sage.rings.finite_rings: Update # needs

Author: Matthias Koeppe

src/sage/rings/finite_rings/element_pari_ffelt.pyx

@@ -1333,9 +1333,10 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):
 
         EXAMPLES::
 
+            sage: # needs sage.libs.gap
             sage: F = FiniteField(2^3, 'aa', impl='pari_ffelt')
             sage: aa = F.multiplicative_generator()
-            sage: gap(aa) # indirect doctest
+            sage: gap(aa)  # indirect doctest
             Z(2^3)
             sage: b = F.multiplicative_generator()
             sage: a = b^3
@@ -1350,6 +1351,7 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):
 
         You can specify the instance of the Gap interpreter that is used::
 
+            sage: # needs sage.libs.gap
             sage: F = FiniteField(next_prime(200)^2, 'a', impl='pari_ffelt')
             sage: a = F.multiplicative_generator()
             sage: a._gap_ (gap)
@@ -1359,6 +1361,7 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):
 
         Gap only supports relatively small finite fields::
 
+            sage: # needs sage.libs.gap
             sage: F = FiniteField(next_prime(1000)^2, 'a', impl='pari_ffelt')
             sage: a = F.multiplicative_generator()
             sage: a._gap_init_()

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -4,9 +4,9 @@ Base class for finite fields
 
 TESTS::
 
-    sage: K.<a> = NumberField(x^2 + 1)
-    sage: F = K.factor(3)[0][0].residue_field()
-    sage: loads(dumps(F)) == F
+    sage: K.<a> = NumberField(x^2 + 1)                                                  # needs sage.rings.number_field
+    sage: F = K.factor(3)[0][0].residue_field()                                         # needs sage.rings.number_field
+    sage: loads(dumps(F)) == F                                                          # needs sage.rings.number_field
     True
 
 AUTHORS:

src/sage/rings/finite_rings/finite_field_constructor.py

@@ -73,7 +73,7 @@
 
 ::
 
-    sage: k = GF(5^2,'c'); type(k)
+    sage: k = GF(5^2,'c'); type(k)                                                      # needs sage.libs.linbox
     <class 'sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category'>
 
 One can also give the cardinality `q=p^n` as the tuple `(p,n)`::
@@ -83,7 +83,7 @@
 
 ::
 
-    sage: k = GF(2^16,'c'); type(k)
+    sage: k = GF(2^16,'c'); type(k)                                                     # needs sage.libs.ntl
     <class 'sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e_with_category'>
 
 ::
@@ -125,9 +125,9 @@
 
 ::
 
-    sage: k = GF(9,'alpha'); type(k)
+    sage: k = GF(9,'alpha'); type(k)                                                    # needs sage.libs.linbox
     <class 'sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category'>
-    sage: k.base_ring()
+    sage: k.base_ring()                                                                 # needs sage.libs.linbox
     Finite Field of size 3
 
 ::
@@ -508,12 +508,12 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
         """
         EXAMPLES::
 
-            sage: GF.create_key_and_extra_args(9, 'a')
+            sage: GF.create_key_and_extra_args(9, 'a')                                  # needs sage.libs.linbox
             ((9, ('a',), x^2 + 2*x + 2, 'givaro', 3, 2, True, None, 'poly', True, True, True), {})
 
         The order `q` can also be given as a pair `(p,n)`::
 
-            sage: GF.create_key_and_extra_args((3, 2), 'a')
+            sage: GF.create_key_and_extra_args((3, 2), 'a')                             # needs sage.libs.linbox
             ((9, ('a',), x^2 + 2*x + 2, 'givaro', 3, 2, True, None, 'poly', True, True, True), {})
 
         We do not take invalid keyword arguments and raise a value error
@@ -527,28 +527,28 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
         Moreover, ``repr`` and ``elem_cache`` are ignored when not
         using givaro::
 
-            sage: GF.create_key_and_extra_args(16, 'a', impl='ntl', repr='poly')
+            sage: GF.create_key_and_extra_args(16, 'a', impl='ntl', repr='poly')        # needs sage.libs.ntl
             ((16, ('a',), x^4 + x + 1, 'ntl', 2, 4, True, None, None, None, True, True), {})
-            sage: GF.create_key_and_extra_args(16, 'a', impl='ntl', elem_cache=False)
+            sage: GF.create_key_and_extra_args(16, 'a', impl='ntl', elem_cache=False)   # needs sage.libs.ntl
             ((16, ('a',), x^4 + x + 1, 'ntl', 2, 4, True, None, None, None, True, True), {})
-            sage: GF(16, impl='ntl') is GF(16, impl='ntl', repr='foo')
+            sage: GF(16, impl='ntl') is GF(16, impl='ntl', repr='foo')                  # needs sage.libs.ntl
             True
 
         We handle extra arguments for the givaro finite field and
         create unique objects for their defaults::
 
-            sage: GF(25, impl='givaro') is GF(25, impl='givaro', repr='poly')
+            sage: GF(25, impl='givaro') is GF(25, impl='givaro', repr='poly')           # needs sage.libs.linbox
             True
-            sage: GF(25, impl='givaro') is GF(25, impl='givaro', elem_cache=True)
+            sage: GF(25, impl='givaro') is GF(25, impl='givaro', elem_cache=True)       # needs sage.libs.linbox
             True
-            sage: GF(625, impl='givaro') is GF(625, impl='givaro', elem_cache=False)
+            sage: GF(625, impl='givaro') is GF(625, impl='givaro', elem_cache=False)    # needs sage.libs.linbox
             True
 
         We explicitly take ``structure``, ``implementation`` and ``prec`` attributes
         for compatibility with :class:`~sage.categories.pushout.AlgebraicExtensionFunctor`
         but we ignore them as they are not used, see :trac:`21433`::
 
-            sage: GF.create_key_and_extra_args(9, 'a', structure=None)
+            sage: GF.create_key_and_extra_args(9, 'a', structure=None)                  # needs sage.libs.linbox
             ((9, ('a',), x^2 + 2*x + 2, 'givaro', 3, 2, True, None, 'poly', True, True, True), {})
 
         TESTS::
@@ -684,8 +684,8 @@ def create_object(self, version, key, **kwds):
         We try to create finite fields with various implementations::
 
             sage: k = GF(2, impl='modn')
-            sage: k = GF(2, impl='givaro')
-            sage: k = GF(2, impl='ntl')
+            sage: k = GF(2, impl='givaro')                                              # needs sage.libs.linbox
+            sage: k = GF(2, impl='ntl')                                                 # needs sage.libs.ntl
             sage: k = GF(2, impl='pari')
             Traceback (most recent call last):
             ...
@@ -698,18 +698,18 @@ def create_object(self, version, key, **kwds):
             Traceback (most recent call last):
             ...
             ValueError: the 'modn' implementation requires a prime order
-            sage: k.<a> = GF(2^15, impl='givaro')
-            sage: k.<a> = GF(2^15, impl='ntl')
+            sage: k.<a> = GF(2^15, impl='givaro')                                       # needs sage.libs.linbox
+            sage: k.<a> = GF(2^15, impl='ntl')                                          # needs sage.libs.ntl
             sage: k.<a> = GF(2^15, impl='pari')
             sage: k.<a> = GF(3^60, impl='modn')
             Traceback (most recent call last):
             ...
             ValueError: the 'modn' implementation requires a prime order
-            sage: k.<a> = GF(3^60, impl='givaro')
+            sage: k.<a> = GF(3^60, impl='givaro')                                       # needs sage.libs.linbox
             Traceback (most recent call last):
             ...
             ValueError: q must be < 2^16
-            sage: k.<a> = GF(3^60, impl='ntl')
+            sage: k.<a> = GF(3^60, impl='ntl')                                          # needs sage.libs.ntl
             Traceback (most recent call last):
             ...
             ValueError: q must be a 2-power