gh-38180: `sage.interfaces`: More `lazy_import`
    
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This includes some updates for low-level doctests so that they do not
trip over `LazyImport` objects.

- Cherry-picked from #35095 / #36380

### 📝 Checklist

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- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: #38180
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee

Author: Release Manager

src/sage/categories/pushout.py

@@ -3976,14 +3976,20 @@ class BlackBoxConstructionFunctor(ConstructionFunctor):
     EXAMPLES::
 
         sage: from sage.categories.pushout import BlackBoxConstructionFunctor
+
+        sage: # needs sage.libs.gap
+        sage: from sage.interfaces.gap import gap
         sage: FG = BlackBoxConstructionFunctor(gap)
-        sage: FS = BlackBoxConstructionFunctor(singular)
         sage: FG
         BlackBoxConstructionFunctor
-        sage: FG(ZZ)                                                                    # needs sage.libs.gap
+        sage: FG(ZZ)
         Integers
-        sage: FG(ZZ).parent()                                                           # needs sage.libs.gap
+        sage: FG(ZZ).parent()
         Gap
+        sage: FG == loads(dumps(FG))
+        True
+
+        sage: FS = BlackBoxConstructionFunctor(singular)
         sage: FS(QQ['t'])                                                               # needs sage.libs.singular
         polynomial ring, over a field, global ordering
         //   coefficients: QQ
@@ -3993,8 +3999,6 @@ class BlackBoxConstructionFunctor(ConstructionFunctor):
         //        block   2 : ordering C
         sage: FG == FS                                                                  # needs sage.libs.gap sage.libs.singular
         False
-        sage: FG == loads(dumps(FG))                                                    # needs sage.libs.gap
-        True
     """
     rank = 100
 

src/sage/doctest/forker.py

@@ -1579,6 +1579,7 @@ def report_unexpected_exception(self, out, test, example, exc_info):
 
         EXAMPLES::
 
+            sage: from sage.interfaces.sage0 import sage0
             sage: sage0.quit()
             sage: _ = sage0.eval("import doctest, sys, os, multiprocessing, subprocess")
             sage: _ = sage0.eval("from sage.doctest.parsing import SageOutputChecker")

src/sage/interfaces/all.py

@@ -1,32 +1,32 @@
 # interfaces to other interpreters
 
-from sage.interfaces.sage0 import sage0, sage0_version, Sage
-from sage.interfaces.gap import gap, gap_reset_workspace, Gap
-from sage.interfaces.gp import gp, gp_version, Gp
 # import problems
-# from maxima_lib import maxima_lib
-from sage.interfaces.maxima import maxima, Maxima
-from sage.interfaces.singular import singular, singular_version, Singular
-
-from sage.interfaces.magma import magma, Magma
-from sage.interfaces.polymake import polymake
+try:
+    # from maxima_lib import maxima_lib
+    from sage.interfaces.maxima import maxima, Maxima
+except ImportError:
+    pass
 
 from sage.misc.lazy_import import lazy_import
 
+lazy_import('sage.interfaces.sage0', ['sage0', 'sage0_version', 'Sage'])
 lazy_import('sage.interfaces.axiom', ['Axiom', 'axiom'])
 lazy_import('sage.interfaces.ecm', ['ECM', 'ecm'])
 lazy_import('sage.interfaces.four_ti_2', 'four_ti_2')
 lazy_import('sage.interfaces.fricas', ['FriCAS', 'fricas'])
 lazy_import('sage.interfaces.frobby', 'frobby')
+lazy_import('sage.interfaces.gap', ['gap', 'gap_reset_workspace', 'Gap'])
 lazy_import('sage.interfaces.gap3', ['gap3', 'gap3_version', 'Gap3'])
 lazy_import('sage.interfaces.genus2reduction', ['genus2reduction', 'Genus2reduction'])
 lazy_import('sage.interfaces.gfan', ['gfan', 'Gfan'])
 lazy_import('sage.interfaces.giac', ['giac', 'Giac'])
 lazy_import('sage.interfaces.gnuplot', 'gnuplot')
+lazy_import('sage.interfaces.gp', ['gp', 'gp_version', 'Gp'])
 lazy_import('sage.interfaces.kash', ['kash', 'kash_version', 'Kash'])
 lazy_import('sage.interfaces.lie', ['lie', 'LiE'])
 lazy_import('sage.interfaces.lisp', ['lisp', 'Lisp'])
 lazy_import('sage.interfaces.macaulay2', ['macaulay2', 'Macaulay2'])
+lazy_import('sage.interfaces.magma', ['magma', 'Magma'])
 lazy_import('sage.interfaces.magma_free', 'magma_free')
 lazy_import('sage.interfaces.maple', ['maple', 'Maple'])
 lazy_import('sage.interfaces.mathematica', ['mathematica', 'Mathematica'])
@@ -35,12 +35,14 @@
 lazy_import('sage.interfaces.mupad', ['mupad', 'Mupad'])  # NOT functional yet
 lazy_import('sage.interfaces.mwrank', ['mwrank', 'Mwrank'])
 lazy_import('sage.interfaces.octave', ['octave', 'Octave'])
+lazy_import('sage.interfaces.polymake', 'polymake')
 lazy_import('sage.interfaces.povray', 'povray')
 lazy_import('sage.interfaces.psage', 'PSage')
 lazy_import('sage.interfaces.qepcad', ['qepcad', 'qepcad_version', 'qepcad_formula'])
 lazy_import('sage.interfaces.r', ['r', 'R', 'r_version'])
 lazy_import('sage.interfaces.read_data', 'read_data')
 lazy_import('sage.interfaces.scilab', 'scilab')
+lazy_import('sage.interfaces.singular', ['singular', 'singular_version', 'Singular'])
 lazy_import('sage.interfaces.tachyon', 'tachyon_rt')
 
 # The following variable is used by sage-shell-mode in emacs:

src/sage/interfaces/expect.py

@@ -928,6 +928,7 @@ def _eval_line(self, line, allow_use_file=True, wait_for_prompt=True, restart_if
 
         TESTS::
 
+            sage: from sage.interfaces.singular import singular
             sage: singular._eval_line('def a=3;')
             ''
             sage: singular('a')

src/sage/interfaces/gap.py

@@ -644,6 +644,7 @@ def _eval_line(self, line, allow_use_file=True, wait_for_prompt=True, restart_if
 
         TESTS::
 
+            sage: from sage.interfaces.gap import gap
             sage: gap._eval_line('2+2;')
             '4'
 
@@ -1124,6 +1125,7 @@ def __reduce__(self):
         """
         EXAMPLES::
 
+            sage: from sage.interfaces.gap import gap
             sage: gap.__reduce__()
             (<function reduce_load_GAP at 0x...>, ())
             sage: f, args = _

src/sage/interfaces/gp.py

@@ -270,7 +270,7 @@ def _repr_(self):
 
         EXAMPLES::
 
-            sage: gp # indirect doctest
+            sage: gp  # indirect doctest
             PARI/GP interpreter
         """
         return 'PARI/GP interpreter'
@@ -279,6 +279,7 @@ def __reduce__(self):
         """
         EXAMPLES::
 
+            sage: from sage.interfaces.gp import gp
             sage: gp.__reduce__()
             (<function reduce_load_GP at 0x...>, ())
             sage: f, args = _

src/sage/interfaces/interface.py

@@ -638,6 +638,7 @@ def __getattr__(self, attrname):
         TESTS::
 
             sage: from sage.structure.parent_base import ParentWithBase
+            sage: from sage.interfaces.singular import singular
             sage: ParentWithBase.__getattribute__(singular, '_coerce_map_from_')
             <bound method Singular._coerce_map_from_ of Singular>
         """

src/sage/interfaces/magma.py

@@ -397,6 +397,7 @@ def __reduce__(self):
 
         EXAMPLES::
 
+            sage: from sage.interfaces.magma import magma
             sage: loads(dumps(magma)) is magma
             True
 

src/sage/interfaces/polymake.py

@@ -155,6 +155,7 @@ def __reduce__(self):
         """
         EXAMPLES::
 
+            sage: from sage.interfaces.polymake import polymake
             sage: loads(dumps(polymake)) is polymake
             True
 

src/sage/interfaces/singular.py

@@ -468,6 +468,7 @@ def __reduce__(self):
         """
         EXAMPLES::
 
+            sage: from sage.interfaces.singular import singular
             sage: singular.__reduce__()
             (<function reduce_load_Singular at 0x...>, ())
         """