sagemathgh-38096: sage.combinat, sage.games: Use more `lazy_impor…

…t` in all.py files

    
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This helps with the modularization, but is also desirable for reducing
the start-up time of Sage.
- Cherry-picked from sagemath#37900

Related: sagemath#35520

### 📝 Checklist

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- [ ] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: sagemath#38096
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee

src/sage/categories/weyl_groups.py

@@ -572,9 +572,10 @@ def stanley_symmetric_function(self):
 
             - [Pon2010]_
             """
-            import sage.combinat.sf
             from sage.rings.rational_field import QQ
-            m = sage.combinat.sf.sf.SymmetricFunctions(QQ).monomial()
+            from sage.combinat.sf.sf import SymmetricFunctions
+
+            m = SymmetricFunctions(QQ).monomial()
             return m.from_polynomial_exp(self.stanley_symmetric_function_as_polynomial())
 
         @cached_in_parent_method

src/sage/combinat/ncsf_qsym/all.py

@@ -11,5 +11,10 @@
 from sage.misc.namespace_package import install_doc
 install_doc(__package__, __doc__)
 
-from sage.combinat.ncsf_qsym.qsym import QuasiSymmetricFunctions
-from sage.combinat.ncsf_qsym.ncsf import NonCommutativeSymmetricFunctions
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.combinat.ncsf_qsym.qsym', 'QuasiSymmetricFunctions')
+lazy_import('sage.combinat.ncsf_qsym.ncsf', 'NonCommutativeSymmetricFunctions')
+
+del install_doc
+del lazy_import

src/sage/combinat/ncsym/all.py

@@ -11,5 +11,10 @@
 from sage.misc.namespace_package import install_doc
 install_doc(__package__, __doc__)
 
-from sage.combinat.ncsym.ncsym import SymmetricFunctionsNonCommutingVariables
-from sage.combinat.ncsym.dual import SymmetricFunctionsNonCommutingVariablesDual
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.combinat.ncsym.ncsym', 'SymmetricFunctionsNonCommutingVariables')
+lazy_import('sage.combinat.ncsym.dual', 'SymmetricFunctionsNonCommutingVariablesDual')
+
+del install_doc
+del lazy_import

src/sage/combinat/root_system/all.py

@@ -122,9 +122,9 @@
 from sage.misc.lazy_import import lazy_import
 
 from sage.combinat.root_system.cartan_type import CartanType
-from sage.combinat.root_system.dynkin_diagram import DynkinDiagram
-from sage.combinat.root_system.cartan_matrix import CartanMatrix
-from sage.combinat.root_system.coxeter_matrix import CoxeterMatrix
+lazy_import('sage.combinat.root_system.dynkin_diagram', 'DynkinDiagram')
+lazy_import('sage.combinat.root_system.cartan_matrix', 'CartanMatrix')
+lazy_import('sage.combinat.root_system.coxeter_matrix', 'CoxeterMatrix')
 from sage.combinat.root_system.coxeter_type import CoxeterType
 from sage.combinat.root_system.root_system import RootSystem, WeylDim
 lazy_import('sage.combinat.root_system.weyl_group', ['WeylGroup',
@@ -138,5 +138,9 @@
                                                           'WeightRing'])
 from sage.combinat.root_system.branching_rules import BranchingRule, branching_rule_from_plethysm, branching_rule
 
-lazy_import('sage.combinat.root_system.non_symmetric_macdonald_polynomials', 'NonSymmetricMacdonaldPolynomials')
-lazy_import('sage.combinat.root_system.integrable_representations', 'IntegrableRepresentation')
+lazy_import('sage.combinat.root_system.non_symmetric_macdonald_polynomials',
+            'NonSymmetricMacdonaldPolynomials')
+lazy_import('sage.combinat.root_system.integrable_representations',
+            'IntegrableRepresentation')
+del lazy_import
+del install_doc

src/sage/combinat/words/all.py

@@ -43,11 +43,16 @@
 from sage.misc.namespace_package import install_doc
 install_doc(__package__, __doc__)
 
+from sage.misc.lazy_import import lazy_import
+
 from sage.combinat.words.alphabet import Alphabet, build_alphabet
 from sage.combinat.words.morphism import WordMorphism
-from sage.combinat.words.paths import WordPaths
+lazy_import('sage.combinat.words.paths', 'WordPaths')
 from sage.combinat.words.word import Word
 from sage.combinat.words.word_options import WordOptions
 from sage.combinat.words.word_generators import words
 from sage.combinat.words.words import Words, FiniteWords, InfiniteWords
 from sage.combinat.words.lyndon_word import LyndonWord, LyndonWords, StandardBracketedLyndonWords
+
+del install_doc
+del lazy_import

src/sage/games/all.py

@@ -1,2 +1,6 @@
-from sage.games.sudoku import Sudoku, sudoku
-from sage.games.hexad import Minimog
+
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.games.sudoku', ['Sudoku', 'sudoku'])
+lazy_import('sage.games.hexad', ['Minimog'])
+del lazy_import

src/sage/structure/parent.pyx

@@ -2143,7 +2143,7 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
 
             sage: # needs sage.combinat sage.modules
             sage: R = QQ['q,t'].fraction_field()
-            sage: Sym = sage.combinat.sf.sf.SymmetricFunctions(R)
+            sage: Sym = SymmetricFunctions(R)
             sage: H = Sym.macdonald().H()
             sage: P = Sym.macdonald().P()
             sage: m = Sym.monomial()
@@ -2180,7 +2180,7 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
 
             sage: # needs sage.combinat sage.modules
             sage: R = QQ['q,t'].fraction_field()
-            sage: Sym = sage.combinat.sf.sf.SymmetricFunctions(R)
+            sage: Sym = SymmetricFunctions(R)
             sage: P = Sym.macdonald().P()
             sage: Ht = Sym.macdonald().Ht()
             sage: Ht._internal_coerce_map_from(P)