sage.rings.padics: Update # needs

src/sage/features/sagemath.py

@@ -389,16 +389,28 @@ def __init__(self):
         """
         JoinFeature.__init__(self, 'sage.libs.gap',
                              [PythonModule('sage.libs.gap.libgap'),
-                              PythonModule('sage.interfaces.gap')])
+                              PythonModule('sage.interfaces.gap'),
+                              PythonModule('sage.groups.matrix_gps.finitely_generated_gap'),
+                              PythonModule('sage.groups.matrix_gps.group_element_gap'),
+                              PythonModule('sage.groups.matrix_gps.heisenberg'),
+                              PythonModule('sage.groups.matrix_gps.isometries'),
+                              PythonModule('sage.groups.matrix_gps.linear_gap'),
+                              PythonModule('sage.groups.matrix_gps.matrix_group_gap'),
+                              PythonModule('sage.groups.matrix_gps.named_group_gap'),
+                              PythonModule('sage.groups.matrix_gps.orthogonal_gap'),
+                              PythonModule('sage.groups.matrix_gps.symplectic_gap'),
+                              PythonModule('sage.groups.matrix_gps.unitary_gap'),
+                              PythonModule('sage.matrix.matrix_gap'),
+                              PythonModule('sage.rings.universal_cyclotomic_field')])
 
 
 class sage__libs__linbox(JoinFeature):
     r"""
     A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.linbox`
     and other modules depending on Givaro, FFLAS-FFPACK, LinBox.
 
-    In addition to the modularization purposes that this tag serves,
-    it also provides attribution to the upstream project.
+    In addition to the modularization purposes that this tag serves, it also provides attribution
+    to the upstream project.
 
     TESTS::
 
@@ -415,7 +427,9 @@ def __init__(self):
             True
         """
         JoinFeature.__init__(self, 'sage.libs.linbox',
-                             [PythonModule('sage.rings.finite_rings.element_givaro')],
+                             [PythonModule('sage.rings.finite_rings.element_givaro'),
+                              PythonModule('sage.matrix.matrix_modn_dense_float'),
+                              PythonModule('sage.matrix.matrix_modn_dense_double')],
                              spkg='sagemath_linbox', type='standard')
 
 
@@ -442,7 +456,8 @@ def __init__(self):
             True
         """
         JoinFeature.__init__(self, 'sage.libs.m4ri',
-                             [PythonModule('sage.matrix.matrix_gf2e_dense')],
+                             [PythonModule('sage.matrix.matrix_gf2e_dense'),
+                              PythonModule('sage.matrix.matrix_mod2_dense')],
                              spkg='sagemath_m4ri', type='standard')
 
 
@@ -708,7 +723,8 @@ def __init__(self):
         """
         JoinFeature.__init__(self, 'sage.rings.finite_rings',
                              [PythonModule('sage.rings.finite_rings.element_pari_ffelt'),
-                              PythonModule('sage.rings.algebraic_closure_finite_field')],
+                              PythonModule('sage.rings.algebraic_closure_finite_field'),
+                              sage__libs__pari()],
                              type='standard')
 
 
@@ -784,16 +800,19 @@ class sage__rings__number_field(JoinFeature):
         sage: CC(zeta)
         0.913545457642601 + 0.406736643075800*I
 
-    Doctests that make use of the algebraic field ``QQbar``, the algebraic real field ``AA``,
-    or the universal cyclotomic field should be marked likewise::
+    Doctests that make use of the algebraic field ``QQbar`` or the algebraic real field ``AA``
+    should be marked likewise::
 
         sage: # needs sage.rings.number_field
         sage: AA(-1)^(1/3)
         -1
         sage: QQbar(-1)^(1/3)
         0.500000000000000? + 0.866025403784439?*I
 
-        sage: # needs sage.rings.number_field
+    Use of the universal cyclotomic field should be marked
+    ``# needs sage.libs.gap sage.rings.number_field``.
+
+        sage: # needs sage.libs.gap sage.rings.number_field
         sage: UCF = UniversalCyclotomicField(); UCF
         Universal Cyclotomic Field
         sage: E = UCF.gen

src/sage/rings/abc.pyx

@@ -66,13 +66,13 @@ class UniversalCyclotomicField(Field):
     EXAMPLES::
 
         sage: import sage.rings.abc
-        sage: K = UniversalCyclotomicField()                                            # needs sage.rings.number_field
-        sage: isinstance(K, sage.rings.abc.UniversalCyclotomicField)                    # needs sage.rings.number_field
+        sage: K = UniversalCyclotomicField()                                            # needs sage.libs.gap sage.rings.number_field
+        sage: isinstance(K, sage.rings.abc.UniversalCyclotomicField)                    # needs sage.libs.gap sage.rings.number_field
         True
 
     By design, there is a unique direct subclass::
 
-        sage: sage.rings.abc.UniversalCyclotomicField.__subclasses__()                  # needs sage.rings.number_field
+        sage: sage.rings.abc.UniversalCyclotomicField.__subclasses__()                  # needs sage.libs.gap sage.rings.number_field
         [<class 'sage.rings.universal_cyclotomic_field.UniversalCyclotomicField'>]
 
         sage: len(sage.rings.abc.NumberField_cyclotomic.__subclasses__()) <= 1

src/sage/rings/complex_arb.pyx

@@ -4014,7 +4014,7 @@ cdef class ComplexBall(RingElement):
              [2.2882956833435e+50 +/- ...e+36],
              [1.2807602335816e+51 +/- ...e+37])
             sage: ai, aip, bi, bip = CBF(1,2).airy()
-            sage: (ai * bip - bi * aip) * CBF(pi)
+            sage: (ai * bip - bi * aip) * CBF(pi)                                       # needs sage.symbolic
             [1.0000000000000 +/- ...e-15] + [+/- ...e-16]*I
 
         """

src/sage/rings/complex_double.pyx

@@ -796,11 +796,11 @@ cdef class ComplexDoubleElement(FieldElement):
 
         EXAMPLES::
 
-            sage: CDF(1.2) > CDF(i)
+            sage: CDF(1.2) > CDF(i)                                                     # needs sage.symbolic
             True
             sage: CDF(1) < CDF(2)
             True
-            sage: CDF(1 + i) > CDF(-1 - i)
+            sage: CDF(1 + i) > CDF(-1 - i)                                              # needs sage.symbolic
             True
 
         ::
@@ -2551,11 +2551,12 @@ cdef class ComplexToCDF(Morphism):
 
     EXAMPLES::
 
-        sage: import numpy                                                              # needs numpy
-        sage: f = CDF.coerce_map_from(numpy.complex_)                                   # needs numpy
-        sage: f(numpy.complex_(I))                                                      # needs numpy
+        sage: # needs numpy
+        sage: import numpy
+        sage: f = CDF.coerce_map_from(numpy.complex_)
+        sage: f(numpy.complex_(I))
         1.0*I
-        sage: f(numpy.complex_(I)).parent()                                             # needs numpy
+        sage: f(numpy.complex_(I)).parent()
         Complex Double Field
     """
     def __init__(self, R):

src/sage/rings/complex_interval_field.py

@@ -484,19 +484,19 @@ def _coerce_map_from_(self, S):
             Coercion map:
               From: Set of Python objects of class 'int'
               To:   Complex Interval Field with 53 bits of precision
-            sage: CIF.coerce_map_from(GaussianIntegers())
+            sage: CIF.coerce_map_from(GaussianIntegers())                               # needs sage.rings.number_field
             Conversion via _complex_mpfi_ method map:
               From: Gaussian Integers in Number Field in I with defining polynomial x^2 + 1 with I = 1*I
               To:   Complex Interval Field with 53 bits of precision
-            sage: CIF.coerce_map_from(QQbar)
+            sage: CIF.coerce_map_from(QQbar)                                            # needs sage.rings.number_field
             Conversion via _complex_mpfi_ method map:
               From: Algebraic Field
               To:   Complex Interval Field with 53 bits of precision
-            sage: CIF.coerce_map_from(AA)
+            sage: CIF.coerce_map_from(AA)                                               # needs sage.rings.number_field
             Conversion via _complex_mpfi_ method map:
               From: Algebraic Real Field
               To:   Complex Interval Field with 53 bits of precision
-            sage: CIF.coerce_map_from(UniversalCyclotomicField())
+            sage: CIF.coerce_map_from(UniversalCyclotomicField())                       # needs sage.libs.gap sage.rings.number_field
             Conversion via _complex_mpfi_ method map:
               From: Universal Cyclotomic Field
               To:   Complex Interval Field with 53 bits of precision
@@ -532,9 +532,9 @@ def _repr_(self):
 
         EXAMPLES::
 
-            sage: ComplexIntervalField() # indirect doctest
+            sage: ComplexIntervalField()  # indirect doctest
             Complex Interval Field with 53 bits of precision
-            sage: ComplexIntervalField(100) # indirect doctest
+            sage: ComplexIntervalField(100)  # indirect doctest
             Complex Interval Field with 100 bits of precision
         """
         return "Complex Interval Field with %s bits of precision" % self._prec

src/sage/rings/continued_fraction.py

@@ -157,7 +157,7 @@
 
 Nevertheless, the tail is preserved under invertible integer homographies::
 
-    sage: # needs sage.rings.number_field
+    sage: # needs sage.modular sage.rings.number_field
     sage: apply_homography =  lambda m,z: (m[0,0]*z + m[0,1]) / (m[1,0]*z + m[1,1])
     sage: m1 = SL2Z([60,13,83,18])
     sage: m2 = SL2Z([27,80,28,83])

src/sage/rings/derivation.py

@@ -1580,16 +1580,15 @@ def __init__(self, parent, arg=None):
 
         TESTS::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: from sage.rings.derivation import RingDerivationWithoutTwist_wrapper
             sage: R.<x,y> = GF(5)[]
             sage: S = R.quo([x^5, y^5])
             sage: M = S.derivation_module()
             sage: der = M.random_element()
             sage: isinstance(der, RingDerivationWithoutTwist_wrapper)
             True
-
-            sage: TestSuite(der).run()                                                  # needs sage.rings.finite_rings
+            sage: TestSuite(der).run()
 
         """
         if isinstance(arg, list) and len(arg) == 1 and isinstance(arg[0], RingDerivation):
@@ -1620,7 +1619,7 @@ def _add_(self, other):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: Dx = S.derivation(x)
@@ -1637,7 +1636,7 @@ def _sub_(self, other):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: Dx = S.derivation(x)
@@ -1654,7 +1653,7 @@ def _neg_(self):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: Dx = S.derivation(x)
@@ -1670,7 +1669,7 @@ def _lmul_(self, factor):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: Dx = S.derivation(x)
@@ -1688,7 +1687,7 @@ def _rmul_(self, factor):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: Dx = S.derivation(x)
@@ -1707,21 +1706,19 @@ def list(self):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: M = S.derivation_module()
             sage: M.basis()
             Family (d/dx, d/dy)
-
-            sage: S.derivation(x).list()                                                # needs sage.rings.finite_rings
+            sage: S.derivation(x).list()
             [1, 0]
-            sage: S.derivation(y).list()                                                # needs sage.rings.finite_rings
+            sage: S.derivation(y).list()
             [0, 1]
-
-            sage: f = x*S.derivation(x) + y*S.derivation(y); f                          # needs sage.rings.finite_rings
+            sage: f = x*S.derivation(x) + y*S.derivation(y); f
             x*d/dx + y*d/dy
-            sage: f.list()                                                              # needs sage.rings.finite_rings
+            sage: f.list()
             [x, y]
 
         """
@@ -2000,7 +1997,7 @@ def _call_(self, x):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.libs.singular
             sage: R.<X,Y> = GF(5)[]
             sage: S.<x,y> = R.quo([X^5, Y^5])
             sage: f = x^3*S.derivation(); f

src/sage/rings/factorint.pyx

@@ -50,6 +50,8 @@ cpdef aurifeuillian(n, m, F=None, bint check=True) noexcept:
     EXAMPLES::
 
         sage: from sage.rings.factorint import aurifeuillian
+
+        sage: # needs sage.libs.pari sage.rings.real_interval_field
         sage: aurifeuillian(2, 2)
         [5, 13]
         sage: aurifeuillian(2, 2^5)
@@ -58,6 +60,8 @@ cpdef aurifeuillian(n, m, F=None, bint check=True) noexcept:
         [1471, 2851]
         sage: aurifeuillian(15, 1)
         [19231, 142111]
+
+        sage: # needs sage.libs.pari
         sage: aurifeuillian(12, 3)
         Traceback (most recent call last):
         ...
@@ -76,15 +80,17 @@ cpdef aurifeuillian(n, m, F=None, bint check=True) noexcept:
         There is no need to set `F`. It's only for increasing speed
         of :meth:`factor_aurifeuillian()`.
     """
-    from sage.arith.misc import euler_phi
-    from sage.rings.real_mpfi import RealIntervalField
     if check:
         if not n.is_squarefree():
             raise ValueError("n has to be square-free")
         if n < 2:
             raise ValueError("n has to be greater than 1")
         if m < 1:
             raise ValueError("m has to be positive")
+
+    from sage.arith.misc import euler_phi
+    from sage.rings.real_mpfi import RealIntervalField
+
     x = m**2*n
     cdef Py_ssize_t y = euler_phi(2*n)//2
     if F is None:
@@ -129,7 +135,7 @@ cpdef factor_aurifeuillian(n, check=True) noexcept:
 
     EXAMPLES::
 
-        sage: # needs sage.libs.pari
+        sage: # needs sage.libs.pari sage.rings.real_interval_field
         sage: from sage.rings.factorint import factor_aurifeuillian as fa
         sage: fa(2^6 + 1)
         [5, 13]
@@ -148,7 +154,8 @@ cpdef factor_aurifeuillian(n, check=True) noexcept:
 
     TESTS::
 
-        sage: for n in [2,3,5,6,30,31,33]:                                              # needs sage.libs.pari
+        sage: # needs sage.libs.pari sage.rings.real_interval_field
+        sage: for n in [2,3,5,6,30,31,33]:
         ....:     for m in [8,96,109201283]:
         ....:         s = -1 if n % 4 == 1 else 1
         ....:         y = (m^2*n)^n + s