# Ticket #11362: trac11362.ipynb

File trac11362.ipynb, 7.5 KB (added by , 17 months ago) |
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1 | { |

2 | "cells": [ |

3 | { |

4 | "cell_type": "code", |

5 | "execution_count": 1, |

6 | "metadata": {}, |

7 | "outputs": [], |

8 | "source": [ |

9 | "S = GF(8)\n", |

10 | "T = S.multiplication_table()" |

11 | ] |

12 | }, |

13 | { |

14 | "cell_type": "code", |

15 | "execution_count": 2, |

16 | "metadata": {}, |

17 | "outputs": [ |

18 | { |

19 | "data": { |

20 | "text/plain": [ |

21 | "* a b c d e f g h\n", |

22 | " +----------------\n", |

23 | "a| a a a a a a a a\n", |

24 | "b| a b c d e f g h\n", |

25 | "c| a c e g d b h f\n", |

26 | "d| a d g f h e b c\n", |

27 | "e| a e d h g c f b\n", |

28 | "f| a f b e c h d g\n", |

29 | "g| a g h b f d c e\n", |

30 | "h| a h f c b g e d\n" |

31 | ] |

32 | }, |

33 | "execution_count": 2, |

34 | "metadata": {}, |

35 | "output_type": "execute_result" |

36 | } |

37 | ], |

38 | "source": [ |

39 | "T" |

40 | ] |

41 | }, |

42 | { |

43 | "cell_type": "code", |

44 | "execution_count": 3, |

45 | "metadata": {}, |

46 | "outputs": [ |

47 | { |

48 | "data": { |

49 | "text/plain": [ |

50 | "{\\setlength{\\arraycolsep}{2ex}\n", |

51 | "\\begin{array}{r|*{8}{r}}\n", |

52 | "\\multicolumn{1}{c|}{\\ast}&a&b&c&d&e&f&g&h\\\\\\hline\n", |

53 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

54 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

55 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

56 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

57 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

58 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

59 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

60 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

61 | "\\end{array}}" |

62 | ] |

63 | }, |

64 | "execution_count": 3, |

65 | "metadata": {}, |

66 | "output_type": "execute_result" |

67 | } |

68 | ], |

69 | "source": [ |

70 | "latex(T)" |

71 | ] |

72 | }, |

73 | { |

74 | "cell_type": "code", |

75 | "execution_count": 4, |

76 | "metadata": {}, |

77 | "outputs": [ |

78 | { |

79 | "data": { |

80 | "text/html": [ |

81 | "\\begin{array}{r|*{8}{r}}\n", |

82 | "\\hfil\\ast\\hfil&a&b&c&d&e&f&g&h\\\\\\hline\n", |

83 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

84 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

85 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

86 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

87 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

88 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

89 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

90 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

91 | "\\end{array}" |

92 | ], |

93 | "text/latex": [ |

94 | "\\[ {\\setlength{\\arraycolsep}{2ex}\n", |

95 | "\\begin{array}{r|*{8}{r}}\n", |

96 | "\\multicolumn{1}{c|}{\\ast}&a&b&c&d&e&f&g&h\\\\\\hline\n", |

97 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

98 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

99 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

100 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

101 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

102 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

103 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

104 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

105 | "\\end{array}} \\]" |

106 | ], |

107 | "text/plain": [ |

108 | "* a b c d e f g h\n", |

109 | " +----------------\n", |

110 | "a| a a a a a a a a\n", |

111 | "b| a b c d e f g h\n", |

112 | "c| a c e g d b h f\n", |

113 | "d| a d g f h e b c\n", |

114 | "e| a e d h g c f b\n", |

115 | "f| a f b e c h d g\n", |

116 | "g| a g h b f d c e\n", |

117 | "h| a h f c b g e d\n" |

118 | ] |

119 | }, |

120 | "metadata": {}, |

121 | "output_type": "display_data" |

122 | } |

123 | ], |

124 | "source": [ |

125 | "show(T)" |

126 | ] |

127 | }, |

128 | { |

129 | "cell_type": "code", |

130 | "execution_count": 5, |

131 | "metadata": {}, |

132 | "outputs": [ |

133 | { |

134 | "data": { |

135 | "text/html": [ |

136 | "\\begin{array}{r|*{8}{r}}\n", |

137 | "\\hfil\\ast\\hfil&a&b&c&d&e&f&g&h\\\\\\hline\n", |

138 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

139 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

140 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

141 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

142 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

143 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

144 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

145 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

146 | "\\end{array}" |

147 | ], |

148 | "text/latex": [ |

149 | "\\[ {\\setlength{\\arraycolsep}{2ex}\n", |

150 | "\\begin{array}{r|*{8}{r}}\n", |

151 | "\\multicolumn{1}{c|}{\\ast}&a&b&c&d&e&f&g&h\\\\\\hline\n", |

152 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

153 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

154 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

155 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

156 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

157 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

158 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

159 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

160 | "\\end{array}} \\]" |

161 | ], |

162 | "text/plain": [ |

163 | "* a b c d e f g h\n", |

164 | " +----------------\n", |

165 | "a| a a a a a a a a\n", |

166 | "b| a b c d e f g h\n", |

167 | "c| a c e g d b h f\n", |

168 | "d| a d g f h e b c\n", |

169 | "e| a e d h g c f b\n", |

170 | "f| a f b e c h d g\n", |

171 | "g| a g h b f d c e\n", |

172 | "h| a h f c b g e d\n" |

173 | ] |

174 | }, |

175 | "metadata": {}, |

176 | "output_type": "display_data" |

177 | } |

178 | ], |

179 | "source": [ |

180 | "pretty_print(T)" |

181 | ] |

182 | }, |

183 | { |

184 | "cell_type": "code", |

185 | "execution_count": 6, |

186 | "metadata": {}, |

187 | "outputs": [], |

188 | "source": [ |

189 | "f = sqrt(x)/x+2" |

190 | ] |

191 | }, |

192 | { |

193 | "cell_type": "code", |

194 | "execution_count": 7, |

195 | "metadata": {}, |

196 | "outputs": [ |

197 | { |

198 | "data": { |

199 | "text/plain": [ |

200 | "1/sqrt(x) + 2" |

201 | ] |

202 | }, |

203 | "execution_count": 7, |

204 | "metadata": {}, |

205 | "output_type": "execute_result" |

206 | } |

207 | ], |

208 | "source": [ |

209 | "f" |

210 | ] |

211 | }, |

212 | { |

213 | "cell_type": "code", |

214 | "execution_count": 8, |

215 | "metadata": {}, |

216 | "outputs": [], |

217 | "source": [ |

218 | "%display latex" |

219 | ] |

220 | }, |

221 | { |

222 | "cell_type": "code", |

223 | "execution_count": 9, |

224 | "metadata": {}, |

225 | "outputs": [ |

226 | { |

227 | "data": { |

228 | "text/html": [ |

229 | "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{\\sqrt{x}} + 2\\]</html>" |

230 | ], |

231 | "text/latex": [ |

232 | "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{\\sqrt{x}} + 2$$" |

233 | ], |

234 | "text/plain": [ |

235 | "1/sqrt(x) + 2" |

236 | ] |

237 | }, |

238 | "execution_count": 9, |

239 | "metadata": {}, |

240 | "output_type": "execute_result" |

241 | } |

242 | ], |

243 | "source": [ |

244 | "f" |

245 | ] |

246 | }, |

247 | { |

248 | "cell_type": "code", |

249 | "execution_count": 10, |

250 | "metadata": {}, |

251 | "outputs": [ |

252 | { |

253 | "data": { |

254 | "text/html": [ |

255 | "\\begin{array}{r|*{8}{r}}\n", |

256 | "\\hfil\\ast\\hfil&a&b&c&d&e&f&g&h\\\\\\hline\n", |

257 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

258 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

259 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

260 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

261 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

262 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

263 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

264 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

265 | "\\end{array}" |

266 | ], |

267 | "text/latex": [ |

268 | "\\[ {\\setlength{\\arraycolsep}{2ex}\n", |

269 | "\\begin{array}{r|*{8}{r}}\n", |

270 | "\\multicolumn{1}{c|}{\\ast}&a&b&c&d&e&f&g&h\\\\\\hline\n", |

271 | "{}a&a&a&a&a&a&a&a&a\\\\\n", |

272 | "{}b&a&b&c&d&e&f&g&h\\\\\n", |

273 | "{}c&a&c&e&g&d&b&h&f\\\\\n", |

274 | "{}d&a&d&g&f&h&e&b&c\\\\\n", |

275 | "{}e&a&e&d&h&g&c&f&b\\\\\n", |

276 | "{}f&a&f&b&e&c&h&d&g\\\\\n", |

277 | "{}g&a&g&h&b&f&d&c&e\\\\\n", |

278 | "{}h&a&h&f&c&b&g&e&d\\\\\n", |

279 | "\\end{array}} \\]" |

280 | ], |

281 | "text/plain": [ |

282 | "* a b c d e f g h\n", |

283 | " +----------------\n", |

284 | "a| a a a a a a a a\n", |

285 | "b| a b c d e f g h\n", |

286 | "c| a c e g d b h f\n", |

287 | "d| a d g f h e b c\n", |

288 | "e| a e d h g c f b\n", |

289 | "f| a f b e c h d g\n", |

290 | "g| a g h b f d c e\n", |

291 | "h| a h f c b g e d\n" |

292 | ] |

293 | }, |

294 | "execution_count": 10, |

295 | "metadata": {}, |

296 | "output_type": "execute_result" |

297 | } |

298 | ], |

299 | "source": [ |

300 | "T" |

301 | ] |

302 | }, |

303 | { |

304 | "cell_type": "code", |

305 | "execution_count": null, |

306 | "metadata": {}, |

307 | "outputs": [], |

308 | "source": [] |

309 | } |

310 | ], |

311 | "metadata": { |

312 | "kernelspec": { |

313 | "display_name": "SageMath 9.4", |

314 | "language": "sage", |

315 | "name": "sagemath" |

316 | }, |

317 | "language_info": { |

318 | "codemirror_mode": { |

319 | "name": "ipython", |

320 | "version": 3 |

321 | }, |

322 | "file_extension": ".py", |

323 | "mimetype": "text/x-python", |

324 | "name": "python", |

325 | "nbconvert_exporter": "python", |

326 | "pygments_lexer": "ipython3", |

327 | "version": "3.9.6" |

328 | } |

329 | }, |

330 | "nbformat": 4, |

331 | "nbformat_minor": 4 |

332 | } |