# Ticket #9958: Doctest_failures_Sage-4.7.2.alpha2_Linux_x86_SSE3-individual_tests_rerun-segfaults-verbose.log

File Doctest_failures_Sage-4.7.2.alpha2_Linux_x86_SSE3-individual_tests_rerun-segfaults-verbose.log, 74.9 KB (added by , 10 years ago) |
---|

Line | |
---|---|

1 | sage -t -long -verbose "devel/sage/sage/rings/morphism.pyx" |

2 | Trying: |

3 | set_random_seed(0L) |

4 | Expecting nothing |

5 | ok |

6 | Trying: |

7 | change_warning_output(sys.stdout) |

8 | Expecting nothing |

9 | ok |

10 | Trying: |

11 | H = Hom(ZZ, QQ)###line 11:_sage_ >>> H = Hom(ZZ, QQ) |

12 | Expecting nothing |

13 | ok |

14 | Trying: |

15 | phi = H([Integer(1)])###line 12:_sage_ >>> phi = H([1]) |

16 | Expecting nothing |

17 | ok |

18 | Trying: |

19 | phi(Integer(10))###line 13:_sage_ >>> phi(10) |

20 | Expecting: |

21 | 10 |

22 | ok |

23 | Trying: |

24 | phi(Integer(3)/Integer(1))###line 15:_sage_ >>> phi(3/1) |

25 | Expecting: |

26 | 3 |

27 | ok |

28 | Trying: |

29 | phi(Integer(2)/Integer(3))###line 17:_sage_ >>> phi(2/3) |

30 | Expecting: |

31 | Traceback (most recent call last): |

32 | ... |

33 | TypeError: 2/3 fails to convert into the map's domain Integer Ring, but a `pushforward` method is not properly implemented |

34 | ok |

35 | Trying: |

36 | H = Hom(QQ, ZZ)###line 24:_sage_ >>> H = Hom(QQ, ZZ) |

37 | Expecting nothing |

38 | ok |

39 | Trying: |

40 | H([Integer(1)])###line 25:_sage_ >>> H([1]) |

41 | Expecting: |

42 | Traceback (most recent call last): |

43 | ... |

44 | TypeError: images do not define a valid homomorphism |

45 | ok |

46 | Trying: |

47 | H = Hom(ZZ, GF(Integer(9), 'a'))###line 34:_sage_ >>> H = Hom(ZZ, GF(9, 'a')) |

48 | Expecting nothing |

49 | ok |

50 | Trying: |

51 | phi = H([Integer(1)])###line 35:_sage_ >>> phi = H([1]) |

52 | Expecting nothing |

53 | ok |

54 | Trying: |

55 | phi(Integer(5))###line 36:_sage_ >>> phi(5) |

56 | Expecting: |

57 | 2 |

58 | ok |

59 | Trying: |

60 | psi = H([Integer(4)])###line 38:_sage_ >>> psi = H([4]) |

61 | Expecting nothing |

62 | ok |

63 | Trying: |

64 | psi(Integer(5))###line 39:_sage_ >>> psi(5) |

65 | Expecting: |

66 | 2 |

67 | ok |

68 | Trying: |

69 | R, x = PolynomialRing(ZZ, 'x').objgen()###line 46:_sage_ >>> R, x = PolynomialRing(ZZ, 'x').objgen() |

70 | Expecting nothing |

71 | ok |

72 | Trying: |

73 | phi = R.hom([Integer(2)], GF(Integer(5)))###line 47:_sage_ >>> phi = R.hom([2], GF(5)) |

74 | Expecting nothing |

75 | ok |

76 | Trying: |

77 | phi###line 48:_sage_ >>> phi |

78 | Expecting: |

79 | Ring morphism: |

80 | From: Univariate Polynomial Ring in x over Integer Ring |

81 | To: Finite Field of size 5 |

82 | Defn: x |--> 2 |

83 | ok |

84 | Trying: |

85 | phi(x + Integer(12))###line 53:_sage_ >>> phi(x + 12) |

86 | Expecting: |

87 | 4 |

88 | ok |

89 | Trying: |

90 | f = RR.hom([RR(Integer(1))]); f###line 60:_sage_ >>> f = RR.hom([RR(1)]); f |

91 | Expecting: |

92 | Ring endomorphism of Real Field with 53 bits of precision |

93 | Defn: 1.00000000000000 |--> 1.00000000000000 |

94 | ok |

95 | Trying: |

96 | f(RealNumber('2.5'))###line 63:_sage_ >>> f(2.5) |

97 | Expecting: |

98 | 2.50000000000000 |

99 | ok |

100 | Trying: |

101 | f = RR.hom( [RealNumber('2.0')] )###line 65:_sage_ >>> f = RR.hom( [2.0] ) |

102 | Expecting: |

103 | Traceback (most recent call last): |

104 | ... |

105 | TypeError: images do not define a valid homomorphism |

106 | ok |

107 | Trying: |

108 | R200 = RealField(Integer(200))###line 74:_sage_ >>> R200 = RealField(200) |

109 | Expecting nothing |

110 | ok |

111 | Trying: |

112 | f = RR.hom( R200 )###line 75:_sage_ >>> f = RR.hom( R200 ) |

113 | Expecting: |

114 | Traceback (most recent call last): |

115 | ... |

116 | TypeError: Natural coercion morphism from Real Field with 53 bits of precision to Real Field with 200 bits of precision not defined. |

117 | ok |

118 | Trying: |

119 | f = RR.hom( RealField(Integer(15)) )###line 82:_sage_ >>> f = RR.hom( RealField(15) ) |

120 | Expecting nothing |

121 | ok |

122 | Trying: |

123 | f(RealNumber('2.5'))###line 83:_sage_ >>> f(2.5) |

124 | Expecting: |

125 | 2.500 |

126 | ok |

127 | Trying: |

128 | f(RR.pi())###line 85:_sage_ >>> f(RR.pi()) |

129 | Expecting: |

130 | 3.142 |

131 | ok |

132 | Trying: |

133 | i = RR.hom([CC(Integer(1))]); i###line 90:_sage_ >>> i = RR.hom([CC(1)]); i |

134 | Expecting: |

135 | Ring morphism: |

136 | From: Real Field with 53 bits of precision |

137 | To: Complex Field with 53 bits of precision |

138 | Defn: 1.00000000000000 |--> 1.00000000000000 |

139 | ok |

140 | Trying: |

141 | i(RR('3.1'))###line 95:_sage_ >>> i(RR('3.1')) |

142 | Expecting: |

143 | 3.10000000000000 |

144 | ok |

145 | Trying: |

146 | R = PolynomialRing(QQ,Integer(3), names=('x', 'y', 'z',)); (x, y, z,) = R._first_ngens(3)###line 100:_sage_ >>> R.<x,y,z> = PolynomialRing(QQ,3) |

147 | Expecting nothing |

148 | ok |

149 | Trying: |

150 | phi = R.hom([y,z,x**Integer(2)]); phi###line 101:_sage_ >>> phi = R.hom([y,z,x^2]); phi |

151 | Expecting: |

152 | Ring endomorphism of Multivariate Polynomial Ring in x, y, z over Rational Field |

153 | Defn: x |--> y |

154 | y |--> z |

155 | z |--> x^2 |

156 | ok |

157 | Trying: |

158 | phi(x+y+z)###line 106:_sage_ >>> phi(x+y+z) |

159 | Expecting: |

160 | x^2 + y + z |

161 | ok |

162 | Trying: |

163 | R = PolynomialRing(QQ, names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 112:_sage_ >>> R.<x,y> = PolynomialRing(QQ) |

164 | Expecting nothing |

165 | ok |

166 | Trying: |

167 | S = quo(R, ideal(Integer(1) + y**Integer(2)), names=('a', 'b',)); (a, b,) = S._first_ngens(2)###line 113:_sage_ >>> S.<a,b> = quo(R, ideal(1 + y^2)) |

168 | Expecting nothing |

169 | ok |

170 | Trying: |

171 | phi = S.hom([a**Integer(2), -b])###line 114:_sage_ >>> phi = S.hom([a^2, -b]) |

172 | Expecting nothing |

173 | ok |

174 | Trying: |

175 | phi###line 115:_sage_ >>> phi |

176 | Expecting: |

177 | Ring endomorphism of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (y^2 + 1) |

178 | Defn: a |--> a^2 |

179 | b |--> -b |

180 | ok |

181 | Trying: |

182 | phi(b)###line 119:_sage_ >>> phi(b) |

183 | Expecting: |

184 | -b |

185 | ok |

186 | Trying: |

187 | phi(a**Integer(2) + b**Integer(2))###line 121:_sage_ >>> phi(a^2 + b^2) |

188 | Expecting: |

189 | a^4 - 1 |

190 | ok |

191 | Trying: |

192 | R = ZZ.quo(Integer(8)*ZZ)###line 127:_sage_ >>> R = ZZ.quo(8*ZZ) |

193 | Expecting nothing |

194 | ok |

195 | Trying: |

196 | pi = R.cover()###line 128:_sage_ >>> pi = R.cover() |

197 | Expecting nothing |

198 | ok |

199 | Trying: |

200 | pi###line 129:_sage_ >>> pi |

201 | Expecting: |

202 | Ring morphism: |

203 | From: Integer Ring |

204 | To: Ring of integers modulo 8 |

205 | Defn: Natural quotient map |

206 | ok |

207 | Trying: |

208 | pi.domain()###line 134:_sage_ >>> pi.domain() |

209 | Expecting: |

210 | Integer Ring |

211 | ok |

212 | Trying: |

213 | pi.codomain()###line 136:_sage_ >>> pi.codomain() |

214 | Expecting: |

215 | Ring of integers modulo 8 |

216 | ok |

217 | Trying: |

218 | pi(Integer(10))###line 138:_sage_ >>> pi(10) |

219 | Expecting: |

220 | 2 |

221 | ok |

222 | Trying: |

223 | pi.lift()###line 140:_sage_ >>> pi.lift() |

224 | Expecting: |

225 | Set-theoretic ring morphism: |

226 | From: Ring of integers modulo 8 |

227 | To: Integer Ring |

228 | Defn: Choice of lifting map |

229 | ok |

230 | Trying: |

231 | pi.lift(Integer(13))###line 145:_sage_ >>> pi.lift(13) |

232 | Expecting: |

233 | 5 |

234 | ok |

235 | Trying: |

236 | k = GF(Integer(2))###line 152:_sage_ >>> k = GF(2) |

237 | Expecting nothing |

238 | ok |

239 | Trying: |

240 | i = k.hom(GF(Integer(4), 'a'))###line 153:_sage_ >>> i = k.hom(GF(4, 'a')) |

241 | Expecting nothing |

242 | ok |

243 | Trying: |

244 | i###line 154:_sage_ >>> i |

245 | Expecting: |

246 | Ring Coercion morphism: |

247 | From: Finite Field of size 2 |

248 | To: Finite Field in a of size 2^2 |

249 | ok |

250 | Trying: |

251 | i(Integer(0))###line 158:_sage_ >>> i(0) |

252 | Expecting: |

253 | 0 |

254 | ok |

255 | Trying: |

256 | a = i(Integer(1)); a.parent()###line 160:_sage_ >>> a = i(1); a.parent() |

257 | Expecting: |

258 | Finite Field in a of size 2^2 |

259 | ok |

260 | Trying: |

261 | pi = ZZ.hom(k)###line 168:_sage_ >>> pi = ZZ.hom(k) |

262 | Expecting nothing |

263 | ok |

264 | Trying: |

265 | pi###line 169:_sage_ >>> pi |

266 | Expecting: |

267 | Ring Coercion morphism: |

268 | From: Integer Ring |

269 | To: Finite Field of size 2 |

270 | ok |

271 | Trying: |

272 | f = i * pi###line 173:_sage_ >>> f = i * pi |

273 | Expecting nothing |

274 | ok |

275 | Trying: |

276 | f###line 174:_sage_ >>> f |

277 | Expecting: |

278 | Composite map: |

279 | From: Integer Ring |

280 | To: Finite Field in a of size 2^2 |

281 | Defn: Ring Coercion morphism: |

282 | From: Integer Ring |

283 | To: Finite Field of size 2 |

284 | then |

285 | Ring Coercion morphism: |

286 | From: Finite Field of size 2 |

287 | To: Finite Field in a of size 2^2 |

288 | ok |

289 | Trying: |

290 | a = f(Integer(5)); a###line 185:_sage_ >>> a = f(5); a |

291 | Expecting: |

292 | 1 |

293 | ok |

294 | Trying: |

295 | a.parent()###line 187:_sage_ >>> a.parent() |

296 | Expecting: |

297 | Finite Field in a of size 2^2 |

298 | ok |

299 | Trying: |

300 | phi = QQ.hom(Qp(Integer(3), print_mode = 'series'))###line 194:_sage_ >>> phi = QQ.hom(Qp(3, print_mode = 'series')) |

301 | Expecting nothing |

302 | ok |

303 | Trying: |

304 | phi###line 195:_sage_ >>> phi |

305 | Expecting: |

306 | Ring Coercion morphism: |

307 | From: Rational Field |

308 | To: 3-adic Field with capped relative precision 20 |

309 | ok |

310 | Trying: |

311 | phi.codomain()###line 199:_sage_ >>> phi.codomain() |

312 | Expecting: |

313 | 3-adic Field with capped relative precision 20 |

314 | ok |

315 | Trying: |

316 | phi(Integer(394))###line 201:_sage_ >>> phi(394) |

317 | Expecting: |

318 | 1 + 2*3 + 3^2 + 2*3^3 + 3^4 + 3^5 + O(3^20) |

319 | ok |

320 | Trying: |

321 | R = PolynomialRing(QQ, names=('x',)); (x,) = R._first_ngens(1)###line 209:_sage_ >>> R.<x> = PolynomialRing(QQ) |

322 | Expecting nothing |

323 | ok |

324 | Trying: |

325 | S = R.quo(x**Integer(2)-Integer(2), names=('sqrt2',)); (sqrt2,) = S._first_ngens(1)###line 210:_sage_ >>> S.<sqrt2> = R.quo(x^2-2) |

326 | Expecting nothing |

327 | ok |

328 | Trying: |

329 | sqrt2**Integer(2)###line 211:_sage_ >>> sqrt2^2 |

330 | Expecting: |

331 | 2 |

332 | ok |

333 | Trying: |

334 | (Integer(3)+sqrt2)**Integer(10)###line 213:_sage_ >>> (3+sqrt2)^10 |

335 | Expecting: |

336 | 993054*sqrt2 + 1404491 |

337 | ok |

338 | Trying: |

339 | c = S.hom([-sqrt2])###line 215:_sage_ >>> c = S.hom([-sqrt2]) |

340 | Expecting nothing |

341 | ok |

342 | Trying: |

343 | c(Integer(1)+sqrt2)###line 216:_sage_ >>> c(1+sqrt2) |

344 | Expecting: |

345 | -sqrt2 + 1 |

346 | ok |

347 | Trying: |

348 | (Integer(1) - sqrt2)**Integer(2)###line 221:_sage_ >>> (1 - sqrt2)^2 |

349 | Expecting: |

350 | -2*sqrt2 + 3 |

351 | ok |

352 | Trying: |

353 | c = S.hom([Integer(1)-sqrt2]) # this is not valid###line 223:_sage_ >>> c = S.hom([1-sqrt2]) # this is not valid |

354 | Expecting: |

355 | Traceback (most recent call last): |

356 | ... |

357 | TypeError: images do not define a valid homomorphism |

358 | ok |

359 | Trying: |

360 | R = PowerSeriesRing(QQ, names=('t',)); (t,) = R._first_ngens(1); R###line 232:_sage_ >>> R.<t> = PowerSeriesRing(QQ); R |

361 | Expecting: |

362 | Power Series Ring in t over Rational Field |

363 | ok |

364 | Trying: |

365 | f = R.hom([t**Integer(2)]); f###line 234:_sage_ >>> f = R.hom([t^2]); f |

366 | Expecting: |

367 | Ring endomorphism of Power Series Ring in t over Rational Field |

368 | Defn: t |--> t^2 |

369 | ok |

370 | Trying: |

371 | R.set_default_prec(Integer(10))###line 237:_sage_ >>> R.set_default_prec(10) |

372 | Expecting nothing |

373 | ok |

374 | Trying: |

375 | s = Integer(1)/(Integer(1) + t); s###line 238:_sage_ >>> s = 1/(1 + t); s |

376 | Expecting: |

377 | 1 - t + t^2 - t^3 + t^4 - t^5 + t^6 - t^7 + t^8 - t^9 + O(t^10) |

378 | ok |

379 | Trying: |

380 | f(s)###line 240:_sage_ >>> f(s) |

381 | Expecting: |

382 | 1 - t^2 + t^4 - t^6 + t^8 - t^10 + t^12 - t^14 + t^16 - t^18 + O(t^20) |

383 | ok |

384 | Trying: |

385 | R = PowerSeriesRing(GF(Integer(5)), names=('t',)); (t,) = R._first_ngens(1)###line 247:_sage_ >>> R.<t> = PowerSeriesRing(GF(5)) |

386 | Expecting nothing |

387 | ok |

388 | Trying: |

389 | f = R.hom([t**Integer(5)]); f###line 248:_sage_ >>> f = R.hom([t^5]); f |

390 | Expecting: |

391 | Ring endomorphism of Power Series Ring in t over Finite Field of size 5 |

392 | Defn: t |--> t^5 |

393 | ok |

394 | Trying: |

395 | a = Integer(2) + t + Integer(3)*t**Integer(2) + Integer(4)*t**Integer(3) + O(t**Integer(4))###line 251:_sage_ >>> a = 2 + t + 3*t^2 + 4*t^3 + O(t^4) |

396 | Expecting nothing |

397 | ok |

398 | Trying: |

399 | b = Integer(1) + t + Integer(2)*t**Integer(2) + t**Integer(3) + O(t**Integer(5))###line 252:_sage_ >>> b = 1 + t + 2*t^2 + t^3 + O(t^5) |

400 | Expecting nothing |

401 | ok |

402 | Trying: |

403 | f(a)###line 253:_sage_ >>> f(a) |

404 | Expecting: |

405 | 2 + t^5 + 3*t^10 + 4*t^15 + O(t^20) |

406 | ok |

407 | Trying: |

408 | f(b)###line 255:_sage_ >>> f(b) |

409 | Expecting: |

410 | 1 + t^5 + 2*t^10 + t^15 + O(t^25) |

411 | ok |

412 | Trying: |

413 | f(a*b)###line 257:_sage_ >>> f(a*b) |

414 | Expecting: |

415 | 2 + 3*t^5 + 3*t^10 + t^15 + O(t^20) |

416 | ok |

417 | Trying: |

418 | f(a)*f(b)###line 259:_sage_ >>> f(a)*f(b) |

419 | Expecting: |

420 | 2 + 3*t^5 + 3*t^10 + t^15 + O(t^20) |

421 | ok |

422 | Trying: |

423 | R = LaurentSeriesRing(QQ, names=('t',)); (t,) = R._first_ngens(1)###line 266:_sage_ >>> R.<t> = LaurentSeriesRing(QQ) |

424 | Expecting nothing |

425 | ok |

426 | Trying: |

427 | f = R.hom([t**Integer(3) + t]); f###line 267:_sage_ >>> f = R.hom([t^3 + t]); f |

428 | Expecting: |

429 | Ring endomorphism of Laurent Series Ring in t over Rational Field |

430 | Defn: t |--> t + t^3 |

431 | ok |

432 | Trying: |

433 | R.set_default_prec(Integer(10))###line 270:_sage_ >>> R.set_default_prec(10) |

434 | Expecting nothing |

435 | ok |

436 | Trying: |

437 | s = Integer(2)/t**Integer(2) + Integer(1)/(Integer(1) + t); s###line 271:_sage_ >>> s = 2/t^2 + 1/(1 + t); s |

438 | Expecting: |

439 | 2*t^-2 + 1 - t + t^2 - t^3 + t^4 - t^5 + t^6 - t^7 + t^8 - t^9 + O(t^10) |

440 | ok |

441 | Trying: |

442 | f(s)###line 273:_sage_ >>> f(s) |

443 | Expecting: |

444 | 2*t^-2 - 3 - t + 7*t^2 - 2*t^3 - 5*t^4 - 4*t^5 + 16*t^6 - 9*t^7 + O(t^8) |

445 | ok |

446 | Trying: |

447 | f = R.hom([t**Integer(3)]); f###line 275:_sage_ >>> f = R.hom([t^3]); f |

448 | Expecting: |

449 | Ring endomorphism of Laurent Series Ring in t over Rational Field |

450 | Defn: t |--> t^3 |

451 | ok |

452 | Trying: |

453 | f(s)###line 278:_sage_ >>> f(s) |

454 | Expecting: |

455 | 2*t^-6 + 1 - t^3 + t^6 - t^9 + t^12 - t^15 + t^18 - t^21 + t^24 - t^27 |

456 | ok |

457 | Trying: |

458 | s = Integer(2)/t**Integer(2) + Integer(1)/(Integer(1) + t); s###line 280:_sage_ >>> s = 2/t^2 + 1/(1 + t); s |

459 | Expecting: |

460 | 2*t^-2 + 1 - t + t^2 - t^3 + t^4 - t^5 + t^6 - t^7 + t^8 - t^9 + O(t^10) |

461 | ok |

462 | Trying: |

463 | f(s)###line 282:_sage_ >>> f(s) |

464 | Expecting: |

465 | 2*t^-6 + 1 - t^3 + t^6 - t^9 + t^12 - t^15 + t^18 - t^21 + t^24 - t^27 |

466 | ok |

467 | Trying: |

468 | R.hom([Integer(1)/t])###line 289:_sage_ >>> R.hom([1/t]) |

469 | Expecting: |

470 | Traceback (most recent call last): |

471 | ... |

472 | TypeError: images do not define a valid homomorphism |

473 | ok |

474 | Trying: |

475 | R.hom([Integer(1)])###line 293:_sage_ >>> R.hom([1]) |

476 | Expecting: |

477 | Traceback (most recent call last): |

478 | ... |

479 | TypeError: images do not define a valid homomorphism |

480 | ok |

481 | Trying: |

482 | K = CyclotomicField(Integer(7), names=('zeta7',)); (zeta7,) = K._first_ngens(1)###line 302:_sage_ >>> K.<zeta7> = CyclotomicField(7) |

483 | Expecting nothing |

484 | ok |

485 | Trying: |

486 | c = K.hom([Integer(1)/zeta7]); c###line 303:_sage_ >>> c = K.hom([1/zeta7]); c |

487 | Expecting: |

488 | Ring endomorphism of Cyclotomic Field of order 7 and degree 6 |

489 | Defn: zeta7 |--> -zeta7^5 - zeta7^4 - zeta7^3 - zeta7^2 - zeta7 - 1 |

490 | ok |

491 | Trying: |

492 | a = (Integer(1)+zeta7)**Integer(5); a###line 306:_sage_ >>> a = (1+zeta7)^5; a |

493 | Expecting: |

494 | zeta7^5 + 5*zeta7^4 + 10*zeta7^3 + 10*zeta7^2 + 5*zeta7 + 1 |

495 | ok |

496 | Trying: |

497 | c(a)###line 308:_sage_ >>> c(a) |

498 | Expecting: |

499 | 5*zeta7^5 + 5*zeta7^4 - 4*zeta7^2 - 5*zeta7 - 4 |

500 | ok |

501 | Trying: |

502 | c(zeta7 + Integer(1)/zeta7) # this element is obviously fixed by inversion###line 310:_sage_ >>> c(zeta7 + 1/zeta7) # this element is obviously fixed by inversion |

503 | Expecting: |

504 | -zeta7^5 - zeta7^4 - zeta7^3 - zeta7^2 - 1 |

505 | ok |

506 | Trying: |

507 | zeta7 + Integer(1)/zeta7###line 312:_sage_ >>> zeta7 + 1/zeta7 |

508 | Expecting: |

509 | -zeta7^5 - zeta7^4 - zeta7^3 - zeta7^2 - 1 |

510 | ok |

511 | Trying: |

512 | R = PolynomialRing(QQ, names=('x',)); (x,) = R._first_ngens(1)###line 319:_sage_ >>> R.<x> = PolynomialRing(QQ) |

513 | Expecting nothing |

514 | ok |

515 | Trying: |

516 | K = NumberField(x**Integer(3) - Integer(2), names=('beta',)); (beta,) = K._first_ngens(1)###line 320:_sage_ >>> K.<beta> = NumberField(x^3 - 2) |

517 | Expecting nothing |

518 | ok |

519 | Trying: |

520 | alpha = RR(Integer(2))**(Integer(1)/Integer(3)); alpha###line 321:_sage_ >>> alpha = RR(2)^(1/3); alpha |

521 | Expecting: |

522 | 1.25992104989487 |

523 | ok |

524 | Trying: |

525 | i = K.hom([alpha],check=False); i###line 323:_sage_ >>> i = K.hom([alpha],check=False); i |

526 | Expecting: |

527 | Ring morphism: |

528 | From: Number Field in beta with defining polynomial x^3 - 2 |

529 | To: Real Field with 53 bits of precision |

530 | Defn: beta |--> 1.25992104989487 |

531 | ok |

532 | Trying: |

533 | i(beta)###line 328:_sage_ >>> i(beta) |

534 | Expecting: |

535 | 1.25992104989487 |

536 | ok |

537 | Trying: |

538 | i(beta**Integer(3))###line 330:_sage_ >>> i(beta^3) |

539 | Expecting: |

540 | 2.00000000000000 |

541 | ok |

542 | Trying: |

543 | i(beta**Integer(2) + Integer(1))###line 332:_sage_ >>> i(beta^2 + 1) |

544 | Expecting: |

545 | 2.58740105196820 |

546 | ok |

547 | Trying: |

548 | K = QQ # by the way :-)###line 337:_sage_ >>> K = QQ # by the way :-) |

549 | Expecting nothing |

550 | ok |

551 | Trying: |

552 | R = K['a, b, c, d']; (a, b, c, d,) = R._first_ngens(4); R###line 338:_sage_ >>> R.<a,b,c,d> = K[]; R |

553 | Expecting: |

554 | Multivariate Polynomial Ring in a, b, c, d over Rational Field |

555 | ok |

556 | Trying: |

557 | S = K['u']; (u,) = S._first_ngens(1); S###line 340:_sage_ >>> S.<u> = K[]; S |

558 | Expecting: |

559 | Univariate Polynomial Ring in u over Rational Field |

560 | ok |

561 | Trying: |

562 | f = R.hom([Integer(0),Integer(0),Integer(0),u], S); f###line 342:_sage_ >>> f = R.hom([0,0,0,u], S); f |

563 | Expecting: |

564 | Ring morphism: |

565 | From: Multivariate Polynomial Ring in a, b, c, d over Rational Field |

566 | To: Univariate Polynomial Ring in u over Rational Field |

567 | Defn: a |--> 0 |

568 | b |--> 0 |

569 | c |--> 0 |

570 | d |--> u |

571 | ok |

572 | Trying: |

573 | f(a+b+c+d)###line 350:_sage_ >>> f(a+b+c+d) |

574 | Expecting: |

575 | u |

576 | ok |

577 | Trying: |

578 | f( (a+b+c+d)**Integer(2) )###line 352:_sage_ >>> f( (a+b+c+d)^2 ) |

579 | Expecting: |

580 | u^2 |

581 | ok |

582 | Trying: |

583 | H = Hom(ZZ, QQ)###line 357:_sage_ >>> H = Hom(ZZ, QQ) |

584 | Expecting nothing |

585 | ok |

586 | Trying: |

587 | H == loads(dumps(H))###line 358:_sage_ >>> H == loads(dumps(H)) |

588 | Expecting: |

589 | True |

590 | ok |

591 | Trying: |

592 | K = CyclotomicField(Integer(7), names=('zeta7',)); (zeta7,) = K._first_ngens(1)###line 363:_sage_ >>> K.<zeta7> = CyclotomicField(7) |

593 | Expecting nothing |

594 | ok |

595 | Trying: |

596 | c = K.hom([Integer(1)/zeta7])###line 364:_sage_ >>> c = K.hom([1/zeta7]) |

597 | Expecting nothing |

598 | ok |

599 | Trying: |

600 | c == loads(dumps(c))###line 365:_sage_ >>> c == loads(dumps(c)) |

601 | Expecting: |

602 | True |

603 | ok |

604 | Trying: |

605 | R = PowerSeriesRing(GF(Integer(5)), names=('t',)); (t,) = R._first_ngens(1)###line 370:_sage_ >>> R.<t> = PowerSeriesRing(GF(5)) |

606 | Expecting nothing |

607 | ok |

608 | Trying: |

609 | f = R.hom([t**Integer(5)])###line 371:_sage_ >>> f = R.hom([t^5]) |

610 | Expecting nothing |

611 | ok |

612 | Trying: |

613 | f == loads(dumps(f))###line 372:_sage_ >>> f == loads(dumps(f)) |

614 | Expecting: |

615 | True |

616 | ok |

617 | Trying: |

618 | sig_on_count() |

619 | Expecting: |

620 | 0 |

621 | ok |

622 | Trying: |

623 | set_random_seed(0L) |

624 | Expecting nothing |

625 | ok |

626 | Trying: |

627 | change_warning_output(sys.stdout) |

628 | Expecting nothing |

629 | ok |

630 | Trying: |

631 | f = Zmod(Integer(8)).cover()###line 397:_sage_ >>> f = Zmod(8).cover() |

632 | Expecting nothing |

633 | ok |

634 | Trying: |

635 | sage.rings.morphism.is_RingHomomorphism(f)###line 398:_sage_ >>> sage.rings.morphism.is_RingHomomorphism(f) |

636 | Expecting: |

637 | True |

638 | ok |

639 | Trying: |

640 | sage.rings.morphism.is_RingHomomorphism(Integer(2)/Integer(3))###line 400:_sage_ >>> sage.rings.morphism.is_RingHomomorphism(2/3) |

641 | Expecting: |

642 | False |

643 | ok |

644 | Trying: |

645 | sig_on_count() |

646 | Expecting: |

647 | 0 |

648 | ok |

649 | Trying: |

650 | set_random_seed(0L) |

651 | Expecting nothing |

652 | ok |

653 | Trying: |

654 | change_warning_output(sys.stdout) |

655 | Expecting nothing |

656 | ok |

657 | Trying: |

658 | sig_on_count() |

659 | Expecting: |

660 | 0 |

661 | ok |

662 | Trying: |

663 | set_random_seed(0L) |

664 | Expecting nothing |

665 | ok |

666 | Trying: |

667 | change_warning_output(sys.stdout) |

668 | Expecting nothing |

669 | ok |

670 | Trying: |

671 | f = ZZ.hom(Zmod(Integer(6))); f###line 560:_sage_ >>> f = ZZ.hom(Zmod(6)); f |

672 | Expecting: |

673 | Ring Coercion morphism: |

674 | From: Integer Ring |

675 | To: Ring of integers modulo 6 |

676 | ok |

677 | Trying: |

678 | isinstance(f, sage.rings.morphism.RingHomomorphism)###line 564:_sage_ >>> isinstance(f, sage.rings.morphism.RingHomomorphism) |

679 | Expecting: |

680 | True |

681 | ok |

682 | Trying: |

683 | sig_on_count() |

684 | Expecting: |

685 | 0 |

686 | ok |

687 | Trying: |

688 | set_random_seed(0L) |

689 | Expecting nothing |

690 | ok |

691 | Trying: |

692 | change_warning_output(sys.stdout) |

693 | Expecting nothing |

694 | ok |

695 | Trying: |

696 | bool(ZZ.hom(QQ,[Integer(1)]))###line 581:_sage_ >>> bool(ZZ.hom(QQ,[1])) |

697 | Expecting: |

698 | True |

699 | ok |

700 | Trying: |

701 | R1 = Zmod(Integer(1))###line 586:_sage_ >>> R1 = Zmod(1) |

702 | Expecting nothing |

703 | ok |

704 | Trying: |

705 | phi = R1.hom(R1, [Integer(1)])###line 587:_sage_ >>> phi = R1.hom(R1, [1]) |

706 | Expecting nothing |

707 | ok |

708 | Trying: |

709 | bool(phi)###line 588:_sage_ >>> bool(phi) |

710 | Expecting: |

711 | False |

712 | ok |

713 | Trying: |

714 | bool(ZZ.hom(R1, [Integer(1)]))###line 590:_sage_ >>> bool(ZZ.hom(R1, [1])) |

715 | Expecting: |

716 | False |

717 | ok |

718 | Trying: |

719 | sig_on_count() |

720 | Expecting: |

721 | 0 |

722 | ok |

723 | Trying: |

724 | set_random_seed(0L) |

725 | Expecting nothing |

726 | ok |

727 | Trying: |

728 | change_warning_output(sys.stdout) |

729 | Expecting nothing |

730 | ok |

731 | Trying: |

732 | phi = ZZ.hom(QQ,[Integer(1)])###line 605:_sage_ >>> phi = ZZ.hom(QQ,[1]) |

733 | Expecting nothing |

734 | ok |

735 | Trying: |

736 | phi._repr_type()###line 606:_sage_ >>> phi._repr_type() |

737 | Expecting: |

738 | 'Ring Coercion' |

739 | ok |

740 | Trying: |

741 | sage.rings.morphism.RingHomomorphism._repr_type(phi)###line 608:_sage_ >>> sage.rings.morphism.RingHomomorphism._repr_type(phi) |

742 | Expecting: |

743 | 'Ring' |

744 | ok |

745 | Trying: |

746 | sig_on_count() |

747 | Expecting: |

748 | 0 |

749 | ok |

750 | Trying: |

751 | set_random_seed(0L) |

752 | Expecting nothing |

753 | ok |

754 | Trying: |

755 | change_warning_output(sys.stdout) |

756 | Expecting nothing |

757 | ok |

758 | Trying: |

759 | f = ZZ.hom(Zmod(Integer(7)))###line 628:_sage_ >>> f = ZZ.hom(Zmod(7)) |

760 | Expecting nothing |

761 | ok |

762 | Trying: |

763 | f._set_lift(Zmod(Integer(7)).lift())###line 629:_sage_ >>> f._set_lift(Zmod(7).lift()) |

764 | Expecting nothing |

765 | ok |

766 | Trying: |

767 | f.lift()###line 630:_sage_ >>> f.lift() |

768 | Expecting: |

769 | Set-theoretic ring morphism: |

770 | From: Ring of integers modulo 7 |

771 | To: Integer Ring |

772 | Defn: Choice of lifting map |

773 | ok |

774 | Trying: |

775 | sig_on_count() |

776 | Expecting: |

777 | 0 |

778 | ok |

779 | Trying: |

780 | set_random_seed(0L) |

781 | Expecting nothing |

782 | ok |

783 | Trying: |

784 | change_warning_output(sys.stdout) |

785 | Expecting nothing |

786 | ok |

787 | Trying: |

788 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 665:_sage_ >>> R.<x,y> = QQ[] |

789 | Expecting nothing |

790 | ok |

791 | Trying: |

792 | S = QQ['a, b']; (a, b,) = S._first_ngens(2)###line 666:_sage_ >>> S.<a,b> = QQ[] |

793 | Expecting nothing |

794 | ok |

795 | Trying: |

796 | f = R.hom([a+b,a-b])###line 667:_sage_ >>> f = R.hom([a+b,a-b]) |

797 | Expecting nothing |

798 | ok |

799 | Trying: |

800 | g = S.hom(Frac(S))###line 668:_sage_ >>> g = S.hom(Frac(S)) |

801 | Expecting nothing |

802 | ok |

803 | Trying: |

804 | g*f###line 669:_sage_ >>> g*f |

805 | Expecting: |

806 | Ring morphism: |

807 | From: Multivariate Polynomial Ring in x, y over Rational Field |

808 | To: Fraction Field of Multivariate Polynomial Ring in a, b over Rational Field |

809 | Defn: x |--> a + b |

810 | y |--> a - b |

811 | ok |

812 | Trying: |

813 | from sage.categories.morphism import SetMorphism###line 675:_sage_ >>> from sage.categories.morphism import SetMorphism |

814 | Expecting nothing |

815 | ok |

816 | Trying: |

817 | h = SetMorphism(Hom(R,S,Rings()), lambda p: p[Integer(0)])###line 676:_sage_ >>> h = SetMorphism(Hom(R,S,Rings()), lambda p: p[0]) |

818 | Expecting nothing |

819 | ok |

820 | Trying: |

821 | g*h###line 677:_sage_ >>> g*h |

822 | Expecting: |

823 | Composite map: |

824 | From: Multivariate Polynomial Ring in x, y over Rational Field |

825 | To: Fraction Field of Multivariate Polynomial Ring in a, b over Rational Field |

826 | Defn: Generic morphism: |

827 | From: Multivariate Polynomial Ring in x, y over Rational Field |

828 | To: Multivariate Polynomial Ring in a, b over Rational Field |

829 | then |

830 | Ring Coercion morphism: |

831 | From: Multivariate Polynomial Ring in a, b over Rational Field |

832 | To: Fraction Field of Multivariate Polynomial Ring in a, b over Rational Field |

833 | ok |

834 | Trying: |

835 | sig_on_count() |

836 | Expecting: |

837 | 0 |

838 | ok |

839 | Trying: |

840 | set_random_seed(0L) |

841 | Expecting nothing |

842 | ok |

843 | Trying: |

844 | change_warning_output(sys.stdout) |

845 | Expecting nothing |

846 | ok |

847 | Trying: |

848 | f = ZZ.hom(QQ)###line 712:_sage_ >>> f = ZZ.hom(QQ) |

849 | Expecting nothing |

850 | ok |

851 | Trying: |

852 | f.is_injective()###line 713:_sage_ >>> f.is_injective() |

853 | Expecting: |

854 | Traceback (most recent call last): |

855 | ... |

856 | NotImplementedError |

857 | ok |

858 | Trying: |

859 | sig_on_count() |

860 | Expecting: |

861 | 0 |

862 | ok |

863 | Trying: |

864 | set_random_seed(0L) |

865 | Expecting nothing |

866 | ok |

867 | Trying: |

868 | change_warning_output(sys.stdout) |

869 | Expecting nothing |

870 | ok |

871 | Trying: |

872 | h = Hom(ZZ, QQ)###line 736:_sage_ >>> h = Hom(ZZ, QQ) |

873 | Expecting nothing |

874 | ok |

875 | Trying: |

876 | f = h.natural_map()###line 737:_sage_ >>> f = h.natural_map() |

877 | Expecting nothing |

878 | ok |

879 | Trying: |

880 | f.is_zero()###line 738:_sage_ >>> f.is_zero() |

881 | Expecting: |

882 | False |

883 | ok |

884 | Trying: |

885 | R = Integers(Integer(1))###line 745:_sage_ >>> R = Integers(1) |

886 | Expecting nothing |

887 | ok |

888 | Trying: |

889 | R###line 746:_sage_ >>> R |

890 | Expecting: |

891 | Ring of integers modulo 1 |

892 | ok |

893 | Trying: |

894 | h = Hom(ZZ, R)###line 748:_sage_ >>> h = Hom(ZZ, R) |

895 | Expecting nothing |

896 | ok |

897 | Trying: |

898 | f = h.natural_map()###line 749:_sage_ >>> f = h.natural_map() |

899 | Expecting nothing |

900 | ok |

901 | Trying: |

902 | f.is_zero()###line 750:_sage_ >>> f.is_zero() |

903 | Expecting: |

904 | True |

905 | ok |

906 | Trying: |

907 | h = Hom(ZZ, GF(Integer(2)))###line 757:_sage_ >>> h = Hom(ZZ, GF(2)) |

908 | Expecting nothing |

909 | ok |

910 | Trying: |

911 | f = h.natural_map()###line 758:_sage_ >>> f = h.natural_map() |

912 | Expecting nothing |

913 | ok |

914 | Trying: |

915 | f.is_zero()###line 759:_sage_ >>> f.is_zero() |

916 | Expecting: |

917 | False |

918 | ok |

919 | Trying: |

920 | sig_on_count() |

921 | Expecting: |

922 | 0 |

923 | ok |

924 | Trying: |

925 | set_random_seed(0L) |

926 | Expecting nothing |

927 | ok |

928 | Trying: |

929 | change_warning_output(sys.stdout) |

930 | Expecting nothing |

931 | ok |

932 | Trying: |

933 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2); f = S.cover()###line 771:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]); f = S.cover() |

934 | Expecting nothing |

935 | ok |

936 | Trying: |

937 | f.pushforward(R.ideal([x,Integer(3)*x+x*y+y**Integer(2)]))###line 772:_sage_ >>> f.pushforward(R.ideal([x,3*x+x*y+y^2])) |

938 | Expecting: |

939 | Ideal (xx, xx*yy + 3*xx) of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y^2) |

940 | ok |

941 | Trying: |

942 | sig_on_count() |

943 | Expecting: |

944 | 0 |

945 | ok |

946 | Trying: |

947 | set_random_seed(0L) |

948 | Expecting nothing |

949 | ok |

950 | Trying: |

951 | change_warning_output(sys.stdout) |

952 | Expecting nothing |

953 | ok |

954 | Trying: |

955 | f = ZZ.hom(ZZ)###line 789:_sage_ >>> f = ZZ.hom(ZZ) |

956 | Expecting nothing |

957 | ok |

958 | Trying: |

959 | f.inverse_image(ZZ.ideal(Integer(2)))###line 790:_sage_ >>> f.inverse_image(ZZ.ideal(2)) |

960 | Expecting: |

961 | Traceback (most recent call last): |

962 | ... |

963 | NotImplementedError |

964 | ok |

965 | Trying: |

966 | sig_on_count() |

967 | Expecting: |

968 | 0 |

969 | ok |

970 | Trying: |

971 | set_random_seed(0L) |

972 | Expecting nothing |

973 | ok |

974 | Trying: |

975 | change_warning_output(sys.stdout) |

976 | Expecting nothing |

977 | ok |

978 | Trying: |

979 | sig_on_count() |

980 | Expecting: |

981 | 0 |

982 | ok |

983 | Trying: |

984 | set_random_seed(0L) |

985 | Expecting nothing |

986 | ok |

987 | Trying: |

988 | change_warning_output(sys.stdout) |

989 | Expecting nothing |

990 | ok |

991 | Trying: |

992 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 806:_sage_ >>> R.<x,y> = QQ[] |

993 | Expecting nothing |

994 | ok |

995 | Trying: |

996 | f = R.hom([x,x])###line 807:_sage_ >>> f = R.hom([x,x]) |

997 | Expecting nothing |

998 | ok |

999 | Trying: |

1000 | f(x+y)###line 808:_sage_ >>> f(x+y) |

1001 | Expecting: |

1002 | 2*x |

1003 | ok |

1004 | Trying: |

1005 | f.lift()###line 810:_sage_ >>> f.lift() |

1006 | Expecting: |

1007 | Traceback (most recent call last): |

1008 | ... |

1009 | ValueError: no lift map defined |

1010 | ok |

1011 | Trying: |

1012 | g = R.hom(R)###line 814:_sage_ >>> g = R.hom(R) |

1013 | Expecting nothing |

1014 | ok |

1015 | Trying: |

1016 | f._set_lift(g)###line 815:_sage_ >>> f._set_lift(g) |

1017 | Expecting nothing |

1018 | ok |

1019 | Trying: |

1020 | f.lift() == g###line 816:_sage_ >>> f.lift() == g |

1021 | Expecting: |

1022 | True |

1023 | ok |

1024 | Trying: |

1025 | f.lift(x)###line 818:_sage_ >>> f.lift(x) |

1026 | Expecting: |

1027 | x |

1028 | ok |

1029 | Trying: |

1030 | sig_on_count() |

1031 | Expecting: |

1032 | 0 |

1033 | ok |

1034 | Trying: |

1035 | set_random_seed(0L) |

1036 | Expecting nothing |

1037 | ok |

1038 | Trying: |

1039 | change_warning_output(sys.stdout) |

1040 | Expecting nothing |

1041 | ok |

1042 | Trying: |

1043 | f = ZZ.hom(QQ); f # indirect doctest###line 836:_sage_ >>> f = ZZ.hom(QQ); f # indirect doctest |

1044 | Expecting: |

1045 | Ring Coercion morphism: |

1046 | From: Integer Ring |

1047 | To: Rational Field |

1048 | ok |

1049 | Trying: |

1050 | f == loads(dumps(f))###line 841:_sage_ >>> f == loads(dumps(f)) |

1051 | Expecting: |

1052 | True |

1053 | ok |

1054 | Trying: |

1055 | sig_on_count() |

1056 | Expecting: |

1057 | 0 |

1058 | ok |

1059 | Trying: |

1060 | set_random_seed(0L) |

1061 | Expecting nothing |

1062 | ok |

1063 | Trying: |

1064 | change_warning_output(sys.stdout) |

1065 | Expecting nothing |

1066 | ok |

1067 | Trying: |

1068 | f = ZZ.hom(QQ)###line 855:_sage_ >>> f = ZZ.hom(QQ) |

1069 | Expecting nothing |

1070 | ok |

1071 | Trying: |

1072 | type(f)###line 856:_sage_ >>> type(f) |

1073 | Expecting: |

1074 | <type 'sage.rings.morphism.RingHomomorphism_coercion'> |

1075 | ok |

1076 | Trying: |

1077 | f._repr_type()###line 858:_sage_ >>> f._repr_type() |

1078 | Expecting: |

1079 | 'Ring Coercion' |

1080 | ok |

1081 | Trying: |

1082 | sig_on_count() |

1083 | Expecting: |

1084 | 0 |

1085 | ok |

1086 | Trying: |

1087 | set_random_seed(0L) |

1088 | Expecting nothing |

1089 | ok |

1090 | Trying: |

1091 | change_warning_output(sys.stdout) |

1092 | Expecting nothing |

1093 | ok |

1094 | Trying: |

1095 | f = ZZ.hom(QQ)###line 872:_sage_ >>> f = ZZ.hom(QQ) |

1096 | Expecting nothing |

1097 | ok |

1098 | Trying: |

1099 | g = ZZ.hom(ZZ)###line 873:_sage_ >>> g = ZZ.hom(ZZ) |

1100 | Expecting nothing |

1101 | ok |

1102 | Trying: |

1103 | f == g###line 874:_sage_ >>> f == g |

1104 | Expecting: |

1105 | False |

1106 | ok |

1107 | Trying: |

1108 | f > g###line 876:_sage_ >>> f > g |

1109 | Expecting: |

1110 | True |

1111 | ok |

1112 | Trying: |

1113 | f < g###line 878:_sage_ >>> f < g |

1114 | Expecting: |

1115 | False |

1116 | ok |

1117 | Trying: |

1118 | h = Zmod(Integer(6)).lift()###line 880:_sage_ >>> h = Zmod(6).lift() |

1119 | Expecting nothing |

1120 | ok |

1121 | Trying: |

1122 | f == h###line 881:_sage_ >>> f == h |

1123 | Expecting: |

1124 | False |

1125 | ok |

1126 | Trying: |

1127 | sig_on_count() |

1128 | Expecting: |

1129 | 0 |

1130 | ok |

1131 | Trying: |

1132 | set_random_seed(0L) |

1133 | Expecting nothing |

1134 | ok |

1135 | Trying: |

1136 | change_warning_output(sys.stdout) |

1137 | Expecting nothing |

1138 | ok |

1139 | Trying: |

1140 | f = ZZ.hom(QQ); type(f)###line 898:_sage_ >>> f = ZZ.hom(QQ); type(f) |

1141 | Expecting: |

1142 | <type 'sage.rings.morphism.RingHomomorphism_coercion'> |

1143 | ok |

1144 | Trying: |

1145 | f(Integer(2)) == Integer(2)###line 900:_sage_ >>> f(2) == 2 |

1146 | Expecting: |

1147 | True |

1148 | ok |

1149 | Trying: |

1150 | type(f(Integer(2))) # indirect doctest###line 902:_sage_ >>> type(f(2)) # indirect doctest |

1151 | Expecting: |

1152 | <type 'sage.rings.rational.Rational'> |

1153 | ok |

1154 | Trying: |

1155 | sig_on_count() |

1156 | Expecting: |

1157 | 0 |

1158 | ok |

1159 | Trying: |

1160 | set_random_seed(0L) |

1161 | Expecting nothing |

1162 | ok |

1163 | Trying: |

1164 | change_warning_output(sys.stdout) |

1165 | Expecting nothing |

1166 | ok |

1167 | Trying: |

1168 | sig_on_count() |

1169 | Expecting: |

1170 | 0 |

1171 | ok |

1172 | Trying: |

1173 | set_random_seed(0L) |

1174 | Expecting nothing |

1175 | ok |

1176 | Trying: |

1177 | change_warning_output(sys.stdout) |

1178 | Expecting nothing |

1179 | ok |

1180 | Trying: |

1181 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 917:_sage_ >>> R.<x,y> = QQ[] |

1182 | Expecting nothing |

1183 | ok |

1184 | Trying: |

1185 | phi = R.hom([x,x+y]); phi###line 918:_sage_ >>> phi = R.hom([x,x+y]); phi |

1186 | Expecting: |

1187 | Ring endomorphism of Multivariate Polynomial Ring in x, y over Rational Field |

1188 | Defn: x |--> x |

1189 | y |--> x + y |

1190 | ok |

1191 | Trying: |

1192 | type(phi)###line 922:_sage_ >>> type(phi) |

1193 | Expecting: |

1194 | <type 'sage.rings.morphism.RingHomomorphism_im_gens'> |

1195 | ok |

1196 | Trying: |

1197 | S = R.quotient(x - y, names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2)###line 927:_sage_ >>> S.<xx,yy> = R.quotient(x - y) |

1198 | Expecting nothing |

1199 | ok |

1200 | Trying: |

1201 | phi = S.hom([xx+Integer(1),xx+Integer(1)])###line 928:_sage_ >>> phi = S.hom([xx+1,xx+1]) |

1202 | Expecting nothing |

1203 | ok |

1204 | Trying: |

1205 | phi = S.hom([xx+Integer(1),xx-Integer(1)])###line 932:_sage_ >>> phi = S.hom([xx+1,xx-1]) |

1206 | Expecting: |

1207 | Traceback (most recent call last): |

1208 | ... |

1209 | TypeError: images do not define a valid homomorphism |

1210 | ok |

1211 | Trying: |

1212 | phi = S.hom([xx+Integer(1),xx-Integer(1)],check=False)###line 941:_sage_ >>> phi = S.hom([xx+1,xx-1],check=False) |

1213 | Expecting: |

1214 | Traceback (most recent call last): |

1215 | ... |

1216 | TypeError: images do not define a valid homomorphism |

1217 | ok |

1218 | Trying: |

1219 | sig_on_count() |

1220 | Expecting: |

1221 | 0 |

1222 | ok |

1223 | Trying: |

1224 | set_random_seed(0L) |

1225 | Expecting nothing |

1226 | ok |

1227 | Trying: |

1228 | change_warning_output(sys.stdout) |

1229 | Expecting nothing |

1230 | ok |

1231 | Trying: |

1232 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 968:_sage_ >>> R.<x,y> = QQ[] |

1233 | Expecting nothing |

1234 | ok |

1235 | Trying: |

1236 | f = R.hom([x,x+y])###line 969:_sage_ >>> f = R.hom([x,x+y]) |

1237 | Expecting nothing |

1238 | ok |

1239 | Trying: |

1240 | f.im_gens()###line 970:_sage_ >>> f.im_gens() |

1241 | Expecting: |

1242 | [x, x + y] |

1243 | ok |

1244 | Trying: |

1245 | f.im_gens()[Integer(0)] = Integer(5)###line 976:_sage_ >>> f.im_gens()[0] = 5 |

1246 | Expecting nothing |

1247 | ok |

1248 | Trying: |

1249 | f.im_gens()###line 977:_sage_ >>> f.im_gens() |

1250 | Expecting: |

1251 | [x, x + y] |

1252 | ok |

1253 | Trying: |

1254 | sig_on_count() |

1255 | Expecting: |

1256 | 0 |

1257 | ok |

1258 | Trying: |

1259 | set_random_seed(0L) |

1260 | Expecting nothing |

1261 | ok |

1262 | Trying: |

1263 | change_warning_output(sys.stdout) |

1264 | Expecting nothing |

1265 | ok |

1266 | Trying: |

1267 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); f = R.hom([x,x+y]); g = R.hom([y,x])###line 996:_sage_ >>> R.<x,y> = QQ[]; f = R.hom([x,x+y]); g = R.hom([y,x]) |

1268 | Expecting nothing |

1269 | ok |

1270 | Trying: |

1271 | cmp(f,g) # indirect doctest###line 997:_sage_ >>> cmp(f,g) # indirect doctest |

1272 | Expecting: |

1273 | 1 |

1274 | ok |

1275 | Trying: |

1276 | cmp(g,f)###line 999:_sage_ >>> cmp(g,f) |

1277 | Expecting: |

1278 | -1 |

1279 | ok |

1280 | Trying: |

1281 | sig_on_count() |

1282 | Expecting: |

1283 | 0 |

1284 | ok |

1285 | Trying: |

1286 | set_random_seed(0L) |

1287 | Expecting nothing |

1288 | ok |

1289 | Trying: |

1290 | change_warning_output(sys.stdout) |

1291 | Expecting nothing |

1292 | ok |

1293 | Trying: |

1294 | R = QQ['x']; (x,) = R._first_ngens(1)###line 1013:_sage_ >>> R.<x> = QQ[] |

1295 | Expecting nothing |

1296 | ok |

1297 | Trying: |

1298 | Q = R.quotient(x**Integer(2) + x + Integer(1), names=('a',)); (a,) = Q._first_ngens(1)###line 1014:_sage_ >>> Q.<a> = R.quotient(x^2 + x + 1) |

1299 | Expecting nothing |

1300 | ok |

1301 | Trying: |

1302 | f1 = R.hom([a])###line 1015:_sage_ >>> f1 = R.hom([a]) |

1303 | Expecting nothing |

1304 | ok |

1305 | Trying: |

1306 | f2 = R.hom([a + a**Integer(2) + a + Integer(1)])###line 1016:_sage_ >>> f2 = R.hom([a + a^2 + a + 1]) |

1307 | Expecting nothing |

1308 | ok |

1309 | Trying: |

1310 | f1 == f2###line 1017:_sage_ >>> f1 == f2 |

1311 | Expecting: |

1312 | True |

1313 | ok |

1314 | Trying: |

1315 | f1 == R.hom([a**Integer(2)])###line 1019:_sage_ >>> f1 == R.hom([a^2]) |

1316 | Expecting: |

1317 | False |

1318 | ok |

1319 | Trying: |

1320 | f1(x**Integer(3) + x)###line 1021:_sage_ >>> f1(x^3 + x) |

1321 | Expecting: |

1322 | a + 1 |

1323 | ok |

1324 | Trying: |

1325 | f2(x**Integer(3) + x)###line 1023:_sage_ >>> f2(x^3 + x) |

1326 | Expecting: |

1327 | a + 1 |

1328 | ok |

1329 | Trying: |

1330 | loads(dumps(f2)) == f2###line 1028:_sage_ >>> loads(dumps(f2)) == f2 |

1331 | Expecting: |

1332 | True |

1333 | ok |

1334 | Trying: |

1335 | R = GF(Integer(7))['x, y']; (x, y,) = R._first_ngens(2)###line 1037:_sage_ >>> R.<x,y> = GF(7)[] |

1336 | Expecting nothing |

1337 | ok |

1338 | Trying: |

1339 | Q = R.quotient([x**Integer(2) + x + Integer(1), y**Integer(2) + y + Integer(1)], names=('a', 'b',)); (a, b,) = Q._first_ngens(2)###line 1038:_sage_ >>> Q.<a,b> = R.quotient([x^2 + x + 1, y^2 + y + 1]) |

1340 | Expecting nothing |

1341 | ok |

1342 | Trying: |

1343 | f1 = R.hom([a, b])###line 1039:_sage_ >>> f1 = R.hom([a, b]) |

1344 | Expecting nothing |

1345 | ok |

1346 | Trying: |

1347 | f2 = R.hom([a + a**Integer(2) + a + Integer(1), b + b**Integer(2) + b + Integer(1)])###line 1040:_sage_ >>> f2 = R.hom([a + a^2 + a + 1, b + b^2 + b + 1]) |

1348 | Expecting nothing |

1349 | ok |

1350 | Trying: |

1351 | f1 == f2###line 1041:_sage_ >>> f1 == f2 |

1352 | Expecting: |

1353 | True |

1354 | ok |

1355 | Trying: |

1356 | f1 == R.hom([b,a])###line 1043:_sage_ >>> f1 == R.hom([b,a]) |

1357 | Expecting: |

1358 | False |

1359 | ok |

1360 | Trying: |

1361 | x**Integer(3) + x + y**Integer(2)###line 1045:_sage_ >>> x^3 + x + y^2 |

1362 | Expecting: |

1363 | x^3 + y^2 + x |

1364 | ok |

1365 | Trying: |

1366 | f1(x**Integer(3) + x + y**Integer(2))###line 1047:_sage_ >>> f1(x^3 + x + y^2) |

1367 | Expecting: |

1368 | a - b |

1369 | ok |

1370 | Trying: |

1371 | f2(x**Integer(3) + x + y**Integer(2))###line 1049:_sage_ >>> f2(x^3 + x + y^2) |

1372 | Expecting: |

1373 | a - b |

1374 | ok |

1375 | Trying: |

1376 | loads(dumps(f2)) == f2###line 1054:_sage_ >>> loads(dumps(f2)) == f2 |

1377 | Expecting: |

1378 | True |

1379 | ok |

1380 | Trying: |

1381 | sig_on_count() |

1382 | Expecting: |

1383 | 0 |

1384 | ok |

1385 | Trying: |

1386 | set_random_seed(0L) |

1387 | Expecting nothing |

1388 | ok |

1389 | Trying: |

1390 | change_warning_output(sys.stdout) |

1391 | Expecting nothing |

1392 | ok |

1393 | Trying: |

1394 | f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))###line 416:_sage_ >>> f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ)) |

1395 | Expecting nothing |

1396 | ok |

1397 | Trying: |

1398 | type(f)###line 417:_sage_ >>> type(f) |

1399 | Expecting: |

1400 | <type 'sage.rings.morphism.RingMap'> |

1401 | ok |

1402 | Trying: |

1403 | sig_on_count() |

1404 | Expecting: |

1405 | 0 |

1406 | ok |

1407 | Trying: |

1408 | set_random_seed(0L) |

1409 | Expecting nothing |

1410 | ok |

1411 | Trying: |

1412 | change_warning_output(sys.stdout) |

1413 | Expecting nothing |

1414 | ok |

1415 | Trying: |

1416 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); f = R.hom([x**Integer(2),x+y])###line 1067:_sage_ >>> R.<x,y> = QQ[]; f = R.hom([x^2,x+y]) |

1417 | Expecting nothing |

1418 | ok |

1419 | Trying: |

1420 | print f._repr_defn()###line 1068:_sage_ >>> print f._repr_defn() |

1421 | Expecting: |

1422 | x |--> x^2 |

1423 | y |--> x + y |

1424 | ok |

1425 | Trying: |

1426 | sig_on_count() |

1427 | Expecting: |

1428 | 0 |

1429 | ok |

1430 | Trying: |

1431 | set_random_seed(0L) |

1432 | Expecting nothing |

1433 | ok |

1434 | Trying: |

1435 | change_warning_output(sys.stdout) |

1436 | Expecting nothing |

1437 | ok |

1438 | Trying: |

1439 | R = ZZ['x, y, z']; (x, y, z,) = R._first_ngens(3); f = R.hom([Integer(2)*x,z,y])###line 1083:_sage_ >>> R.<x,y,z> = ZZ[]; f = R.hom([2*x,z,y]) |

1440 | Expecting nothing |

1441 | ok |

1442 | Trying: |

1443 | f(x+Integer(2)*y+Integer(3)*z) # indirect doctest###line 1084:_sage_ >>> f(x+2*y+3*z) # indirect doctest |

1444 | Expecting: |

1445 | 2*x + 3*y + 2*z |

1446 | ok |

1447 | Trying: |

1448 | sig_on_count() |

1449 | Expecting: |

1450 | 0 |

1451 | ok |

1452 | Trying: |

1453 | set_random_seed(0L) |

1454 | Expecting nothing |

1455 | ok |

1456 | Trying: |

1457 | change_warning_output(sys.stdout) |

1458 | Expecting nothing |

1459 | ok |

1460 | Trying: |

1461 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 1102:_sage_ >>> R.<x,y> = QQ[] |

1462 | Expecting nothing |

1463 | ok |

1464 | Trying: |

1465 | S = QQ['z']; (z,) = S._first_ngens(1)###line 1103:_sage_ >>> S.<z> = QQ[] |

1466 | Expecting nothing |

1467 | ok |

1468 | Trying: |

1469 | f = R.hom([Integer(2)*z,Integer(3)*z],S)###line 1104:_sage_ >>> f = R.hom([2*z,3*z],S) |

1470 | Expecting nothing |

1471 | ok |

1472 | Trying: |

1473 | PR = R['t']; (t,) = PR._first_ngens(1)###line 1109:_sage_ >>> PR.<t> = R[] |

1474 | Expecting nothing |

1475 | ok |

1476 | Trying: |

1477 | PS = S['t']###line 1110:_sage_ >>> PS = S['t'] |

1478 | Expecting nothing |

1479 | ok |

1480 | Trying: |

1481 | Pf = PR.hom(f,PS)###line 1111:_sage_ >>> Pf = PR.hom(f,PS) |

1482 | Expecting nothing |

1483 | ok |

1484 | Trying: |

1485 | Pf###line 1112:_sage_ >>> Pf |

1486 | Expecting: |

1487 | Ring morphism: |

1488 | From: Univariate Polynomial Ring in t over Multivariate Polynomial Ring in x, y over Rational Field |

1489 | To: Univariate Polynomial Ring in t over Univariate Polynomial Ring in z over Rational Field |

1490 | Defn: Induced from base ring by |

1491 | Ring morphism: |

1492 | From: Multivariate Polynomial Ring in x, y over Rational Field |

1493 | To: Univariate Polynomial Ring in z over Rational Field |

1494 | Defn: x |--> 2*z |

1495 | y |--> 3*z |

1496 | ok |

1497 | Trying: |

1498 | p = (x - Integer(4)*y + Integer(1)/Integer(13))*t**Integer(2) + (Integer(1)/Integer(2)*x**Integer(2) - Integer(1)/Integer(3)*y**Integer(2))*t + Integer(2)*y**Integer(2) + x###line 1122:_sage_ >>> p = (x - 4*y + 1/13)*t^2 + (1/2*x^2 - 1/3*y^2)*t + 2*y^2 + x |

1499 | Expecting nothing |

1500 | ok |

1501 | Trying: |

1502 | Pf(p)###line 1123:_sage_ >>> Pf(p) |

1503 | Expecting: |

1504 | (-10*z + 1/13)*t^2 - z^2*t + 18*z^2 + 2*z |

1505 | ok |

1506 | Trying: |

1507 | MR = MatrixSpace(R,Integer(2),Integer(2))###line 1128:_sage_ >>> MR = MatrixSpace(R,2,2) |

1508 | Expecting nothing |

1509 | ok |

1510 | Trying: |

1511 | MS = MatrixSpace(S,Integer(2),Integer(2))###line 1129:_sage_ >>> MS = MatrixSpace(S,2,2) |

1512 | Expecting nothing |

1513 | ok |

1514 | Trying: |

1515 | M = MR([x**Integer(2) + Integer(1)/Integer(7)*x*y - y**Integer(2), - Integer(1)/Integer(2)*y**Integer(2) + Integer(2)*y + Integer(1)/Integer(6), Integer(4)*x**Integer(2) - Integer(14)*x, Integer(1)/Integer(2)*y**Integer(2) + Integer(13)/Integer(4)*x - Integer(2)/Integer(11)*y])###line 1130:_sage_ >>> M = MR([x^2 + 1/7*x*y - y^2, - 1/2*y^2 + 2*y + 1/6, 4*x^2 - 14*x, 1/2*y^2 + 13/4*x - 2/11*y]) |

1516 | Expecting nothing |

1517 | ok |

1518 | Trying: |

1519 | Mf = MR.hom(f,MS)###line 1131:_sage_ >>> Mf = MR.hom(f,MS) |

1520 | Expecting nothing |

1521 | ok |

1522 | Trying: |

1523 | Mf###line 1132:_sage_ >>> Mf |

1524 | Expecting: |

1525 | Ring morphism: |

1526 | From: Full MatrixSpace of 2 by 2 dense matrices over Multivariate Polynomial Ring in x, y over Rational Field |

1527 | To: Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in z over Rational Field |

1528 | Defn: Induced from base ring by |

1529 | Ring morphism: |

1530 | From: Multivariate Polynomial Ring in x, y over Rational Field |

1531 | To: Univariate Polynomial Ring in z over Rational Field |

1532 | Defn: x |--> 2*z |

1533 | y |--> 3*z |

1534 | ok |

1535 | Trying: |

1536 | Mf(M)###line 1142:_sage_ >>> Mf(M) |

1537 | Expecting: |

1538 | [ -29/7*z^2 -9/2*z^2 + 6*z + 1/6] |

1539 | [ 16*z^2 - 28*z 9/2*z^2 + 131/22*z] |

1540 | ok |

1541 | Trying: |

1542 | MPR = MatrixSpace(PR, Integer(2))###line 1148:_sage_ >>> MPR = MatrixSpace(PR, 2) |

1543 | Expecting nothing |

1544 | ok |

1545 | Trying: |

1546 | MPS = MatrixSpace(PS, Integer(2))###line 1149:_sage_ >>> MPS = MatrixSpace(PS, 2) |

1547 | Expecting nothing |

1548 | ok |

1549 | Trying: |

1550 | M = MPR([(- x + y)*t**Integer(2) + Integer(58)*t - Integer(3)*x**Integer(2) + x*y, (- Integer(1)/Integer(7)*x*y - Integer(1)/Integer(40)*x)*t**Integer(2) + (Integer(5)*x**Integer(2) + y**Integer(2))*t + Integer(2)*y, (- Integer(1)/Integer(3)*y + Integer(1))*t**Integer(2) + Integer(1)/Integer(3)*x*y + y**Integer(2) + Integer(5)/Integer(2)*y + Integer(1)/Integer(4), (x + Integer(6)*y + Integer(1))*t**Integer(2)])###line 1150:_sage_ >>> M = MPR([(- x + y)*t^2 + 58*t - 3*x^2 + x*y, (- 1/7*x*y - 1/40*x)*t^2 + (5*x^2 + y^2)*t + 2*y, (- 1/3*y + 1)*t^2 + 1/3*x*y + y^2 + 5/2*y + 1/4, (x + 6*y + 1)*t^2]) |

1551 | Expecting nothing |

1552 | ok |

1553 | Trying: |

1554 | MPf = MPR.hom(f,MPS); MPf###line 1151:_sage_ >>> MPf = MPR.hom(f,MPS); MPf |

1555 | Expecting: |

1556 | Ring morphism: |

1557 | From: Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in t over Multivariate Polynomial Ring in x, y over Rational Field |

1558 | To: Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in t over Univariate Polynomial Ring in z over Rational Field |

1559 | Defn: Induced from base ring by |

1560 | Ring morphism: |

1561 | From: Univariate Polynomial Ring in t over Multivariate Polynomial Ring in x, y over Rational Field |

1562 | To: Univariate Polynomial Ring in t over Univariate Polynomial Ring in z over Rational Field |

1563 | Defn: Induced from base ring by |

1564 | Ring morphism: |

1565 | From: Multivariate Polynomial Ring in x, y over Rational Field |

1566 | To: Univariate Polynomial Ring in z over Rational Field |

1567 | Defn: x |--> 2*z |

1568 | y |--> 3*z |

1569 | ok |

1570 | Trying: |

1571 | MPf(M)###line 1165:_sage_ >>> MPf(M) |

1572 | Expecting: |

1573 | [ z*t^2 + 58*t - 6*z^2 (-6/7*z^2 - 1/20*z)*t^2 + 29*z^2*t + 6*z] |

1574 | [ (-z + 1)*t^2 + 11*z^2 + 15/2*z + 1/4 (20*z + 1)*t^2] |

1575 | ok |

1576 | Trying: |

1577 | sig_on_count() |

1578 | Expecting: |

1579 | 0 |

1580 | ok |

1581 | Trying: |

1582 | set_random_seed(0L) |

1583 | Expecting nothing |

1584 | ok |

1585 | Trying: |

1586 | change_warning_output(sys.stdout) |

1587 | Expecting nothing |

1588 | ok |

1589 | Trying: |

1590 | from sage.rings.morphism import RingHomomorphism_from_base###line 1175:_sage_ >>> from sage.rings.morphism import RingHomomorphism_from_base |

1591 | Expecting nothing |

1592 | ok |

1593 | Trying: |

1594 | R = ZZ['x']; (x,) = R._first_ngens(1)###line 1176:_sage_ >>> R.<x> = ZZ[] |

1595 | Expecting nothing |

1596 | ok |

1597 | Trying: |

1598 | f = R.hom([Integer(2)*x],R)###line 1177:_sage_ >>> f = R.hom([2*x],R) |

1599 | Expecting nothing |

1600 | ok |

1601 | Trying: |

1602 | P = MatrixSpace(R,Integer(2)).Hom(MatrixSpace(R,Integer(2)))###line 1178:_sage_ >>> P = MatrixSpace(R,2).Hom(MatrixSpace(R,2)) |

1603 | Expecting nothing |

1604 | ok |

1605 | Trying: |

1606 | g = RingHomomorphism_from_base(P,f)###line 1179:_sage_ >>> g = RingHomomorphism_from_base(P,f) |

1607 | Expecting nothing |

1608 | ok |

1609 | Trying: |

1610 | g###line 1180:_sage_ >>> g |

1611 | Expecting: |

1612 | Ring endomorphism of Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in x over Integer Ring |

1613 | Defn: Induced from base ring by |

1614 | Ring endomorphism of Univariate Polynomial Ring in x over Integer Ring |

1615 | Defn: x |--> 2*x |

1616 | ok |

1617 | Trying: |

1618 | P = MatrixSpace(R,Integer(2)).Hom(R['t'])###line 1189:_sage_ >>> P = MatrixSpace(R,2).Hom(R['t']) |

1619 | Expecting nothing |

1620 | ok |

1621 | Trying: |

1622 | g = RingHomomorphism_from_base(P,f)###line 1190:_sage_ >>> g = RingHomomorphism_from_base(P,f) |

1623 | Expecting: |

1624 | Traceback (most recent call last): |

1625 | ... |

1626 | ValueError: Domain and codomain must have the same functorial construction over their base rings |

1627 | ok |

1628 | Trying: |

1629 | sig_on_count() |

1630 | Expecting: |

1631 | 0 |

1632 | ok |

1633 | Trying: |

1634 | set_random_seed(0L) |

1635 | Expecting nothing |

1636 | ok |

1637 | Trying: |

1638 | change_warning_output(sys.stdout) |

1639 | Expecting nothing |

1640 | ok |

1641 | Trying: |

1642 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 1213:_sage_ >>> R.<x,y> = QQ[] |

1643 | Expecting nothing |

1644 | ok |

1645 | Trying: |

1646 | S = QQ['z']; (z,) = S._first_ngens(1)###line 1214:_sage_ >>> S.<z> = QQ[] |

1647 | Expecting nothing |

1648 | ok |

1649 | Trying: |

1650 | f = R.hom([Integer(2)*z,Integer(3)*z],S)###line 1215:_sage_ >>> f = R.hom([2*z,3*z],S) |

1651 | Expecting nothing |

1652 | ok |

1653 | Trying: |

1654 | MR = MatrixSpace(R,Integer(2))###line 1216:_sage_ >>> MR = MatrixSpace(R,2) |

1655 | Expecting nothing |

1656 | ok |

1657 | Trying: |

1658 | MS = MatrixSpace(S,Integer(2))###line 1217:_sage_ >>> MS = MatrixSpace(S,2) |

1659 | Expecting nothing |

1660 | ok |

1661 | Trying: |

1662 | g = MR.hom(f,MS)###line 1218:_sage_ >>> g = MR.hom(f,MS) |

1663 | Expecting nothing |

1664 | ok |

1665 | Trying: |

1666 | g.underlying_map() == f###line 1219:_sage_ >>> g.underlying_map() == f |

1667 | Expecting: |

1668 | True |

1669 | ok |

1670 | Trying: |

1671 | sig_on_count() |

1672 | Expecting: |

1673 | 0 |

1674 | ok |

1675 | Trying: |

1676 | set_random_seed(0L) |

1677 | Expecting nothing |

1678 | ok |

1679 | Trying: |

1680 | change_warning_output(sys.stdout) |

1681 | Expecting nothing |

1682 | ok |

1683 | Trying: |

1684 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); f = R.hom([x,x+y]); g = R.hom([y,x])###line 1239:_sage_ >>> R.<x,y> = QQ[]; f = R.hom([x,x+y]); g = R.hom([y,x]) |

1685 | Expecting nothing |

1686 | ok |

1687 | Trying: |

1688 | S = R['z']; (z,) = S._first_ngens(1)###line 1240:_sage_ >>> S.<z> = R[] |

1689 | Expecting nothing |

1690 | ok |

1691 | Trying: |

1692 | fS = S.hom(f,S); gS = S.hom(g,S)###line 1241:_sage_ >>> fS = S.hom(f,S); gS = S.hom(g,S) |

1693 | Expecting nothing |

1694 | ok |

1695 | Trying: |

1696 | cmp(fS,gS) # indirect doctest###line 1242:_sage_ >>> cmp(fS,gS) # indirect doctest |

1697 | Expecting: |

1698 | 1 |

1699 | ok |

1700 | Trying: |

1701 | cmp(gS,fS) # indirect doctest###line 1244:_sage_ >>> cmp(gS,fS) # indirect doctest |

1702 | Expecting: |

1703 | -1 |

1704 | ok |

1705 | Trying: |

1706 | sig_on_count() |

1707 | Expecting: |

1708 | 0 |

1709 | ok |

1710 | Trying: |

1711 | set_random_seed(0L) |

1712 | Expecting nothing |

1713 | ok |

1714 | Trying: |

1715 | change_warning_output(sys.stdout) |

1716 | Expecting nothing |

1717 | ok |

1718 | Trying: |

1719 | R = QQ['x']; (x,) = R._first_ngens(1)###line 1256:_sage_ >>> R.<x> = QQ[] |

1720 | Expecting nothing |

1721 | ok |

1722 | Trying: |

1723 | Q = R.quotient(x**Integer(2) + x + Integer(1), names=('a',)); (a,) = Q._first_ngens(1)###line 1257:_sage_ >>> Q.<a> = R.quotient(x^2 + x + 1) |

1724 | Expecting nothing |

1725 | ok |

1726 | Trying: |

1727 | f1 = R.hom([a])###line 1258:_sage_ >>> f1 = R.hom([a]) |

1728 | Expecting nothing |

1729 | ok |

1730 | Trying: |

1731 | f2 = R.hom([a + a**Integer(2) + a + Integer(1)])###line 1259:_sage_ >>> f2 = R.hom([a + a^2 + a + 1]) |

1732 | Expecting nothing |

1733 | ok |

1734 | Trying: |

1735 | PR = R['s, t']; (s, t,) = PR._first_ngens(2)###line 1260:_sage_ >>> PR.<s,t> = R[] |

1736 | Expecting nothing |

1737 | ok |

1738 | Trying: |

1739 | PQ = Q['s','t']###line 1261:_sage_ >>> PQ = Q['s','t'] |

1740 | Expecting nothing |

1741 | ok |

1742 | Trying: |

1743 | f1P = PR.hom(f1,PQ)###line 1262:_sage_ >>> f1P = PR.hom(f1,PQ) |

1744 | Expecting nothing |

1745 | ok |

1746 | Trying: |

1747 | f2P = PR.hom(f2,PQ)###line 1263:_sage_ >>> f2P = PR.hom(f2,PQ) |

1748 | Expecting nothing |

1749 | ok |

1750 | Trying: |

1751 | f1P == f2P###line 1264:_sage_ >>> f1P == f2P |

1752 | Expecting: |

1753 | True |

1754 | ok |

1755 | Trying: |

1756 | f1P == loads(dumps(f1P))###line 1269:_sage_ >>> f1P == loads(dumps(f1P)) |

1757 | Expecting: |

1758 | True |

1759 | ok |

1760 | Trying: |

1761 | R = GF(Integer(7))['x, y']; (x, y,) = R._first_ngens(2)###line 1278:_sage_ >>> R.<x,y> = GF(7)[] |

1762 | Expecting nothing |

1763 | ok |

1764 | Trying: |

1765 | Q = R.quotient([x**Integer(2) + x + Integer(1), y**Integer(2) + y + Integer(1)], names=('a', 'b',)); (a, b,) = Q._first_ngens(2)###line 1279:_sage_ >>> Q.<a,b> = R.quotient([x^2 + x + 1, y^2 + y + 1]) |

1766 | Expecting nothing |

1767 | ok |

1768 | Trying: |

1769 | f1 = R.hom([a, b])###line 1280:_sage_ >>> f1 = R.hom([a, b]) |

1770 | Expecting nothing |

1771 | ok |

1772 | Trying: |

1773 | f2 = R.hom([a + a**Integer(2) + a + Integer(1), b + b**Integer(2) + b + Integer(1)])###line 1281:_sage_ >>> f2 = R.hom([a + a^2 + a + 1, b + b^2 + b + 1]) |

1774 | Expecting nothing |

1775 | ok |

1776 | Trying: |

1777 | MR = MatrixSpace(R,Integer(2))###line 1282:_sage_ >>> MR = MatrixSpace(R,2) |

1778 | Expecting nothing |

1779 | ok |

1780 | Trying: |

1781 | MQ = MatrixSpace(Q,Integer(2))###line 1283:_sage_ >>> MQ = MatrixSpace(Q,2) |

1782 | Expecting nothing |

1783 | ok |

1784 | Trying: |

1785 | f1M = MR.hom(f1,MQ)###line 1284:_sage_ >>> f1M = MR.hom(f1,MQ) |

1786 | Expecting nothing |

1787 | ok |

1788 | Trying: |

1789 | f2M = MR.hom(f2,MQ)###line 1285:_sage_ >>> f2M = MR.hom(f2,MQ) |

1790 | Expecting nothing |

1791 | ok |

1792 | Trying: |

1793 | f1M == f2M###line 1286:_sage_ >>> f1M == f2M |

1794 | Expecting: |

1795 | True |

1796 | ok |

1797 | Trying: |

1798 | f1M == loads(dumps(f1M))###line 1291:_sage_ >>> f1M == loads(dumps(f1M)) |

1799 | Expecting: |

1800 | True |

1801 | ok |

1802 | Trying: |

1803 | sig_on_count() |

1804 | Expecting: |

1805 | 0 |

1806 | ok |

1807 | Trying: |

1808 | set_random_seed(0L) |

1809 | Expecting nothing |

1810 | ok |

1811 | Trying: |

1812 | change_warning_output(sys.stdout) |

1813 | Expecting nothing |

1814 | ok |

1815 | Trying: |

1816 | R1 = ZZ['x, y']; (x, y,) = R1._first_ngens(2)###line 1310:_sage_ >>> R1.<x,y> = ZZ[] |

1817 | Expecting nothing |

1818 | ok |

1819 | Trying: |

1820 | f = R1.hom([x+y,x-y])###line 1311:_sage_ >>> f = R1.hom([x+y,x-y]) |

1821 | Expecting nothing |

1822 | ok |

1823 | Trying: |

1824 | R2 = MatrixSpace(FractionField(R1)['t'],Integer(2))###line 1312:_sage_ >>> R2 = MatrixSpace(FractionField(R1)['t'],2) |

1825 | Expecting nothing |

1826 | ok |

1827 | Trying: |

1828 | g = R2.hom(f,R2)###line 1313:_sage_ >>> g = R2.hom(f,R2) |

1829 | Expecting nothing |

1830 | ok |

1831 | Trying: |

1832 | g #indirect doctest###line 1314:_sage_ >>> g #indirect doctest |

1833 | Expecting: |

1834 | Ring endomorphism of Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in t over Fraction Field of Multivariate Polynomial Ring in x, y over Integer Ring |

1835 | Defn: Induced from base ring by |

1836 | Ring endomorphism of Univariate Polynomial Ring in t over Fraction Field of Multivariate Polynomial Ring in x, y over Integer Ring |

1837 | Defn: Induced from base ring by |

1838 | Ring endomorphism of Fraction Field of Multivariate Polynomial Ring in x, y over Integer Ring |

1839 | Defn: x |--> x + y |

1840 | y |--> x - y |

1841 | ok |

1842 | Trying: |

1843 | sig_on_count() |

1844 | Expecting: |

1845 | 0 |

1846 | ok |

1847 | Trying: |

1848 | set_random_seed(0L) |

1849 | Expecting nothing |

1850 | ok |

1851 | Trying: |

1852 | change_warning_output(sys.stdout) |

1853 | Expecting nothing |

1854 | ok |

1855 | Trying: |

1856 | sig_on_count() |

1857 | Expecting: |

1858 | 0 |

1859 | ok |

1860 | Trying: |

1861 | set_random_seed(0L) |

1862 | Expecting nothing |

1863 | ok |

1864 | Trying: |

1865 | change_warning_output(sys.stdout) |

1866 | Expecting nothing |

1867 | ok |

1868 | Trying: |

1869 | R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 1354:_sage_ >>> R.<x,y> = PolynomialRing(QQ, 2) |

1870 | Expecting nothing |

1871 | ok |

1872 | Trying: |

1873 | S = R.quo(x**Integer(2) + y**Integer(2), names=('a', 'b',)); (a, b,) = S._first_ngens(2)###line 1355:_sage_ >>> S.<a,b> = R.quo(x^2 + y^2) |

1874 | Expecting nothing |

1875 | ok |

1876 | Trying: |

1877 | phi = S.cover(); phi###line 1356:_sage_ >>> phi = S.cover(); phi |

1878 | Expecting: |

1879 | Ring morphism: |

1880 | From: Multivariate Polynomial Ring in x, y over Rational Field |

1881 | To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2) |

1882 | Defn: Natural quotient map |

1883 | ok |

1884 | Trying: |

1885 | phi(x+y)###line 1361:_sage_ >>> phi(x+y) |

1886 | Expecting: |

1887 | a + b |

1888 | ok |

1889 | Trying: |

1890 | sig_on_count() |

1891 | Expecting: |

1892 | 0 |

1893 | ok |

1894 | Trying: |

1895 | set_random_seed(0L) |

1896 | Expecting nothing |

1897 | ok |

1898 | Trying: |

1899 | change_warning_output(sys.stdout) |

1900 | Expecting nothing |

1901 | ok |

1902 | Trying: |

1903 | f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))###line 426:_sage_ >>> f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ)) |

1904 | Expecting nothing |

1905 | ok |

1906 | Trying: |

1907 | type(f)###line 427:_sage_ >>> type(f) |

1908 | Expecting: |

1909 | <type 'sage.rings.morphism.RingMap'> |

1910 | ok |

1911 | Trying: |

1912 | f._repr_type()###line 429:_sage_ >>> f._repr_type() |

1913 | Expecting: |

1914 | 'Set-theoretic ring' |

1915 | ok |

1916 | Trying: |

1917 | f###line 431:_sage_ >>> f |

1918 | Expecting: |

1919 | Set-theoretic ring endomorphism of Integer Ring |

1920 | ok |

1921 | Trying: |

1922 | sig_on_count() |

1923 | Expecting: |

1924 | 0 |

1925 | ok |

1926 | Trying: |

1927 | set_random_seed(0L) |

1928 | Expecting nothing |

1929 | ok |

1930 | Trying: |

1931 | change_warning_output(sys.stdout) |

1932 | Expecting nothing |

1933 | ok |

1934 | Trying: |

1935 | f = Zmod(Integer(6)).cover(); f # implicit test###line 1370:_sage_ >>> f = Zmod(6).cover(); f # implicit test |

1936 | Expecting: |

1937 | Ring morphism: |

1938 | From: Integer Ring |

1939 | To: Ring of integers modulo 6 |

1940 | Defn: Natural quotient map |

1941 | ok |

1942 | Trying: |

1943 | type(f)###line 1375:_sage_ >>> type(f) |

1944 | Expecting: |

1945 | <type 'sage.rings.morphism.RingHomomorphism_cover'> |

1946 | ok |

1947 | Trying: |

1948 | sig_on_count() |

1949 | Expecting: |

1950 | 0 |

1951 | ok |

1952 | Trying: |

1953 | set_random_seed(0L) |

1954 | Expecting nothing |

1955 | ok |

1956 | Trying: |

1957 | change_warning_output(sys.stdout) |

1958 | Expecting nothing |

1959 | ok |

1960 | Trying: |

1961 | f = Zmod(Integer(6)).cover()###line 1387:_sage_ >>> f = Zmod(6).cover() |

1962 | Expecting nothing |

1963 | ok |

1964 | Trying: |

1965 | type(f)###line 1388:_sage_ >>> type(f) |

1966 | Expecting: |

1967 | <type 'sage.rings.morphism.RingHomomorphism_cover'> |

1968 | ok |

1969 | Trying: |

1970 | f(-Integer(5)) # indirect doctest###line 1390:_sage_ >>> f(-5) # indirect doctest |

1971 | Expecting: |

1972 | 1 |

1973 | ok |

1974 | Trying: |

1975 | f._call_(Integer(1)/Integer(2))###line 1400:_sage_ >>> f._call_(1/2) |

1976 | Expecting: |

1977 | Traceback (most recent call last): |

1978 | ... |

1979 | ZeroDivisionError: Inverse does not exist. |

1980 | ok |

1981 | Trying: |

1982 | f(Integer(1)/Integer(2))###line 1404:_sage_ >>> f(1/2) |

1983 | Expecting: |

1984 | Traceback (most recent call last): |

1985 | ... |

1986 | TypeError: 1/2 fails to convert into the map's domain Integer Ring, but a `pushforward` method is not properly implemented |

1987 | ok |

1988 | Trying: |

1989 | sig_on_count() |

1990 | Expecting: |

1991 | 0 |

1992 | ok |

1993 | Trying: |

1994 | set_random_seed(0L) |

1995 | Expecting nothing |

1996 | ok |

1997 | Trying: |

1998 | change_warning_output(sys.stdout) |

1999 | Expecting nothing |

2000 | ok |

2001 | Trying: |

2002 | f = Zmod(Integer(6)).cover()###line 1417:_sage_ >>> f = Zmod(6).cover() |

2003 | Expecting nothing |

2004 | ok |

2005 | Trying: |

2006 | f._repr_defn()###line 1418:_sage_ >>> f._repr_defn() |

2007 | Expecting: |

2008 | 'Natural quotient map' |

2009 | ok |

2010 | Trying: |

2011 | type(f)###line 1420:_sage_ >>> type(f) |

2012 | Expecting: |

2013 | <type 'sage.rings.morphism.RingHomomorphism_cover'> |

2014 | ok |

2015 | Trying: |

2016 | sig_on_count() |

2017 | Expecting: |

2018 | 0 |

2019 | ok |

2020 | Trying: |

2021 | set_random_seed(0L) |

2022 | Expecting nothing |

2023 | ok |

2024 | Trying: |

2025 | change_warning_output(sys.stdout) |

2026 | Expecting nothing |

2027 | ok |

2028 | Trying: |

2029 | f = Zmod(Integer(6)).cover()###line 1432:_sage_ >>> f = Zmod(6).cover() |

2030 | Expecting nothing |

2031 | ok |

2032 | Trying: |

2033 | f.kernel()###line 1433:_sage_ >>> f.kernel() |

2034 | Expecting: |

2035 | Principal ideal (6) of Integer Ring |

2036 | ok |

2037 | Trying: |

2038 | sig_on_count() |

2039 | Expecting: |

2040 | 0 |

2041 | ok |

2042 | Trying: |

2043 | set_random_seed(0L) |

2044 | Expecting nothing |

2045 | ok |

2046 | Trying: |

2047 | change_warning_output(sys.stdout) |

2048 | Expecting nothing |

2049 | ok |

2050 | Trying: |

2051 | R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 1442:_sage_ >>> R.<x,y> = PolynomialRing(QQ, 2) |

2052 | Expecting nothing |

2053 | ok |

2054 | Trying: |

2055 | S = R.quo(x**Integer(2) + y**Integer(2), names=('a', 'b',)); (a, b,) = S._first_ngens(2)###line 1443:_sage_ >>> S.<a,b> = R.quo(x^2 + y^2) |

2056 | Expecting nothing |

2057 | ok |

2058 | Trying: |

2059 | phi = S.cover()###line 1444:_sage_ >>> phi = S.cover() |

2060 | Expecting nothing |

2061 | ok |

2062 | Trying: |

2063 | phi == loads(dumps(phi))###line 1445:_sage_ >>> phi == loads(dumps(phi)) |

2064 | Expecting: |

2065 | True |

2066 | ok |

2067 | Trying: |

2068 | phi == R.quo(x**Integer(2) + y**Integer(3)).cover()###line 1447:_sage_ >>> phi == R.quo(x^2 + y^3).cover() |

2069 | Expecting: |

2070 | False |

2071 | ok |

2072 | Trying: |

2073 | sig_on_count() |

2074 | Expecting: |

2075 | 0 |

2076 | ok |

2077 | Trying: |

2078 | set_random_seed(0L) |

2079 | Expecting nothing |

2080 | ok |

2081 | Trying: |

2082 | change_warning_output(sys.stdout) |

2083 | Expecting nothing |

2084 | ok |

2085 | Trying: |

2086 | R = PolynomialRing(QQ, Integer(3), names=('x', 'y', 'z',)); (x, y, z,) = R._first_ngens(3)###line 1478:_sage_ >>> R.<x, y, z> = PolynomialRing(QQ, 3) |

2087 | Expecting nothing |

2088 | ok |

2089 | Trying: |

2090 | S = R.quo(x**Integer(3) + y**Integer(3) + z**Integer(3), names=('a', 'b', 'c',)); (a, b, c,) = S._first_ngens(3)###line 1479:_sage_ >>> S.<a, b, c> = R.quo(x^3 + y^3 + z^3) |

2091 | Expecting nothing |

2092 | ok |

2093 | Trying: |

2094 | phi = S.hom([b, c, a]); phi###line 1480:_sage_ >>> phi = S.hom([b, c, a]); phi |

2095 | Expecting: |

2096 | Ring endomorphism of Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (x^3 + y^3 + z^3) |

2097 | Defn: a |--> b |

2098 | b |--> c |

2099 | c |--> a |

2100 | ok |

2101 | Trying: |

2102 | phi(a+b+c)###line 1485:_sage_ >>> phi(a+b+c) |

2103 | Expecting: |

2104 | a + b + c |

2105 | ok |

2106 | Trying: |

2107 | loads(dumps(phi)) == phi###line 1487:_sage_ >>> loads(dumps(phi)) == phi |

2108 | Expecting: |

2109 | True |

2110 | ok |

2111 | Trying: |

2112 | S.hom([b**Integer(2), c**Integer(2), a**Integer(2)])###line 1496:_sage_ >>> S.hom([b^2, c^2, a^2]) |

2113 | Expecting: |

2114 | Traceback (most recent call last): |

2115 | ... |

2116 | TypeError: images do not define a valid homomorphism |

2117 | ok |

2118 | Trying: |

2119 | sig_on_count() |

2120 | Expecting: |

2121 | 0 |

2122 | ok |

2123 | Trying: |

2124 | set_random_seed(0L) |

2125 | Expecting nothing |

2126 | ok |

2127 | Trying: |

2128 | change_warning_output(sys.stdout) |

2129 | Expecting nothing |

2130 | ok |

2131 | Trying: |

2132 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2); S.hom([yy,xx])###line 1505:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]); S.hom([yy,xx]) |

2133 | Expecting: |

2134 | Ring endomorphism of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y^2) |

2135 | Defn: xx |--> yy |

2136 | yy |--> xx |

2137 | ok |

2138 | Trying: |

2139 | sig_on_count() |

2140 | Expecting: |

2141 | 0 |

2142 | ok |

2143 | Trying: |

2144 | set_random_seed(0L) |

2145 | Expecting nothing |

2146 | ok |

2147 | Trying: |

2148 | change_warning_output(sys.stdout) |

2149 | Expecting nothing |

2150 | ok |

2151 | Trying: |

2152 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2); f = S.hom([yy,xx])###line 1540:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]); f = S.hom([yy,xx]) |

2153 | Expecting nothing |

2154 | ok |

2155 | Trying: |

2156 | f._phi()###line 1541:_sage_ >>> f._phi() |

2157 | Expecting: |

2158 | Ring morphism: |

2159 | From: Multivariate Polynomial Ring in x, y over Rational Field |

2160 | To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y^2) |

2161 | Defn: x |--> yy |

2162 | y |--> xx |

2163 | ok |

2164 | Trying: |

2165 | sig_on_count() |

2166 | Expecting: |

2167 | 0 |

2168 | ok |

2169 | Trying: |

2170 | set_random_seed(0L) |

2171 | Expecting nothing |

2172 | ok |

2173 | Trying: |

2174 | change_warning_output(sys.stdout) |

2175 | Expecting nothing |

2176 | ok |

2177 | Trying: |

2178 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2)###line 1557:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]) |

2179 | Expecting nothing |

2180 | ok |

2181 | Trying: |

2182 | S.hom([yy,xx]).morphism_from_cover()###line 1558:_sage_ >>> S.hom([yy,xx]).morphism_from_cover() |

2183 | Expecting: |

2184 | Ring morphism: |

2185 | From: Multivariate Polynomial Ring in x, y over Rational Field |

2186 | To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y^2) |

2187 | Defn: x |--> yy |

2188 | y |--> xx |

2189 | ok |

2190 | Trying: |

2191 | sig_on_count() |

2192 | Expecting: |

2193 | 0 |

2194 | ok |

2195 | Trying: |

2196 | set_random_seed(0L) |

2197 | Expecting nothing |

2198 | ok |

2199 | Trying: |

2200 | change_warning_output(sys.stdout) |

2201 | Expecting nothing |

2202 | ok |

2203 | Trying: |

2204 | R = PolynomialRing(GF(Integer(19)), Integer(3), names=('x', 'y', 'z',)); (x, y, z,) = R._first_ngens(3)###line 1571:_sage_ >>> R.<x, y, z> = PolynomialRing(GF(19), 3) |

2205 | Expecting nothing |

2206 | ok |

2207 | Trying: |

2208 | S = R.quo(x**Integer(3) + y**Integer(3) + z**Integer(3), names=('a', 'b', 'c',)); (a, b, c,) = S._first_ngens(3)###line 1572:_sage_ >>> S.<a, b, c> = R.quo(x^3 + y^3 + z^3) |

2209 | Expecting nothing |

2210 | ok |

2211 | Trying: |

2212 | phi = S.hom([b, c, a])###line 1573:_sage_ >>> phi = S.hom([b, c, a]) |

2213 | Expecting nothing |

2214 | ok |

2215 | Trying: |

2216 | psi = S.hom([c, b, a])###line 1574:_sage_ >>> psi = S.hom([c, b, a]) |

2217 | Expecting nothing |

2218 | ok |

2219 | Trying: |

2220 | f = S.hom([b, c, a + a**Integer(3) + b**Integer(3) + c**Integer(3)])###line 1575:_sage_ >>> f = S.hom([b, c, a + a^3 + b^3 + c^3]) |

2221 | Expecting nothing |

2222 | ok |

2223 | Trying: |

2224 | phi == psi###line 1576:_sage_ >>> phi == psi |

2225 | Expecting: |

2226 | False |

2227 | ok |

2228 | Trying: |

2229 | phi == f###line 1578:_sage_ >>> phi == f |

2230 | Expecting: |

2231 | True |

2232 | ok |

2233 | Trying: |

2234 | sig_on_count() |

2235 | Expecting: |

2236 | 0 |

2237 | ok |

2238 | Trying: |

2239 | set_random_seed(0L) |

2240 | Expecting nothing |

2241 | ok |

2242 | Trying: |

2243 | change_warning_output(sys.stdout) |

2244 | Expecting nothing |

2245 | ok |

2246 | Trying: |

2247 | R, (x,y) = PolynomialRing(QQ, Integer(2), 'xy').objgens()###line 446:_sage_ >>> R, (x,y) = PolynomialRing(QQ, 2, 'xy').objgens() |

2248 | Expecting nothing |

2249 | ok |

2250 | Trying: |

2251 | S = R.quo( (x**Integer(2) + y**Integer(2), y) , names=('xbar', 'ybar',)); (xbar, ybar,) = S._first_ngens(2)###line 447:_sage_ >>> S.<xbar,ybar> = R.quo( (x^2 + y^2, y) ) |

2252 | Expecting nothing |

2253 | ok |

2254 | Trying: |

2255 | S.lift()###line 448:_sage_ >>> S.lift() |

2256 | Expecting: |

2257 | Set-theoretic ring morphism: |

2258 | From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2, y) |

2259 | To: Multivariate Polynomial Ring in x, y over Rational Field |

2260 | Defn: Choice of lifting map |

2261 | ok |

2262 | Trying: |

2263 | S.lift() == Integer(0)###line 453:_sage_ >>> S.lift() == 0 |

2264 | Expecting: |

2265 | False |

2266 | ok |

2267 | Trying: |

2268 | sig_on_count() |

2269 | Expecting: |

2270 | 0 |

2271 | ok |

2272 | Trying: |

2273 | set_random_seed(0L) |

2274 | Expecting nothing |

2275 | ok |

2276 | Trying: |

2277 | change_warning_output(sys.stdout) |

2278 | Expecting nothing |

2279 | ok |

2280 | Trying: |

2281 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2); f = S.hom([yy,xx])###line 1591:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]); f = S.hom([yy,xx]) |

2282 | Expecting nothing |

2283 | ok |

2284 | Trying: |

2285 | print f._repr_defn()###line 1592:_sage_ >>> print f._repr_defn() |

2286 | Expecting: |

2287 | xx |--> yy |

2288 | yy |--> xx |

2289 | ok |

2290 | Trying: |

2291 | sig_on_count() |

2292 | Expecting: |

2293 | 0 |

2294 | ok |

2295 | Trying: |

2296 | set_random_seed(0L) |

2297 | Expecting nothing |

2298 | ok |

2299 | Trying: |

2300 | change_warning_output(sys.stdout) |

2301 | Expecting nothing |

2302 | ok |

2303 | Trying: |

2304 | R = QQ['x, y']; (x, y,) = R._first_ngens(2); S = R.quo([x**Integer(2),y**Integer(2)], names=('xx', 'yy',)); (xx, yy,) = S._first_ngens(2); f = S.hom([yy,xx])###line 1607:_sage_ >>> R.<x,y> = QQ[]; S.<xx,yy> = R.quo([x^2,y^2]); f = S.hom([yy,xx]) |

2305 | Expecting nothing |

2306 | ok |

2307 | Trying: |

2308 | f(Integer(3)*x + (Integer(1)/Integer(2))*y) # indirect doctest###line 1608:_sage_ >>> f(3*x + (1/2)*y) # indirect doctest |

2309 | Expecting: |

2310 | 1/2*xx + 3*yy |

2311 | ok |

2312 | Trying: |

2313 | sig_on_count() |

2314 | Expecting: |

2315 | 0 |

2316 | ok |

2317 | Trying: |

2318 | set_random_seed(0L) |

2319 | Expecting nothing |

2320 | ok |

2321 | Trying: |

2322 | change_warning_output(sys.stdout) |

2323 | Expecting nothing |

2324 | ok |

2325 | Trying: |

2326 | f = Zmod(Integer(8)).lift() # indirect doctest###line 462:_sage_ >>> f = Zmod(8).lift() # indirect doctest |

2327 | Expecting nothing |

2328 | ok |

2329 | Trying: |

2330 | f(Integer(3))###line 463:_sage_ >>> f(3) |

2331 | Expecting: |

2332 | 3 |

2333 | ok |

2334 | Trying: |

2335 | type(f(Integer(3)))###line 465:_sage_ >>> type(f(3)) |

2336 | Expecting: |

2337 | <type 'sage.rings.integer.Integer'> |

2338 | ok |

2339 | Trying: |

2340 | type(f)###line 467:_sage_ >>> type(f) |

2341 | Expecting: |

2342 | <type 'sage.rings.morphism.RingMap_lift'> |

2343 | ok |

2344 | Trying: |

2345 | sig_on_count() |

2346 | Expecting: |

2347 | 0 |

2348 | ok |

2349 | Trying: |

2350 | set_random_seed(0L) |

2351 | Expecting nothing |

2352 | ok |

2353 | Trying: |

2354 | change_warning_output(sys.stdout) |

2355 | Expecting nothing |

2356 | ok |

2357 | Trying: |

2358 | f = Zmod(Integer(8)).lift()###line 495:_sage_ >>> f = Zmod(8).lift() |

2359 | Expecting nothing |

2360 | ok |

2361 | Trying: |

2362 | g = Zmod(Integer(10)).lift()###line 496:_sage_ >>> g = Zmod(10).lift() |

2363 | Expecting nothing |

2364 | ok |

2365 | Trying: |

2366 | f == f###line 497:_sage_ >>> f == f |

2367 | Expecting: |

2368 | True |

2369 | ok |

2370 | Trying: |

2371 | f == g###line 499:_sage_ >>> f == g |

2372 | Expecting: |

2373 | False |

2374 | ok |

2375 | Trying: |

2376 | f < g###line 501:_sage_ >>> f < g |

2377 | Expecting: |

2378 | True |

2379 | ok |

2380 | Trying: |

2381 | f > g###line 503:_sage_ >>> f > g |

2382 | Expecting: |

2383 | False |

2384 | ok |

2385 | Trying: |

2386 | Zmod(Integer(8)).lift() == Integer(1)###line 508:_sage_ >>> Zmod(8).lift() == 1 |

2387 | Expecting: |

2388 | False |

2389 | ok |

2390 | Trying: |

2391 | sig_on_count() |

2392 | Expecting: |

2393 | 0 |

2394 | ok |

2395 | Trying: |

2396 | set_random_seed(0L) |

2397 | Expecting nothing |

2398 | ok |

2399 | Trying: |

2400 | change_warning_output(sys.stdout) |

2401 | Expecting nothing |

2402 | ok |

2403 | Trying: |

2404 | f = Zmod(Integer(8)).lift()###line 525:_sage_ >>> f = Zmod(8).lift() |

2405 | Expecting nothing |

2406 | ok |

2407 | Trying: |

2408 | f._repr_defn()###line 526:_sage_ >>> f._repr_defn() |

2409 | Expecting: |

2410 | 'Choice of lifting map' |

2411 | ok |

2412 | Trying: |

2413 | f###line 528:_sage_ >>> f |

2414 | Expecting: |

2415 | Set-theoretic ring morphism: |

2416 | From: Ring of integers modulo 8 |

2417 | To: Integer Ring |

2418 | Defn: Choice of lifting map |

2419 | ok |

2420 | Trying: |

2421 | sig_on_count() |

2422 | Expecting: |

2423 | 0 |

2424 | ok |

2425 | Trying: |

2426 | set_random_seed(0L) |

2427 | Expecting nothing |

2428 | ok |

2429 | Trying: |

2430 | change_warning_output(sys.stdout) |

2431 | Expecting nothing |

2432 | ok |

2433 | Trying: |

2434 | f = Zmod(Integer(8)).lift()###line 542:_sage_ >>> f = Zmod(8).lift() |

2435 | Expecting nothing |

2436 | ok |

2437 | Trying: |

2438 | type(f)###line 543:_sage_ >>> type(f) |

2439 | Expecting: |

2440 | <type 'sage.rings.morphism.RingMap_lift'> |

2441 | ok |

2442 | Trying: |

2443 | f(-Integer(1)) # indirect doctest###line 545:_sage_ >>> f(-1) # indirect doctest |

2444 | Expecting: |

2445 | 7 |

2446 | ok |

2447 | Trying: |

2448 | type(f(-Integer(1)))###line 547:_sage_ >>> type(f(-1)) |

2449 | Expecting: |

2450 | <type 'sage.rings.integer.Integer'> |

2451 | ok |

2452 | Trying: |

2453 | sig_on_count() |

2454 | Expecting: |

2455 | 0 |

2456 | ok |

2457 | 3 items had no tests: |

2458 | __main__ |

2459 | __main__.change_warning_output |

2460 | __main__.warning_function |

2461 | 52 items passed all tests: |

2462 | 120 tests in __main__.example_0 |

2463 | 6 tests in __main__.example_1 |

2464 | 3 tests in __main__.example_10 |

2465 | 5 tests in __main__.example_11 |

2466 | 8 tests in __main__.example_12 |

2467 | 6 tests in __main__.example_13 |

2468 | 6 tests in __main__.example_14 |

2469 | 11 tests in __main__.example_15 |

2470 | 5 tests in __main__.example_16 |

2471 | 14 tests in __main__.example_17 |

2472 | 5 tests in __main__.example_18 |

2473 | 5 tests in __main__.example_19 |

2474 | 3 tests in __main__.example_2 |

2475 | 11 tests in __main__.example_20 |

2476 | 5 tests in __main__.example_21 |

2477 | 6 tests in __main__.example_22 |

2478 | 10 tests in __main__.example_23 |

2479 | 6 tests in __main__.example_24 |

2480 | 3 tests in __main__.example_25 |

2481 | 10 tests in __main__.example_26 |

2482 | 8 tests in __main__.example_27 |

2483 | 6 tests in __main__.example_28 |

2484 | 22 tests in __main__.example_29 |

2485 | 5 tests in __main__.example_3 |

2486 | 5 tests in __main__.example_30 |

2487 | 5 tests in __main__.example_31 |

2488 | 23 tests in __main__.example_32 |

2489 | 11 tests in __main__.example_33 |

2490 | 10 tests in __main__.example_34 |

2491 | 8 tests in __main__.example_35 |

2492 | 23 tests in __main__.example_36 |

2493 | 8 tests in __main__.example_37 |

2494 | 3 tests in __main__.example_38 |

2495 | 7 tests in __main__.example_39 |

2496 | 7 tests in __main__.example_4 |

2497 | 5 tests in __main__.example_40 |

2498 | 8 tests in __main__.example_41 |

2499 | 6 tests in __main__.example_42 |

2500 | 5 tests in __main__.example_43 |

2501 | 8 tests in __main__.example_44 |

2502 | 9 tests in __main__.example_45 |

2503 | 4 tests in __main__.example_46 |

2504 | 5 tests in __main__.example_47 |

2505 | 5 tests in __main__.example_48 |

2506 | 10 tests in __main__.example_49 |

2507 | 7 tests in __main__.example_5 |

2508 | 5 tests in __main__.example_50 |

2509 | 5 tests in __main__.example_51 |

2510 | 7 tests in __main__.example_6 |

2511 | 10 tests in __main__.example_7 |

2512 | 6 tests in __main__.example_8 |

2513 | 7 tests in __main__.example_9 |

2514 | 511 tests in 55 items. |

2515 | 511 passed and 0 failed. |

2516 | Test passed. |

2517 | Segmentation fault |

2518 | [8.6 s] |

2519 | |

2520 | ---------------------------------------------------------------------- |

2521 | The following tests failed: |

2522 | |

2523 | |

2524 | sage -t -long -verbose "devel/sage/sage/rings/morphism.pyx" |

2525 | Total time for all tests: 8.6 seconds |

2526 | sage -t -long -verbose "devel/sage/sage/rings/homset.py" |

2527 | Trying: |

2528 | set_random_seed(0L) |

2529 | Expecting nothing |

2530 | ok |

2531 | Trying: |

2532 | change_warning_output(sys.stdout) |

2533 | Expecting nothing |

2534 | ok |

2535 | Trying: |

2536 | sig_on_count() |

2537 | Expecting: |

2538 | 0 |

2539 | ok |

2540 | Trying: |

2541 | set_random_seed(0L) |

2542 | Expecting nothing |

2543 | ok |

2544 | Trying: |

2545 | change_warning_output(sys.stdout) |

2546 | Expecting nothing |

2547 | ok |

2548 | Trying: |

2549 | sig_on_count() |

2550 | Expecting: |

2551 | 0 |

2552 | ok |

2553 | Trying: |

2554 | set_random_seed(0L) |

2555 | Expecting nothing |

2556 | ok |

2557 | Trying: |

2558 | change_warning_output(sys.stdout) |

2559 | Expecting nothing |

2560 | ok |

2561 | Trying: |

2562 | H = Hom(ZZ, QQ)###line 82:_sage_ >>> H = Hom(ZZ, QQ) |

2563 | Expecting nothing |

2564 | ok |

2565 | Trying: |

2566 | phi = H([])###line 83:_sage_ >>> phi = H([]) |

2567 | Expecting: |

2568 | Traceback (most recent call last): |

2569 | ... |

2570 | TypeError: images do not define a valid homomorphism |

2571 | ok |

2572 | Trying: |

2573 | H = Hom(ZZ, QQ)###line 90:_sage_ >>> H = Hom(ZZ, QQ) |

2574 | Expecting nothing |

2575 | ok |

2576 | Trying: |

2577 | H == loads(dumps(H))###line 91:_sage_ >>> H == loads(dumps(H)) |

2578 | Expecting: |

2579 | True |

2580 | ok |

2581 | Trying: |

2582 | sig_on_count() |

2583 | Expecting: |

2584 | 0 |

2585 | ok |

2586 | Trying: |

2587 | set_random_seed(0L) |

2588 | Expecting nothing |

2589 | ok |

2590 | Trying: |

2591 | change_warning_output(sys.stdout) |

2592 | Expecting nothing |

2593 | ok |

2594 | Trying: |

2595 | R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 116:_sage_ >>> R.<x,y> = PolynomialRing(QQ, 2) |

2596 | Expecting nothing |

2597 | ok |

2598 | Trying: |

2599 | S = R.quotient(x**Integer(2) + y**Integer(2), names=('a', 'b',)); (a, b,) = S._first_ngens(2)###line 117:_sage_ >>> S.<a,b> = R.quotient(x^2 + y^2) |

2600 | Expecting nothing |

2601 | ok |

2602 | Trying: |

2603 | phi = S.hom([b,a]); phi###line 118:_sage_ >>> phi = S.hom([b,a]); phi |

2604 | Expecting: |

2605 | Ring endomorphism of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2) |

2606 | Defn: a |--> b |

2607 | b |--> a |

2608 | ok |

2609 | Trying: |

2610 | phi(a)###line 122:_sage_ >>> phi(a) |

2611 | Expecting: |

2612 | b |

2613 | ok |

2614 | Trying: |

2615 | phi(b)###line 124:_sage_ >>> phi(b) |

2616 | Expecting: |

2617 | a |

2618 | ok |

2619 | Trying: |

2620 | R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 133:_sage_ >>> R.<x,y> = PolynomialRing(QQ, 2) |

2621 | Expecting nothing |

2622 | ok |

2623 | Trying: |

2624 | S = R.quotient(x**Integer(2) + y**Integer(2), names=('a', 'b',)); (a, b,) = S._first_ngens(2)###line 134:_sage_ >>> S.<a,b> = R.quotient(x^2 + y^2) |

2625 | Expecting nothing |

2626 | ok |

2627 | Trying: |

2628 | H = S.Hom(R)###line 135:_sage_ >>> H = S.Hom(R) |

2629 | Expecting nothing |

2630 | ok |

2631 | Trying: |

2632 | H == loads(dumps(H))###line 136:_sage_ >>> H == loads(dumps(H)) |

2633 | Expecting: |

2634 | True |

2635 | ok |

2636 | Trying: |

2637 | phi = S.hom([b,a])###line 141:_sage_ >>> phi = S.hom([b,a]) |

2638 | Expecting nothing |

2639 | ok |

2640 | Trying: |

2641 | phi == loads(dumps(phi))###line 142:_sage_ >>> phi == loads(dumps(phi)) |

2642 | Expecting: |

2643 | True |

2644 | ok |

2645 | Trying: |

2646 | sig_on_count() |

2647 | Expecting: |

2648 | 0 |

2649 | ok |

2650 | Segmentation fault |

2651 | [4.8 s] |

2652 | |

2653 | ---------------------------------------------------------------------- |

2654 | The following tests failed: |

2655 | |

2656 | |

2657 | sage -t -long -verbose "devel/sage/sage/rings/homset.py" |

2658 | Total time for all tests: 4.9 seconds |

2659 | |

2660 | sage -t -long -verbose "devel/sage/sage/schemes/generic/scheme.py" |

2661 | Trying: |

2662 | set_random_seed(0L) |

2663 | Expecting nothing |

2664 | ok |

2665 | Trying: |

2666 | change_warning_output(sys.stdout) |

2667 | Expecting nothing |

2668 | ok |

2669 | Trying: |

2670 | sig_on_count() |

2671 | Expecting: |

2672 | 0 |

2673 | ok |

2674 | Trying: |

2675 | set_random_seed(0L) |

2676 | Expecting nothing |

2677 | ok |

2678 | Trying: |

2679 | change_warning_output(sys.stdout) |

2680 | Expecting nothing |

2681 | ok |

2682 | Trying: |

2683 | from sage.schemes.generic.scheme import is_Scheme###line 39:_sage_ >>> from sage.schemes.generic.scheme import is_Scheme |

2684 | Expecting nothing |

2685 | ok |

2686 | Trying: |

2687 | is_Scheme(Integer(5))###line 40:_sage_ >>> is_Scheme(5) |

2688 | Expecting: |

2689 | False |

2690 | ok |

2691 | Trying: |

2692 | X = Spec(QQ)###line 42:_sage_ >>> X = Spec(QQ) |

2693 | Expecting nothing |

2694 | ok |

2695 | Trying: |

2696 | is_Scheme(X)###line 43:_sage_ >>> is_Scheme(X) |

2697 | Expecting: |

2698 | True |

2699 | ok |

2700 | Trying: |

2701 | sig_on_count() |

2702 | Expecting: |

2703 | 0 |

2704 | ok |

2705 | Trying: |

2706 | set_random_seed(0L) |

2707 | Expecting nothing |

2708 | ok |

2709 | Trying: |

2710 | change_warning_output(sys.stdout) |

2711 | Expecting nothing |

2712 | ok |

2713 | Trying: |

2714 | X = Spec(QQ)###line 274:_sage_ >>> X = Spec(QQ) |

2715 | Expecting nothing |

2716 | ok |

2717 | Trying: |

2718 | X._homset_class()###line 275:_sage_ >>> X._homset_class() |

2719 | Expecting: |

2720 | Traceback (most recent call last): |

2721 | ... |

2722 | NotImplementedError |

2723 | ok |

2724 | Trying: |

2725 | sig_on_count() |

2726 | Expecting: |

2727 | 0 |

2728 | ok |

2729 | Trying: |

2730 | set_random_seed(0L) |

2731 | Expecting nothing |

2732 | ok |

2733 | Trying: |

2734 | change_warning_output(sys.stdout) |

2735 | Expecting nothing |

2736 | ok |

2737 | Trying: |

2738 | A = AffineSpace(Integer(3), ZZ)###line 289:_sage_ >>> A = AffineSpace(3, ZZ) |

2739 | Expecting nothing |

2740 | ok |

2741 | Trying: |

2742 | A###line 290:_sage_ >>> A |

2743 | Expecting: |

2744 | Affine Space of dimension 3 over Integer Ring |

2745 | ok |

2746 | Trying: |

2747 | A/QQ###line 292:_sage_ >>> A/QQ |

2748 | Expecting: |

2749 | Affine Space of dimension 3 over Rational Field |

2750 | ok |

2751 | Trying: |

2752 | A/GF(Integer(7))###line 294:_sage_ >>> A/GF(7) |

2753 | Expecting: |

2754 | Affine Space of dimension 3 over Finite Field of size 7 |

2755 | ok |

2756 | Trying: |

2757 | sig_on_count() |

2758 | Expecting: |

2759 | 0 |

2760 | ok |

2761 | Trying: |

2762 | set_random_seed(0L) |

2763 | Expecting nothing |

2764 | ok |

2765 | Trying: |

2766 | change_warning_output(sys.stdout) |

2767 | Expecting nothing |

2768 | ok |

2769 | Trying: |

2770 | A = AffineSpace(Integer(4), QQ)###line 305:_sage_ >>> A = AffineSpace(4, QQ) |

2771 | Expecting nothing |

2772 | ok |

2773 | Trying: |

2774 | A.base_ring()###line 306:_sage_ >>> A.base_ring() |

2775 | Expecting: |

2776 | Rational Field |

2777 | ok |

2778 | Trying: |

2779 | X = Spec(QQ)###line 311:_sage_ >>> X = Spec(QQ) |

2780 | Expecting nothing |

2781 | ok |

2782 | Trying: |

2783 | X.base_ring()###line 312:_sage_ >>> X.base_ring() |

2784 | Expecting: |

2785 | Integer Ring |

2786 | ok |

2787 | Trying: |

2788 | sig_on_count() |

2789 | Expecting: |

2790 | 0 |

2791 | ok |

2792 | Trying: |

2793 | set_random_seed(0L) |

2794 | Expecting nothing |

2795 | ok |

2796 | Trying: |

2797 | change_warning_output(sys.stdout) |

2798 | Expecting nothing |

2799 | ok |

2800 | Trying: |

2801 | A = AffineSpace(Integer(4), QQ)###line 332:_sage_ >>> A = AffineSpace(4, QQ) |

2802 | Expecting nothing |

2803 | ok |

2804 | Trying: |

2805 | A.base_scheme()###line 333:_sage_ >>> A.base_scheme() |

2806 | Expecting: |

2807 | Spectrum of Rational Field |

2808 | ok |

2809 | Trying: |

2810 | X = Spec(QQ)###line 338:_sage_ >>> X = Spec(QQ) |

2811 | Expecting nothing |

2812 | ok |

2813 | Trying: |

2814 | X.base_scheme()###line 339:_sage_ >>> X.base_scheme() |

2815 | Expecting: |

2816 | Spectrum of Integer Ring |

2817 | ok |

2818 | Trying: |

2819 | sig_on_count() |

2820 | Expecting: |

2821 | 0 |

2822 | ok |

2823 | Trying: |

2824 | set_random_seed(0L) |

2825 | Expecting nothing |

2826 | ok |

2827 | Trying: |

2828 | change_warning_output(sys.stdout) |

2829 | Expecting nothing |

2830 | ok |

2831 | Trying: |

2832 | A = AffineSpace(Integer(4), QQ)###line 362:_sage_ >>> A = AffineSpace(4, QQ) |

2833 | Expecting nothing |

2834 | ok |

2835 | Trying: |

2836 | A.base_morphism()###line 363:_sage_ >>> A.base_morphism() |

2837 | Expecting: |

2838 | Scheme morphism: |

2839 | From: Affine Space of dimension 4 over Rational Field |

2840 | To: Spectrum of Rational Field |

2841 | Defn: Structure map |

2842 | ok |

2843 | Trying: |

2844 | X = Spec(QQ)###line 371:_sage_ >>> X = Spec(QQ) |

2845 | Expecting nothing |

2846 | ok |

2847 | Trying: |

2848 | X.base_morphism()###line 372:_sage_ >>> X.base_morphism() |

2849 | Expecting: |

2850 | Scheme morphism: |

2851 | From: Spectrum of Rational Field |

2852 | To: Spectrum of Integer Ring |

2853 | Defn: Structure map |

2854 | ok |

2855 | Trying: |

2856 | sig_on_count() |

2857 | Expecting: |

2858 | 0 |

2859 | ok |

2860 | Trying: |

2861 | set_random_seed(0L) |

2862 | Expecting nothing |

2863 | ok |

2864 | Trying: |

2865 | change_warning_output(sys.stdout) |

2866 | Expecting nothing |

2867 | ok |

2868 | Trying: |

2869 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 400:_sage_ >>> R.<x, y> = QQ[] |

2870 | Expecting nothing |

2871 | ok |

2872 | Trying: |

2873 | I = (x**Integer(2) - y**Integer(2))*R###line 401:_sage_ >>> I = (x^2 - y^2)*R |

2874 | Expecting nothing |

2875 | ok |

2876 | Trying: |

2877 | X = Spec(R.quotient(I))###line 402:_sage_ >>> X = Spec(R.quotient(I)) |

2878 | Expecting nothing |

2879 | ok |

2880 | Trying: |

2881 | X.coordinate_ring()###line 403:_sage_ >>> X.coordinate_ring() |

2882 | Expecting: |

2883 | Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 - y^2) |

2884 | ok |

2885 | Trying: |

2886 | sig_on_count() |

2887 | Expecting: |

2888 | 0 |

2889 | ok |

2890 | Trying: |

2891 | set_random_seed(0L) |

2892 | Expecting nothing |

2893 | ok |

2894 | Trying: |

2895 | change_warning_output(sys.stdout) |

2896 | Expecting nothing |

2897 | ok |

2898 | Trying: |

2899 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 417:_sage_ >>> R.<x, y> = QQ[] |

2900 | Expecting nothing |

2901 | ok |

2902 | Trying: |

2903 | I = (x**Integer(2) - y**Integer(2))*R###line 418:_sage_ >>> I = (x^2 - y^2)*R |

2904 | Expecting nothing |

2905 | ok |

2906 | Trying: |

2907 | X = Spec(R.quotient(I))###line 419:_sage_ >>> X = Spec(R.quotient(I)) |

2908 | Expecting nothing |

2909 | ok |

2910 | Trying: |

2911 | X.dimension_absolute()###line 420:_sage_ >>> X.dimension_absolute() |

2912 | Expecting: |

2913 | Traceback (most recent call last): |

2914 | ... |

2915 | NotImplementedError |

2916 | ok |

2917 | Trying: |

2918 | X.dimension()###line 424:_sage_ >>> X.dimension() |

2919 | Expecting: |

2920 | Traceback (most recent call last): |

2921 | ... |

2922 | NotImplementedError |

2923 | ok |

2924 | Trying: |

2925 | sig_on_count() |

2926 | Expecting: |

2927 | 0 |

2928 | ok |

2929 | Trying: |

2930 | set_random_seed(0L) |

2931 | Expecting nothing |

2932 | ok |

2933 | Trying: |

2934 | change_warning_output(sys.stdout) |

2935 | Expecting nothing |

2936 | ok |

2937 | Trying: |

2938 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 439:_sage_ >>> R.<x, y> = QQ[] |

2939 | Expecting nothing |

2940 | ok |

2941 | Trying: |

2942 | I = (x**Integer(2) - y**Integer(2))*R###line 440:_sage_ >>> I = (x^2 - y^2)*R |

2943 | Expecting nothing |

2944 | ok |

2945 | Trying: |

2946 | X = Spec(R.quotient(I))###line 441:_sage_ >>> X = Spec(R.quotient(I)) |

2947 | Expecting nothing |

2948 | ok |

2949 | Trying: |

2950 | X.dimension_relative()###line 442:_sage_ >>> X.dimension_relative() |

2951 | Expecting: |

2952 | Traceback (most recent call last): |

2953 | ... |

2954 | NotImplementedError |

2955 | ok |

2956 | Trying: |

2957 | sig_on_count() |

2958 | Expecting: |

2959 | 0 |

2960 | ok |

2961 | Trying: |

2962 | set_random_seed(0L) |

2963 | Expecting nothing |

2964 | ok |

2965 | Trying: |

2966 | change_warning_output(sys.stdout) |

2967 | Expecting nothing |

2968 | ok |

2969 | Trying: |

2970 | X = Spec(QQ)###line 455:_sage_ >>> X = Spec(QQ) |

2971 | Expecting nothing |

2972 | ok |

2973 | Trying: |

2974 | X.identity_morphism()###line 456:_sage_ >>> X.identity_morphism() |

2975 | Expecting: |

2976 | Scheme endomorphism of Spectrum of Rational Field |

2977 | Defn: Identity map |

2978 | ok |

2979 | Trying: |

2980 | sig_on_count() |

2981 | Expecting: |

2982 | 0 |

2983 | ok |

2984 | Trying: |

2985 | set_random_seed(0L) |

2986 | Expecting nothing |

2987 | ok |

2988 | Trying: |

2989 | change_warning_output(sys.stdout) |

2990 | Expecting nothing |

2991 | ok |

2992 | Trying: |

2993 | P = ProjectiveSpace(ZZ, Integer(3))###line 471:_sage_ >>> P = ProjectiveSpace(ZZ, 3) |

2994 | Expecting nothing |

2995 | ok |

2996 | Trying: |

2997 | P.hom(Spec(ZZ))###line 472:_sage_ >>> P.hom(Spec(ZZ)) |

2998 | Expecting: |

2999 | Scheme morphism: |

3000 | From: Projective Space of dimension 3 over Integer Ring |

3001 | To: Spectrum of Integer Ring |

3002 | Defn: Structure map |

3003 | ok |

3004 | Trying: |

3005 | sig_on_count() |

3006 | Expecting: |

3007 | 0 |

3008 | ok |

3009 | Trying: |

3010 | set_random_seed(0L) |

3011 | Expecting nothing |

3012 | ok |

3013 | Trying: |

3014 | change_warning_output(sys.stdout) |

3015 | Expecting nothing |

3016 | ok |

3017 | Trying: |

3018 | R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 59:_sage_ >>> R.<x, y> = QQ[] |

3019 | Expecting nothing |

3020 | ok |

3021 | Trying: |

3022 | I = (x**Integer(2) - y**Integer(2))*R###line 60:_sage_ >>> I = (x^2 - y^2)*R |

3023 | Expecting nothing |

3024 | ok |

3025 | Trying: |

3026 | RmodI = R.quotient(I)###line 61:_sage_ >>> RmodI = R.quotient(I) |

3027 | Expecting nothing |

3028 | ok |

3029 | Trying: |

3030 | X = Spec(RmodI)###line 62:_sage_ >>> X = Spec(RmodI) |

3031 | Expecting nothing |

3032 | ok |

3033 | Trying: |

3034 | TestSuite(X).run(skip = ["_test_an_element", "_test_elements", "_test_some_elements", "_test_category"]) # See #7946###line 63:_sage_ >>> TestSuite(X).run(skip = ["_test_an_element", "_test_elements", "_test_some_elements", "_test_category"]) # See #7946 |

3035 | Expecting nothing |

3036 | ok |

3037 | Trying: |

3038 | ProjectiveSpace(Integer(4), QQ).category()###line 67:_sage_ >>> ProjectiveSpace(4, QQ).category() |

3039 | Expecting: |

3040 | Category of schemes over Spectrum of Rational Field |

3041 | ok |

3042 | Trying: |

3043 | sig_on_count() |

3044 | Expecting: |

3045 | 0 |

3046 | ok |

3047 | Trying: |

3048 | set_random_seed(0L) |

3049 | Expecting nothing |

3050 | ok |

3051 | Trying: |

3052 | change_warning_output(sys.stdout) |

3053 | Expecting nothing |

3054 | ok |

3055 | Trying: |

3056 | P = ProjectiveSpace(ZZ, Integer(3))###line 491:_sage_ >>> P = ProjectiveSpace(ZZ, 3) |

3057 | Expecting nothing |

3058 | ok |

3059 | Trying: |

3060 | S = Spec(ZZ)###line 492:_sage_ >>> S = Spec(ZZ) |

3061 | Expecting nothing |

3062 | ok |

3063 | Trying: |

3064 | S._Hom_(P)###line 493:_sage_ >>> S._Hom_(P) |

3065 | Expecting: |

3066 | Set of points of Projective Space of dimension 3 over Integer Ring defined over Integer Ring |

3067 | ok |

3068 | Trying: |

3069 | sig_on_count() |

3070 | Expecting: |

3071 | 0 |

3072 | ok |

3073 | /home/leif/Sage/sage-4.7.2.alpha2-gcc-4.5.1/local/lib/libcsage.so(print_backtrace+0x3b)[0xb736f2db] |

3074 | /home/leif/Sage/sage-4.7.2.alpha2-gcc-4.5.1/local/lib/libcsage.so(sigdie+0x17)[0xb736f31b] |

3075 | /home/leif/Sage/sage-4.7.2.alpha2-gcc-4.5.1/local/lib/libcsage.so(sage_signal_handler+0x21b)[0xb736ee92] |

3076 | [0xb784c400] |

3077 | |

3078 | ------------------------------------------------------------------------ |

3079 | Unhandled SIGSEGV: A segmentation fault occurred in Sage. |

3080 | This probably occurred because a *compiled* component of Sage has a bug |

3081 | in it and is not properly wrapped with sig_on(), sig_off(). You might |

3082 | want to run Sage under gdb with 'sage -gdb' to debug this. |

3083 | Sage will now terminate. |

3084 | ------------------------------------------------------------------------ |

3085 | Segmentation fault |

3086 | [5.0 s] |

3087 | |

3088 | ---------------------------------------------------------------------- |

3089 | The following tests failed: |

3090 | |

3091 | |

3092 | sage -t -long -verbose "devel/sage/sage/schemes/generic/scheme.py" |

3093 | Total time for all tests: 5.1 seconds |