $ivar != $vartest |
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52 | error=失败 |
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53 | !exit |
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54 | !endif |
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55 | |||
56 | newvar=!item 1 of $newvariables |
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57 | vv=!varlist nofn $methparm2 |
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58 | vtest=!listcomplement $ivar,e,pi,euler in $vv |
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59 | !if $vtest!=$empty |
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60 | error=\(h($ivar)) 只能是 \($ivar) 的函数. |
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61 | !exit |
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62 | !endif |
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63 | hprime=!exec maxima diff($methparm2,$ivar); |
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64 | !if $hprime=$empty |
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65 | :bad_data |
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66 | error=bad_data |
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67 | !exit |
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68 | !endif |
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69 | vv=!varlist nofn $methparm3 |
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70 | vtest=!listcomplement $newvar,e,pi,euler in $vv |
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71 | !if $vtest!=$empty |
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72 | error=\(f($newvar)) 只能是 \($newvar) 的函数. |
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73 | !exit |
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74 | !endif |
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75 | substed=!mathsubst $newvar=($methparm2) in $methparm3 |
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76 | !read deduc/sub/checkzero ($substed)*($hprime)-($iker)\ |
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77 | diff($methparm3,$newvar) |
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78 | !distribute lines $out into ztest,difftest |
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79 | !if $ztest=$empty or $difftest=$empty |
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80 | !goto bad_data |
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81 | !endif |
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82 | !if $ztest!=yes |
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83 | error=把错误公式应用于变量替换! |
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84 | !advance penalty |
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85 | !exit |
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86 | !endif |
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87 | |||
88 | !read deduc/sub/simplify $methparm3\ |
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89 | ($methparm3)*($newvar) |
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90 | !distribute lines $out into newker,res |
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91 | !if $newker=$empty or $res=$empty |
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92 | !goto bad_data |
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93 | !endif |
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94 | !if strictintegrate iswordof $m_options and $difftest=yes |
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95 | error=你不能把 \(f($newvar)) 取成常数. \ |
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96 | 请换一个方法. |
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97 | !exit |
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98 | !endif |
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99 | |||
100 | !if $difftest=yes |
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101 | newobject1=($res) |
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102 | !else |
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103 | newobject1=integrate($newker,$newvar) |
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104 | !endif |
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105 | oldobject=0,1 |
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106 | newobject0=$newvar=$methparm2 |
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107 | methexp=\($newvar=$methparm2) |
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108 | variables=$variables,$newvar |
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109 | !exit |
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110 |