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 leif, 10 years ago)

Pentium4 Prescott (SSE3 / PNI, 32-bit), GCC 4.5.1, native code, -mfpmath=sse, Ubuntu 9.04 x86 (The three segfaulting files tested in verbose mode.)

Line 
1sage -t -long -verbose "devel/sage/sage/rings/morphism.pyx"
2Trying:
3    set_random_seed(0L)
4Expecting nothing
5ok
6Trying:
7    change_warning_output(sys.stdout)
8Expecting nothing
9ok
10Trying:
11    H = Hom(ZZ, QQ)###line 11:_sage_    >>> H = Hom(ZZ, QQ)
12Expecting nothing
13ok
14Trying:
15    phi = H([Integer(1)])###line 12:_sage_    >>> phi = H([1])
16Expecting nothing
17ok
18Trying:
19    phi(Integer(10))###line 13:_sage_    >>> phi(10)
20Expecting:
21    10
22ok
23Trying:
24    phi(Integer(3)/Integer(1))###line 15:_sage_    >>> phi(3/1)
25Expecting:
26    3
27ok
28Trying:
29    phi(Integer(2)/Integer(3))###line 17:_sage_    >>> phi(2/3)
30Expecting:
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
34ok
35Trying:
36    H = Hom(QQ, ZZ)###line 24:_sage_    >>> H = Hom(QQ, ZZ)
37Expecting nothing
38ok
39Trying:
40    H([Integer(1)])###line 25:_sage_    >>> H([1])
41Expecting:
42    Traceback (most recent call last):
43    ...
44    TypeError: images do not define a valid homomorphism
45ok
46Trying:
47    H = Hom(ZZ, GF(Integer(9), 'a'))###line 34:_sage_    >>> H = Hom(ZZ, GF(9, 'a'))
48Expecting nothing
49ok
50Trying:
51    phi = H([Integer(1)])###line 35:_sage_    >>> phi = H([1])
52Expecting nothing
53ok
54Trying:
55    phi(Integer(5))###line 36:_sage_    >>> phi(5)
56Expecting:
57    2
58ok
59Trying:
60    psi = H([Integer(4)])###line 38:_sage_    >>> psi = H([4])
61Expecting nothing
62ok
63Trying:
64    psi(Integer(5))###line 39:_sage_    >>> psi(5)
65Expecting:
66    2
67ok
68Trying:
69    R, x = PolynomialRing(ZZ, 'x').objgen()###line 46:_sage_    >>> R, x = PolynomialRing(ZZ, 'x').objgen()
70Expecting nothing
71ok
72Trying:
73    phi = R.hom([Integer(2)], GF(Integer(5)))###line 47:_sage_    >>> phi = R.hom([2], GF(5))
74Expecting nothing
75ok
76Trying:
77    phi###line 48:_sage_    >>> phi
78Expecting:
79    Ring morphism:
80      From: Univariate Polynomial Ring in x over Integer Ring
81      To:   Finite Field of size 5
82      Defn: x |--> 2
83ok
84Trying:
85    phi(x + Integer(12))###line 53:_sage_    >>> phi(x + 12)
86Expecting:
87    4
88ok
89Trying:
90    f = RR.hom([RR(Integer(1))]); f###line 60:_sage_    >>> f = RR.hom([RR(1)]); f
91Expecting:
92    Ring endomorphism of Real Field with 53 bits of precision
93      Defn: 1.00000000000000 |--> 1.00000000000000
94ok
95Trying:
96    f(RealNumber('2.5'))###line 63:_sage_    >>> f(2.5)
97Expecting:
98    2.50000000000000
99ok
100Trying:
101    f = RR.hom( [RealNumber('2.0')] )###line 65:_sage_    >>> f = RR.hom( [2.0] )
102Expecting:
103    Traceback (most recent call last):
104    ...
105    TypeError: images do not define a valid homomorphism
106ok
107Trying:
108    R200 = RealField(Integer(200))###line 74:_sage_    >>> R200 = RealField(200)
109Expecting nothing
110ok
111Trying:
112    f = RR.hom( R200 )###line 75:_sage_    >>> f = RR.hom( R200 )
113Expecting:
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.
117ok
118Trying:
119    f = RR.hom( RealField(Integer(15)) )###line 82:_sage_    >>> f = RR.hom( RealField(15) )
120Expecting nothing
121ok
122Trying:
123    f(RealNumber('2.5'))###line 83:_sage_    >>> f(2.5)
124Expecting:
125    2.500
126ok
127Trying:
128    f(RR.pi())###line 85:_sage_    >>> f(RR.pi())
129Expecting:
130    3.142
131ok
132Trying:
133    i = RR.hom([CC(Integer(1))]); i###line 90:_sage_    >>> i = RR.hom([CC(1)]); i
134Expecting:
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
139ok
140Trying:
141    i(RR('3.1'))###line 95:_sage_    >>> i(RR('3.1'))
142Expecting:
143    3.10000000000000
144ok
145Trying:
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)
147Expecting nothing
148ok
149Trying:
150    phi = R.hom([y,z,x**Integer(2)]); phi###line 101:_sage_    >>> phi = R.hom([y,z,x^2]); phi
151Expecting:
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
156ok
157Trying:
158    phi(x+y+z)###line 106:_sage_    >>> phi(x+y+z)
159Expecting:
160    x^2 + y + z
161ok
162Trying:
163    R = PolynomialRing(QQ, names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 112:_sage_    >>> R.<x,y> = PolynomialRing(QQ)
164Expecting nothing
165ok
166Trying:
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))
168Expecting nothing
169ok
170Trying:
171    phi = S.hom([a**Integer(2), -b])###line 114:_sage_    >>> phi = S.hom([a^2, -b])
172Expecting nothing
173ok
174Trying:
175    phi###line 115:_sage_    >>> phi
176Expecting:
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
180ok
181Trying:
182    phi(b)###line 119:_sage_    >>> phi(b)
183Expecting:
184    -b
185ok
186Trying:
187    phi(a**Integer(2) + b**Integer(2))###line 121:_sage_    >>> phi(a^2 + b^2)
188Expecting:
189    a^4 - 1
190ok
191Trying:
192    R = ZZ.quo(Integer(8)*ZZ)###line 127:_sage_    >>> R = ZZ.quo(8*ZZ)
193Expecting nothing
194ok
195Trying:
196    pi = R.cover()###line 128:_sage_    >>> pi = R.cover()
197Expecting nothing
198ok
199Trying:
200    pi###line 129:_sage_    >>> pi
201Expecting:
202    Ring morphism:
203      From: Integer Ring
204      To:   Ring of integers modulo 8
205      Defn: Natural quotient map
206ok
207Trying:
208    pi.domain()###line 134:_sage_    >>> pi.domain()
209Expecting:
210    Integer Ring
211ok
212Trying:
213    pi.codomain()###line 136:_sage_    >>> pi.codomain()
214Expecting:
215    Ring of integers modulo 8
216ok
217Trying:
218    pi(Integer(10))###line 138:_sage_    >>> pi(10)
219Expecting:
220    2
221ok
222Trying:
223    pi.lift()###line 140:_sage_    >>> pi.lift()
224Expecting:
225    Set-theoretic ring morphism:
226      From: Ring of integers modulo 8
227      To:   Integer Ring
228      Defn: Choice of lifting map
229ok
230Trying:
231    pi.lift(Integer(13))###line 145:_sage_    >>> pi.lift(13)
232Expecting:
233    5
234ok
235Trying:
236    k = GF(Integer(2))###line 152:_sage_    >>> k = GF(2)
237Expecting nothing
238ok
239Trying:
240    i = k.hom(GF(Integer(4), 'a'))###line 153:_sage_    >>> i = k.hom(GF(4, 'a'))
241Expecting nothing
242ok
243Trying:
244    i###line 154:_sage_    >>> i
245Expecting:
246    Ring Coercion morphism:
247      From: Finite Field of size 2
248      To:   Finite Field in a of size 2^2
249ok
250Trying:
251    i(Integer(0))###line 158:_sage_    >>> i(0)
252Expecting:
253    0
254ok
255Trying:
256    a = i(Integer(1)); a.parent()###line 160:_sage_    >>> a = i(1); a.parent()
257Expecting:
258    Finite Field in a of size 2^2
259ok
260Trying:
261    pi = ZZ.hom(k)###line 168:_sage_    >>> pi = ZZ.hom(k)
262Expecting nothing
263ok
264Trying:
265    pi###line 169:_sage_    >>> pi
266Expecting:
267    Ring Coercion morphism:
268      From: Integer Ring
269      To:   Finite Field of size 2
270ok
271Trying:
272    f = i * pi###line 173:_sage_    >>> f = i * pi
273Expecting nothing
274ok
275Trying:
276    f###line 174:_sage_    >>> f
277Expecting:
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
288ok
289Trying:
290    a = f(Integer(5)); a###line 185:_sage_    >>> a = f(5); a
291Expecting:
292    1
293ok
294Trying:
295    a.parent()###line 187:_sage_    >>> a.parent()
296Expecting:
297    Finite Field in a of size 2^2
298ok
299Trying:
300    phi = QQ.hom(Qp(Integer(3), print_mode = 'series'))###line 194:_sage_    >>> phi = QQ.hom(Qp(3, print_mode = 'series'))
301Expecting nothing
302ok
303Trying:
304    phi###line 195:_sage_    >>> phi
305Expecting:
306    Ring Coercion morphism:
307      From: Rational Field
308      To:   3-adic Field with capped relative precision 20
309ok
310Trying:
311    phi.codomain()###line 199:_sage_    >>> phi.codomain()
312Expecting:
313    3-adic Field with capped relative precision 20
314ok
315Trying:
316    phi(Integer(394))###line 201:_sage_    >>> phi(394)
317Expecting:
318    1 + 2*3 + 3^2 + 2*3^3 + 3^4 + 3^5 + O(3^20)
319ok
320Trying:
321    R = PolynomialRing(QQ, names=('x',)); (x,) = R._first_ngens(1)###line 209:_sage_    >>> R.<x> = PolynomialRing(QQ)
322Expecting nothing
323ok
324Trying:
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)
326Expecting nothing
327ok
328Trying:
329    sqrt2**Integer(2)###line 211:_sage_    >>> sqrt2^2
330Expecting:
331    2
332ok
333Trying:
334    (Integer(3)+sqrt2)**Integer(10)###line 213:_sage_    >>> (3+sqrt2)^10
335Expecting:
336    993054*sqrt2 + 1404491
337ok
338Trying:
339    c = S.hom([-sqrt2])###line 215:_sage_    >>> c = S.hom([-sqrt2])
340Expecting nothing
341ok
342Trying:
343    c(Integer(1)+sqrt2)###line 216:_sage_    >>> c(1+sqrt2)
344Expecting:
345    -sqrt2 + 1
346ok
347Trying:
348    (Integer(1) - sqrt2)**Integer(2)###line 221:_sage_    >>> (1 - sqrt2)^2
349Expecting:
350    -2*sqrt2 + 3
351ok
352Trying:
353    c = S.hom([Integer(1)-sqrt2])    # this is not valid###line 223:_sage_    >>> c = S.hom([1-sqrt2])    # this is not valid
354Expecting:
355    Traceback (most recent call last):
356    ...
357    TypeError: images do not define a valid homomorphism
358ok
359Trying:
360    R = PowerSeriesRing(QQ, names=('t',)); (t,) = R._first_ngens(1); R###line 232:_sage_    >>> R.<t> = PowerSeriesRing(QQ); R
361Expecting:
362    Power Series Ring in t over Rational Field
363ok
364Trying:
365    f = R.hom([t**Integer(2)]); f###line 234:_sage_    >>> f = R.hom([t^2]); f
366Expecting:
367    Ring endomorphism of Power Series Ring in t over Rational Field
368      Defn: t |--> t^2
369ok
370Trying:
371    R.set_default_prec(Integer(10))###line 237:_sage_    >>> R.set_default_prec(10)
372Expecting nothing
373ok
374Trying:
375    s = Integer(1)/(Integer(1) + t); s###line 238:_sage_    >>> s = 1/(1 + t); s
376Expecting:
377    1 - t + t^2 - t^3 + t^4 - t^5 + t^6 - t^7 + t^8 - t^9 + O(t^10)
378ok
379Trying:
380    f(s)###line 240:_sage_    >>> f(s)
381Expecting:
382    1 - t^2 + t^4 - t^6 + t^8 - t^10 + t^12 - t^14 + t^16 - t^18 + O(t^20)
383ok
384Trying:
385    R = PowerSeriesRing(GF(Integer(5)), names=('t',)); (t,) = R._first_ngens(1)###line 247:_sage_    >>> R.<t> = PowerSeriesRing(GF(5))
386Expecting nothing
387ok
388Trying:
389    f = R.hom([t**Integer(5)]); f###line 248:_sage_    >>> f = R.hom([t^5]); f
390Expecting:
391    Ring endomorphism of Power Series Ring in t over Finite Field of size 5
392      Defn: t |--> t^5
393ok
394Trying:
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)
396Expecting nothing
397ok
398Trying:
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)
400Expecting nothing
401ok
402Trying:
403    f(a)###line 253:_sage_    >>> f(a)
404Expecting:
405    2 + t^5 + 3*t^10 + 4*t^15 + O(t^20)
406ok
407Trying:
408    f(b)###line 255:_sage_    >>> f(b)
409Expecting:
410    1 + t^5 + 2*t^10 + t^15 + O(t^25)
411ok
412Trying:
413    f(a*b)###line 257:_sage_    >>> f(a*b)
414Expecting:
415    2 + 3*t^5 + 3*t^10 + t^15 + O(t^20)
416ok
417Trying:
418    f(a)*f(b)###line 259:_sage_    >>> f(a)*f(b)
419Expecting:
420    2 + 3*t^5 + 3*t^10 + t^15 + O(t^20)
421ok
422Trying:
423    R = LaurentSeriesRing(QQ, names=('t',)); (t,) = R._first_ngens(1)###line 266:_sage_    >>> R.<t> = LaurentSeriesRing(QQ)
424Expecting nothing
425ok
426Trying:
427    f = R.hom([t**Integer(3) + t]); f###line 267:_sage_    >>> f = R.hom([t^3 + t]); f
428Expecting:
429    Ring endomorphism of Laurent Series Ring in t over Rational Field
430      Defn: t |--> t + t^3
431ok
432Trying:
433    R.set_default_prec(Integer(10))###line 270:_sage_    >>> R.set_default_prec(10)
434Expecting nothing
435ok
436Trying:
437    s = Integer(2)/t**Integer(2) + Integer(1)/(Integer(1) + t); s###line 271:_sage_    >>> s = 2/t^2 + 1/(1 + t); s
438Expecting:
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)
440ok
441Trying:
442    f(s)###line 273:_sage_    >>> f(s)
443Expecting:
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)
445ok
446Trying:
447    f = R.hom([t**Integer(3)]); f###line 275:_sage_    >>> f = R.hom([t^3]); f
448Expecting:
449    Ring endomorphism of Laurent Series Ring in t over Rational Field
450      Defn: t |--> t^3
451ok
452Trying:
453    f(s)###line 278:_sage_    >>> f(s)
454Expecting:
455    2*t^-6 + 1 - t^3 + t^6 - t^9 + t^12 - t^15 + t^18 - t^21 + t^24 - t^27
456ok
457Trying:
458    s = Integer(2)/t**Integer(2) + Integer(1)/(Integer(1) + t); s###line 280:_sage_    >>> s = 2/t^2 + 1/(1 + t); s
459Expecting:
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)
461ok
462Trying:
463    f(s)###line 282:_sage_    >>> f(s)
464Expecting:
465    2*t^-6 + 1 - t^3 + t^6 - t^9 + t^12 - t^15 + t^18 - t^21 + t^24 - t^27
466ok
467Trying:
468    R.hom([Integer(1)/t])###line 289:_sage_    >>> R.hom([1/t])
469Expecting:
470    Traceback (most recent call last):
471    ...
472    TypeError: images do not define a valid homomorphism
473ok
474Trying:
475    R.hom([Integer(1)])###line 293:_sage_    >>> R.hom([1])
476Expecting:
477    Traceback (most recent call last):
478    ...
479    TypeError: images do not define a valid homomorphism
480ok
481Trying:
482    K = CyclotomicField(Integer(7), names=('zeta7',)); (zeta7,) = K._first_ngens(1)###line 302:_sage_    >>> K.<zeta7> = CyclotomicField(7)
483Expecting nothing
484ok
485Trying:
486    c = K.hom([Integer(1)/zeta7]); c###line 303:_sage_    >>> c = K.hom([1/zeta7]); c
487Expecting:
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
490ok
491Trying:
492    a = (Integer(1)+zeta7)**Integer(5); a###line 306:_sage_    >>> a = (1+zeta7)^5; a
493Expecting:
494    zeta7^5 + 5*zeta7^4 + 10*zeta7^3 + 10*zeta7^2 + 5*zeta7 + 1
495ok
496Trying:
497    c(a)###line 308:_sage_    >>> c(a)
498Expecting:
499    5*zeta7^5 + 5*zeta7^4 - 4*zeta7^2 - 5*zeta7 - 4
500ok
501Trying:
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
503Expecting:
504    -zeta7^5 - zeta7^4 - zeta7^3 - zeta7^2 - 1
505ok
506Trying:
507    zeta7 + Integer(1)/zeta7###line 312:_sage_    >>> zeta7 + 1/zeta7
508Expecting:
509    -zeta7^5 - zeta7^4 - zeta7^3 - zeta7^2 - 1
510ok
511Trying:
512    R = PolynomialRing(QQ, names=('x',)); (x,) = R._first_ngens(1)###line 319:_sage_    >>> R.<x> = PolynomialRing(QQ)
513Expecting nothing
514ok
515Trying:
516    K = NumberField(x**Integer(3) - Integer(2), names=('beta',)); (beta,) = K._first_ngens(1)###line 320:_sage_    >>> K.<beta> = NumberField(x^3 - 2)
517Expecting nothing
518ok
519Trying:
520    alpha = RR(Integer(2))**(Integer(1)/Integer(3)); alpha###line 321:_sage_    >>> alpha = RR(2)^(1/3); alpha
521Expecting:
522    1.25992104989487
523ok
524Trying:
525    i = K.hom([alpha],check=False); i###line 323:_sage_    >>> i = K.hom([alpha],check=False); i
526Expecting:
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
531ok
532Trying:
533    i(beta)###line 328:_sage_    >>> i(beta)
534Expecting:
535    1.25992104989487
536ok
537Trying:
538    i(beta**Integer(3))###line 330:_sage_    >>> i(beta^3)
539Expecting:
540    2.00000000000000
541ok
542Trying:
543    i(beta**Integer(2) + Integer(1))###line 332:_sage_    >>> i(beta^2 + 1)
544Expecting:
545    2.58740105196820
546ok
547Trying:
548    K = QQ # by the way :-)###line 337:_sage_    >>> K = QQ # by the way :-)
549Expecting nothing
550ok
551Trying:
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
553Expecting:
554    Multivariate Polynomial Ring in a, b, c, d over Rational Field
555ok
556Trying:
557    S = K['u']; (u,) = S._first_ngens(1); S###line 340:_sage_    >>> S.<u> = K[]; S
558Expecting:
559    Univariate Polynomial Ring in u over Rational Field
560ok
561Trying:
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
563Expecting:
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
571ok
572Trying:
573    f(a+b+c+d)###line 350:_sage_    >>> f(a+b+c+d)
574Expecting:
575    u
576ok
577Trying:
578    f( (a+b+c+d)**Integer(2) )###line 352:_sage_    >>> f( (a+b+c+d)^2 )
579Expecting:
580    u^2
581ok
582Trying:
583    H = Hom(ZZ, QQ)###line 357:_sage_    >>> H = Hom(ZZ, QQ)
584Expecting nothing
585ok
586Trying:
587    H == loads(dumps(H))###line 358:_sage_    >>> H == loads(dumps(H))
588Expecting:
589    True
590ok
591Trying:
592    K = CyclotomicField(Integer(7), names=('zeta7',)); (zeta7,) = K._first_ngens(1)###line 363:_sage_    >>> K.<zeta7> = CyclotomicField(7)
593Expecting nothing
594ok
595Trying:
596    c = K.hom([Integer(1)/zeta7])###line 364:_sage_    >>> c = K.hom([1/zeta7])
597Expecting nothing
598ok
599Trying:
600    c == loads(dumps(c))###line 365:_sage_    >>> c == loads(dumps(c))
601Expecting:
602    True
603ok
604Trying:
605    R = PowerSeriesRing(GF(Integer(5)), names=('t',)); (t,) = R._first_ngens(1)###line 370:_sage_    >>> R.<t> = PowerSeriesRing(GF(5))
606Expecting nothing
607ok
608Trying:
609    f = R.hom([t**Integer(5)])###line 371:_sage_    >>> f = R.hom([t^5])
610Expecting nothing
611ok
612Trying:
613    f == loads(dumps(f))###line 372:_sage_    >>> f == loads(dumps(f))
614Expecting:
615    True
616ok
617Trying:
618    sig_on_count()
619Expecting:
620    0
621ok
622Trying:
623    set_random_seed(0L)
624Expecting nothing
625ok
626Trying:
627    change_warning_output(sys.stdout)
628Expecting nothing
629ok
630Trying:
631    f = Zmod(Integer(8)).cover()###line 397:_sage_    >>> f = Zmod(8).cover()
632Expecting nothing
633ok
634Trying:
635    sage.rings.morphism.is_RingHomomorphism(f)###line 398:_sage_    >>> sage.rings.morphism.is_RingHomomorphism(f)
636Expecting:
637    True
638ok
639Trying:
640    sage.rings.morphism.is_RingHomomorphism(Integer(2)/Integer(3))###line 400:_sage_    >>> sage.rings.morphism.is_RingHomomorphism(2/3)
641Expecting:
642    False
643ok
644Trying:
645    sig_on_count()
646Expecting:
647    0
648ok
649Trying:
650    set_random_seed(0L)
651Expecting nothing
652ok
653Trying:
654    change_warning_output(sys.stdout)
655Expecting nothing
656ok
657Trying:
658    sig_on_count()
659Expecting:
660    0
661ok
662Trying:
663    set_random_seed(0L)
664Expecting nothing
665ok
666Trying:
667    change_warning_output(sys.stdout)
668Expecting nothing
669ok
670Trying:
671    f = ZZ.hom(Zmod(Integer(6))); f###line 560:_sage_    >>> f = ZZ.hom(Zmod(6)); f
672Expecting:
673    Ring Coercion morphism:
674      From: Integer Ring
675      To:   Ring of integers modulo 6
676ok
677Trying:
678    isinstance(f, sage.rings.morphism.RingHomomorphism)###line 564:_sage_    >>> isinstance(f, sage.rings.morphism.RingHomomorphism)
679Expecting:
680    True
681ok
682Trying:
683    sig_on_count()
684Expecting:
685    0
686ok
687Trying:
688    set_random_seed(0L)
689Expecting nothing
690ok
691Trying:
692    change_warning_output(sys.stdout)
693Expecting nothing
694ok
695Trying:
696    bool(ZZ.hom(QQ,[Integer(1)]))###line 581:_sage_    >>> bool(ZZ.hom(QQ,[1]))
697Expecting:
698    True
699ok
700Trying:
701    R1 = Zmod(Integer(1))###line 586:_sage_    >>> R1 = Zmod(1)
702Expecting nothing
703ok
704Trying:
705    phi = R1.hom(R1, [Integer(1)])###line 587:_sage_    >>> phi = R1.hom(R1, [1])
706Expecting nothing
707ok
708Trying:
709    bool(phi)###line 588:_sage_    >>> bool(phi)
710Expecting:
711    False
712ok
713Trying:
714    bool(ZZ.hom(R1, [Integer(1)]))###line 590:_sage_    >>> bool(ZZ.hom(R1, [1]))
715Expecting:
716    False
717ok
718Trying:
719    sig_on_count()
720Expecting:
721    0
722ok
723Trying:
724    set_random_seed(0L)
725Expecting nothing
726ok
727Trying:
728    change_warning_output(sys.stdout)
729Expecting nothing
730ok
731Trying:
732    phi = ZZ.hom(QQ,[Integer(1)])###line 605:_sage_    >>> phi = ZZ.hom(QQ,[1])
733Expecting nothing
734ok
735Trying:
736    phi._repr_type()###line 606:_sage_    >>> phi._repr_type()
737Expecting:
738    'Ring Coercion'
739ok
740Trying:
741    sage.rings.morphism.RingHomomorphism._repr_type(phi)###line 608:_sage_    >>> sage.rings.morphism.RingHomomorphism._repr_type(phi)
742Expecting:
743    'Ring'
744ok
745Trying:
746    sig_on_count()
747Expecting:
748    0
749ok
750Trying:
751    set_random_seed(0L)
752Expecting nothing
753ok
754Trying:
755    change_warning_output(sys.stdout)
756Expecting nothing
757ok
758Trying:
759    f = ZZ.hom(Zmod(Integer(7)))###line 628:_sage_    >>> f = ZZ.hom(Zmod(7))
760Expecting nothing
761ok
762Trying:
763    f._set_lift(Zmod(Integer(7)).lift())###line 629:_sage_    >>> f._set_lift(Zmod(7).lift())
764Expecting nothing
765ok
766Trying:
767    f.lift()###line 630:_sage_    >>> f.lift()
768Expecting:
769    Set-theoretic ring morphism:
770      From: Ring of integers modulo 7
771      To:   Integer Ring
772      Defn: Choice of lifting map
773ok
774Trying:
775    sig_on_count()
776Expecting:
777    0
778ok
779Trying:
780    set_random_seed(0L)
781Expecting nothing
782ok
783Trying:
784    change_warning_output(sys.stdout)
785Expecting nothing
786ok
787Trying:
788    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 665:_sage_    >>> R.<x,y> = QQ[]
789Expecting nothing
790ok
791Trying:
792    S = QQ['a, b']; (a, b,) = S._first_ngens(2)###line 666:_sage_    >>> S.<a,b> = QQ[]
793Expecting nothing
794ok
795Trying:
796    f = R.hom([a+b,a-b])###line 667:_sage_    >>> f = R.hom([a+b,a-b])
797Expecting nothing
798ok
799Trying:
800    g = S.hom(Frac(S))###line 668:_sage_    >>> g = S.hom(Frac(S))
801Expecting nothing
802ok
803Trying:
804    g*f###line 669:_sage_    >>> g*f
805Expecting:
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
811ok
812Trying:
813    from sage.categories.morphism import SetMorphism###line 675:_sage_    >>> from sage.categories.morphism import SetMorphism
814Expecting nothing
815ok
816Trying:
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])
818Expecting nothing
819ok
820Trying:
821    g*h###line 677:_sage_    >>> g*h
822Expecting:
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
833ok
834Trying:
835    sig_on_count()
836Expecting:
837    0
838ok
839Trying:
840    set_random_seed(0L)
841Expecting nothing
842ok
843Trying:
844    change_warning_output(sys.stdout)
845Expecting nothing
846ok
847Trying:
848    f = ZZ.hom(QQ)###line 712:_sage_    >>> f = ZZ.hom(QQ)
849Expecting nothing
850ok
851Trying:
852    f.is_injective()###line 713:_sage_    >>> f.is_injective()
853Expecting:
854    Traceback (most recent call last):
855    ...
856    NotImplementedError
857ok
858Trying:
859    sig_on_count()
860Expecting:
861    0
862ok
863Trying:
864    set_random_seed(0L)
865Expecting nothing
866ok
867Trying:
868    change_warning_output(sys.stdout)
869Expecting nothing
870ok
871Trying:
872    h = Hom(ZZ, QQ)###line 736:_sage_    >>> h = Hom(ZZ, QQ)
873Expecting nothing
874ok
875Trying:
876    f = h.natural_map()###line 737:_sage_    >>> f = h.natural_map()
877Expecting nothing
878ok
879Trying:
880    f.is_zero()###line 738:_sage_    >>> f.is_zero()
881Expecting:
882    False
883ok
884Trying:
885    R = Integers(Integer(1))###line 745:_sage_    >>> R = Integers(1)
886Expecting nothing
887ok
888Trying:
889    R###line 746:_sage_    >>> R
890Expecting:
891    Ring of integers modulo 1
892ok
893Trying:
894    h = Hom(ZZ, R)###line 748:_sage_    >>> h = Hom(ZZ, R)
895Expecting nothing
896ok
897Trying:
898    f = h.natural_map()###line 749:_sage_    >>> f = h.natural_map()
899Expecting nothing
900ok
901Trying:
902    f.is_zero()###line 750:_sage_    >>> f.is_zero()
903Expecting:
904    True
905ok
906Trying:
907    h = Hom(ZZ, GF(Integer(2)))###line 757:_sage_    >>> h = Hom(ZZ, GF(2))
908Expecting nothing
909ok
910Trying:
911    f = h.natural_map()###line 758:_sage_    >>> f = h.natural_map()
912Expecting nothing
913ok
914Trying:
915    f.is_zero()###line 759:_sage_    >>> f.is_zero()
916Expecting:
917    False
918ok
919Trying:
920    sig_on_count()
921Expecting:
922    0
923ok
924Trying:
925    set_random_seed(0L)
926Expecting nothing
927ok
928Trying:
929    change_warning_output(sys.stdout)
930Expecting nothing
931ok
932Trying:
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()
934Expecting nothing
935ok
936Trying:
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]))
938Expecting:
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)
940ok
941Trying:
942    sig_on_count()
943Expecting:
944    0
945ok
946Trying:
947    set_random_seed(0L)
948Expecting nothing
949ok
950Trying:
951    change_warning_output(sys.stdout)
952Expecting nothing
953ok
954Trying:
955    f = ZZ.hom(ZZ)###line 789:_sage_    >>> f = ZZ.hom(ZZ)
956Expecting nothing
957ok
958Trying:
959    f.inverse_image(ZZ.ideal(Integer(2)))###line 790:_sage_    >>> f.inverse_image(ZZ.ideal(2))
960Expecting:
961    Traceback (most recent call last):
962    ...
963    NotImplementedError
964ok
965Trying:
966    sig_on_count()
967Expecting:
968    0
969ok
970Trying:
971    set_random_seed(0L)
972Expecting nothing
973ok
974Trying:
975    change_warning_output(sys.stdout)
976Expecting nothing
977ok
978Trying:
979    sig_on_count()
980Expecting:
981    0
982ok
983Trying:
984    set_random_seed(0L)
985Expecting nothing
986ok
987Trying:
988    change_warning_output(sys.stdout)
989Expecting nothing
990ok
991Trying:
992    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 806:_sage_    >>> R.<x,y> = QQ[]
993Expecting nothing
994ok
995Trying:
996    f = R.hom([x,x])###line 807:_sage_    >>> f = R.hom([x,x])
997Expecting nothing
998ok
999Trying:
1000    f(x+y)###line 808:_sage_    >>> f(x+y)
1001Expecting:
1002    2*x
1003ok
1004Trying:
1005    f.lift()###line 810:_sage_    >>> f.lift()
1006Expecting:
1007    Traceback (most recent call last):
1008    ...
1009    ValueError: no lift map defined
1010ok
1011Trying:
1012    g = R.hom(R)###line 814:_sage_    >>> g = R.hom(R)
1013Expecting nothing
1014ok
1015Trying:
1016    f._set_lift(g)###line 815:_sage_    >>> f._set_lift(g)
1017Expecting nothing
1018ok
1019Trying:
1020    f.lift() == g###line 816:_sage_    >>> f.lift() == g
1021Expecting:
1022    True
1023ok
1024Trying:
1025    f.lift(x)###line 818:_sage_    >>> f.lift(x)
1026Expecting:
1027    x
1028ok
1029Trying:
1030    sig_on_count()
1031Expecting:
1032    0
1033ok
1034Trying:
1035    set_random_seed(0L)
1036Expecting nothing
1037ok
1038Trying:
1039    change_warning_output(sys.stdout)
1040Expecting nothing
1041ok
1042Trying:
1043    f = ZZ.hom(QQ); f                    # indirect doctest###line 836:_sage_    >>> f = ZZ.hom(QQ); f                    # indirect doctest
1044Expecting:
1045    Ring Coercion morphism:
1046      From: Integer Ring
1047      To:   Rational Field
1048ok
1049Trying:
1050    f == loads(dumps(f))###line 841:_sage_    >>> f == loads(dumps(f))
1051Expecting:
1052    True
1053ok
1054Trying:
1055    sig_on_count()
1056Expecting:
1057    0
1058ok
1059Trying:
1060    set_random_seed(0L)
1061Expecting nothing
1062ok
1063Trying:
1064    change_warning_output(sys.stdout)
1065Expecting nothing
1066ok
1067Trying:
1068    f = ZZ.hom(QQ)###line 855:_sage_    >>> f = ZZ.hom(QQ)
1069Expecting nothing
1070ok
1071Trying:
1072    type(f)###line 856:_sage_    >>> type(f)
1073Expecting:
1074    <type 'sage.rings.morphism.RingHomomorphism_coercion'>
1075ok
1076Trying:
1077    f._repr_type()###line 858:_sage_    >>> f._repr_type()
1078Expecting:
1079    'Ring Coercion'
1080ok
1081Trying:
1082    sig_on_count()
1083Expecting:
1084    0
1085ok
1086Trying:
1087    set_random_seed(0L)
1088Expecting nothing
1089ok
1090Trying:
1091    change_warning_output(sys.stdout)
1092Expecting nothing
1093ok
1094Trying:
1095    f = ZZ.hom(QQ)###line 872:_sage_    >>> f = ZZ.hom(QQ)
1096Expecting nothing
1097ok
1098Trying:
1099    g = ZZ.hom(ZZ)###line 873:_sage_    >>> g = ZZ.hom(ZZ)
1100Expecting nothing
1101ok
1102Trying:
1103    f == g###line 874:_sage_    >>> f == g
1104Expecting:
1105    False
1106ok
1107Trying:
1108    f > g###line 876:_sage_    >>> f > g
1109Expecting:
1110    True
1111ok
1112Trying:
1113    f < g###line 878:_sage_    >>> f < g
1114Expecting:
1115    False
1116ok
1117Trying:
1118    h = Zmod(Integer(6)).lift()###line 880:_sage_    >>> h = Zmod(6).lift()
1119Expecting nothing
1120ok
1121Trying:
1122    f == h###line 881:_sage_    >>> f == h
1123Expecting:
1124    False
1125ok
1126Trying:
1127    sig_on_count()
1128Expecting:
1129    0
1130ok
1131Trying:
1132    set_random_seed(0L)
1133Expecting nothing
1134ok
1135Trying:
1136    change_warning_output(sys.stdout)
1137Expecting nothing
1138ok
1139Trying:
1140    f = ZZ.hom(QQ); type(f)###line 898:_sage_    >>> f = ZZ.hom(QQ); type(f)
1141Expecting:
1142    <type 'sage.rings.morphism.RingHomomorphism_coercion'>
1143ok
1144Trying:
1145    f(Integer(2)) == Integer(2)###line 900:_sage_    >>> f(2) == 2
1146Expecting:
1147    True
1148ok
1149Trying:
1150    type(f(Integer(2)))          # indirect doctest###line 902:_sage_    >>> type(f(2))          # indirect doctest
1151Expecting:
1152    <type 'sage.rings.rational.Rational'>
1153ok
1154Trying:
1155    sig_on_count()
1156Expecting:
1157    0
1158ok
1159Trying:
1160    set_random_seed(0L)
1161Expecting nothing
1162ok
1163Trying:
1164    change_warning_output(sys.stdout)
1165Expecting nothing
1166ok
1167Trying:
1168    sig_on_count()
1169Expecting:
1170    0
1171ok
1172Trying:
1173    set_random_seed(0L)
1174Expecting nothing
1175ok
1176Trying:
1177    change_warning_output(sys.stdout)
1178Expecting nothing
1179ok
1180Trying:
1181    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 917:_sage_    >>> R.<x,y> = QQ[]
1182Expecting nothing
1183ok
1184Trying:
1185    phi = R.hom([x,x+y]); phi###line 918:_sage_    >>> phi = R.hom([x,x+y]); phi
1186Expecting:
1187    Ring endomorphism of Multivariate Polynomial Ring in x, y over Rational Field
1188      Defn: x |--> x
1189            y |--> x + y
1190ok
1191Trying:
1192    type(phi)###line 922:_sage_    >>> type(phi)
1193Expecting:
1194    <type 'sage.rings.morphism.RingHomomorphism_im_gens'>
1195ok
1196Trying:
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)
1198Expecting nothing
1199ok
1200Trying:
1201    phi = S.hom([xx+Integer(1),xx+Integer(1)])###line 928:_sage_    >>> phi = S.hom([xx+1,xx+1])
1202Expecting nothing
1203ok
1204Trying:
1205    phi = S.hom([xx+Integer(1),xx-Integer(1)])###line 932:_sage_    >>> phi = S.hom([xx+1,xx-1])
1206Expecting:
1207    Traceback (most recent call last):
1208    ...
1209    TypeError: images do not define a valid homomorphism
1210ok
1211Trying:
1212    phi = S.hom([xx+Integer(1),xx-Integer(1)],check=False)###line 941:_sage_    >>> phi = S.hom([xx+1,xx-1],check=False)
1213Expecting:
1214    Traceback (most recent call last):
1215    ...
1216    TypeError: images do not define a valid homomorphism
1217ok
1218Trying:
1219    sig_on_count()
1220Expecting:
1221    0
1222ok
1223Trying:
1224    set_random_seed(0L)
1225Expecting nothing
1226ok
1227Trying:
1228    change_warning_output(sys.stdout)
1229Expecting nothing
1230ok
1231Trying:
1232    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 968:_sage_    >>> R.<x,y> = QQ[]
1233Expecting nothing
1234ok
1235Trying:
1236    f = R.hom([x,x+y])###line 969:_sage_    >>> f = R.hom([x,x+y])
1237Expecting nothing
1238ok
1239Trying:
1240    f.im_gens()###line 970:_sage_    >>> f.im_gens()
1241Expecting:
1242    [x, x + y]
1243ok
1244Trying:
1245    f.im_gens()[Integer(0)] = Integer(5)###line 976:_sage_    >>> f.im_gens()[0] = 5
1246Expecting nothing
1247ok
1248Trying:
1249    f.im_gens()###line 977:_sage_    >>> f.im_gens()
1250Expecting:
1251    [x, x + y]
1252ok
1253Trying:
1254    sig_on_count()
1255Expecting:
1256    0
1257ok
1258Trying:
1259    set_random_seed(0L)
1260Expecting nothing
1261ok
1262Trying:
1263    change_warning_output(sys.stdout)
1264Expecting nothing
1265ok
1266Trying:
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])
1268Expecting nothing
1269ok
1270Trying:
1271    cmp(f,g)             # indirect doctest###line 997:_sage_    >>> cmp(f,g)             # indirect doctest
1272Expecting:
1273    1
1274ok
1275Trying:
1276    cmp(g,f)###line 999:_sage_    >>> cmp(g,f)
1277Expecting:
1278    -1
1279ok
1280Trying:
1281    sig_on_count()
1282Expecting:
1283    0
1284ok
1285Trying:
1286    set_random_seed(0L)
1287Expecting nothing
1288ok
1289Trying:
1290    change_warning_output(sys.stdout)
1291Expecting nothing
1292ok
1293Trying:
1294    R = QQ['x']; (x,) = R._first_ngens(1)###line 1013:_sage_    >>> R.<x> = QQ[]
1295Expecting nothing
1296ok
1297Trying:
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)
1299Expecting nothing
1300ok
1301Trying:
1302    f1 = R.hom([a])###line 1015:_sage_    >>> f1 = R.hom([a])
1303Expecting nothing
1304ok
1305Trying:
1306    f2 = R.hom([a + a**Integer(2) + a + Integer(1)])###line 1016:_sage_    >>> f2 = R.hom([a + a^2 + a + 1])
1307Expecting nothing
1308ok
1309Trying:
1310    f1 == f2###line 1017:_sage_    >>> f1 == f2
1311Expecting:
1312    True
1313ok
1314Trying:
1315    f1 == R.hom([a**Integer(2)])###line 1019:_sage_    >>> f1 == R.hom([a^2])
1316Expecting:
1317    False
1318ok
1319Trying:
1320    f1(x**Integer(3) + x)###line 1021:_sage_    >>> f1(x^3 + x)
1321Expecting:
1322    a + 1
1323ok
1324Trying:
1325    f2(x**Integer(3) + x)###line 1023:_sage_    >>> f2(x^3 + x)
1326Expecting:
1327    a + 1
1328ok
1329Trying:
1330    loads(dumps(f2)) == f2###line 1028:_sage_    >>> loads(dumps(f2)) == f2
1331Expecting:
1332    True
1333ok
1334Trying:
1335    R = GF(Integer(7))['x, y']; (x, y,) = R._first_ngens(2)###line 1037:_sage_    >>> R.<x,y> = GF(7)[]
1336Expecting nothing
1337ok
1338Trying:
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])
1340Expecting nothing
1341ok
1342Trying:
1343    f1 = R.hom([a, b])###line 1039:_sage_    >>> f1 = R.hom([a, b])
1344Expecting nothing
1345ok
1346Trying:
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])
1348Expecting nothing
1349ok
1350Trying:
1351    f1 == f2###line 1041:_sage_    >>> f1 == f2
1352Expecting:
1353    True
1354ok
1355Trying:
1356    f1 == R.hom([b,a])###line 1043:_sage_    >>> f1 == R.hom([b,a])
1357Expecting:
1358    False
1359ok
1360Trying:
1361    x**Integer(3) + x + y**Integer(2)###line 1045:_sage_    >>> x^3 + x + y^2
1362Expecting:
1363    x^3 + y^2 + x
1364ok
1365Trying:
1366    f1(x**Integer(3) + x + y**Integer(2))###line 1047:_sage_    >>> f1(x^3 + x + y^2)
1367Expecting:
1368    a - b
1369ok
1370Trying:
1371    f2(x**Integer(3) + x + y**Integer(2))###line 1049:_sage_    >>> f2(x^3 + x + y^2)
1372Expecting:
1373    a - b
1374ok
1375Trying:
1376    loads(dumps(f2)) == f2###line 1054:_sage_    >>> loads(dumps(f2)) == f2
1377Expecting:
1378    True
1379ok
1380Trying:
1381    sig_on_count()
1382Expecting:
1383    0
1384ok
1385Trying:
1386    set_random_seed(0L)
1387Expecting nothing
1388ok
1389Trying:
1390    change_warning_output(sys.stdout)
1391Expecting nothing
1392ok
1393Trying:
1394    f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))###line 416:_sage_    >>> f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))
1395Expecting nothing
1396ok
1397Trying:
1398    type(f)###line 417:_sage_    >>> type(f)
1399Expecting:
1400    <type 'sage.rings.morphism.RingMap'>
1401ok
1402Trying:
1403    sig_on_count()
1404Expecting:
1405    0
1406ok
1407Trying:
1408    set_random_seed(0L)
1409Expecting nothing
1410ok
1411Trying:
1412    change_warning_output(sys.stdout)
1413Expecting nothing
1414ok
1415Trying:
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])
1417Expecting nothing
1418ok
1419Trying:
1420    print f._repr_defn()###line 1068:_sage_    >>> print f._repr_defn()
1421Expecting:
1422    x |--> x^2
1423    y |--> x + y
1424ok
1425Trying:
1426    sig_on_count()
1427Expecting:
1428    0
1429ok
1430Trying:
1431    set_random_seed(0L)
1432Expecting nothing
1433ok
1434Trying:
1435    change_warning_output(sys.stdout)
1436Expecting nothing
1437ok
1438Trying:
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])
1440Expecting nothing
1441ok
1442Trying:
1443    f(x+Integer(2)*y+Integer(3)*z)             # indirect doctest###line 1084:_sage_    >>> f(x+2*y+3*z)             # indirect doctest
1444Expecting:
1445    2*x + 3*y + 2*z
1446ok
1447Trying:
1448    sig_on_count()
1449Expecting:
1450    0
1451ok
1452Trying:
1453    set_random_seed(0L)
1454Expecting nothing
1455ok
1456Trying:
1457    change_warning_output(sys.stdout)
1458Expecting nothing
1459ok
1460Trying:
1461    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 1102:_sage_    >>> R.<x,y> = QQ[]
1462Expecting nothing
1463ok
1464Trying:
1465    S = QQ['z']; (z,) = S._first_ngens(1)###line 1103:_sage_    >>> S.<z> = QQ[]
1466Expecting nothing
1467ok
1468Trying:
1469    f = R.hom([Integer(2)*z,Integer(3)*z],S)###line 1104:_sage_    >>> f = R.hom([2*z,3*z],S)
1470Expecting nothing
1471ok
1472Trying:
1473    PR = R['t']; (t,) = PR._first_ngens(1)###line 1109:_sage_    >>> PR.<t> = R[]
1474Expecting nothing
1475ok
1476Trying:
1477    PS = S['t']###line 1110:_sage_    >>> PS = S['t']
1478Expecting nothing
1479ok
1480Trying:
1481    Pf = PR.hom(f,PS)###line 1111:_sage_    >>> Pf = PR.hom(f,PS)
1482Expecting nothing
1483ok
1484Trying:
1485    Pf###line 1112:_sage_    >>> Pf
1486Expecting:
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
1496ok
1497Trying:
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
1499Expecting nothing
1500ok
1501Trying:
1502    Pf(p)###line 1123:_sage_    >>> Pf(p)
1503Expecting:
1504    (-10*z + 1/13)*t^2 - z^2*t + 18*z^2 + 2*z
1505ok
1506Trying:
1507    MR = MatrixSpace(R,Integer(2),Integer(2))###line 1128:_sage_    >>> MR = MatrixSpace(R,2,2)
1508Expecting nothing
1509ok
1510Trying:
1511    MS = MatrixSpace(S,Integer(2),Integer(2))###line 1129:_sage_    >>> MS = MatrixSpace(S,2,2)
1512Expecting nothing
1513ok
1514Trying:
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])
1516Expecting nothing
1517ok
1518Trying:
1519    Mf = MR.hom(f,MS)###line 1131:_sage_    >>> Mf = MR.hom(f,MS)
1520Expecting nothing
1521ok
1522Trying:
1523    Mf###line 1132:_sage_    >>> Mf
1524Expecting:
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
1534ok
1535Trying:
1536    Mf(M)###line 1142:_sage_    >>> Mf(M)
1537Expecting:
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]
1540ok
1541Trying:
1542    MPR = MatrixSpace(PR, Integer(2))###line 1148:_sage_    >>> MPR = MatrixSpace(PR, 2)
1543Expecting nothing
1544ok
1545Trying:
1546    MPS = MatrixSpace(PS, Integer(2))###line 1149:_sage_    >>> MPS = MatrixSpace(PS, 2)
1547Expecting nothing
1548ok
1549Trying:
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])
1551Expecting nothing
1552ok
1553Trying:
1554    MPf = MPR.hom(f,MPS); MPf###line 1151:_sage_    >>> MPf = MPR.hom(f,MPS); MPf
1555Expecting:
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
1569ok
1570Trying:
1571    MPf(M)###line 1165:_sage_    >>> MPf(M)
1572Expecting:
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]
1575ok
1576Trying:
1577    sig_on_count()
1578Expecting:
1579    0
1580ok
1581Trying:
1582    set_random_seed(0L)
1583Expecting nothing
1584ok
1585Trying:
1586    change_warning_output(sys.stdout)
1587Expecting nothing
1588ok
1589Trying:
1590    from sage.rings.morphism import RingHomomorphism_from_base###line 1175:_sage_    >>> from sage.rings.morphism import RingHomomorphism_from_base
1591Expecting nothing
1592ok
1593Trying:
1594    R = ZZ['x']; (x,) = R._first_ngens(1)###line 1176:_sage_    >>> R.<x> = ZZ[]
1595Expecting nothing
1596ok
1597Trying:
1598    f = R.hom([Integer(2)*x],R)###line 1177:_sage_    >>> f = R.hom([2*x],R)
1599Expecting nothing
1600ok
1601Trying:
1602    P = MatrixSpace(R,Integer(2)).Hom(MatrixSpace(R,Integer(2)))###line 1178:_sage_    >>> P = MatrixSpace(R,2).Hom(MatrixSpace(R,2))
1603Expecting nothing
1604ok
1605Trying:
1606    g = RingHomomorphism_from_base(P,f)###line 1179:_sage_    >>> g = RingHomomorphism_from_base(P,f)
1607Expecting nothing
1608ok
1609Trying:
1610    g###line 1180:_sage_    >>> g
1611Expecting:
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
1616ok
1617Trying:
1618    P = MatrixSpace(R,Integer(2)).Hom(R['t'])###line 1189:_sage_    >>> P = MatrixSpace(R,2).Hom(R['t'])
1619Expecting nothing
1620ok
1621Trying:
1622    g = RingHomomorphism_from_base(P,f)###line 1190:_sage_    >>> g = RingHomomorphism_from_base(P,f)
1623Expecting:
1624    Traceback (most recent call last):
1625    ...
1626    ValueError: Domain and codomain must have the same functorial construction over their base rings
1627ok
1628Trying:
1629    sig_on_count()
1630Expecting:
1631    0
1632ok
1633Trying:
1634    set_random_seed(0L)
1635Expecting nothing
1636ok
1637Trying:
1638    change_warning_output(sys.stdout)
1639Expecting nothing
1640ok
1641Trying:
1642    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 1213:_sage_    >>> R.<x,y> = QQ[]
1643Expecting nothing
1644ok
1645Trying:
1646    S = QQ['z']; (z,) = S._first_ngens(1)###line 1214:_sage_    >>> S.<z> = QQ[]
1647Expecting nothing
1648ok
1649Trying:
1650    f = R.hom([Integer(2)*z,Integer(3)*z],S)###line 1215:_sage_    >>> f = R.hom([2*z,3*z],S)
1651Expecting nothing
1652ok
1653Trying:
1654    MR = MatrixSpace(R,Integer(2))###line 1216:_sage_    >>> MR = MatrixSpace(R,2)
1655Expecting nothing
1656ok
1657Trying:
1658    MS = MatrixSpace(S,Integer(2))###line 1217:_sage_    >>> MS = MatrixSpace(S,2)
1659Expecting nothing
1660ok
1661Trying:
1662    g = MR.hom(f,MS)###line 1218:_sage_    >>> g = MR.hom(f,MS)
1663Expecting nothing
1664ok
1665Trying:
1666    g.underlying_map() == f###line 1219:_sage_    >>> g.underlying_map() == f
1667Expecting:
1668    True
1669ok
1670Trying:
1671    sig_on_count()
1672Expecting:
1673    0
1674ok
1675Trying:
1676    set_random_seed(0L)
1677Expecting nothing
1678ok
1679Trying:
1680    change_warning_output(sys.stdout)
1681Expecting nothing
1682ok
1683Trying:
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])
1685Expecting nothing
1686ok
1687Trying:
1688    S = R['z']; (z,) = S._first_ngens(1)###line 1240:_sage_    >>> S.<z> = R[]
1689Expecting nothing
1690ok
1691Trying:
1692    fS = S.hom(f,S); gS = S.hom(g,S)###line 1241:_sage_    >>> fS = S.hom(f,S); gS = S.hom(g,S)
1693Expecting nothing
1694ok
1695Trying:
1696    cmp(fS,gS)   # indirect doctest###line 1242:_sage_    >>> cmp(fS,gS)   # indirect doctest
1697Expecting:
1698    1
1699ok
1700Trying:
1701    cmp(gS,fS)   # indirect doctest###line 1244:_sage_    >>> cmp(gS,fS)   # indirect doctest
1702Expecting:
1703    -1
1704ok
1705Trying:
1706    sig_on_count()
1707Expecting:
1708    0
1709ok
1710Trying:
1711    set_random_seed(0L)
1712Expecting nothing
1713ok
1714Trying:
1715    change_warning_output(sys.stdout)
1716Expecting nothing
1717ok
1718Trying:
1719    R = QQ['x']; (x,) = R._first_ngens(1)###line 1256:_sage_    >>> R.<x> = QQ[]
1720Expecting nothing
1721ok
1722Trying:
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)
1724Expecting nothing
1725ok
1726Trying:
1727    f1 = R.hom([a])###line 1258:_sage_    >>> f1 = R.hom([a])
1728Expecting nothing
1729ok
1730Trying:
1731    f2 = R.hom([a + a**Integer(2) + a + Integer(1)])###line 1259:_sage_    >>> f2 = R.hom([a + a^2 + a + 1])
1732Expecting nothing
1733ok
1734Trying:
1735    PR = R['s, t']; (s, t,) = PR._first_ngens(2)###line 1260:_sage_    >>> PR.<s,t> = R[]
1736Expecting nothing
1737ok
1738Trying:
1739    PQ = Q['s','t']###line 1261:_sage_    >>> PQ = Q['s','t']
1740Expecting nothing
1741ok
1742Trying:
1743    f1P = PR.hom(f1,PQ)###line 1262:_sage_    >>> f1P = PR.hom(f1,PQ)
1744Expecting nothing
1745ok
1746Trying:
1747    f2P = PR.hom(f2,PQ)###line 1263:_sage_    >>> f2P = PR.hom(f2,PQ)
1748Expecting nothing
1749ok
1750Trying:
1751    f1P == f2P###line 1264:_sage_    >>> f1P == f2P
1752Expecting:
1753    True
1754ok
1755Trying:
1756    f1P == loads(dumps(f1P))###line 1269:_sage_    >>> f1P == loads(dumps(f1P))
1757Expecting:
1758    True
1759ok
1760Trying:
1761    R = GF(Integer(7))['x, y']; (x, y,) = R._first_ngens(2)###line 1278:_sage_    >>> R.<x,y> = GF(7)[]
1762Expecting nothing
1763ok
1764Trying:
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])
1766Expecting nothing
1767ok
1768Trying:
1769    f1 = R.hom([a, b])###line 1280:_sage_    >>> f1 = R.hom([a, b])
1770Expecting nothing
1771ok
1772Trying:
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])
1774Expecting nothing
1775ok
1776Trying:
1777    MR = MatrixSpace(R,Integer(2))###line 1282:_sage_    >>> MR = MatrixSpace(R,2)
1778Expecting nothing
1779ok
1780Trying:
1781    MQ = MatrixSpace(Q,Integer(2))###line 1283:_sage_    >>> MQ = MatrixSpace(Q,2)
1782Expecting nothing
1783ok
1784Trying:
1785    f1M = MR.hom(f1,MQ)###line 1284:_sage_    >>> f1M = MR.hom(f1,MQ)
1786Expecting nothing
1787ok
1788Trying:
1789    f2M = MR.hom(f2,MQ)###line 1285:_sage_    >>> f2M = MR.hom(f2,MQ)
1790Expecting nothing
1791ok
1792Trying:
1793    f1M == f2M###line 1286:_sage_    >>> f1M == f2M
1794Expecting:
1795    True
1796ok
1797Trying:
1798    f1M == loads(dumps(f1M))###line 1291:_sage_    >>> f1M == loads(dumps(f1M))
1799Expecting:
1800    True
1801ok
1802Trying:
1803    sig_on_count()
1804Expecting:
1805    0
1806ok
1807Trying:
1808    set_random_seed(0L)
1809Expecting nothing
1810ok
1811Trying:
1812    change_warning_output(sys.stdout)
1813Expecting nothing
1814ok
1815Trying:
1816    R1 = ZZ['x, y']; (x, y,) = R1._first_ngens(2)###line 1310:_sage_    >>> R1.<x,y> = ZZ[]
1817Expecting nothing
1818ok
1819Trying:
1820    f = R1.hom([x+y,x-y])###line 1311:_sage_    >>> f = R1.hom([x+y,x-y])
1821Expecting nothing
1822ok
1823Trying:
1824    R2 = MatrixSpace(FractionField(R1)['t'],Integer(2))###line 1312:_sage_    >>> R2 = MatrixSpace(FractionField(R1)['t'],2)
1825Expecting nothing
1826ok
1827Trying:
1828    g = R2.hom(f,R2)###line 1313:_sage_    >>> g = R2.hom(f,R2)
1829Expecting nothing
1830ok
1831Trying:
1832    g         #indirect doctest###line 1314:_sage_    >>> g         #indirect doctest
1833Expecting:
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
1841ok
1842Trying:
1843    sig_on_count()
1844Expecting:
1845    0
1846ok
1847Trying:
1848    set_random_seed(0L)
1849Expecting nothing
1850ok
1851Trying:
1852    change_warning_output(sys.stdout)
1853Expecting nothing
1854ok
1855Trying:
1856    sig_on_count()
1857Expecting:
1858    0
1859ok
1860Trying:
1861    set_random_seed(0L)
1862Expecting nothing
1863ok
1864Trying:
1865    change_warning_output(sys.stdout)
1866Expecting nothing
1867ok
1868Trying:
1869    R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 1354:_sage_    >>> R.<x,y> = PolynomialRing(QQ, 2)
1870Expecting nothing
1871ok
1872Trying:
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)
1874Expecting nothing
1875ok
1876Trying:
1877    phi = S.cover(); phi###line 1356:_sage_    >>> phi = S.cover(); phi
1878Expecting:
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
1883ok
1884Trying:
1885    phi(x+y)###line 1361:_sage_    >>> phi(x+y)
1886Expecting:
1887    a + b
1888ok
1889Trying:
1890    sig_on_count()
1891Expecting:
1892    0
1893ok
1894Trying:
1895    set_random_seed(0L)
1896Expecting nothing
1897ok
1898Trying:
1899    change_warning_output(sys.stdout)
1900Expecting nothing
1901ok
1902Trying:
1903    f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))###line 426:_sage_    >>> f = sage.rings.morphism.RingMap(ZZ.Hom(ZZ))
1904Expecting nothing
1905ok
1906Trying:
1907    type(f)###line 427:_sage_    >>> type(f)
1908Expecting:
1909    <type 'sage.rings.morphism.RingMap'>
1910ok
1911Trying:
1912    f._repr_type()###line 429:_sage_    >>> f._repr_type()
1913Expecting:
1914    'Set-theoretic ring'
1915ok
1916Trying:
1917    f###line 431:_sage_    >>> f
1918Expecting:
1919    Set-theoretic ring endomorphism of Integer Ring
1920ok
1921Trying:
1922    sig_on_count()
1923Expecting:
1924    0
1925ok
1926Trying:
1927    set_random_seed(0L)
1928Expecting nothing
1929ok
1930Trying:
1931    change_warning_output(sys.stdout)
1932Expecting nothing
1933ok
1934Trying:
1935    f = Zmod(Integer(6)).cover(); f    # implicit test###line 1370:_sage_    >>> f = Zmod(6).cover(); f    # implicit test
1936Expecting:
1937    Ring morphism:
1938      From: Integer Ring
1939      To:   Ring of integers modulo 6
1940      Defn: Natural quotient map
1941ok
1942Trying:
1943    type(f)###line 1375:_sage_    >>> type(f)
1944Expecting:
1945    <type 'sage.rings.morphism.RingHomomorphism_cover'>
1946ok
1947Trying:
1948    sig_on_count()
1949Expecting:
1950    0
1951ok
1952Trying:
1953    set_random_seed(0L)
1954Expecting nothing
1955ok
1956Trying:
1957    change_warning_output(sys.stdout)
1958Expecting nothing
1959ok
1960Trying:
1961    f = Zmod(Integer(6)).cover()###line 1387:_sage_    >>> f = Zmod(6).cover()
1962Expecting nothing
1963ok
1964Trying:
1965    type(f)###line 1388:_sage_    >>> type(f)
1966Expecting:
1967    <type 'sage.rings.morphism.RingHomomorphism_cover'>
1968ok
1969Trying:
1970    f(-Integer(5))                 # indirect doctest###line 1390:_sage_    >>> f(-5)                 # indirect doctest
1971Expecting:
1972    1
1973ok
1974Trying:
1975    f._call_(Integer(1)/Integer(2))###line 1400:_sage_    >>> f._call_(1/2)
1976Expecting:
1977    Traceback (most recent call last):
1978    ...
1979    ZeroDivisionError: Inverse does not exist.
1980ok
1981Trying:
1982    f(Integer(1)/Integer(2))###line 1404:_sage_    >>> f(1/2)
1983Expecting:
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
1987ok
1988Trying:
1989    sig_on_count()
1990Expecting:
1991    0
1992ok
1993Trying:
1994    set_random_seed(0L)
1995Expecting nothing
1996ok
1997Trying:
1998    change_warning_output(sys.stdout)
1999Expecting nothing
2000ok
2001Trying:
2002    f = Zmod(Integer(6)).cover()###line 1417:_sage_    >>> f = Zmod(6).cover()
2003Expecting nothing
2004ok
2005Trying:
2006    f._repr_defn()###line 1418:_sage_    >>> f._repr_defn()
2007Expecting:
2008    'Natural quotient map'
2009ok
2010Trying:
2011    type(f)###line 1420:_sage_    >>> type(f)
2012Expecting:
2013    <type 'sage.rings.morphism.RingHomomorphism_cover'>
2014ok
2015Trying:
2016    sig_on_count()
2017Expecting:
2018    0
2019ok
2020Trying:
2021    set_random_seed(0L)
2022Expecting nothing
2023ok
2024Trying:
2025    change_warning_output(sys.stdout)
2026Expecting nothing
2027ok
2028Trying:
2029    f = Zmod(Integer(6)).cover()###line 1432:_sage_    >>> f = Zmod(6).cover()
2030Expecting nothing
2031ok
2032Trying:
2033    f.kernel()###line 1433:_sage_    >>> f.kernel()
2034Expecting:
2035    Principal ideal (6) of Integer Ring
2036ok
2037Trying:
2038    sig_on_count()
2039Expecting:
2040    0
2041ok
2042Trying:
2043    set_random_seed(0L)
2044Expecting nothing
2045ok
2046Trying:
2047    change_warning_output(sys.stdout)
2048Expecting nothing
2049ok
2050Trying:
2051    R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 1442:_sage_    >>> R.<x,y> = PolynomialRing(QQ, 2)
2052Expecting nothing
2053ok
2054Trying:
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)
2056Expecting nothing
2057ok
2058Trying:
2059    phi = S.cover()###line 1444:_sage_    >>> phi = S.cover()
2060Expecting nothing
2061ok
2062Trying:
2063    phi == loads(dumps(phi))###line 1445:_sage_    >>> phi == loads(dumps(phi))
2064Expecting:
2065    True
2066ok
2067Trying:
2068    phi == R.quo(x**Integer(2) + y**Integer(3)).cover()###line 1447:_sage_    >>> phi == R.quo(x^2 + y^3).cover()
2069Expecting:
2070    False
2071ok
2072Trying:
2073    sig_on_count()
2074Expecting:
2075    0
2076ok
2077Trying:
2078    set_random_seed(0L)
2079Expecting nothing
2080ok
2081Trying:
2082    change_warning_output(sys.stdout)
2083Expecting nothing
2084ok
2085Trying:
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)
2087Expecting nothing
2088ok
2089Trying:
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)
2091Expecting nothing
2092ok
2093Trying:
2094    phi = S.hom([b, c, a]); phi###line 1480:_sage_    >>> phi = S.hom([b, c, a]); phi
2095Expecting:
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
2100ok
2101Trying:
2102    phi(a+b+c)###line 1485:_sage_    >>> phi(a+b+c)
2103Expecting:
2104    a + b + c
2105ok
2106Trying:
2107    loads(dumps(phi)) == phi###line 1487:_sage_    >>> loads(dumps(phi)) == phi
2108Expecting:
2109    True
2110ok
2111Trying:
2112    S.hom([b**Integer(2), c**Integer(2), a**Integer(2)])###line 1496:_sage_    >>> S.hom([b^2, c^2, a^2])
2113Expecting:
2114    Traceback (most recent call last):
2115    ...
2116    TypeError: images do not define a valid homomorphism
2117ok
2118Trying:
2119    sig_on_count()
2120Expecting:
2121    0
2122ok
2123Trying:
2124    set_random_seed(0L)
2125Expecting nothing
2126ok
2127Trying:
2128    change_warning_output(sys.stdout)
2129Expecting nothing
2130ok
2131Trying:
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])
2133Expecting:
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
2137ok
2138Trying:
2139    sig_on_count()
2140Expecting:
2141    0
2142ok
2143Trying:
2144    set_random_seed(0L)
2145Expecting nothing
2146ok
2147Trying:
2148    change_warning_output(sys.stdout)
2149Expecting nothing
2150ok
2151Trying:
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])
2153Expecting nothing
2154ok
2155Trying:
2156    f._phi()###line 1541:_sage_    >>> f._phi()
2157Expecting:
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
2163ok
2164Trying:
2165    sig_on_count()
2166Expecting:
2167    0
2168ok
2169Trying:
2170    set_random_seed(0L)
2171Expecting nothing
2172ok
2173Trying:
2174    change_warning_output(sys.stdout)
2175Expecting nothing
2176ok
2177Trying:
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])
2179Expecting nothing
2180ok
2181Trying:
2182    S.hom([yy,xx]).morphism_from_cover()###line 1558:_sage_    >>> S.hom([yy,xx]).morphism_from_cover()
2183Expecting:
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
2189ok
2190Trying:
2191    sig_on_count()
2192Expecting:
2193    0
2194ok
2195Trying:
2196    set_random_seed(0L)
2197Expecting nothing
2198ok
2199Trying:
2200    change_warning_output(sys.stdout)
2201Expecting nothing
2202ok
2203Trying:
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)
2205Expecting nothing
2206ok
2207Trying:
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)
2209Expecting nothing
2210ok
2211Trying:
2212    phi = S.hom([b, c, a])###line 1573:_sage_    >>> phi = S.hom([b, c, a])
2213Expecting nothing
2214ok
2215Trying:
2216    psi = S.hom([c, b, a])###line 1574:_sage_    >>> psi = S.hom([c, b, a])
2217Expecting nothing
2218ok
2219Trying:
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])
2221Expecting nothing
2222ok
2223Trying:
2224    phi == psi###line 1576:_sage_    >>> phi == psi
2225Expecting:
2226    False
2227ok
2228Trying:
2229    phi == f###line 1578:_sage_    >>> phi == f
2230Expecting:
2231    True
2232ok
2233Trying:
2234    sig_on_count()
2235Expecting:
2236    0
2237ok
2238Trying:
2239    set_random_seed(0L)
2240Expecting nothing
2241ok
2242Trying:
2243    change_warning_output(sys.stdout)
2244Expecting nothing
2245ok
2246Trying:
2247    R, (x,y) = PolynomialRing(QQ, Integer(2), 'xy').objgens()###line 446:_sage_    >>> R, (x,y) = PolynomialRing(QQ, 2, 'xy').objgens()
2248Expecting nothing
2249ok
2250Trying:
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) )
2252Expecting nothing
2253ok
2254Trying:
2255    S.lift()###line 448:_sage_    >>> S.lift()
2256Expecting:
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
2261ok
2262Trying:
2263    S.lift() == Integer(0)###line 453:_sage_    >>> S.lift() == 0
2264Expecting:
2265    False
2266ok
2267Trying:
2268    sig_on_count()
2269Expecting:
2270    0
2271ok
2272Trying:
2273    set_random_seed(0L)
2274Expecting nothing
2275ok
2276Trying:
2277    change_warning_output(sys.stdout)
2278Expecting nothing
2279ok
2280Trying:
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])
2282Expecting nothing
2283ok
2284Trying:
2285    print f._repr_defn()###line 1592:_sage_    >>> print f._repr_defn()
2286Expecting:
2287    xx |--> yy
2288    yy |--> xx
2289ok
2290Trying:
2291    sig_on_count()
2292Expecting:
2293    0
2294ok
2295Trying:
2296    set_random_seed(0L)
2297Expecting nothing
2298ok
2299Trying:
2300    change_warning_output(sys.stdout)
2301Expecting nothing
2302ok
2303Trying:
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])
2305Expecting nothing
2306ok
2307Trying:
2308    f(Integer(3)*x + (Integer(1)/Integer(2))*y)   # indirect doctest###line 1608:_sage_    >>> f(3*x + (1/2)*y)   # indirect doctest
2309Expecting:
2310    1/2*xx + 3*yy
2311ok
2312Trying:
2313    sig_on_count()
2314Expecting:
2315    0
2316ok
2317Trying:
2318    set_random_seed(0L)
2319Expecting nothing
2320ok
2321Trying:
2322    change_warning_output(sys.stdout)
2323Expecting nothing
2324ok
2325Trying:
2326    f = Zmod(Integer(8)).lift()          # indirect doctest###line 462:_sage_    >>> f = Zmod(8).lift()          # indirect doctest
2327Expecting nothing
2328ok
2329Trying:
2330    f(Integer(3))###line 463:_sage_    >>> f(3)
2331Expecting:
2332    3
2333ok
2334Trying:
2335    type(f(Integer(3)))###line 465:_sage_    >>> type(f(3))
2336Expecting:
2337    <type 'sage.rings.integer.Integer'>
2338ok
2339Trying:
2340    type(f)###line 467:_sage_    >>> type(f)
2341Expecting:
2342    <type 'sage.rings.morphism.RingMap_lift'>
2343ok
2344Trying:
2345    sig_on_count()
2346Expecting:
2347    0
2348ok
2349Trying:
2350    set_random_seed(0L)
2351Expecting nothing
2352ok
2353Trying:
2354    change_warning_output(sys.stdout)
2355Expecting nothing
2356ok
2357Trying:
2358    f = Zmod(Integer(8)).lift()###line 495:_sage_    >>> f = Zmod(8).lift()
2359Expecting nothing
2360ok
2361Trying:
2362    g = Zmod(Integer(10)).lift()###line 496:_sage_    >>> g = Zmod(10).lift()
2363Expecting nothing
2364ok
2365Trying:
2366    f == f###line 497:_sage_    >>> f == f
2367Expecting:
2368    True
2369ok
2370Trying:
2371    f == g###line 499:_sage_    >>> f == g
2372Expecting:
2373    False
2374ok
2375Trying:
2376    f < g###line 501:_sage_    >>> f < g
2377Expecting:
2378    True
2379ok
2380Trying:
2381    f > g###line 503:_sage_    >>> f > g
2382Expecting:
2383    False
2384ok
2385Trying:
2386    Zmod(Integer(8)).lift() == Integer(1)###line 508:_sage_    >>> Zmod(8).lift() == 1
2387Expecting:
2388    False
2389ok
2390Trying:
2391    sig_on_count()
2392Expecting:
2393    0
2394ok
2395Trying:
2396    set_random_seed(0L)
2397Expecting nothing
2398ok
2399Trying:
2400    change_warning_output(sys.stdout)
2401Expecting nothing
2402ok
2403Trying:
2404    f = Zmod(Integer(8)).lift()###line 525:_sage_    >>> f = Zmod(8).lift()
2405Expecting nothing
2406ok
2407Trying:
2408    f._repr_defn()###line 526:_sage_    >>> f._repr_defn()
2409Expecting:
2410    'Choice of lifting map'
2411ok
2412Trying:
2413    f###line 528:_sage_    >>> f
2414Expecting:
2415    Set-theoretic ring morphism:
2416      From: Ring of integers modulo 8
2417      To:   Integer Ring
2418      Defn: Choice of lifting map
2419ok
2420Trying:
2421    sig_on_count()
2422Expecting:
2423    0
2424ok
2425Trying:
2426    set_random_seed(0L)
2427Expecting nothing
2428ok
2429Trying:
2430    change_warning_output(sys.stdout)
2431Expecting nothing
2432ok
2433Trying:
2434    f = Zmod(Integer(8)).lift()###line 542:_sage_    >>> f = Zmod(8).lift()
2435Expecting nothing
2436ok
2437Trying:
2438    type(f)###line 543:_sage_    >>> type(f)
2439Expecting:
2440    <type 'sage.rings.morphism.RingMap_lift'>
2441ok
2442Trying:
2443    f(-Integer(1))                       # indirect doctest###line 545:_sage_    >>> f(-1)                       # indirect doctest
2444Expecting:
2445    7
2446ok
2447Trying:
2448    type(f(-Integer(1)))###line 547:_sage_    >>> type(f(-1))
2449Expecting:
2450    <type 'sage.rings.integer.Integer'>
2451ok
2452Trying:
2453    sig_on_count()
2454Expecting:
2455    0
2456ok
24573 items had no tests:
2458    __main__
2459    __main__.change_warning_output
2460    __main__.warning_function
246152 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
2514511 tests in 55 items.
2515511 passed and 0 failed.
2516Test passed.
2517Segmentation fault
2518         [8.6 s]
2519 
2520----------------------------------------------------------------------
2521The following tests failed:
2522
2523
2524        sage -t -long -verbose "devel/sage/sage/rings/morphism.pyx"
2525Total time for all tests: 8.6 seconds
2526sage -t -long -verbose "devel/sage/sage/rings/homset.py"   
2527Trying:
2528    set_random_seed(0L)
2529Expecting nothing
2530ok
2531Trying:
2532    change_warning_output(sys.stdout)
2533Expecting nothing
2534ok
2535Trying:
2536    sig_on_count()
2537Expecting:
2538    0
2539ok
2540Trying:
2541    set_random_seed(0L)
2542Expecting nothing
2543ok
2544Trying:
2545    change_warning_output(sys.stdout)
2546Expecting nothing
2547ok
2548Trying:
2549    sig_on_count()
2550Expecting:
2551    0
2552ok
2553Trying:
2554    set_random_seed(0L)
2555Expecting nothing
2556ok
2557Trying:
2558    change_warning_output(sys.stdout)
2559Expecting nothing
2560ok
2561Trying:
2562    H = Hom(ZZ, QQ)###line 82:_sage_    >>> H = Hom(ZZ, QQ)
2563Expecting nothing
2564ok
2565Trying:
2566    phi = H([])###line 83:_sage_    >>> phi = H([])
2567Expecting:
2568    Traceback (most recent call last):
2569    ...
2570    TypeError: images do not define a valid homomorphism
2571ok
2572Trying:
2573    H = Hom(ZZ, QQ)###line 90:_sage_    >>> H = Hom(ZZ, QQ)
2574Expecting nothing
2575ok
2576Trying:
2577    H == loads(dumps(H))###line 91:_sage_    >>> H == loads(dumps(H))
2578Expecting:
2579    True
2580ok
2581Trying:
2582    sig_on_count()
2583Expecting:
2584    0
2585ok
2586Trying:
2587    set_random_seed(0L)
2588Expecting nothing
2589ok
2590Trying:
2591    change_warning_output(sys.stdout)
2592Expecting nothing
2593ok
2594Trying:
2595    R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 116:_sage_    >>> R.<x,y> = PolynomialRing(QQ, 2)
2596Expecting nothing
2597ok
2598Trying:
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)
2600Expecting nothing
2601ok
2602Trying:
2603    phi = S.hom([b,a]); phi###line 118:_sage_    >>> phi = S.hom([b,a]); phi
2604Expecting:
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
2608ok
2609Trying:
2610    phi(a)###line 122:_sage_    >>> phi(a)
2611Expecting:
2612    b
2613ok
2614Trying:
2615    phi(b)###line 124:_sage_    >>> phi(b)
2616Expecting:
2617    a
2618ok
2619Trying:
2620    R = PolynomialRing(QQ, Integer(2), names=('x', 'y',)); (x, y,) = R._first_ngens(2)###line 133:_sage_    >>> R.<x,y> = PolynomialRing(QQ, 2)
2621Expecting nothing
2622ok
2623Trying:
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)
2625Expecting nothing
2626ok
2627Trying:
2628    H = S.Hom(R)###line 135:_sage_    >>> H = S.Hom(R)
2629Expecting nothing
2630ok
2631Trying:
2632    H == loads(dumps(H))###line 136:_sage_    >>> H == loads(dumps(H))
2633Expecting:
2634    True
2635ok
2636Trying:
2637    phi = S.hom([b,a])###line 141:_sage_    >>> phi = S.hom([b,a])
2638Expecting nothing
2639ok
2640Trying:
2641    phi == loads(dumps(phi))###line 142:_sage_    >>> phi == loads(dumps(phi))
2642Expecting:
2643    True
2644ok
2645Trying:
2646    sig_on_count()
2647Expecting:
2648    0
2649ok
2650Segmentation fault
2651         [4.8 s]
2652 
2653----------------------------------------------------------------------
2654The following tests failed:
2655
2656
2657        sage -t -long -verbose "devel/sage/sage/rings/homset.py"
2658Total time for all tests: 4.9 seconds
2659
2660sage -t -long -verbose "devel/sage/sage/schemes/generic/scheme.py"
2661Trying:
2662    set_random_seed(0L)
2663Expecting nothing
2664ok
2665Trying:
2666    change_warning_output(sys.stdout)
2667Expecting nothing
2668ok
2669Trying:
2670    sig_on_count()
2671Expecting:
2672    0
2673ok
2674Trying:
2675    set_random_seed(0L)
2676Expecting nothing
2677ok
2678Trying:
2679    change_warning_output(sys.stdout)
2680Expecting nothing
2681ok
2682Trying:
2683    from sage.schemes.generic.scheme import is_Scheme###line 39:_sage_    >>> from sage.schemes.generic.scheme import is_Scheme
2684Expecting nothing
2685ok
2686Trying:
2687    is_Scheme(Integer(5))###line 40:_sage_    >>> is_Scheme(5)
2688Expecting:
2689    False
2690ok
2691Trying:
2692    X = Spec(QQ)###line 42:_sage_    >>> X = Spec(QQ)
2693Expecting nothing
2694ok
2695Trying:
2696    is_Scheme(X)###line 43:_sage_    >>> is_Scheme(X)
2697Expecting:
2698    True
2699ok
2700Trying:
2701    sig_on_count()
2702Expecting:
2703    0
2704ok
2705Trying:
2706    set_random_seed(0L)
2707Expecting nothing
2708ok
2709Trying:
2710    change_warning_output(sys.stdout)
2711Expecting nothing
2712ok
2713Trying:
2714    X = Spec(QQ)###line 274:_sage_    >>> X = Spec(QQ)
2715Expecting nothing
2716ok
2717Trying:
2718    X._homset_class()###line 275:_sage_    >>> X._homset_class()
2719Expecting:
2720    Traceback (most recent call last):
2721    ...
2722    NotImplementedError
2723ok
2724Trying:
2725    sig_on_count()
2726Expecting:
2727    0
2728ok
2729Trying:
2730    set_random_seed(0L)
2731Expecting nothing
2732ok
2733Trying:
2734    change_warning_output(sys.stdout)
2735Expecting nothing
2736ok
2737Trying:
2738    A = AffineSpace(Integer(3), ZZ)###line 289:_sage_    >>> A = AffineSpace(3, ZZ)
2739Expecting nothing
2740ok
2741Trying:
2742    A###line 290:_sage_    >>> A
2743Expecting:
2744    Affine Space of dimension 3 over Integer Ring
2745ok
2746Trying:
2747    A/QQ###line 292:_sage_    >>> A/QQ
2748Expecting:
2749    Affine Space of dimension 3 over Rational Field
2750ok
2751Trying:
2752    A/GF(Integer(7))###line 294:_sage_    >>> A/GF(7)
2753Expecting:
2754    Affine Space of dimension 3 over Finite Field of size 7
2755ok
2756Trying:
2757    sig_on_count()
2758Expecting:
2759    0
2760ok
2761Trying:
2762    set_random_seed(0L)
2763Expecting nothing
2764ok
2765Trying:
2766    change_warning_output(sys.stdout)
2767Expecting nothing
2768ok
2769Trying:
2770    A = AffineSpace(Integer(4), QQ)###line 305:_sage_    >>> A = AffineSpace(4, QQ)
2771Expecting nothing
2772ok
2773Trying:
2774    A.base_ring()###line 306:_sage_    >>> A.base_ring()
2775Expecting:
2776    Rational Field
2777ok
2778Trying:
2779    X = Spec(QQ)###line 311:_sage_    >>> X = Spec(QQ)
2780Expecting nothing
2781ok
2782Trying:
2783    X.base_ring()###line 312:_sage_    >>> X.base_ring()
2784Expecting:
2785    Integer Ring
2786ok
2787Trying:
2788    sig_on_count()
2789Expecting:
2790    0
2791ok
2792Trying:
2793    set_random_seed(0L)
2794Expecting nothing
2795ok
2796Trying:
2797    change_warning_output(sys.stdout)
2798Expecting nothing
2799ok
2800Trying:
2801    A = AffineSpace(Integer(4), QQ)###line 332:_sage_    >>> A = AffineSpace(4, QQ)
2802Expecting nothing
2803ok
2804Trying:
2805    A.base_scheme()###line 333:_sage_    >>> A.base_scheme()
2806Expecting:
2807    Spectrum of Rational Field
2808ok
2809Trying:
2810    X = Spec(QQ)###line 338:_sage_    >>> X = Spec(QQ)
2811Expecting nothing
2812ok
2813Trying:
2814    X.base_scheme()###line 339:_sage_    >>> X.base_scheme()
2815Expecting:
2816    Spectrum of Integer Ring
2817ok
2818Trying:
2819    sig_on_count()
2820Expecting:
2821    0
2822ok
2823Trying:
2824    set_random_seed(0L)
2825Expecting nothing
2826ok
2827Trying:
2828    change_warning_output(sys.stdout)
2829Expecting nothing
2830ok
2831Trying:
2832    A = AffineSpace(Integer(4), QQ)###line 362:_sage_    >>> A = AffineSpace(4, QQ)
2833Expecting nothing
2834ok
2835Trying:
2836    A.base_morphism()###line 363:_sage_    >>> A.base_morphism()
2837Expecting:
2838    Scheme morphism:
2839      From: Affine Space of dimension 4 over Rational Field
2840      To:   Spectrum of Rational Field
2841      Defn: Structure map
2842ok
2843Trying:
2844    X = Spec(QQ)###line 371:_sage_    >>> X = Spec(QQ)
2845Expecting nothing
2846ok
2847Trying:
2848    X.base_morphism()###line 372:_sage_    >>> X.base_morphism()
2849Expecting:
2850    Scheme morphism:
2851      From: Spectrum of Rational Field
2852      To:   Spectrum of Integer Ring
2853      Defn: Structure map
2854ok
2855Trying:
2856    sig_on_count()
2857Expecting:
2858    0
2859ok
2860Trying:
2861    set_random_seed(0L)
2862Expecting nothing
2863ok
2864Trying:
2865    change_warning_output(sys.stdout)
2866Expecting nothing
2867ok
2868Trying:
2869    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 400:_sage_    >>> R.<x, y> = QQ[]
2870Expecting nothing
2871ok
2872Trying:
2873    I = (x**Integer(2) - y**Integer(2))*R###line 401:_sage_    >>> I = (x^2 - y^2)*R
2874Expecting nothing
2875ok
2876Trying:
2877    X = Spec(R.quotient(I))###line 402:_sage_    >>> X = Spec(R.quotient(I))
2878Expecting nothing
2879ok
2880Trying:
2881    X.coordinate_ring()###line 403:_sage_    >>> X.coordinate_ring()
2882Expecting:
2883    Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 - y^2)
2884ok
2885Trying:
2886    sig_on_count()
2887Expecting:
2888    0
2889ok
2890Trying:
2891    set_random_seed(0L)
2892Expecting nothing
2893ok
2894Trying:
2895    change_warning_output(sys.stdout)
2896Expecting nothing
2897ok
2898Trying:
2899    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 417:_sage_    >>> R.<x, y> = QQ[]
2900Expecting nothing
2901ok
2902Trying:
2903    I = (x**Integer(2) - y**Integer(2))*R###line 418:_sage_    >>> I = (x^2 - y^2)*R
2904Expecting nothing
2905ok
2906Trying:
2907    X = Spec(R.quotient(I))###line 419:_sage_    >>> X = Spec(R.quotient(I))
2908Expecting nothing
2909ok
2910Trying:
2911    X.dimension_absolute()###line 420:_sage_    >>> X.dimension_absolute()
2912Expecting:
2913    Traceback (most recent call last):
2914    ...
2915    NotImplementedError
2916ok
2917Trying:
2918    X.dimension()###line 424:_sage_    >>> X.dimension()
2919Expecting:
2920    Traceback (most recent call last):
2921    ...
2922    NotImplementedError
2923ok
2924Trying:
2925    sig_on_count()
2926Expecting:
2927    0
2928ok
2929Trying:
2930    set_random_seed(0L)
2931Expecting nothing
2932ok
2933Trying:
2934    change_warning_output(sys.stdout)
2935Expecting nothing
2936ok
2937Trying:
2938    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 439:_sage_    >>> R.<x, y> = QQ[]
2939Expecting nothing
2940ok
2941Trying:
2942    I = (x**Integer(2) - y**Integer(2))*R###line 440:_sage_    >>> I = (x^2 - y^2)*R
2943Expecting nothing
2944ok
2945Trying:
2946    X = Spec(R.quotient(I))###line 441:_sage_    >>> X = Spec(R.quotient(I))
2947Expecting nothing
2948ok
2949Trying:
2950    X.dimension_relative()###line 442:_sage_    >>> X.dimension_relative()
2951Expecting:
2952    Traceback (most recent call last):
2953    ...
2954    NotImplementedError
2955ok
2956Trying:
2957    sig_on_count()
2958Expecting:
2959    0
2960ok
2961Trying:
2962    set_random_seed(0L)
2963Expecting nothing
2964ok
2965Trying:
2966    change_warning_output(sys.stdout)
2967Expecting nothing
2968ok
2969Trying:
2970    X = Spec(QQ)###line 455:_sage_    >>> X = Spec(QQ)
2971Expecting nothing
2972ok
2973Trying:
2974    X.identity_morphism()###line 456:_sage_    >>> X.identity_morphism()
2975Expecting:
2976    Scheme endomorphism of Spectrum of Rational Field
2977      Defn: Identity map
2978ok
2979Trying:
2980    sig_on_count()
2981Expecting:
2982    0
2983ok
2984Trying:
2985    set_random_seed(0L)
2986Expecting nothing
2987ok
2988Trying:
2989    change_warning_output(sys.stdout)
2990Expecting nothing
2991ok
2992Trying:
2993    P = ProjectiveSpace(ZZ, Integer(3))###line 471:_sage_    >>> P = ProjectiveSpace(ZZ, 3)
2994Expecting nothing
2995ok
2996Trying:
2997    P.hom(Spec(ZZ))###line 472:_sage_    >>> P.hom(Spec(ZZ))
2998Expecting:
2999    Scheme morphism:
3000      From: Projective Space of dimension 3 over Integer Ring
3001      To:   Spectrum of Integer Ring
3002      Defn: Structure map
3003ok
3004Trying:
3005    sig_on_count()
3006Expecting:
3007    0
3008ok
3009Trying:
3010    set_random_seed(0L)
3011Expecting nothing
3012ok
3013Trying:
3014    change_warning_output(sys.stdout)
3015Expecting nothing
3016ok
3017Trying:
3018    R = QQ['x, y']; (x, y,) = R._first_ngens(2)###line 59:_sage_    >>> R.<x, y> = QQ[]
3019Expecting nothing
3020ok
3021Trying:
3022    I = (x**Integer(2) - y**Integer(2))*R###line 60:_sage_    >>> I = (x^2 - y^2)*R
3023Expecting nothing
3024ok
3025Trying:
3026    RmodI = R.quotient(I)###line 61:_sage_    >>> RmodI = R.quotient(I)
3027Expecting nothing
3028ok
3029Trying:
3030    X = Spec(RmodI)###line 62:_sage_    >>> X = Spec(RmodI)
3031Expecting nothing
3032ok
3033Trying:
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
3035Expecting nothing
3036ok
3037Trying:
3038    ProjectiveSpace(Integer(4), QQ).category()###line 67:_sage_    >>> ProjectiveSpace(4, QQ).category()
3039Expecting:
3040    Category of schemes over Spectrum of Rational Field
3041ok
3042Trying:
3043    sig_on_count()
3044Expecting:
3045    0
3046ok
3047Trying:
3048    set_random_seed(0L)
3049Expecting nothing
3050ok
3051Trying:
3052    change_warning_output(sys.stdout)
3053Expecting nothing
3054ok
3055Trying:
3056    P = ProjectiveSpace(ZZ, Integer(3))###line 491:_sage_    >>> P = ProjectiveSpace(ZZ, 3)
3057Expecting nothing
3058ok
3059Trying:
3060    S = Spec(ZZ)###line 492:_sage_    >>> S = Spec(ZZ)
3061Expecting nothing
3062ok
3063Trying:
3064    S._Hom_(P)###line 493:_sage_    >>> S._Hom_(P)
3065Expecting:
3066    Set of points of Projective Space of dimension 3 over Integer Ring defined over Integer Ring
3067ok
3068Trying:
3069    sig_on_count()
3070Expecting:
3071    0
3072ok
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------------------------------------------------------------------------
3079Unhandled SIGSEGV: A segmentation fault occurred in Sage.
3080This probably occurred because a *compiled* component of Sage has a bug
3081in it and is not properly wrapped with sig_on(), sig_off(). You might
3082want to run Sage under gdb with 'sage -gdb' to debug this.
3083Sage will now terminate.
3084------------------------------------------------------------------------
3085Segmentation fault
3086         [5.0 s]
3087 
3088----------------------------------------------------------------------
3089The following tests failed:
3090
3091
3092        sage -t -long -verbose "devel/sage/sage/schemes/generic/scheme.py"
3093Total time for all tests: 5.1 seconds