gh-36052: `sage.rings.{padics,valuation}`: Modularization fixes, `# needs`
    
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- Part of: #29705
- Cherry-picked from: #35095
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URL: #36052
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe

Author: Release Manager

src/sage/rings/padics/factory.py

@@ -975,10 +975,10 @@ def Qq(q, prec=None, type='capped-rel', modulus=None, names=None,
 
     2. The modulus can also be given as a **symbolic expression**. ::
 
-        sage: x = var('x')
-        sage: X.<a> = Qq(27, modulus = x^3 + 2*x + 1); X.modulus()
+        sage: x = var('x')                                                              # needs sage.symbolic
+        sage: X.<a> = Qq(27, modulus = x^3 + 2*x + 1); X.modulus()                      # needs sage.symbolic
         (1 + O(3^20))*x^3 + O(3^20)*x^2 + (2 + O(3^20))*x + 1 + O(3^20)
-        sage: X == R
+        sage: X == R                                                                    # needs sage.symbolic
         True
 
       By default, the polynomial chosen is the standard lift of the
@@ -2225,10 +2225,10 @@ def Zq(q, prec=None, type='capped-rel', modulus=None, names=None,
 
     2. The modulus can also be given as a **symbolic expression**. ::
 
-        sage: x = var('x')
-        sage: X.<a> = Zq(27, modulus = x^3 + 2*x + 1); X.modulus()
+        sage: x = var('x')                                                              # needs sage.symbolic
+        sage: X.<a> = Zq(27, modulus = x^3 + 2*x + 1); X.modulus()                      # needs sage.symbolic
         (1 + O(3^20))*x^3 + O(3^20)*x^2 + (2 + O(3^20))*x + 1 + O(3^20)
-        sage: X == R
+        sage: X == R                                                                    # needs sage.symbolic
         True
 
       By default, the polynomial chosen is the standard lift of the

src/sage/rings/padics/local_generic.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.padics
+# sage.doctest: needs sage.rings.padics
 r"""
 Local Generic
 

src/sage/rings/padics/local_generic_element.pyx

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.padics
+# sage.doctest: needs sage.rings.padics
 """
 Local Generic Element
 

src/sage/rings/padics/misc.py

@@ -91,25 +91,25 @@ def gauss_sum(a, p, f, prec=20, factored=False, algorithm='pari', parent=None):
     In this example, we verify that `g_3(0) = -1`::
 
         sage: from sage.rings.padics.misc import gauss_sum
-        sage: -gauss_sum(0, 3, 1)                                                       # optional - sage.rings.padics
+        sage: -gauss_sum(0, 3, 1)                                                       # needs sage.rings.padics
         1 + O(pi^40)
 
     Next, we verify that `g_5(a) g_5(-a) = 5 (-1)^a`::
 
         sage: from sage.rings.padics.misc import gauss_sum
-        sage: gauss_sum(2,5,1)^2 - 5                                                    # optional - sage.rings.padics
+        sage: gauss_sum(2,5,1)^2 - 5                                                    # needs sage.rings.padics
         O(pi^84)
-        sage: gauss_sum(1,5,1)*gauss_sum(3,5,1) + 5                                     # optional - sage.rings.padics
+        sage: gauss_sum(1,5,1)*gauss_sum(3,5,1) + 5                                     # needs sage.rings.padics
         O(pi^84)
 
     Finally, we compute a non-trivial value::
 
         sage: from sage.rings.padics.misc import gauss_sum
-        sage: gauss_sum(2,13,2)                                                         # optional - sage.rings.padics
+        sage: gauss_sum(2,13,2)                                                         # needs sage.rings.padics
         6*pi^2 + 7*pi^14 + 11*pi^26 + 3*pi^62 + 6*pi^74 + 3*pi^86 + 5*pi^98 +
         pi^110 + 7*pi^134 + 9*pi^146 + 4*pi^158 + 6*pi^170 + 4*pi^194 +
         pi^206 + 6*pi^218 + 9*pi^230 + O(pi^242)
-        sage: gauss_sum(2,13,2, prec=5, factored=True)                                  # optional - sage.rings.padics
+        sage: gauss_sum(2,13,2, prec=5, factored=True)                                  # needs sage.rings.padics
         (2, 6 + 6*13 + 10*13^2 + O(13^5))
 
     .. SEEALSO::

src/sage/rings/padics/padic_base_generic.py

@@ -433,11 +433,11 @@ def plot(self, max_points=2500, **args):
 
         EXAMPLES::
 
-            sage: Zp(3).plot()
+            sage: Zp(3).plot()                                                          # needs sage.plot
             Graphics object consisting of 1 graphics primitive
-            sage: Zp(5).plot(max_points=625)
+            sage: Zp(5).plot(max_points=625)                                            # needs sage.plot
             Graphics object consisting of 1 graphics primitive
-            sage: Zp(23).plot(rgbcolor=(1,0,0))
+            sage: Zp(23).plot(rgbcolor=(1,0,0))                                         # needs sage.plot
             Graphics object consisting of 1 graphics primitive
         """
         if 'pointsize' not in args:

src/sage/rings/padics/padic_generic.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.padics
+# sage.doctest: needs sage.rings.padics
 r"""
 `p`-adic Generic
 
@@ -36,7 +36,6 @@
 from sage.rings.ring import PrincipalIdealDomain
 from sage.rings.integer import Integer
 from sage.rings.infinity import Infinity
-from sage.rings.padics.padic_printing import pAdicPrinter
 from sage.rings.padics.precision_error import PrecisionError
 from sage.misc.cachefunc import cached_method
 from sage.structure.richcmp import richcmp_not_equal
@@ -59,6 +58,8 @@ def __init__(self, base, p, prec, print_mode, names, element_class, category=Non
 
             sage: R = Zp(17)  # indirect doctest
         """
+        from sage.rings.padics.padic_printing import pAdicPrinter
+
         if category is None:
             if self.is_field():
                 category = Fields()
@@ -1896,6 +1897,8 @@ def local_print_mode(obj, print_options, pos=None, ram_name=None):
 
         For more documentation see :class:`sage.structure.parent_gens.localvars`.
     """
+    from sage.rings.padics.padic_printing import pAdicPrinter
+
     if isinstance(print_options, str):
         print_options = {'mode': print_options}
     elif not isinstance(print_options, dict):

src/sage/rings/padics/padic_lattice_element.py

@@ -17,10 +17,11 @@
     sage: R3 = QpLC(2)
     sage: R4 = QpLF(2)
 
-    sage: TestSuite(R1).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
-    sage: TestSuite(R2).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
-    sage: TestSuite(R3).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
-    sage: TestSuite(R4).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
+    sage: # long time
+    sage: TestSuite(R1).run(skip=['_test_teichmuller', '_test_matrix_smith'])
+    sage: TestSuite(R2).run(skip=['_test_teichmuller', '_test_matrix_smith'])
+    sage: TestSuite(R3).run(skip=['_test_teichmuller', '_test_matrix_smith'])
+    sage: TestSuite(R4).run(skip=['_test_teichmuller', '_test_matrix_smith'])
 """
 
 # ****************************************************************************