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Matthias Koeppe
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src/sage/rings/finite_rings: Use more block tags
1 parent e9630a6 commit 8a823ff

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5 files changed

+151
-120
lines changed

5 files changed

+151
-120
lines changed

‎src/sage/rings/finite_rings/hom_prime_finite_field.pyx

Lines changed: 5 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -79,13 +79,14 @@ cdef class FiniteFieldHomomorphism_prime(FiniteFieldHomomorphism_generic):
7979
"""
8080
TESTS::
8181
82+
sage: # needs sage.rings.finite_rings
8283
sage: from sage.rings.finite_rings.hom_prime_finite_field import FiniteFieldHomomorphism_prime
8384
sage: k = GF(3)
84-
sage: K.<t> = GF(3^5) # needs sage.rings.finite_rings
85-
sage: f = FiniteFieldHomomorphism_prime(Hom(k, K)) # needs sage.rings.finite_rings
86-
sage: a = f(4); a # needs sage.rings.finite_rings
85+
sage: K.<t> = GF(3^5)
86+
sage: f = FiniteFieldHomomorphism_prime(Hom(k, K))
87+
sage: a = f(4); a
8788
1
88-
sage: a.parent() # needs sage.rings.finite_rings
89+
sage: a.parent()
8990
Finite Field in t of size 3^5
9091
"""
9192
return self._codomain._element_constructor(x)

‎src/sage/rings/finite_rings/integer_mod.pyx

Lines changed: 63 additions & 47 deletions
Original file line numberDiff line numberDiff line change
@@ -547,14 +547,15 @@ cdef class IntegerMod_abstract(FiniteRingElement):
547547
548548
EXAMPLES::
549549
550+
sage: # needs sage.libs.gap
550551
sage: a = Mod(2,19)
551-
sage: gap(a) # needs sage.libs.gap
552+
sage: gap(a)
552553
Z(19)
553-
sage: gap(Mod(3, next_prime(10000))) # needs sage.libs.gap
554+
sage: gap(Mod(3, next_prime(10000)))
554555
Z(10007)^6190
555-
sage: gap(Mod(3, next_prime(100000))) # needs sage.libs.gap
556+
sage: gap(Mod(3, next_prime(100000)))
556557
ZmodpZObj( 3, 100003 )
557-
sage: gap(Mod(4, 48)) # needs sage.libs.gap
558+
sage: gap(Mod(4, 48))
558559
ZmodnZObj( 4, 48 )
559560
"""
560561
return '%s*One(ZmodnZ(%s))' % (self, self.__modulus.sageInteger)
@@ -565,11 +566,12 @@ cdef class IntegerMod_abstract(FiniteRingElement):
565566
566567
EXAMPLES::
567568
569+
sage: # optional - magma
568570
sage: a = Integers(15)(4)
569-
sage: b = magma(a) # optional - magma
570-
sage: b.Type() # optional - magma
571+
sage: b = magma(a)
572+
sage: b.Type()
571573
RngIntResElt
572-
sage: b^2 # optional - magma
574+
sage: b^2
573575
1
574576
"""
575577
return '%s!%s'%(self.parent()._magma_init_(magma), self)
@@ -585,14 +587,14 @@ cdef class IntegerMod_abstract(FiniteRingElement):
585587
sage: a._axiom_init_()
586588
'4 :: IntegerMod(15)'
587589
588-
sage: aa = axiom(a); aa #optional - axiom
590+
sage: aa = axiom(a); aa # optional - axiom
589591
4
590-
sage: aa.type() #optional - axiom
592+
sage: aa.type() # optional - axiom
591593
IntegerMod 15
592594
593-
sage: aa = fricas(a); aa #optional - fricas
595+
sage: aa = fricas(a); aa # optional - fricas
594596
4
595-
sage: aa.typeOf() #optional - fricas
597+
sage: aa.typeOf() # optional - fricas
596598
IntegerMod(15)
597599
598600
"""
@@ -654,12 +656,13 @@ cdef class IntegerMod_abstract(FiniteRingElement):
654656
655657
EXAMPLES::
656658
659+
sage: # needs sage.libs.pari
657660
sage: r = Integers(125)
658-
sage: b = r.multiplicative_generator()^3 # needs sage.libs.pari
659-
sage: a = b^17 # needs sage.libs.pari
660-
sage: a.log(b) # needs sage.libs.pari
661+
sage: b = r.multiplicative_generator()^3
662+
sage: a = b^17
663+
sage: a.log(b)
661664
17
662-
sage: a.log() # needs sage.libs.pari
665+
sage: a.log()
663666
51
664667
665668
A bigger example::
@@ -702,12 +705,13 @@ cdef class IntegerMod_abstract(FiniteRingElement):
702705
703706
We test against a bug (side effect on PARI) fixed in :trac:`9438`::
704707
708+
sage: # needs sage.libs.pari
705709
sage: R.<a, b> = QQ[]
706-
sage: pari(b) # needs sage.libs.pari
710+
sage: pari(b)
707711
b
708-
sage: GF(7)(5).log() # needs sage.rings.finite_rings
712+
sage: GF(7)(5).log()
709713
5
710-
sage: pari(b) # needs sage.libs.pari
714+
sage: pari(b)
711715
b
712716
713717
We test that :trac:`23927` is fixed::
@@ -1034,22 +1038,24 @@ cdef class IntegerMod_abstract(FiniteRingElement):
10341038
10351039
sage: Mod(3, 17).is_square()
10361040
False
1037-
sage: Mod(9, 17).is_square() # needs sage.libs.pari
1041+
1042+
sage: # needs sage.libs.pari
1043+
sage: Mod(9, 17).is_square()
10381044
True
1039-
sage: Mod(9, 17*19^2).is_square() # needs sage.libs.pari
1045+
sage: Mod(9, 17*19^2).is_square()
10401046
True
1041-
sage: Mod(-1, 17^30).is_square() # needs sage.libs.pari
1047+
sage: Mod(-1, 17^30).is_square()
10421048
True
1043-
sage: Mod(1/9, next_prime(2^40)).is_square() # needs sage.libs.pari
1049+
sage: Mod(1/9, next_prime(2^40)).is_square()
10441050
True
1045-
sage: Mod(1/25, next_prime(2^90)).is_square() # needs sage.libs.pari
1051+
sage: Mod(1/25, next_prime(2^90)).is_square()
10461052
True
10471053
10481054
TESTS::
10491055
1050-
sage: Mod(1/25, 2^8).is_square() # needs sage.libs.pari
1056+
sage: Mod(1/25, 2^8).is_square() # needs sage.libs.pari
10511057
True
1052-
sage: Mod(1/25, 2^40).is_square() # needs sage.libs.pari
1058+
sage: Mod(1/25, 2^40).is_square() # needs sage.libs.pari
10531059
True
10541060
10551061
sage: for p,q,r in cartesian_product_iterator([[3,5],[11,13],[17,19]]): # long time, needs sage.libs.pari
@@ -1130,16 +1136,18 @@ cdef class IntegerMod_abstract(FiniteRingElement):
11301136
86
11311137
sage: mod(7, 18).sqrt()
11321138
5
1133-
sage: a = mod(14, 5^60).sqrt() # needs sage.libs.pari
1134-
sage: a*a # needs sage.libs.pari
1139+
1140+
sage: # needs sage.libs.pari
1141+
sage: a = mod(14, 5^60).sqrt()
1142+
sage: a*a
11351143
14
11361144
sage: mod(15, 389).sqrt(extend=False)
11371145
Traceback (most recent call last):
11381146
...
11391147
ValueError: self must be a square
1140-
sage: Mod(1/9, next_prime(2^40)).sqrt()^(-2) # needs sage.libs.pari
1148+
sage: Mod(1/9, next_prime(2^40)).sqrt()^(-2)
11411149
9
1142-
sage: Mod(1/25, next_prime(2^90)).sqrt()^(-2) # needs sage.libs.pari
1150+
sage: Mod(1/25, next_prime(2^90)).sqrt()^(-2)
11431151
25
11441152
11451153
::
@@ -1154,7 +1162,8 @@ cdef class IntegerMod_abstract(FiniteRingElement):
11541162
sage: y = x.sqrt(); y
11551163
sqrt359
11561164
sage: y.parent()
1157-
Univariate Quotient Polynomial Ring in sqrt359 over Ring of integers modulo 360 with modulus x^2 + 1
1165+
Univariate Quotient Polynomial Ring in sqrt359 over
1166+
Ring of integers modulo 360 with modulus x^2 + 1
11581167
sage: y^2
11591168
359
11601169
@@ -1173,15 +1182,16 @@ cdef class IntegerMod_abstract(FiniteRingElement):
11731182
11741183
::
11751184
1185+
sage: # needs sage.libs.pari
11761186
sage: R = Integers(5*13^3*37); R
11771187
Ring of integers modulo 406445
1178-
sage: v = R(-1).sqrt(all=True); v # needs sage.libs.pari
1188+
sage: v = R(-1).sqrt(all=True); v
11791189
[78853, 111808, 160142, 193097, 213348, 246303, 294637, 327592]
1180-
sage: [x^2 for x in v] # needs sage.libs.pari
1190+
sage: [x^2 for x in v]
11811191
[406444, 406444, 406444, 406444, 406444, 406444, 406444, 406444]
1182-
sage: v = R(169).sqrt(all=True); min(v), -max(v), len(v) # needs sage.libs.pari
1192+
sage: v = R(169).sqrt(all=True); min(v), -max(v), len(v)
11831193
(13, 13, 104)
1184-
sage: all(x^2 == 169 for x in v) # needs sage.libs.pari
1194+
sage: all(x^2 == 169 for x in v)
11851195
True
11861196
11871197
::
@@ -1391,17 +1401,20 @@ cdef class IntegerMod_abstract(FiniteRingElement):
13911401
5
13921402
sage: K(23).nth_root(3)
13931403
29
1394-
sage: mod(225, 2^5*3^2).nth_root(4, all=True) # needs sage.rings.padics
1404+
1405+
sage: # needs sage.rings.padics
1406+
sage: mod(225, 2^5*3^2).nth_root(4, all=True)
13951407
[225, 129, 33, 63, 255, 159, 9, 201, 105, 279, 183, 87, 81,
13961408
273, 177, 207, 111, 15, 153, 57, 249, 135, 39, 231]
1397-
sage: mod(275, 2^5*7^4).nth_root(7, all=True) # needs sage.rings.padics
1409+
sage: mod(275, 2^5*7^4).nth_root(7, all=True)
13981410
[58235, 25307, 69211, 36283, 3355, 47259, 14331]
1399-
sage: mod(1,8).nth_root(2, all=True) # needs sage.rings.padics
1411+
sage: mod(1,8).nth_root(2, all=True)
14001412
[1, 7, 5, 3]
14011413
sage: mod(4,8).nth_root(2, all=True)
14021414
[2, 6]
1403-
sage: mod(1,16).nth_root(4, all=True) # needs sage.rings.padics
1415+
sage: mod(1,16).nth_root(4, all=True)
14041416
[1, 15, 13, 3, 9, 7, 5, 11]
1417+
14051418
sage: (mod(22,31)^200).nth_root(200)
14061419
5
14071420
sage: mod(3,6).nth_root(0, all=True)
@@ -1582,7 +1595,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
15821595
15831596
TESTS::
15841597
1585-
sage: for n in range(2,100): # long time
1598+
sage: for n in range(2,100): # long time
15861599
....: K = Integers(n)
15871600
....: elist = list(range(1,min(2*n+2,100)))
15881601
....: for e in random_sublist(elist, 5/len(elist)):
@@ -2914,16 +2927,18 @@ cdef class IntegerMod_int(IntegerMod_abstract):
29142927
86
29152928
sage: mod(7, 18).sqrt()
29162929
5
2917-
sage: a = mod(14, 5^60).sqrt() # needs sage.libs.pari
2918-
sage: a*a # needs sage.libs.pari
2930+
2931+
sage: # needs sage.libs.pari
2932+
sage: a = mod(14, 5^60).sqrt()
2933+
sage: a*a
29192934
14
29202935
sage: mod(15, 389).sqrt(extend=False)
29212936
Traceback (most recent call last):
29222937
...
29232938
ValueError: self must be a square
2924-
sage: Mod(1/9, next_prime(2^40)).sqrt()^(-2) # needs sage.libs.pari
2939+
sage: Mod(1/9, next_prime(2^40)).sqrt()^(-2)
29252940
9
2926-
sage: Mod(1/25, next_prime(2^90)).sqrt()^(-2) # needs sage.libs.pari
2941+
sage: Mod(1/25, next_prime(2^90)).sqrt()^(-2)
29272942
25
29282943
29292944
::
@@ -2960,15 +2975,16 @@ cdef class IntegerMod_int(IntegerMod_abstract):
29602975
29612976
::
29622977
2978+
sage: # needs sage.libs.pari
29632979
sage: R = Integers(5*13^3*37); R
29642980
Ring of integers modulo 406445
2965-
sage: v = R(-1).sqrt(all=True); v # needs sage.libs.pari
2981+
sage: v = R(-1).sqrt(all=True); v
29662982
[78853, 111808, 160142, 193097, 213348, 246303, 294637, 327592]
2967-
sage: [x^2 for x in v] # needs sage.libs.pari
2983+
sage: [x^2 for x in v]
29682984
[406444, 406444, 406444, 406444, 406444, 406444, 406444, 406444]
2969-
sage: v = R(169).sqrt(all=True); min(v), -max(v), len(v) # needs sage.libs.pari
2985+
sage: v = R(169).sqrt(all=True); min(v), -max(v), len(v)
29702986
(13, 13, 104)
2971-
sage: all(x^2 == 169 for x in v) # needs sage.libs.pari
2987+
sage: all(x^2 == 169 for x in v)
29722988
True
29732989
29742990
Modulo a power of 2::

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