Annotation of OpenXM/doc/Papers/rims2005-noro.tm, Revision 1.3
1.1 noro 1: <TeXmacs|1.0.6>
2:
3: <style|<tuple|generic|varsession>>
4:
5: <\body>
1.3 ! noro 6: <surround| ||<doc-data|<doc-title|Risa/Asir
! 7: \<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#65B0\>\<#3057\>\<#3044\>\<#5F62\>\<#5F0F\>\<#306E\>\<#6570\>\<#5F0F\>\<#306E\>\<#53D6\>\<#308A\>\<#6271\>\<#3044\>\<#306B\>\<#3064\>\<#3044\>\<#3066\>>|<doc-author-data|<author-name|\<#91CE\>\<#5442\>
1.1 noro 8: \<#6B63\>\<#884C\>, \<#9AD8\>\<#5C71\>\<#4FE1\>\<#6BC5\><next-line>(\<#795E\>\<#6238\>\<#5927\>\<#7406\>)>|<\author-address>
9: \;
1.3 ! noro 10: </author-address>>|<doc-date|<date|>>>>
1.1 noro 11:
1.3 ! noro 12: <assign|NF|<macro|<with|font-family|rm|NF>>>
! 13:
! 14: <assign|ini|<macro|<with|font-family|rm|in>>>
! 15:
! 16: <assign|FN|<macro|<with|font-family|tt|FNODE>>>
! 17:
! 18: <assign|QT|<macro|<with|font-family|tt|QUOTE>>>
! 19:
! 20: <assign|ve|<macro|<vfill><eject>>>
! 21:
! 22: <assign|tmred|<macro|1|<smash|<with|mode|text|<rightarrowfill>><limits><rsub|<with|math-level|1|<arg|1>>><limits><rsup|<with|math-level|1|*>>>>>
! 23:
! 24: <section|Risa/Asir \<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#6570\>\<#5F0F\>\<#306E\>\<#53D6\>\<#308A\>\<#6271\>\<#3044\>>
! 25:
! 26: \<#30E6\>\<#30FC\>\<#30B6\>\<#306B\>\<#3088\>\<#308A\>\<#5165\>\<#529B\>\<#3055\>\<#308C\>\<#305F\>\<#6570\>\<#5F0F\>
! 27: <with|mode|math|\<Rightarrow\>> <FN> \<#3068\>\<#547C\>\<#3070\>\<#308C\>\<#308B\>\<#6728\>\<#69CB\>\<#9020\>\<#306B\>\<#5909\>\<#63DB\>
! 28:
! 29: <with|mode|math|\<Rightarrow\>> <with|font-family|tt|eval()>
! 30: \<#306B\>\<#3088\>\<#308A\>\<#518D\>\<#5E30\>\<#7684\>\<#306B\>Risa
! 31: \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#306B\>\<#5909\>\<#63DB\>
! 32:
! 33: <\itemize>
! 34: <item>Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>
! 35:
! 36: \<#5148\>\<#982D\>\<#306B\>\<#5171\>\<#901A\>\<#306E\>\<#8B58\>\<#5225\>\<#5B50\>\<#30D5\>\<#30A3\>\<#30FC\>\<#30EB\>\<#30C9\>\<#3092\>\<#6301\>\<#3064\>\<#4E00\>\<#7FA4\>\<#306E\>\<#69CB\>\<#9020\>\<#4F53\>
! 37:
! 38: <item>\<#30C8\>\<#30C3\>\<#30D7\>\<#30EC\>\<#30D9\>\<#30EB\>\<#6F14\>\<#7B97\>\<#95A2\>\<#6570\>
1.1 noro 39:
1.3 ! noro 40: \<#8B58\>\<#5225\>\<#5B50\>\<#306B\>\<#3088\>\<#308A\>\<#9069\>\<#5207\>\<#306A\>\<#95A2\>\<#6570\>\<#306B\>\<#632F\>\<#308A\>\<#5206\>\<#3051\>\<#308B\>
1.1 noro 41:
1.3 ! noro 42: <item>Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#306E\>\<#7A2E\>\<#985E\>
1.1 noro 43:
1.3 ! noro 44: \<#6570\>, \<#591A\>\<#9805\>\<#5F0F\>, \<#6709\>\<#7406\>\<#5F0F\>,
! 45: \<#30EA\>\<#30B9\>\<#30C8\>, \<#914D\>\<#5217\>\<#306A\>\<#3069\>30
! 46: \<#7A2E\>\<#985E\>\<#5F31\>
1.1 noro 47:
1.3 ! noro 48: <item>\<#7A2E\>\<#985E\>\<#3054\>\<#3068\>\<#306E\>\<#6F14\>\<#7B97\>
1.1 noro 49:
1.3 ! noro 50: Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>\<#306F\>,
! 51: \<#56FA\>\<#6709\>\<#306E\>\<#65B9\>\<#6CD5\>\<#306B\>\<#3088\>\<#308A\>,
! 52: \<#52B9\>\<#7387\>\<#3088\>\<#3044\>\<#6F14\>\<#7B97\>\<#304C\>\<#9069\>\<#7528\>\<#3067\>\<#304D\>\<#308B\>
! 53: </itemize>
! 54:
! 55: \;
! 56:
! 57: \;
! 58:
! 59: <\with|font-series|bold>
! 60: \<#6B20\>\<#70B9\>
! 61: </with>
! 62:
! 63: <\itemize>
! 64: <item>\<#591A\>\<#9805\>\<#5F0F\>\<#304C\>\<#5F37\>\<#5236\>\<#7684\>\<#306B\>\<#5C55\>\<#958B\>\<#3055\>\<#308C\>\<#3066\>\<#3057\>\<#307E\>\<#3046\>
1.1 noro 65:
1.3 ! noro 66: \<#672C\>\<#6765\>\<#306E\>\<#5165\>\<#529B\>\<#304C\>\<#6301\>\<#3063\>\<#3066\>\<#3044\>\<#305F\>\<#60C5\>\<#5831\>\<#304C\>\<#5931\>\<#308F\>\<#308C\>\<#308B\>.
1.1 noro 67:
1.3 ! noro 68: <item>\<#539F\>\<#5247\>\<#3068\>\<#3057\>\<#3066\>\<#591A\>\<#9805\>\<#5F0F\>\<#306E\>\<#7A4D\>\<#306F\>\<#53EF\>\<#63DB\>\<#3068\>\<#4EEE\>\<#5B9A\>
1.1 noro 69:
1.3 ! noro 70: \<#5FAE\>\<#5206\>\<#4F5C\>\<#7528\>\<#7D20\>\<#306A\>\<#3069\>,
! 71: \<#975E\>\<#53EF\>\<#63DB\>\<#306A\>\<#5BFE\>\<#8C61\>\<#3092\>\<#6271\>\<#3046\>\<#5834\>\<#5408\>\<#306B\>\<#4E0D\>\<#81EA\>\<#7136\>\<#306A\>\<#64CD\>\<#4F5C\>\<#3092\>\<#5F37\>\<#3044\>\<#3089\>\<#308C\>\<#308B\>.
1.1 noro 72:
1.3 ! noro 73: <item>\<#5F0F\>\<#306E\>\<#7C21\>\<#5358\>\<#5316\>\<#306E\>\<#554F\>\<#984C\>
1.1 noro 74:
1.3 ! noro 75: \<#3042\>\<#3089\>\<#3086\>\<#308B\>\<#3082\>\<#306E\>\<#3092\>\<#591A\>\<#9805\>\<#5F0F\>\<#306B\>\<#5909\>\<#63DB\>\<#3057\>\<#3066\>\<#304B\>\<#3089\>\<#7C21\>\<#5358\>\<#5316\>\<#3059\>\<#308B\>\<#306E\>\<#306F\>\<#4E0D\>\<#81EA\>\<#7136\>.
! 76: </itemize>
1.1 noro 77:
78: <\example>
79: \;
80:
81: <with|prog-language|openxm|prog-session|default|<\session>
82: <\folded>
83: <with|font-family|tt|dx> \<#3092\>
84: <with|mode|math|\<partial\>/\<partial\>x>
85: \<#306E\>\<#610F\>\<#5473\>\<#306B\>\<#4F7F\>\<#304A\>\<#3046\>\<#3068\>\<#601D\>\<#3063\>\<#3066\>\<#3082\>
86: <|folded>
87: <\input|openxm] >
88: x*dx
89: </input>
90:
91: <\output>
92: <with|mode|math|x*d*x>
93: </output>
94:
95: <\input|openxm] >
96: dx*x
97: </input>
98:
99: <\output>
100: <with|mode|math|x*d*x>
101: </output>
102:
103: <\input|openxm] >
104: \;
105: </input>
106:
107: <\output>
108: <with|mode|math|0>
109: </output>
110:
111: <\input|openxm] >
112: \;
113: </input>
114: </folded>
115: </session>>
116:
117: \<#306E\>\<#3088\>\<#3046\>\<#306B\>,
118: \<#52DD\>\<#624B\>\<#306B\>\<#9806\>\<#5E8F\>\<#304C\>\<#5909\>\<#3048\>\<#3089\>\<#308C\>\<#3066\>\<#3057\>\<#307E\>\<#3046\>.
119: </example>
120:
1.3 ! noro 121: <\with|font-series|bold>
! 122: \;
! 123:
! 124: \<#76EE\>\<#6A19\>
! 125: </with>
! 126:
! 127: <\itemize>
! 128: <item>\<#6570\>\<#5F0F\>\<#306E\>\<#67D4\>\<#8EDF\>\<#306A\>\<#53D6\>\<#308A\>\<#6271\>\<#3044\>
! 129:
! 130: Maxima, Maple, Mathematica \<#306A\>\<#3069\>\<#306E\>\<#5F97\>\<#610F\>\<#3068\>\<#3059\>\<#308B\>\<#3068\>\<#3053\>\<#308D\>
! 131:
! 132: Risa/Asir \<#306E\>\<#76EE\>\<#6307\>\<#3057\>\<#3066\>\<#304D\>\<#305F\>\<#3082\>\<#306E\>
! 133: : \<#591A\>\<#9805\>\<#5F0F\>\<#6F14\>\<#7B97\>\<#306E\>\<#9AD8\>\<#901F\>\<#51E6\>\<#7406\>\<#3060\>\<#304C\>,
! 134: \<#6271\>\<#3046\>\<#5BFE\>\<#8C61\>\<#304C\>\<#591A\>\<#69D8\>\<#5316\>\<#3057\>\<#3066\>\<#304D\>\<#305F\>
! 135:
! 136: <with|mode|math|\<Rightarrow\>> \<#4E00\>\<#822C\>\<#306E\>\<#6570\>\<#5F0F\>\<#306E\>\<#6F14\>\<#7B97\>\<#304A\>\<#3088\>\<#3073\>\<#7C21\>\<#5358\>\<#5316\>,
! 137: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306B\>\<#3088\>\<#308B\>
! 138: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#306E\>\<#5B9F\>\<#88C5\>
! 139:
! 140: <item>\<#975E\>\<#53EF\>\<#63DB\>\<#4EE3\>\<#6570\>
! 141:
! 142: \<#7279\>\<#306B\>\<#8981\>\<#671B\>\<#304C\>\<#591A\>\<#3044\>\<#8A08\>\<#7B97\>
! 143: <with|mode|math|\<Rightarrow\>> weight
! 144: \<#306E\>\<#6982\>\<#5FF5\>\<#3092\>\<#6301\>\<#3061\>\<#8FBC\>\<#307F\>,
! 145: \<#505C\>\<#6B62\>\<#6027\> \<#3092\>\<#4E0E\>\<#3048\>\<#308B\>\<#30B7\>\<#30F3\>\<#30D7\>\<#30EB\>\<#306A\>\<#57FA\>\<#6E96\>\<#3092\>\<#4E0E\>\<#3048\>\<#308B\>.
! 146: </itemize>
1.1 noro 147:
148: <section|<QT> \<#578B\>>
149:
1.3 ! noro 150: <QT> \<#578B\> = <FN> \<#3092\>\<#30DC\>\<#30C7\>\<#30A3\>\<#90E8\>\<#306B\>\<#6301\>\<#3064\>
! 151: Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>
1.1 noro 152:
153: <subsection|<QT> \<#306E\>\<#5165\>\<#529B\>,
154: \<#57FA\>\<#672C\>\<#64CD\>\<#4F5C\>>
155:
1.3 ! noro 156: <QT> \<#578B\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#64CD\>\<#4F5C\> :
! 157: \<#6728\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#64CD\>\<#4F5C\>
! 158:
! 159: \<#6728\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#4E00\>\<#822C\>\<#7684\>\<#306A\>\<#64CD\>\<#4F5C\>
1.1 noro 160: (\<#5C5E\>\<#6027\>, \<#5B50\>\<#306E\>\<#53D6\>\<#308A\>\<#51FA\>\<#3057\>,
161: \<#6728\>\<#306E\>\<#518D\>\<#69CB\>\<#6210\>\<#306A\>\<#3069\>) \<#3092\>
162: Asir \<#306E\>\<#95A2\>\<#6570\>\<#3068\>\<#3057\>\<#3066\>\<#4E0E\>\<#3048\>\<#308B\>\<#3053\>\<#3068\>\<#3067\>,
163: \<#30E6\>\<#30FC\>\<#30B6\>\<#306B\>\<#3088\>\<#308B\>\<#6570\>\<#5F0F\>\<#306E\>\<#64CD\>\<#4F5C\>\<#304C\>\<#53EF\>\<#80FD\>\<#3068\>\<#306A\>\<#308B\>.
1.3 ! noro 164:
! 165: <QT> \<#578B\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#64CD\>\<#4F5C\> =
1.1 noro 166: \<#5B9F\>\<#969B\>\<#306B\>\<#306F\> <FN>
1.3 ! noro 167: \<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#64CD\>\<#4F5C\>
! 168:
! 169: <FN> \<#306F\>\<#6B21\>\<#306E\>\<#5F62\>\<#3067\>\<#3042\>\<#308B\>.
1.1 noro 170:
171: <\center>
172: (<with|mode|math|i*d> <with|mode|math|a*r*g<rsub|0>>
173: <with|mode|math|a*r*g<rsub|1>> <with|mode|math|\<ldots\>>)
174: </center>
175:
1.3 ! noro 176: (<with|mode|math|a*r*g<rsub|i>> \<#306E\>\<#500B\>\<#6570\>,
1.1 noro 177: \<#578B\>\<#306F\> <with|mode|math|i*d>
1.3 ! noro 178: \<#306B\>\<#3088\>\<#308A\>\<#3055\>\<#307E\>\<#3056\>\<#307E\>)
1.1 noro 179:
180: <\itemize>
181: <item><QT> \<#306E\>\<#5165\>\<#529B\>
182:
183: <QT> \<#306F\> <with|font-family|tt|quote>(<with|mode|math|E*x*p*r>)
184: \<#307E\>\<#305F\>\<#306F\> <with|font-family|tt|`><with|mode|math|E*x*p*r>
185: (\<#30D0\>\<#30C3\>\<#30AF\>\<#30AF\>\<#30A9\>\<#30FC\>\<#30C8\>\<#3064\>\<#304D\>)
186: \<#306B\>\<#3088\>\<#308A\>\<#5165\>\<#529B\>\<#3067\>\<#304D\>\<#308B\>.
187:
188: <item><QT> \<#3068\> Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#306E\>\<#76F8\>\<#4E92\>\<#5909\>\<#63DB\>
189:
190: <with|font-family|tt|objtoquote>(<with|mode|math|O*b*j>),
191: <with|font-family|tt|eval_quote>(<with|mode|math|E*x*p*r>)
192: \<#3067\>\<#884C\>\<#3046\>.
193:
194: <item><QT> \<#306E\>\<#5206\>\<#89E3\>, \<#5408\>\<#6210\>
195:
1.3 ! noro 196: <with|font-family|tt|quote_to_funargs>(<with|mode|math|E*x*p*r>),
1.1 noro 197: <with|font-family|tt|funargs_to_quote>(<with|mode|math|L*i*s*t>)
198: </itemize>
199:
1.3 ! noro 200: <subsection|<FN> \<#306E\>\<#6A19\>\<#6E96\>\<#5F62\>>
! 201:
! 202: <FN> \<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#30DE\>\<#30C3\>\<#30C1\>\<#30F3\>\<#30B0\>,
! 203: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#3092\>\<#5BB9\>\<#6613\>\<#306B\>\<#884C\>\<#3046\>\<#305F\>\<#3081\>
! 204:
! 205: \<#6A19\>\<#6E96\>\<#5F62\>\<#306E\>\<#8A08\>\<#7B97\> :
1.1 noro 206: <with|font-family|tt|qt_normalize>(<with|mode|math|E*x*p*r>[,<with|mode|math|M*o*d*e>])
1.3 ! noro 207: (<with|mode|math|M*o*d*e> : \<#5C55\>\<#958B\>\<#30E2\>\<#30FC\>\<#30C9\>\<#6307\>\<#5B9A\>)
1.1 noro 208:
209: <with|mode|math|n*f> = <with|mode|math|f*o*r*m*u*l*a> <with|mode|math|\|>
210: <with|mode|math|f*u*n*c*t*o*r> (<with|mode|math|n*f> [,
211: <with|mode|math|\<ldots\>>]) <with|mode|math|\|>
212: <with|mode|math|s*u*m_o*f_m*o*n*o*m>
213:
214: <with|mode|math|s*u*m_o*f_m*o*n*o*m> = <with|mode|math|m*o*n*o*m>
215: [<with|mode|math|+> <with|mode|math|\<cdots\>>]
216:
217: <with|mode|math|m*o*n*o*m> = [<with|mode|math|f*o*r*m*u*l*a>
218: <with|mode|math|\<ast\>> ] <with|mode|math|n*f*p*o*w>
219: [<with|mode|math|\<ast\>> <with|mode|math|\<cdots\>>]
220:
221: <with|mode|math|n*f*p*o*w> = <with|mode|math|n*f> <with|mode|math|\|>
222: <with|mode|math|n*f<rsup|n*f>>
223:
224: <with|mode|math|f*o*r*m*u*l*a> = Risa object
225:
1.3 ! noro 226: \<#3059\>\<#306A\>\<#308F\>\<#3061\>, \<#6A19\>\<#6E96\>\<#5F62\>
! 227: <with|mode|math|n*f> = \<#6A19\>\<#6E96\>\<#5F62\>\<#306E\>\<#30D9\>\<#30AD\>\<#7A4D\>\<#306E\>
! 228: Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#4FC2\>\<#6570\>\<#3064\>\<#304D\>\<#306E\>\<#548C\>
! 229:
! 230: \<#548C\>\<#306F\> <FN> \<#3068\>\<#3057\>\<#3066\>\<#306F\>,
! 231: n\<#9805\>\<#548C\>\<#3068\>\<#3057\>\<#3066\>\<#8868\>\<#73FE\>
! 232:
! 233: \<#7A4D\>\<#3082\> n\<#9805\>\<#7A4D\>\<#3068\>\<#3057\>\<#3066\>\<#8868\>\<#73FE\>
! 234:
! 235: <\with|font-series|bold>
! 236: \<#6570\>\<#5B66\>\<#7684\>\<#306B\>\<#3044\>\<#3046\>\<#3068\>\<#6A19\>\<#6E96\>\<#5F62\>\<#3068\>\<#306F\>
! 237: </with>
! 238:
1.1 noro 239: \<#5165\>\<#529B\>\<#3055\>\<#308C\>\<#305F\>\<#6570\>\<#5F0F\>\<#304C\>,
240: Risa \<#30AA\>\<#30D6\>\<#30B8\>\<#30A7\>\<#30AF\>\<#30C8\>\<#3092\>\<#4FC2\>\<#6570\>\<#74B0\>\<#3068\>\<#3059\>\<#308B\>
241: \<#7D50\>\<#5408\>\<#4EE3\>\<#6570\>\<#306E\>\<#5143\>\<#3067\>\<#3042\>\<#308B\>\<#3068\>\<#898B\>\<#306A\>\<#3057\>,
242: \<#548C\>\<#306E\>\<#53EF\>\<#63DB\>\<#6027\>,
243: \<#7A4D\>\<#306E\>\<#7D50\>\<#5408\>\<#6027\>\<#306B\>\<#3088\>\<#308A\>\<#30D5\>\<#30E9\>\<#30C3\>\<#30C8\>\<#306B\>
1.3 ! noro 244: \<#6574\>\<#7406\>\<#3057\>\<#306A\>\<#304A\>\<#3057\>\<#305F\>\<#3082\>\<#306E\>
1.1 noro 245:
246: <\example>
247: <\verbatim>
248: \;
249:
250: <with|prog-language|openxm|prog-session|default|<\session>
251: <\folded>
252: \<#6A19\>\<#6E96\>\<#5F62\>\<#306F\> n
253: \<#9805\>\<#548C\>\<#3067\>\<#8868\>\<#73FE\>\<#3055\>\<#308C\>\<#308B\>
254: <|folded>
255: <\input|openxm] >
256: quotetolist(`x+y+z)
257: </input>
258:
259: <\output>
260: <with|mode|math|[<verbatim|b_op>,<verbatim|+>,[<verbatim|b_op>,<verbatim|+>,[<verbatim|internal>,x],[<verbatim|internal>,y]],[<verbatim|internal>,z]]>
261: </output>
262:
263: <\input|openxm] >
264: quotetolist(qt_normalize(`x+y+z))
265: </input>
266:
267: <\output>
268: <with|mode|math|[<verbatim|n_op>,<verbatim|+>,[<verbatim|internal>,x],[<verbatim|internal>,y],[<verbatim|internal>,z]]>
269: </output>
270:
271: <\input|openxm] >
272: \;
273: </input>
274: </folded>
275: </session>>
276: </verbatim>
277:
278: 2 \<#9805\>\<#6F14\>\<#7B97\>\<#3067\>\<#8868\>\<#73FE\>\<#3055\>\<#308C\>\<#305F\>\<#5F0F\>\<#304C\>,
279: \<#6A19\>\<#6E96\>\<#5F62\>\<#3067\>\<#306F\> n
280: \<#9805\>\<#548C\>\<#3067\>\<#8868\>\<#73FE\>\<#3055\>\<#308C\>\<#3066\>\<#3044\>\<#308B\>\<#3053\>\<#3068\>\<#304C\>\<#5206\>\<#304B\>\<#308B\>.
281: </example>
282:
1.3 ! noro 283: <\with|font-series|bold>
! 284: Mathematica \<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#6A19\>\<#6E96\>\<#5F62\>
! 285: <cite|MMA> \<#3068\>\<#306E\>\<#95A2\>\<#4FC2\>
! 286: </with>
! 287:
! 288: \<#57FA\>\<#672C\>\<#7684\>\<#306B\>\<#540C\>\<#3058\>\<#3067\>\<#3042\>\<#308B\>\<#304C\>,
1.1 noro 289: \<#7A4D\>\<#306E\>\<#53EF\>\<#63DB\>\<#6027\>\<#3092\>\<#4EEE\>\<#5B9A\>\<#3057\>\<#3066\>\<#3044\>\<#306A\>\<#3044\>\<#3053\>\<#3068\>,
290: \<#304A\>\<#3088\>\<#3073\>, \<#4FC2\>\<#6570\>
291: \<#74B0\>\<#3092\>\<#3088\>\<#308A\>\<#4E00\>\<#822C\>\<#7684\>\<#306B\>\<#3057\>\<#3066\>\<#3042\>\<#308B\>\<#70B9\>\<#3067\>\<#7570\>\<#306A\>\<#3063\>\<#3066\>\<#3044\>\<#308B\>.
292:
293: (Mathematica \<#306B\>\<#304A\>\<#3044\>\<#3066\>\<#7A4D\>\<#306E\>
294: <with|font-family|tt|Orderless> \<#5C5E\>\<#6027\>\<#3092\>\<#5916\>\<#3059\>\<#3053\>\<#3068\>\<#3067\>,
295: \<#7A4D\>\<#3092\>\<#975E\>\<#53EF\>\<#63DB\>\<#306B\>\<#3067\>\<#304D\>\<#308B\>\<#304C\>,
296: \<#7C21\>\<#5358\>\<#5316\>\<#306B\>\<#304A\>\<#3044\>\<#3066\>\<#7570\>\<#5E38\>\<#306A\>\<#6319\>\<#52D5\>\<#3092\>\<#793A\>\<#3059\>\<#3088\>\<#3046\>\<#306B\>\<#306A\>\<#308B\>
297: (Ver. 4). Ver. 5 \<#3067\>\<#306F\>, \<#4FC2\>\<#6570\>\<#307E\>\<#3067\>\<#975E\>\<#53EF\>\<#63DB\>\<#306B\>\<#306A\>\<#308B\>.)
298:
1.3 ! noro 299: <\with|font-series|bold>
! 300: \<#6A19\>\<#6E96\>\<#5F62\>+\<#5C55\>\<#958B\>
! 301: </with>
! 302:
! 303: \<#7A4D\>\<#306B\>\<#95A2\>\<#3059\>\<#308B\>\<#5206\>\<#914D\>\<#5247\>\<#3092\>\<#5229\>\<#7528\>\<#3057\>\<#3066\>\<#5C55\>\<#958B\>\<#3055\>\<#308C\>\<#305F\>\<#6A19\>\<#6E96\>\<#5F62\>\<#3092\>\<#5F97\>\<#308B\>\<#3053\>\<#3068\>\<#3082\>\<#3067\>\<#304D\>\<#308B\>.
1.1 noro 304:
305: <\example>
306: \;
307:
308: <with|prog-language|openxm|prog-session|default|<\session>
309: <\folded>
310: \<#6A19\>\<#6E96\>\<#5F62\>\<#3078\>\<#306E\>\<#5909\>\<#63DB\>\<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#5C55\>\<#958B\>
311: <|folded>
312: <\input|openxm] >
313: quotetolist(`(x+y)^2)
314: </input>
315:
316: <\output>
317: <with|mode|math|[<verbatim|b_op>,<verbatim|^>,[<verbatim|u_op>,<verbatim|()>,[<verbatim|b_op>,<verbatim|+>,[<verbatim|internal>,x],[<verbatim|internal>,y]]],[<verbatim|internal>,2]]>
318: </output>
319:
320: <\input|openxm] >
321: quotetolist(qt_normalize(`(x+y)^2))
322: </input>
323:
324: <\output>
325: <with|mode|math|[<verbatim|b_op>,<verbatim|^>,[<verbatim|n_op>,<verbatim|+>,[<verbatim|internal>,x],[<verbatim|internal>,y]],[<verbatim|internal>,2]]>
326: </output>
327:
328: <\input|openxm] >
329: qt_normalize(`(x+y)^2,1)
330: </input>
331:
332: <\output>
1.3 ! noro 333: <with|mode|math|x<rsup|2>+(x*y)+(y<rsup|2>)+(y*x)>
1.1 noro 334: </output>
335:
336: <\input|openxm] >
337: \;
338: </input>
339: </folded>
340: </session>>
341: </example>
342:
343: <subsection|\<#9805\>\<#9806\>\<#5E8F\>\<#304A\>\<#3088\>\<#3073\>\<#4FC2\>\<#6570\>\<#74B0\>\<#306E\>\<#8A2D\>\<#5B9A\>>
344:
1.3 ! noro 345: \<#5358\>\<#9805\>\<#5F0F\>\<#9806\>\<#5E8F\>\<#304A\>\<#3088\>\<#3073\>\<#4FC2\>\<#6570\>\<#74B0\>\<#306F\>\<#53EF\>\<#5909\>
1.1 noro 346:
347: <\itemize>
348: <item>\<#5358\>\<#9805\>\<#5F0F\>\<#9806\>\<#5E8F\>\<#306E\>\<#8A2D\>\<#5B9A\>
349:
1.3 ! noro 350: \<#30C7\>\<#30D5\>\<#30A9\>\<#30EB\>\<#30C8\> :
! 351: \<#3042\>\<#308B\>\<#8F9E\>\<#66F8\>\<#5F0F\>\<#9806\>\<#5E8F\>
! 352:
! 353: <with|font-family|tt|qt_set_ord>(<with|mode|math|V*a*r*L*i*s*t>) :
! 354: \<#57FA\>\<#790E\>\<#3068\>\<#306A\>\<#308B\>\<#4E0D\>\<#5B9A\>\<#5143\>\<#9806\>\<#5E8F\>\<#3092\>\<#4E0E\>\<#3048\>\<#308B\>
1.1 noro 355:
356: <item>\<#4FC2\>\<#6570\>\<#74B0\>\<#306E\>\<#8A2D\>\<#5B9A\>
357:
1.3 ! noro 358: \<#30C7\>\<#30D5\>\<#30A9\>\<#30EB\>\<#30C8\> :
! 359: \<#4FC2\>\<#6570\>\<#74B0\>\<#306F\>\<#6570\>\<#306E\>\<#307F\>
! 360:
! 361: <with|font-family|tt|qt_set_coef>(<with|mode|math|P*a*r*a*m*L*i*s*t>) :
! 362: \<#30D1\>\<#30E9\>\<#30E1\>\<#30BF\>\<#3092\>\<#4FC2\>\<#6570\>\<#74B0\>\<#306B\>\<#8FFD\>\<#52A0\>
! 363: (\<#4FC2\>\<#6570\>\<#74B0\>\<#306F\>\<#6709\>\<#7406\>\<#95A2\>\<#6570\>\<#4F53\>)
1.1 noro 364: </itemize>
365:
366: <\example>
367: <\verbatim>
368: \;
369:
370: <with|prog-language|openxm|prog-session|default|<\session>
1.3 ! noro 371: <\folded>
1.1 noro 372: \<#3044\>\<#304F\>\<#3064\>\<#304B\>\<#306E\>\<#5909\>\<#6570\>\<#3092\>\<#4FC2\>\<#6570\>\<#74B0\>\<#306B\>\<#307E\>\<#308F\>\<#3059\>
1.3 ! noro 373: <|folded>
1.1 noro 374: <\input|openxm] >
375: qt_normalize(`(b*x+a*y)*b*y,1)
376: </input>
377:
378: <\output>
1.3 ! noro 379: <with|mode|math|a*y*b*y+(b*x*b*y)>
1.1 noro 380: </output>
381:
382: <\input|openxm] >
383: qt_set_coef([a,b])
384: </input>
385:
386: <\output>
387: <with|mode|math|[a,b]>
388: </output>
389:
390: <\input|openxm] >
391: qt_normalize(`(b*x+a*y)*b*y,1)
392: </input>
393:
394: <\output>
1.3 ! noro 395: <with|mode|math|(b<rsup|2>)x*y+((b*a)y<rsup|2>)>
1.1 noro 396: </output>
397:
398: <\input|openxm] >
399: \;
400: </input>
401:
402: <\folded>
403: \<#4E0D\>\<#5B9A\>\<#5143\>\<#306E\>\<#9806\>\<#5E8F\>\<#3092\>\<#5909\>\<#3048\>\<#308B\>
404: <|folded>
405: <\input|openxm] >
406: qt_set_ord([y,x])$
407: </input>
408:
409: <\input|openxm] >
410: qt_normalize(`(b*x+a*y)*b*y,1)
411: </input>
412:
413: <\output>
1.3 ! noro 414: <with|mode|math|(b*a)y<rsup|2>+((b<rsup|2>)x*y)>
1.1 noro 415: </output>
416:
417: <\input|openxm] >
418: qt_set_coef([])$
419: </input>
420:
421: <\input|openxm] >
1.3 ! noro 422: qt_set_ord([x,y])$
! 423: </input>
! 424:
! 425: <\input|openxm] >
1.1 noro 426: \;
427: </input>
428: </folded>
1.3 ! noro 429: </folded>
1.1 noro 430: </session>>
431: </verbatim>
432: </example>
433:
434: <section|\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#30DE\>\<#30C3\>\<#30C1\>\<#30F3\>\<#30B0\>\<#306B\>\<#3088\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>>
435:
1.3 ! noro 436: Risa/Asir : \<#4E0D\>\<#5B9A\>\<#5143\>\<#3068\>\<#30D7\>\<#30ED\>\<#30B0\>\<#30E9\>\<#30E0\>\<#5909\>\<#6570\>\<#306F\>\<#660E\>\<#78BA\>\<#306B\>\<#533A\>\<#5225\>\<#3055\>\<#308C\>\<#3066\>\<#3044\>\<#308B\>.
! 437:
! 438: <with|mode|math|\<Rightarrow\>> \<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#5909\>\<#6570\>\<#3068\>\<#3057\>\<#3066\>\<#30D7\>\<#30ED\>\<#30B0\>\<#30E9\>\<#30E0\>\<#5909\>\<#6570\>\<#3092\>\<#7528\>\<#3044\>\<#308B\>
! 439:
! 440: \<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\> = \<#30D7\>\<#30ED\>\<#30B0\>\<#30E9\>\<#30E0\>\<#5909\>\<#6570\>\<#3092\>\<#542B\>\<#3093\>\<#3067\>\<#3082\>\<#3088\>\<#3044\>
! 441: <QT>
! 442:
! 443: <with|font-series|bold|\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#95A2\>\<#6570\>>
1.1 noro 444:
445: <\itemize>
446: <item><with|font-family|tt|nqt_match>(<with|mode|math|E*x*p*r>,<with|mode|math|P*a*t*t*e*n>[,<with|mode|math|M*o*d*e>])
447:
448: <QT> \<#5F0F\> <with|mode|math|E*x*p*r>
449: \<#3068\>\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>
450: <with|mode|math|P*a*t*t*e*r*n> \<#304C\>\<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#3089\>
451: 1 \<#3092\>\<#8FD4\>\<#3059\>. \<#3055\>\<#3089\>\<#306B\>,
452: <with|mode|math|P*a*t*t*e*r*n> \<#4E2D\>\<#306B\>\<#542B\>\<#307E\>\<#308C\>\<#308B\>\<#30D7\>\<#30ED\>\<#30B0\>\<#30E9\>\<#30E0\>\<#5909\>\<#6570\>\<#306B\>\<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#5024\>\<#304C\>\<#5B9F\>\<#969B\>\<#306B\>\<#4EE3\>\<#5165\>\<#3055\>\<#308C\>\<#308B\>.
453:
454: <item><with|font-family|tt|nqt_match_rewrite>(<with|mode|math|E*x*p*r>,<with|mode|math|R*u*l*e>,<with|mode|math|M*o*d*e>)
455:
1.3 ! noro 456: <with|mode|math|R*u*l*e> : [<with|mode|math|P*a*t*t*e*r*n>,<with|mode|math|A*c*t*i*o*n>]
! 457: or [<with|mode|math|P*a*t*t*e*r*n>,<with|mode|math|C*o*n*d*i*t*i*o*n>,<with|mode|math|A*c*t*i*o*n>]
! 458:
1.1 noro 459: <with|mode|math|E*x*p*r> \<#304C\> <with|mode|math|P*a*t*t*e*r*n>
460: \<#306B\>\<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#3089\>,
1.3 ! noro 461: <with|mode|math|A*c*t*i*o*n> \<#304C\>\<#8A55\>\<#4FA1\>\<#3055\>\<#308C\>,
! 462: \<#305D\>\<#306E\>\<#5024\>\<#304C\>\<#8FD4\>\<#308B\>.
! 463:
! 464: <with|mode|math|A*c*t*i*o*n> \<#4E2D\>\<#306E\>\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#5909\>\<#6570\>\<#306F\>\<#5024\>\<#306B\>\<#7F6E\>\<#304D\>\<#63DB\>\<#3048\>\<#3089\>\<#308C\>\<#308B\>.
! 465:
! 466: \<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#306A\>\<#3044\>\<#5834\>\<#5408\>\<#306B\>\<#306F\>
! 467: <with|mode|math|E*x*p*r> \<#305D\>\<#306E\>\<#3082\>\<#306E\>\<#304C\>\<#8FD4\>\<#3055\>\<#308C\>\<#308B\>.
! 468:
! 469: <item><with|font-family|tt|qt_rewrite>(<with|mode|math|E*x*p*r>,<with|mode|math|R*u*l*e*s>,<with|mode|math|M*o*d*e>)
! 470:
! 471: \<#30E6\>\<#30FC\>\<#30B6\>\<#95A2\>\<#6570\>\<#3068\>\<#3057\>\<#3066\>\<#8A18\>\<#8FF0\>\<#3057\>\<#305F\>,
! 472: \<#518D\>\<#5E30\>\<#547C\>\<#3073\>\<#51FA\>\<#3057\>\<#306B\>\<#3088\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#95A2\>\<#6570\>.
! 473: <with|mode|math|R*u*l*e*s> \<#306F\> \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#30EA\>\<#30B9\>\<#30C8\>.
1.1 noro 474: </itemize>
475:
476: <\example>
477: <\verbatim>
478: \;
479:
480: <with|prog-language|openxm|prog-session|default|<\session>
481: <\folded>
482: \<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#5024\>\<#3092\>\<#5909\>\<#6570\>\<#306B\>\<#4EE3\>\<#5165\>
483: <|folded>
484: <\input|openxm] >
485: nqt_match(`x*y*z-3*u,`X*Y+Z)
486: </input>
487:
488: <\output>
489: <with|mode|math|1>
490: </output>
491:
492: <\input|openxm] >
493: [X,Y,Z]
494: </input>
495:
496: <\output>
497: <with|mode|math|[x,y*z,(-3)u]>
498: </output>
499:
500: <\input|openxm] >
501: \;
502: </input>
1.3 ! noro 503:
! 504: <\output>
! 505: <with|mode|math|0>
! 506: </output>
! 507:
! 508: <\input|openxm] >
! 509: \;
! 510: </input>
1.1 noro 511: </folded>
512: </session>>
513:
514: <with|prog-language|openxm|prog-session|default|<\session>
515: <\folded>
516: \<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#3089\>\<#5373\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>
517: <|folded>
518: <\input|openxm] >
519: nqt_match_rewrite(`x*y*z,[`X*Y,`X+Y],1)
520: </input>
521:
522: <\output>
1.3 ! noro 523: <with|mode|math|x+(y*z)>
1.1 noro 524: </output>
525:
526: <\input|openxm] >
527: \;
528: </input>
529: </folded>
530: </session>>
531:
532: \;
533: </verbatim>
534: </example>
535:
1.3 ! noro 536: <\itemize>
! 537: <item>\<#5B9F\>\<#884C\>\<#524D\>\<#306B\>\<#5F15\>\<#6570\>\<#304C\>\<#6A19\>\<#6E96\>\<#5F62\>\<#306B\>\<#5909\>\<#63DB\>\<#3055\>\<#308C\>\<#308B\>
! 538:
! 539: <with|mode|math|M*o*d*e> \<#306F\>\<#305D\>\<#306E\>\<#969B\>\<#306B\>\<#5C55\>\<#958B\>\<#3092\>\<#884C\>\<#3046\>\<#304B\>\<#3069\>\<#3046\>\<#304B\>\<#306E\>\<#6307\>\<#793A\>
! 540:
! 541: <item>\<#6700\>\<#521D\>\<#306B\>\<#30DE\>\<#30C3\>\<#30C1\>\<#3057\>\<#305F\>\<#6642\>\<#70B9\>\<#306E\>\<#60C5\>\<#5831\>\<#304C\>\<#8FD4\>\<#3055\>\<#308C\>\<#308B\>
! 542:
! 543: \<#73FE\>\<#72B6\>\<#3067\>\<#306F\>\<#540C\>\<#4E00\>\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#5909\>\<#6570\>\<#304C\>\<#8907\>\<#6570\>\<#73FE\>\<#308C\>\<#308B\>\<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>\<#5931\>\<#6557\>\<#3059\>\<#308B\>\<#5834\>\<#5408\>\<#3042\>\<#308A\>
! 544:
! 545: <item><with|mode|math|C*o*n*d*i*t*i*o*n> \<#304A\>\<#3088\>\<#3073\>
! 546: <with|mode|math|A*c*t*i*o*n> \<#4E2D\>\<#306E\>\<#95A2\>\<#6570\>\<#547C\>\<#3073\>\<#51FA\>\<#3057\>
! 547:
! 548: \<#3053\>\<#308C\>\<#306B\>\<#3088\>\<#308A\>,
! 549: \<#8907\>\<#96D1\>\<#306A\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3092\>\<#66F8\>\<#304F\>\<#3053\>\<#3068\>\<#304C\>\<#3067\>\<#304D\>,
! 550: \<#307E\>\<#305F\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#6570\>\<#3092\>\<#5C11\>\<#306A\>\<#304F\>\<#62BC\>\<#3048\>\<#308B\>
! 551: \<#3053\>\<#3068\>\<#304C\>\<#3067\>\<#304D\>\<#308B\>.
! 552:
! 553: <item>\<#578B\>\<#5224\>\<#5B9A\>
! 554:
! 555: <with|mode|math|C*o*n*d*i*t*i*o*n> \<#306B\>\<#304A\>\<#3044\>\<#3066\>\<#578B\>\<#5224\>\<#5B9A\>\<#3092\>\<#884C\>\<#3046\>\<#3053\>\<#3068\>\<#306B\>\<#306A\>\<#308B\>.
! 556: </itemize>
1.1 noro 557:
558: <\example>
559: [<with|mode|math|s*l<rsub|2>>\<#306E\>\<#5C55\>\<#958B\>\<#74B0\>]\
560:
561: <\verbatim>
562: <with|prog-language|openxm|prog-session|default|<\session>
563: <\folded>
564: \<#57FA\>\<#672C\>\<#95A2\>\<#4FC2\>\<#5F0F\>\<#306B\>\<#3088\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>
565: <|folded>
566: <\input|openxm] >
567: Rsl=[[`h*e,`e*h+2*e],[`h*f,`f*h-2*f],[`e*f,`f*e+h]]$
568: </input>
569:
570: <\input|openxm] >
571: load("new_rewrite.rr")$
572: </input>
573:
574: <\input|openxm] >
575: qt_rewrite(`e*f^2,Rsl,2)
576: </input>
577:
578: <\output>
1.3 ! noro 579: <with|mode|math|f*f*e+((2)f*h)+((-2)f)>
1.1 noro 580: </output>
581:
582: <\input|openxm] >
583: qt_rewrite(`h*e^3,Rsl,2)
584: </input>
585:
586: <\output>
1.3 ! noro 587: <with|mode|math|e*e*e*h+((6)e*e*e)>
1.1 noro 588: </output>
589:
590: <\input|openxm] >
591: \;
592: </input>
593: </folded>
594: </session>>
595: </verbatim>
596: </example>
597:
598: <section|<FN> \<#306E\>\<#9806\>\<#5E8F\>\<#3065\>\<#3051\>>
599:
1.3 ! noro 600: <\with|font-series|bold>
! 601: \<#4ECA\>\<#56DE\>\<#306E\>\<#5B9F\>\<#88C5\>\<#306E\>\<#76EE\>\<#7684\>
! 602: </with>
! 603:
1.1 noro 604: \<#30E6\>\<#30FC\>\<#30B6\>\<#304C\>\<#6C17\>\<#8EFD\>\<#306B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3092\>\<#4E0E\>\<#3048\>\<#3066\>,
605: \<#4E00\>\<#822C\>\<#306B\>\<#975E\>\<#53EF\>\<#63DB\>\<#306A\>\<#4EE3\>\<#6570\>
1.3 ! noro 606: \<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#8A08\>\<#7B97\>\<#3092\>\<#6C17\>\<#8EFD\>\<#306B\>\<#8A66\>\<#305B\>\<#308B\>\<#3088\>\<#3046\>\<#306A\>\<#74B0\>\<#5883\>\<#3092\>\<#4F5C\>\<#308B\>\<#3053\>\<#3068\>
! 607:
! 608: <\with|font-series|bold>
! 609: \<#7121\>\<#9650\>\<#30EB\>\<#30FC\>\<#30D7\>\<#306B\>\<#9665\>\<#3089\>\<#306A\>\<#3044\>\<#3088\>\<#3046\>\<#306A\>\<#5B9F\>\<#7528\>\<#7684\>\<#306A\>\<#6307\>\<#91DD\>
! 610: </with>
! 611:
1.1 noro 612: <FN> \<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#9806\>\<#5E8F\>\<#3065\>\<#3051\>\<#304A\>\<#3088\>\<#3073\>
613: weight \<#306E\>\<#4F7F\>\<#7528\>\<#3092\>\<#63D0\>\<#6848\>\<#3059\>\<#308B\>.
1.3 ! noro 614:
! 615: \<#591A\>\<#9805\>\<#5F0F\>\<#74B0\>\<#3084\>\<#5FAE\>\<#5206\>\<#4F5C\>\<#7528\>\<#7D20\>\<#74B0\>\<#3067\>\<#7528\>\<#3044\>\<#3089\>\<#308C\>\<#308B\>
! 616: weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#306E\>\<#8003\>\<#3048\>\<#578B\>\<#306E\>\<#81EA\>\<#7136\>\<#306A\>\<#4E00\>\<#822C\>\<#5316\>\<#3067\>\<#3042\>\<#308A\>,
1.1 noro 617: \<#7406\>\<#8AD6\>\<#7684\>\<#306B\>\<#3082\>\<#8208\>\<#5473\>\<#6DF1\>\<#3044\>.
618:
1.3 ! noro 619: <\with|font-series|bold>
! 620: \<#4F8B\> --- \<#53EF\>\<#63DB\>\<#6027\>\<#306E\>\<#5B9A\>\<#7FA9\>
! 621: </with>
! 622:
1.1 noro 623: \<#6570\>\<#5B66\>\<#7684\>\<#306B\>\<#306F\>, \<#4EFB\>\<#610F\>\<#306E\>
1.3 ! noro 624: <with|mode|math|X>, <with|mode|math|Y> \<#306B\>\<#5BFE\>\<#3057\>
! 625: <with|mode|math|X*Y=Y*X> \<#3067\>\<#3088\>\<#3044\>
! 626:
! 627: <with|mode|math|\<Rightarrow\>> <with|mode|math|[`X\<ast\>Y,`Y\<ast\>X]>
! 628: \<#3068\>\<#3044\>\<#3046\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3092\>\<#66F8\>\<#304F\>\<#3068\>\<#505C\>\<#6B62\>\<#3057\>\<#306A\>\<#3044\>.
! 629:
! 630: <\with|font-series|bold>
! 631: \<#6700\>\<#3082\>\<#5B89\>\<#76F4\>\<#306A\>\<#89E3\>\<#6C7A\>\<#65B9\>\<#6CD5\>
! 632: </with>
! 633:
1.1 noro 634: <FN> \<#9593\>\<#306B\>\<#5168\>\<#9806\>\<#5E8F\>\<#3092\>\<#5165\>\<#308C\>\<#3066\>,
635: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#305F\>\<#5834\>\<#5408\>\<#306B\>\<#9806\>\<#5E8F\>\<#304C\>\<#5927\>\<#304D\>\<#304F\>(\<#5C0F\>\<#3055\>\<#304F\>)\<#306A\>\<#308B\>
1.3 ! noro 636: \<#5834\>\<#5408\>\<#306B\>\<#306E\>\<#307F\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#3092\>\<#884C\>\<#3046\>
! 637:
! 638: \<#7A4D\>\<#3092\>\<#69CB\>\<#6210\>\<#3059\>\<#308B\>\<#6709\>\<#9650\>\<#500B\>\<#306E\>
! 639: <FN> \<#306E\>\<#4E26\>\<#3079\>\<#5909\>\<#3048\>\<#306E\>\<#4E2D\>\<#3067\>\<#6700\>\<#3082\>\<#9806\>\<#5E8F\>\<#304C\>\<#4E0A\>(\<#4E0B\>)\<#306E\>\<#3082\>\<#306E\>\<#306B\>\<#5230\>\<#9054\>\<#3059\>\<#308B\>\<#3068\>\<#505C\>\<#6B62\>\<#3059\>\<#308B\>.
1.1 noro 640:
641: <subsection|<FN> \<#306E\> weight\<#3068\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>>
642:
643: \<#4E00\>\<#822C\>\<#306B\> <FN> <with|mode|math|f> \<#306E\> weight
644: <with|mode|math|w(f)> \<#3092\>
645:
646: <\enumerate>
647: <item><with|mode|math|f> \<#304C\> leaf \<#306E\>\<#5834\>\<#5408\>,
648: \<#9069\>\<#5F53\>\<#306A\>\<#5024\>\<#3092\>\<#4E0E\>\<#3048\>\<#308B\>.
649: \<#7279\>\<#306B\>\<#4FC2\>\<#6570\>\<#306E\> weight \<#306F\> 0.
650:
651: <item><with|mode|math|f> \<#304C\> node \<#306E\>\<#5834\>\<#5408\>,
652: <with|mode|math|f> \<#306E\>\<#5B50\>\<#306E\> weight
653: \<#5024\>\<#3092\>\<#5F15\>\<#6570\>\<#3068\>\<#3057\>,
654: \<#8B58\>\<#5225\>\<#5B50\>\<#3067\>\<#6C7A\>\<#3081\>\<#3089\>\<#308C\>\<#305F\>\<#95A2\>\<#6570\>\<#3092\>\<#8A08\>\<#7B97\>\<#3057\>\<#3066\>\<#305D\>\<#306E\>\<#5024\>\<#3092\>\<#3068\>\<#308B\>.
655: </enumerate>
656:
657: \<#306B\>\<#3088\>\<#308A\>\<#518D\>\<#5E30\>\<#7684\>\<#306B\>\<#6C7A\>\<#3081\>\<#308B\>\<#3053\>\<#3068\>\<#304C\>\<#3067\>\<#304D\>\<#308B\>.
658: \<#548C\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>\<#306F\>
659: <with|mode|math|max()>, \<#7A4D\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>\<#306F\>\<#548C\>,
660: \<#30D9\>\<#30AD\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>\<#306F\>\<#7A4D\>\<#3092\>\<#7528\>\<#3044\>\<#308B\>\<#3068\>,
661: \<#6B21\>\<#306E\>\<#3088\>\<#3046\>\<#306B\>\<#306A\>\<#308B\>.
662:
663: <\enumerate>
664: <item><with|mode|math|w(f+g)=max(w(f),w(g))>
665:
666: <item><with|mode|math|w(f*g)=w(f)+w(g)>
667:
668: <item><with|mode|math|w(f<rsup|n>)=n*w(f)>
669: </enumerate>
670:
671: \<#4EE5\>\<#4E0B\>\<#3067\>\<#306F\>, \<#3053\>\<#306E\>\<#3088\>\<#3046\>\<#306A\>
672: weight \<#3092\>\<#6709\>\<#9650\>\<#751F\>\<#6210\>\<#306E\>\<#81EA\>\<#7531\>\<#7D50\>\<#5408\>\<#4EE3\>\<#6570\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>
673: \<#306B\>\<#5FDC\>\<#7528\>\<#3059\>\<#308B\>\<#3053\>\<#3068\>\<#3092\>\<#8003\>\<#3048\>\<#308B\>.
674:
675: \<#4FC2\>\<#6570\>\<#74B0\>\<#3092\> <with|mode|math|K>
676: \<#306E\>\<#4E0A\>\<#3067\> <with|mode|math|z<rsub|1>,\<ldots\>,z<rsub|n>,h>
677: \<#3067\>\<#751F\>\<#6210\>\<#3055\>\<#308C\>\<#308B\>\<#81EA\>\<#7531\>\<#7D50\>\<#5408\>\<#4EE3\>\<#6570\>
678: <with|mode|math|A> \<#3092\>
679:
680: <\equation*>
681: K\<langle\>z<rsub|1>,\<ldots\>,z<rsub|n>,h\<rangle\>
682: </equation*>
683:
1.3 ! noro 684: \<#3068\>\<#66F8\>\<#304F\>.
1.1 noro 685:
686: <\definition>
687: <\with|font-family|rm>
688: <with|mode|math|A> \<#3067\>\<#306E\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>(\<#307E\>\<#305F\>\<#306F\>\<#95A2\>\<#4FC2\>\<#5F0F\>,
689: \<#5DE6\>\<#8FBA\>\<#306F\>\<#5FC5\>\<#305A\>\<#5358\>\<#9805\>\<#5F0F\>)
690: </with>
691:
692: <\equation*>
693: L<rsub|1>\<rightarrow\>R<rsub|1>,\<ldots\>,L<rsub|m>\<rightarrow\>R<rsub|m>
694: </equation*>
695:
696: \<#304C\>, \<#540C\>\<#6B21\>\<#5316\> weight
697: \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\> <with|mode|math|H>
698: \<#306B\>\<#3064\>\<#3044\>\<#3066\>,
699: \<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3067\>\<#3042\>\<#308B\>\<#3068\>\<#306F\>,
700: <with|mode|math|R<rsub|i>> \<#304C\> <with|mode|math|0>
701: \<#3067\>\<#3042\>\<#308B\>\<#304B\>\<#307E\>\<#305F\>\<#306F\>,
702:
703: <\equation*>
704: <with|mode|text|font-family|rm|deg><rsub|H>(L<rsub|i>)=<with|mode|text|font-family|rm|deg><rsub|H>(R<rsub|i><with|mode|text|\<#306E\>\<#4EFB\>\<#610F\>\<#306E\>\<#9805\>>)
705: </equation*>
706:
707: \<#304C\>\<#6210\>\<#7ACB\>\<#3059\>\<#308B\>\<#3053\>\<#3068\>\<#3067\>\<#3042\>\<#308B\>.
708: </definition>
709:
710: \<#3053\>\<#3053\>\<#3067\> <with|mode|math|<with|mode|text|font-family|rm|deg><rsub|H>(<big|prod>z<rsub|i><rsup|e<rsub|i>>)>
711: \<#306F\> <with|mode|math|<big|prod>z<rsub|i><rsup|e<rsub|i>>> \<#306E\>
712: weight <with|mode|math|H> \<#306B\>\<#3064\>\<#3044\>\<#3066\>\<#306E\>(\<#975E\>\<#53EF\>\<#63DB\>\<#6027\>\<#3092\>\<#7121\>\<#8996\>\<#3057\>\<#305F\>)\<#6B21\>\<#6570\>\<#3067\>\<#3042\>\<#308B\>.
713: \<#3064\>\<#307E\>\<#308A\>
714:
715: <\equation*>
716: <with|mode|text|font-family|rm|deg><rsub|H>(<big|prod>z<rsub|i><rsup|e<rsub|i>>)=<big|sum>e<rsub|i>H<rsub|i>
717: </equation*>
718:
719: \<#3068\>\<#5B9A\>\<#7FA9\>\<#3059\>\<#308B\> (<with|mode|math|i>
720: \<#306F\>\<#91CD\>\<#8907\>\<#3057\>\<#3066\>\<#3042\>\<#3089\>\<#308F\>\<#308C\>\<#308B\>\<#3053\>\<#3068\>\<#3082\>\<#3042\>\<#308B\>).
721:
722: <\example>
723: <with|font-family|rm|>
724:
725: <\equation*>
726: z<rsub|2>z<rsub|1>\<rightarrow\>z<rsub|1>z<rsub|2>+h<rsup|2>,h*z<rsub|i>\<rightarrow\>z<rsub|i>h
727: </equation*>
728:
729: \<#306F\> <with|mode|math|H=(1,1,1)> \<#306B\>\<#3064\>\<#3044\>\<#3066\>\<#306E\>\<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3067\>\<#3042\>\<#308B\>.
730: \<#3053\>\<#306E\>\<#4F8B\>\<#306F\> <with|mode|math|x=z<rsub|1>,\<partial\>=z<rsub|2>>
731: \<#3068\>\<#3057\>\<#305F\> 1 \<#5909\>\<#6570\>\<#306E\>\<#540C\>\<#6B21\>\<#5316\>
732: Weyl \<#4EE3\>\<#6570\>\<#306B\>\<#307B\>\<#304B\>\<#306A\>\<#3089\>\<#306A\>\<#3044\>.
733: </example>
734:
1.3 ! noro 735: <\with|font-series|bold>
! 736: \<#4EEE\>\<#5B9A\>
! 737: </with>
! 738:
! 739: <\itemize>
! 740: <item><with|mode|math|H> \<#306E\>\<#3059\>\<#3079\>\<#3066\>\<#306E\>\<#6210\>\<#5206\>\<#306F\>\<#6B63\>
! 741:
! 742: <item><with|mode|math|x<rsub|1>,\<ldots\>,x<rsub|n>,h>
! 743: \<#304B\>\<#3089\>\<#306A\>\<#308B\>\<#30EF\>\<#30FC\>\<#30C9\>\<#306B\>\<#5BFE\>\<#3059\>\<#308B\>
! 744: well order <with|mode|math|\<succ\>> \<#3092\>\<#3072\>\<#3068\>\<#3064\>\<#56FA\>\<#5B9A\>
! 745:
! 746: <item>\<#51FA\>\<#73FE\>\<#3059\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306F\>\<#3068\>\<#304F\>\<#306B\>\<#3053\>\<#3068\>\<#308F\>\<#3089\>\<#306A\>\<#3044\>\<#9650\>\<#308A\>\<#5168\>\<#3066\><with|mode|math|H>
! 747: \<#306B\>\<#3064\>\<#3044\>\<#3066\>\<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>
! 748: </itemize>
1.1 noro 749:
750: <\example>
751: <with|font-family|rm|\<#524D\>\<#306E\>\<#4F8B\>\<#306E\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>>
752:
753: <\equation*>
754: z<rsub|2>z<rsub|1>\<rightarrow\>z<rsub|1>z<rsub|2>+h<rsup|2>,h*z<rsub|i>\<rightarrow\>z<rsub|i>h
755: </equation*>
756:
757: \<#306B\>\<#3055\>\<#3089\>\<#306B\>
758:
759: <\equation*>
760: z<rsub|2><rsup|p+1>\<rightarrow\>0,z<rsub|1>z<rsub|2>\<rightarrow\>p*h<rsup|2>
761: </equation*>
762:
763: \<#3092\>\<#52A0\>\<#3048\>\<#305F\>\<#898F\>\<#5247\>\<#306E\>\<#96C6\>\<#5408\>\<#3092\>
764: <with|mode|math|R<rsub|p>> \<#3068\>\<#66F8\>\<#304F\>.
765: \<#3053\>\<#3053\>\<#3067\> <with|mode|math|p>
766: \<#306F\>\<#81EA\>\<#7136\>\<#6570\>\<#3067\>\<#3042\>\<#308B\>.
767: <with|mode|math|R<rsub|p>> \<#306F\> <with|mode|math|H=(1,1,1)>
768: \<#306B\>\<#3064\>\<#3044\>\<#3066\>\<#306E\>\<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3067\>\<#3042\>\<#308B\>.
769: </example>
770:
771: <\definition>
772: <\with|font-family|rm>
773: <with|mode|math|n> \<#6B21\>\<#5143\>\<#306E\> weight
774: \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>
775: <with|mode|math|w\<in\><with|font-series|bold|R><rsup|n>>
776: \<#304C\>\<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>
777: <with|mode|math|{L<rsub|i>\<rightarrow\>R<rsub|i>}>
778: \<#304A\>\<#3088\>\<#3073\> <with|mode|math|\<succ\>>
779: \<#306B\>\<#3064\>\<#3044\>\<#3066\> \<#6709\>\<#52B9\> weight
780: \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>(admissible weight vector)
781: \<#3067\>\<#3042\>\<#308B\>\<#3068\>\<#306F\>\<#6B21\>\<#306E\>\<#6761\>\<#4EF6\>\<#3092\>\<#307F\>\<#305F\>\<#3059\>
782: \<#3053\>\<#3068\>\<#3067\>\<#3042\>\<#308B\>. \<#4EE5\>\<#4E0B\>
783: <with|mode|math|<wide|w|~>=(w,0)> (<with|mode|math|h>
784: \<#306B\>\<#5BFE\>\<#3059\>\<#308B\> weight \<#3092\> 0
785: \<#306B\>\<#3057\>\<#305F\>\<#3082\>\<#306E\>)
786: \<#3068\>\<#304A\>\<#304F\>.
787: </with>
788:
789: <\enumerate>
790: <item><with|mode|math|<with|mode|text|font-family|rm|deg><rsub|<wide|w|~>>(L<rsub|i>)\<geq\><with|mode|text|font-family|rm|deg><rsub|<wide|w|~>>(R<rsub|i>)>
791:
792: <item>\<#5DE6\>\<#8FBA\>\<#3068\>\<#53F3\>\<#8FBA\>\<#304C\>\<#540C\>\<#3058\>
793: <with|mode|math|w>-\<#6B21\>\<#6570\>\<#3092\>\<#3082\>\<#3064\>\<#3068\>\<#304D\>\<#306F\>
794: \<#53F3\>\<#8FBA\>\<#3067\>\<#5DE6\>\<#8FBA\>\<#3068\>\<#540C\>\<#3058\>
795: <with|mode|math|w>-weight \<#3092\>\<#6301\>\<#3064\>
796: \<#9805\>\<#305F\>\<#3061\>\<#306F\>\<#9806\>\<#5E8F\>
797: <with|mode|math|\<succ\>> \<#3067\>\<#304B\>\<#306A\>\<#3089\>\<#305A\>\<#5C0F\>\<#3055\>\<#3044\>.
798: </enumerate>
799: </definition>
800:
801: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#304C\>\<#3042\>\<#308B\>\<#6B63\>\<#6570\>\<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>
802: <with|mode|math|H> \<#306B\>\<#3064\>\<#3044\>\<#3066\>\<#540C\>\<#6B21\>\<#7684\>\<#3067\>\<#3042\>\<#308B\>\<#3053\>\<#3068\>\<#304B\>\<#3089\>,
803: \<#3053\>\<#308C\>\<#3089\>\<#306E\>\<#6761\>\<#4EF6\>\<#306B\>\<#3088\>\<#308A\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#304C\>\<#505C\>\<#6B62\>\<#6027\>\<#3092\>\<#3082\>\<#3064\>\<#3053\>\<#3068\>\<#304C\>\<#5206\>\<#304B\>\<#308B\>.
804: \<#3055\>\<#3089\>\<#306B\> \<#6B21\>\<#306E\>\<#547D\>\<#984C\>\<#304C\>\<#6210\>\<#308A\>\<#7ACB\>\<#3064\>.
805:
806: <proposition|G-algebra <cite|LEV> \<#306E\>\<#6761\>\<#4EF6\>\<#306E\>\<#3046\>\<#3061\>,
807: well order \<#306E\>\<#5B58\>\<#5728\>\<#6761\>\<#4EF6\>\<#3092\>\<#4EEE\>\<#5B9A\>\<#3057\>\<#306A\>\<#304F\>\<#3066\>\<#3082\>,
808: \<#9069\>\<#5F53\>\<#306A\>\<#540C\>\<#6B21\>\<#5316\>weight\<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>,
809: \<#6709\>\<#52B9\> weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#304C\>\<#5B58\>\<#5728\>\<#3059\>\<#308B\>\<#306A\>\<#3089\>\<#3070\>,
810: <with|mode|math|h> \<#3092\>\<#52A0\>\<#3048\>\<#308B\>\<#6589\>\<#6B21\>\<#5316\>,
811: <with|mode|math|h> \<#3092\> <with|mode|math|1>
812: \<#3068\>\<#304A\>\<#304F\>\<#3053\>\<#3068\>\<#306B\>\<#3088\>\<#308B\>\<#975E\>\<#6589\>\<#5316\>\<#306B\>\<#3088\>\<#308A\>,
813: \<#30B0\>\<#30EC\>\<#30D6\>\<#30CA\>\<#30FC\>\<#57FA\>\<#5E95\>\<#3092\>\<#8A08\>\<#7B97\>\<#3067\>\<#304D\>\<#308B\>\<#3088\>\<#3046\>\<#306B\>\<#306A\>\<#308B\>.>
814:
1.3 ! noro 815: <\with|font-series|bold>
! 816: \<#5FDC\>\<#7528\>\<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#6CE8\>\<#610F\>
! 817: </with>
! 818:
1.1 noro 819: \<#4E0E\>\<#3048\>\<#3089\>\<#308C\>\<#305F\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306B\>\<#5BFE\>\<#3057\>,
820: \<#6709\>\<#52B9\> weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>
821: <with|mode|math|w> \<#3092\>\<#898B\>\<#3064\>\<#3051\>\<#308B\>\<#5FC5\>\<#8981\>\<#304C\>\<#3042\>\<#308B\>.
1.3 ! noro 822:
! 823: <\with|font-series|bold>
! 824: \<#4F8B\> --- \<#4E00\>\<#5909\>\<#6570\>\<#30EF\>\<#30A4\>\<#30EB\>\<#4EE3\>\<#6570\>
! 825: </with>
! 826:
1.1 noro 827: <with|mode|math|w<rsub|1>+w<rsub|2>\<geq\>0>
828: \<#306E\>\<#6761\>\<#4EF6\>\<#3092\>\<#307F\>\<#305F\>\<#3055\>\<#306A\>\<#3044\>\<#3068\>
829: \<#6709\>\<#52B9\> weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#3068\>\<#306A\>\<#3089\>\<#306A\>\<#3044\>.
1.3 ! noro 830:
! 831: <with|mode|math|\<Rightarrow\>> \<#540C\>\<#6642\>\<#5316\> weight
1.1 noro 832: \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#3092\>\<#7528\>\<#3044\>\<#3066\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#53F3\>\<#8FBA\>\<#3092\>\<#6589\>\<#6B21\>\<#5316\>
833: \<#3059\>\<#308C\>\<#3070\>, \<#540C\>\<#6B21\>\<#7684\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#304C\>\<#5F97\>\<#3089\>\<#308C\>\<#308B\>.
834:
1.3 ! noro 835: <\with|font-series|bold>
! 836: \<#73FE\>\<#5728\>\<#306E\>\<#5B9F\>\<#88C5\>
! 837: </with>
! 838:
! 839: <\itemize>
! 840: <item>weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#304C\>\<#8A2D\>\<#5B9A\>\<#3055\>\<#308C\>\<#306A\>\<#3044\>\<#9650\>\<#308A\>,
! 841: weight \<#306B\> \<#3088\>\<#308B\>\<#6BD4\>\<#8F03\>\<#306F\>\<#884C\>\<#308F\>\<#306A\>\<#3044\>.
! 842:
! 843: <item>\<#95A2\>\<#6570\> <with|font-family|tt|qt_set_weight()>
! 844: \<#306B\>\<#3088\>\<#308A\> \<#4E00\>\<#90E8\>\<#306E\>\<#4E0D\>\<#5B9A\>\<#5143\>\<#306B\>\<#5BFE\>\<#3057\>\<#3066\>
! 845: weight \<#304C\>\<#8A2D\>\<#5B9A\>\<#3055\>\<#308C\>\<#308B\>\<#3068\>,
! 846: \<#4ED6\>\<#306E\>\<#4E0D\>\<#5B9A\>\<#5143\>\<#306E\> weight
! 847: \<#306F\>\<#81EA\>\<#52D5\>\<#7684\>\<#306B\> 0
! 848: \<#3068\>\<#306A\>\<#308B\>.
! 849:
! 850: <item>\<#3053\>\<#306E\> weight \<#3092\>\<#7528\>\<#3044\>\<#305F\>
! 851: \<#6B21\>\<#6570\>\<#306E\>\<#6BD4\>\<#8F03\>\<#5F8C\>\<#306B\>\<#73FE\>\<#5728\>\<#8A2D\>\<#5B9A\>
! 852: \<#3055\>\<#308C\>\<#3066\>\<#3044\>\<#308B\>\<#5358\>\<#9805\>\<#5F0F\>\<#9806\>\<#5E8F\>\<#304C\>\<#9069\>\<#7528\>\<#3055\>\<#308C\>\<#308B\>.
! 853: </itemize>
1.1 noro 854:
855: <\example>
856: \;
857:
858: <with|prog-language|openxm|prog-session|default|<\session>
859: <\folded>
860: \<#8CA0\>\<#306E\>weight\<#3092\>\<#3082\>\<#3064\>weight\<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#306B\>\<#3088\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#306E\>\<#4F8B\>
861: <|folded>
862: <\input|openxm] >
863: qt_set_ord([z1,z2,h])$
864: </input>
865:
866: <\input|openxm] >
867: qt_set_weight([[z1,-1],[z2,1]])$
868: </input>
869:
870: <\input|openxm] >
871: Rule1=[[`h*z1,`z1*h], [`h*z2,`z2*h], [`z2*z1,`z1*z2+h^2]] $
872: </input>
873:
874: <\input|openxm] >
875: Rule2=[[`z2*z2,`0], [`z1*z2,`h^2]]$
876: </input>
877:
878: <\input|openxm] >
879: F=`z2^2*(h^2+z1^2)$
880: </input>
881:
882: <\input|openxm] >
883: qt_rewrite(F,Rule1,2)
884: </input>
885:
886: <\output>
887: <with|mode|math|z<rsub|2>z<rsub|2>h*h+z<rsub|1>z<rsub|1>z<rsub|2>z<rsub|2>+(4)z<rsub|1>z<rsub|2>h*h+(2)h*h*h*h>
888: </output>
889:
890: <\input|openxm] >
891: \;
892: </input>
893: </folded>
894: </session>>
895: </example>
896:
897: <\remark>
898: \<#6709\>\<#52B9\> weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#304C\>\<#8CA0\>\<#306E\>\<#6210\>\<#5206\>\<#3092\>\<#3082\>\<#3064\>\<#3068\>\<#975E\>\<#6589\>\<#6B21\>\<#5316\>\<#3057\>\<#305F\>\<#3042\>\<#3068\>\<#306E\>
899: reduction \<#306E\>\<#505C\>\<#6B62\>\<#6027\>\<#306F\>\<#3044\>\<#3048\>\<#306A\>\<#3044\>.
900: </remark>
901:
902: <section|\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#4F8B\>>
903:
904: \<#4EE5\>\<#4E0B\>\<#306B\>, \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#4F8B\>\<#3092\>\<#3044\>\<#304F\>\<#3064\>\<#304B\>\<#7D39\>\<#4ECB\>\<#3059\>\<#308B\>.
905:
906: <\example>
907: [\<#53EF\>\<#63DB\>\<#6027\>]\
908:
909: <\verbatim>
910: <with|prog-language|openxm|prog-session|default|<\session>
911: <\folded>
912: \<#6BD4\>\<#8F03\>\<#95A2\>\<#6570\>\<#306B\>\<#3088\>\<#308B\>\<#6C4E\>\<#7528\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306E\>\<#5B9A\>\<#7FA9\>
913: <|folded>
914: <\input|openxm] >
915: qt_normalize(`(x+y-z)^2,1)
916: </input>
917:
918: <\output>
1.3 ! noro 919: <with|mode|math|x<rsup|2>+(x*y)+(-x*z)+(y<rsup|2>)+(y*x)+(-y*z)+(z<rsup|2>)+(-z*x)+(-z*y)>
1.1 noro 920: </output>
921:
922: <\input|openxm] >
923: Rcomm=[[`X*Y,`nqt_comp(Y*X,X*Y)\<gtr\>0,`Y*X]]$
924: </input>
925:
926: <\input|openxm] >
927: load("new_rewrite.rr")$
928: </input>
929:
930: <\input|openxm] >
931: qt_rewrite(`(x+y-z)^2,Rcomm,1)
932: </input>
933:
934: <\output>
1.3 ! noro 935: <with|mode|math|x<rsup|2>+((2)x*y)+((-2)x*z)+(y<rsup|2>)+((-2)y*z)+(z<rsup|2>)>
1.1 noro 936: </output>
937:
938: <\input|openxm] >
939: \;
940: </input>
941: </folded>
942: </session>>
943: </verbatim>
944:
945: <with|font-family|tt|nqt_comp()> \<#306F\>\<#6BD4\>\<#8F03\>\<#95A2\>\<#6570\>\<#3067\>\<#3042\>\<#308B\>.
946: </example>
947:
948: <\example>
949: [\<#5916\>\<#7A4D\>\<#4EE3\>\<#6570\>]\
950:
951: <\verbatim>
952: <with|prog-language|openxm|prog-session|default|<\session>
953: <\folded>
954: \<#884C\>\<#5217\>\<#5F0F\>\<#306E\>\<#8A08\>\<#7B97\>
955: <|folded>
956: <\input|openxm] >
957: Rext0=[`X*Y,`qt_is_var(X) && qt_is_var(Y) &&
958: nqt_comp(Y,X)\<gtr\>0,`-Y*X]$
959: </input>
960:
961: <\input|openxm] >
962: Rext1=[`X^N,`eval_quote(N)\<gtr\>=2,`0]$
963: </input>
964:
965: <\input|openxm] >
966: Rext2=[`X*X,`0]$
967: </input>
968:
969: <\input|openxm] >
970: Rext=[Rext0,Rext1,Rext2]$
971: </input>
972:
973: <\input|openxm] >
974: qt_set_coef([a,b,c])$
975: </input>
976:
977: <\input|openxm] >
978: qt_rewrite(`(a*x+b*y+c*z)*(b*x+c*y+a*z)*(c*x+a*y+b*z),Rext,1)
979: </input>
980:
981: <\output>
982: <with|mode|math|(-a<rsup|3>+3c*b*a-b<rsup|3>-c<rsup|3>)x*y*z>
983: </output>
984:
985: <\input|openxm] >
986: \;
987: </input>
988: </folded>
989: </session>>
990: </verbatim>
991:
992: \ \<#5909\>\<#6570\>\<#306E\>\<#7A4D\>\<#3092\>\<#4EA4\>\<#4EE3\>\<#7684\>\<#306B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#308B\>\<#898F\>\<#5247\>\<#3092\>\<#5B9A\>\<#7FA9\>\<#3057\>\<#3066\>\<#3044\>\<#308B\>.
993: </example>
994:
995: <\example>
996: [\<#5FAE\>\<#5206\>]\
997:
998: <\verbatim>
999: <with|prog-language|openxm|prog-session|default|<\session>
1000: <\folded>
1001: a \<#3092\>\<#5B9A\>\<#6570\>\<#3068\>\<#898B\>\<#306A\>\<#3059\>
1002: <|folded>
1003: <\input|openxm] >
1004: qt_set_coef([a])$
1005: </input>
1006:
1007: <\input|openxm] >
1008: Rd1=[`d(X+Y),`d(X)+d(Y)]$
1009: </input>
1010:
1011: <\input|openxm] >
1012: Rd2=[`d(X*Y),`d(X)*Y+X*d(Y)]$
1013: </input>
1014:
1015: <\input|openxm] >
1016: Rd3=[`d(N),`qt_is_coef(N),`0]$
1017: </input>
1018:
1019: <\input|openxm] >
1020: Rd=[Rd1,Rd2,Rd3]$
1021: </input>
1022:
1023: <\input|openxm] >
1024: qt_rewrite(`d((x+a*y)^2),Rd,1)
1025: </input>
1026:
1027: <\output>
1028: <with|mode|math|d(x<rsup|2>)+(a)(d(x))y+(a<rsup|2>)(d(y<rsup|2>))+(a)(d(y))x+(a)x(d(y))+(a)y(d(x))>
1029: </output>
1030:
1031: <\input|openxm] >
1032: \;
1033: </input>
1034: </folded>
1035: </session>>
1036: </verbatim>
1037: </example>
1038:
1039: <\example>
1040: [Weyl \<#4EE3\>\<#6570\>]
1041:
1042: <with|prog-language|openxm|prog-session|default|<\session>
1043: <\folded>
1044: Action \<#306B\>\<#30E6\>\<#30FC\>\<#30B6\>\<#5B9A\>\<#7FA9\>\<#95A2\>\<#6570\>\<#3092\>\<#547C\>\<#3073\>\<#51FA\>\<#3059\>\<#4F8B\>
1045: <|folded>
1046: <\input|openxm] >
1047: load("weyl.rr")$
1048: </input>
1049:
1050: <\input|openxm] >
1.3 ! noro 1051: qt_rewrite(`((x*dy+y*dx)^3),Rweyl,1)
! 1052: </input>
! 1053:
! 1054: <\output>
! 1055: <with|mode|math|x<rsup|3>d*y<rsup|3>+((3)x<rsup|2>y*d*x*d*y<rsup|2>)+((3)x<rsup|2>d*x*d*y)+((3)x*y<rsup|2>d*x<rsup|2>d*y)+((3)x*y*d*x<rsup|2>)+((3)x*y*d*y<rsup|2>)+(x*d*y)+(y<rsup|3>d*x<rsup|3>)+((3)y<rsup|2>d*x*d*y)+(y*d*x)>
! 1056: </output>
! 1057:
! 1058: <\input|openxm] >
! 1059: A=(\<less\>\<less\>1,0,0,1\<gtr\>\<gtr\>+\<less\>\<less\>0,1,1,0\<gtr\>\<gtr\>)$
! 1060: </input>
! 1061:
! 1062: <\input|openxm] >
! 1063: A;
! 1064: </input>
! 1065:
! 1066: <\output>
! 1067: <with|mode|math|<underline|x<rsub|1>x<rsub|2>>+x<rsub|0>x<rsub|3>>
! 1068: </output>
! 1069:
! 1070: <\input|openxm] >
! 1071: dp_weyl_mul(dp_weyl_mul(A,A),A)
! 1072: </input>
! 1073:
! 1074: <\output>
! 1075: <with|mode|math|<underline|x<rsub|1><rsup|3>x<rsub|2><rsup|3>>+3x<rsub|0>x<rsub|1><rsup|2>x<rsub|2><rsup|2>x<rsub|3>+3x<rsub|0><rsup|2>x<rsub|1>x<rsub|2>x<rsub|3><rsup|2>+x<rsub|0><rsup|3>x<rsub|3><rsup|3>+3x<rsub|0>x<rsub|1>x<rsub|2><rsup|2>+3x<rsub|0><rsup|2>x<rsub|2>x<rsub|3>+3x<rsub|1><rsup|2>x<rsub|2>x<rsub|3>+3x<rsub|0>x<rsub|1>x<rsub|3><rsup|2>+x<rsub|1>x<rsub|2>+x<rsub|0>x<rsub|3>>
! 1076: </output>
! 1077:
! 1078: <\input|openxm] >
! 1079: \;
1.1 noro 1080: </input>
1081:
1082: <\output>
1.3 ! noro 1083: <with|mode|math|[<verbatim|symbol_table>,[[<verbatim|hypergeometric_2f1>,<verbatim|{}_2
! 1084: F_1>],[<verbatim|hypergeometric_pfq>,<verbatim|{}_p
! 1085: F_q>],[<verbatim|hypergeometric_gamma>,<verbatim|\\Gamma>],[<verbatim|hypergeometric_pochhammer>,<verbatim|{\\rm
! 1086: poch}>]],<verbatim|conv_rule>,7,<verbatim|conv_func>,0,<verbatim|dp_vars>,0,<verbatim|dp_vars_prefix>,0,<verbatim|dp_dvars_prefix>,0,<verbatim|dp_vars_origin>,0,<verbatim|dp_dvars_origin>,0,<verbatim|dp_vars_hweyl>,0,<verbatim|show_lt>,1]>
1.1 noro 1087: </output>
1088:
1089: <\input|openxm] >
1090: \;
1091: </input>
1092: </folded>
1093: </session>>
1094:
1095: <\verbatim>
1096: weyl.rr \<#306E\>\<#5185\>\<#5BB9\>
1097:
1098: def member(V,L) {
1099:
1100: \ \ for ( I = 0; L != [] && V != car(L); L = cdr(L), I++ );
1101:
1102: \ \ return L==[] ? -1 : I;
1103:
1104: }
1105:
1106: def qt_weyl_vmul(X,K,Y,L) {
1107:
1108: \ \ extern WeylV, WeylDV;
1109:
1110: \ \ if ( member(X,WeylV)<with|mode|math|\<gtr\>>= 0 \|\|
1111: member(Y,WeylDV) <with|mode|math|\<gtr\>>= 0 ) return Y^L*X^K;
1112:
1113: \ \ if ( WeylV[I=member(X,WeylDV)] != Y ) return Y^L*X^K;
1114:
1115: \ \ else {
1116:
1117: \ \ \ \ K = eval_quote(K); L = eval_quote(L); M =
1118: K<with|mode|math|\<gtr\>>L?L:K;
1119:
1120: \ \ \ \ for ( T = 1, I = 0; I <with|mode|math|\<less\>>= M; T =
1121: idiv(T*K*L,I+1), I++, L--, L-- \ )
1122:
1123: \ \ \ \ \ \ R += T*Y^L*X^K;
1124:
1125: \ \ \ \ return R;
1126:
1127: \ \ }
1128:
1129: }
1130:
1131: WeylV=[`x,`y,`z]$
1132:
1133: WeylDV=[`dx,`dy,`dz]$
1134:
1135: qt_set_ord(map(eval_quote,append(WeylV,WeylDV)))$
1136:
1137: Rweyl=[[`X^K*Y^L,`qt_is_var(X)&&qt_is_var(Y)&&nqt_comp(Y,X)<with|mode|math|\<gtr\>>0,
1138:
1139: `qt_weyl_vmul(X,K,Y,L)]]$ \ \ \ \ \ \ \ \ \ \ \ \ \ \
1140:
1141: \;
1142: </verbatim>
1143:
1144: <with|mode|math|A*c*t*i*o*n> \<#306B\>\<#30E6\>\<#30FC\>\<#30B6\>\<#5B9A\>\<#7FA9\>\<#95A2\>\<#6570\>\<#3092\>\<#7528\>\<#3044\>\<#308B\>\<#3053\>\<#3068\>\<#306B\>\<#3088\>\<#308A\>,
1145: Weyl \<#4EE3\>\<#6570\>\<#306E\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#3092\>\<#4E00\>\<#3064\>
1146: \<#306B\>\<#307E\>\<#3068\>\<#3081\>\<#3066\>\<#3044\>\<#308B\>.
1147: </example>
1148:
1.3 ! noro 1149: \;
! 1150:
1.1 noro 1151: <section|\<#307E\>\<#3068\>\<#3081\>>
1152:
1.3 ! noro 1153: <\itemize>
! 1154: <item>\<#4E2D\>\<#9593\>\<#7684\>\<#8868\>\<#73FE\>\<#3067\>\<#3042\>\<#308B\>
! 1155: <FN> \<#3092\>\<#30E6\>\<#30FC\>\<#30B6\>\<#8A00\>\<#8A9E\>\<#304B\>\<#3089\>\<#64CD\>\<#4F5C\>\<#3059\>\<#308B\>\<#305F\>\<#3081\>\<#306E\>\<#30A4\>\<#30F3\>\<#30BF\>\<#30D5\>\<#30A7\>\<#30FC\>\<#30B9\>\<#306E\>\<#5B9F\>\<#88C5\>
! 1156:
! 1157: \<#30E6\>\<#30FC\>\<#30B6\>\<#304C\>\<#5B9A\>\<#7FA9\>\<#3059\>\<#308B\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#306B\>\<#3088\>\<#308B\>\<#6570\>\<#5F0F\>\<#306E\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#304C\>\<#53EF\>\<#80FD\>\<#3068\>\<#306A\>\<#3063\>\<#305F\>.
1.1 noro 1158:
1.3 ! noro 1159: <item>\<#4ECA\>\<#5F8C\>\<#306E\>\<#4E88\>\<#5B9A\>
! 1160:
! 1161: \<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#306E\>\<#52B9\>\<#7387\>\<#5411\>\<#4E0A\>,
! 1162: \<#6A19\>\<#6E96\>\<#5F62\>\<#3078\>\<#306E\>\<#5909\>\<#63DB\>\<#3068\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#3092\>\<#4E26\>\<#884C\>\<#3057\>\<#3066\>\<#884C\>\<#3046\>,
! 1163: \<#30D1\>\<#30BF\>\<#30FC\>\<#30F3\>\<#30DE\>\<#30C3\>\<#30C1\>\<#30F3\>\<#30B0\>\<#306E\>\<#6027\>\<#80FD\>\<#5411\>\<#4E0A\>,
! 1164: \<#6A19\>\<#6E96\>\<#7684\>\<#306A\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#898F\>\<#5247\>\<#96C6\>\<#5408\>\<#306E\>\<#63D0\>\<#4F9B\>
! 1165: etc.
! 1166:
! 1167: <item>weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#306B\>\<#3088\>\<#308B\>,
! 1168: \<#81EA\>\<#7531\>\<#7D50\>\<#5408\>\<#4EE3\>\<#6570\>\<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#4E00\>\<#822C\>\<#7684\>\<#306A\>\<#30B0\>\<#30EC\>\<#30D6\>\<#30CA\>\<#57FA\>\<#5E95\>\<#306E\>\<#8A08\>\<#7B97\>
! 1169:
! 1170: \<#3053\>\<#306E\>\<#66F8\>\<#304D\>\<#63DB\>\<#3048\>\<#3068\>weight
! 1171: \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#306B\>\<#3088\>\<#308B\>\<#5358\>\<#9805\>\<#5F0F\>\<#6BD4\>\<#8F03\>\<#3092\>\<#7D44\>\<#307F\>\<#5408\>\<#308F\>\<#305B\>\<#308B\>\<#3053\>\<#3068\>\<#306B\>\<#3088\>\<#308A\>,
! 1172: \<#81EA\>\<#7531\>\<#7D50\>\<#5408\>\<#4EE3\>\<#6570\>\<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#4E00\>\<#822C\>\<#7684\>\<#306A\>\<#30B0\>\<#30EC\>\<#30D6\>\<#30CA\>\<#57FA\>\<#5E95\>\<#306E\>\<#8A08\>\<#7B97\>\<#3092\>\<#8AD6\>\<#3058\>\<#305F\>.
! 1173:
! 1174: <\itemize>
! 1175: <item>\<#5BB9\>\<#6613\>\<#306A\>\<#30D7\>\<#30ED\>\<#30C8\>\<#30BF\>\<#30A4\>\<#30D4\>\<#30F3\>\<#30B0\>
! 1176:
! 1177: Risa/Asir \<#3067\>\<#65B0\>\<#3057\>\<#304F\>\<#5C0E\>\<#5165\>\<#3057\>\<#305F\>,
! 1178: <QT> \<#306B\>\<#5BFE\>\<#3059\>\<#308B\>\<#4E00\>\<#822C\>\<#7684\>\<#306A\>
! 1179: weight \<#30D9\>\<#30AF\>\<#30C8\>\<#30EB\>\<#306E\>\<#30E1\>\<#30AB\>\<#30CB\>\<#30BA\>\<#30E0\>
! 1180: <verbatim| qt_set_weight > \<#306B\>\<#3088\>\<#308A\>\<#308F\>\<#308C\>\<#308F\>\<#308C\>\<#306E\>\<#7406\>\<#8AD6\>\<#3068\>\<#30A2\>\<#30EB\>\<#30B4\>\<#30EA\>\<#30BA\>\<#30E0\>\<#306E\>\<#30D7\>\<#30ED\>\<#30C8\>\<#30BF\>\<#30A4\>
! 1181: \<#30D7\>\<#3092\>\<#5BB9\>\<#6613\>\<#306B\>\<#8A66\>\<#3059\>\<#3053\>\<#3068\>\<#304C\>\<#53EF\>\<#80FD\>\<#3067\>\<#3042\>\<#308B\>.
! 1182:
! 1183: <item><with|mode|math|G>-algebra \<#3088\>\<#308A\>\<#4E00\>\<#822C\>\<#306E\>
! 1184: algebra \<#3092\>\<#6271\>\<#3046\>
! 1185:
! 1186: \<#3053\>\<#3053\>\<#3067\>\<#63D0\>\<#6848\>\<#3057\>\<#305F\>\<#4E00\>\<#822C\>\<#5316\>\<#306F\>
! 1187: Weyl \<#4EE3\>\<#6570\>\<#306E\>\<#540C\>\<#6B21\>\<#5316\>\<#306E\>\<#7406\>\<#8AD6\>\<#3092\>\<#542B\>\<#3080\>.
! 1188:
! 1189: V. Levandovskyy <cite|LEV> \<#306F\> <with|mode|math|G>-algebra
! 1190: \<#306E\>\<#6982\>\<#5FF5\>\<#3092\>\<#5C0E\>\<#5165\>\<#3057\>\<#3066\>,
! 1191: Singular \<#306B\>\<#5B9F\>\<#88C5\>\<#3057\>\<#305F\>\<#304C\>,
! 1192: \<#308F\>\<#308C\>\<#308F\>\<#308C\>\<#306E\>\<#6982\>\<#5FF5\>\<#306F\>\<#540C\>\<#6B21\>\<#5316\>\<#3092\>\<#3068\>\<#304A\>\<#3057\>\<#3066\>,
! 1193: well order \<#3067\>\<#306A\>\<#3044\>\<#5834\>\<#5408\>
! 1194: \<#306B\>\<#3082\>\<#9069\>\<#7528\>\<#3067\>\<#304D\>\<#308B\>.
! 1195:
! 1196: \<#4E00\>\<#822C\>\<#7684\>\<#306A\>\<#67A0\>\<#7D44\>\<#307F\>\<#306E\>\<#5FDC\>\<#7528\>\<#3068\>\<#3057\>\<#3066\>,
! 1197: \<#5C06\>\<#6765\>\<#7684\> \<#306B\>\<#306F\>
! 1198: <with|mode|math|D>-\<#52A0\>\<#7FA4\>\<#306E\>\<#30A2\>\<#30EB\>\<#30B4\>\<#30EA\>\<#30BA\>\<#30E0\>\<#3092\>\<#62E1\>\<#5F35\>\<#3057\>,
! 1199: Calderon-Moreno \<#7B49\>\<#306E\>\<#5C0E\>\<#5165\>\<#3057\>\<#305F\>
! 1200: algebra \<#3092\>\<#5C40\>\<#6240\>\<#7684\>\<#306B\>\<#6271\>\<#3046\>\<#306A\>\<#3069\>\<#306E\>\<#5FDC\>\<#7528\>\<#304C\>\<#898B\>\<#8FBC\>\<#307E\>\<#308C\>\<#308B\>.
! 1201: </itemize>
! 1202: </itemize>
1.2 takayama 1203:
1.1 noro 1204: <\thebibliography|99>
1205: \ <bibitem|MMA> S. Wolfram, The MATHEMATICA Book, Fourth Edition.
1206: Cambridge University Press (1999).
1207:
1208: <bibitem|LEV> V. Levandovskyy, Non-commutative Computer Algebra for
1209: Polynomial Algebras: Gröbner Bases, Applications and Implementation.
1210: Dissertation, Universität Kaiserslautern (2005).
1211: </thebibliography>
1212: </body>
1213:
1214: <\initial>
1215: <\collection>
1216: <associate|font|ipa>
1217: <associate|language|japanese>
1218: <associate|page-medium|automatic>
1.2 takayama 1219: <associate|page-screen-height|768000tmpt>
1220: <associate|page-screen-width|998400tmpt>
1.1 noro 1221: <associate|sfactor|4>
1222: </collection>
1223: </initial>
1224:
1225: <\references>
1226: <\collection>
1227: <associate|auto-1|<tuple|1|?>>
1228: <associate|auto-10|<tuple|6|?>>
1.3 ! noro 1229: <associate|auto-11|<tuple|<with|mode|<quote|math>|<group|\<circ\>>>|?>>
1.1 noro 1230: <associate|auto-2|<tuple|2|?>>
1231: <associate|auto-3|<tuple|2.1|?>>
1232: <associate|auto-4|<tuple|2.2|?>>
1233: <associate|auto-5|<tuple|2.3|?>>
1234: <associate|auto-6|<tuple|3|?>>
1235: <associate|auto-7|<tuple|4|?>>
1236: <associate|auto-8|<tuple|4.1|?>>
1237: <associate|auto-9|<tuple|5|?>>
1238: <associate|bib-LEV|<tuple|LEV|?>>
1239: <associate|bib-MMA|<tuple|MMA|?>>
1240: </collection>
1241: </references>
1242:
1243: <\auxiliary>
1244: <\collection>
1245: <\associate|bib>
1246: MMA
1247:
1248: LEV
1249:
1250: LEV
1251: </associate>
1252: <\associate|toc>
1253: <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Risa/Asir
1254: \<#306B\>\<#304A\>\<#3051\>\<#308B\>\<#6570\>\<#5F0F\>\<#306E\>\<#53D6\>\<#308A\>\<#6271\>\<#3044\>>
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1257:
1258: <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|<with|font-family|<quote|tt>|QUOTE>
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1289:
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1300: <no-break><pageref|auto-11><vspace|0.5fn>
1301: </associate>
1302: </collection>
1303: </auxiliary>
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