sagemathgh-36676: Restructure sage.*.all for modularization, replac…

…e relative by absolute imports

    
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<!-- Describe your changes here in detail -->
We restructure the `all.py` files for modularization.

Guided by the technical constraints outlined in
https://groups.google.com/g/sage-devel/c/ozh-7ZZ848s, sagemath#35095 defines
distribution packages (pip-installable packages) **sagemath-{brial,
combinat, eclib, flint, gap, giac, glpk, graphs, groups, homfly, lcalc,
libbraiding, libecm, linbox, modules, mpmath, ntl, pari, plot,
polyhedra, schemes, singular, standard-no-symbolics, symbolics}**.

When a namespace package such as `sage.misc` is filled by modules from
several distribution packages, we create modules named:
- `src/sage/misc/all__sagemath_environment.py`
- `src/sage/misc/all__sagemath_objects.py`
- `src/sage/misc/all__sagemath_repl.py`

Import statements are moved from `src/sage/misc/all.py` to these files
as appropriate, and `src/sage/misc/all.py` imports `*` from there.

Also some imports are replaced by lazy imports.

The new files provide the top level namespaces for the modularized
distribution packages, thus [enabling modularized testing](https://doc.s
agemath.org/html/en/developer/packaging_sage_library.html#testing-
distribution-packages).

This design was introduced in sagemath#29865 (merged in Jan 2022, early in the
Sage 9.6 development cycle).

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example "Fixes sagemath#12345". -->
- Copied from sagemath#35095.
- Part of sagemath#29705

Moreover, applied a one-line command to replace relative by absolute
imports, thus complementing sagemath#36666, which does not touch `.all*` files.

The changes to other files in `sage.modules` etc. come from the PRs
sagemath#36597, sagemath#36572, sagemath#36588, sagemath#36589 merged here and do not need review.

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appropriately. -->

### 📝 Checklist

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- [x] The title is concise, informative, and self-explanatory.
- [x] 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 accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
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- Depends on sagemath#36597 (merged here to resolve merge conflict)
- Depends on sagemath#36572 (merged here to
resolve merge conflict)
- Depends on sagemath#36588 (merged here to
resolve merge conflict)
- Depends on sagemath#36589 (merged here to
resolve merge conflict)
- Depends on sagemath#36449 (merged here to resolve merge conflict)

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URL: sagemath#36676
Reported by: Matthias Köppe
Reviewer(s): David Coudert, John H. Palmieri, Kwankyu Lee, Matthias Köppe, Tobias Diez

pkgs/sagemath-categories/known-test-failures.json

@@ -26,7 +26,7 @@
         "ntests": 28
     },
     "sage.categories.affine_weyl_groups": {
-        "ntests": 14
+        "ntests": 15
     },
     "sage.categories.algebra_ideals": {
         "failed": true,
@@ -148,7 +148,7 @@
     },
     "sage.categories.coxeter_groups": {
         "failed": true,
-        "ntests": 362
+        "ntests": 363
     },
     "sage.categories.cw_complexes": {
         "failed": true,
@@ -301,7 +301,7 @@
     },
     "sage.categories.finite_complex_reflection_groups": {
         "failed": true,
-        "ntests": 178
+        "ntests": 199
     },
     "sage.categories.finite_coxeter_groups": {
         "ntests": 6
@@ -493,10 +493,6 @@
         "failed": true,
         "ntests": 13
     },
-    "sage.categories.inner_product_spaces": {
-        "failed": true,
-        "ntests": 9
-    },
     "sage.categories.integral_domains": {
         "failed": true,
         "ntests": 22
@@ -783,7 +779,7 @@
     },
     "sage.cpython.debug": {
         "failed": true,
-        "ntests": 14
+        "ntests": 13
     },
     "sage.cpython.dict_del_by_value": {
         "failed": true,
@@ -826,7 +822,6 @@
         "ntests": 321
     },
     "sage.doctest.reporting": {
-        "failed": true,
         "ntests": 124
     },
     "sage.doctest.sources": {
@@ -1091,7 +1086,7 @@
     },
     "sage.misc.sageinspect": {
         "failed": true,
-        "ntests": 329
+        "ntests": 332
     },
     "sage.misc.superseded": {
         "failed": true,
@@ -1124,6 +1119,7 @@
         "ntests": 128
     },
     "sage.repl.configuration": {
+        "failed": true,
         "ntests": 22
     },
     "sage.repl.display.fancy_repr": {
@@ -1149,6 +1145,7 @@
         "ntests": 42
     },
     "sage.repl.inputhook": {
+        "failed": true,
         "ntests": 7
     },
     "sage.repl.interface_magic": {
@@ -1157,7 +1154,7 @@
     },
     "sage.repl.interpreter": {
         "failed": true,
-        "ntests": 118
+        "ntests": 114
     },
     "sage.repl.ipython_extension": {
         "failed": true,
@@ -1188,7 +1185,7 @@
     },
     "sage.repl.load": {
         "failed": true,
-        "ntests": 42
+        "ntests": 38
     },
     "sage.repl.preparse": {
         "failed": true,
@@ -1315,9 +1312,6 @@
     "sage.structure.global_options": {
         "ntests": 145
     },
-    "sage.structure.graphics_file": {
-        "ntests": 8
-    },
     "sage.structure.indexed_generators": {
         "failed": true,
         "ntests": 90

src/doc/en/reference/calculus/index.rst

@@ -23,6 +23,7 @@ Using calculus
 
 - :doc:`More about symbolic variables and functions <sage/calculus/var>`
 - :doc:`Main operations on symbolic expressions <sage/symbolic/expression>`
+- :doc:`sage/calculus/expr`
 - :doc:`Assumptions about symbols and functions <sage/symbolic/assumptions>`
 - :doc:`sage/symbolic/relation`
 - :doc:`sage/symbolic/integration/integral`
@@ -65,6 +66,7 @@ Internal functionality supporting calculus
 
    sage/symbolic/expression
    sage/symbolic/callable
+   sage/calculus/expr
    sage/symbolic/assumptions
    sage/symbolic/relation
    sage/calculus/calculus

src/sage/algebras/all.py

@@ -14,56 +14,12 @@
 #  The full text of the GPL is available at:
 #
 #                  https://www.gnu.org/licenses/
-# ****************************************************************************
-from sage.misc.lazy_import import lazy_import
-
-# old-style class for associative algebras, use Parent instead
-from sage.rings.ring import Algebra
-
-import sage.algebras.catalog as algebras
-
-from .quatalg.all import *
-from .steenrod.all import *
-from .fusion_rings.all import *
-from .lie_algebras.all import *
-from .quantum_groups.all import *
-from .lie_conformal_algebras.all import *
-
-# Algebra base classes
-from .free_algebra import FreeAlgebra
-from .free_algebra_quotient import FreeAlgebraQuotient
-
-from .finite_dimensional_algebras.all import FiniteDimensionalAlgebra
-
-lazy_import('sage.algebras.group_algebra', 'GroupAlgebra')
-
-lazy_import('sage.algebras.iwahori_hecke_algebra', 'IwahoriHeckeAlgebra')
-lazy_import('sage.algebras.affine_nil_temperley_lieb',
-            'AffineNilTemperleyLiebTypeA')
-lazy_import('sage.algebras.nil_coxeter_algebra', 'NilCoxeterAlgebra')
-lazy_import('sage.algebras.schur_algebra', ['SchurAlgebra',
-                                            'SchurTensorModule'])
-
-lazy_import('sage.algebras.hall_algebra', 'HallAlgebra')
-
-lazy_import('sage.algebras.jordan_algebra', 'JordanAlgebra')
-
-lazy_import('sage.algebras.octonion_algebra', 'OctonionAlgebra')
-
-lazy_import('sage.algebras.shuffle_algebra', 'ShuffleAlgebra')
-
-from .clifford_algebra import CliffordAlgebra, ExteriorAlgebra
-from .weyl_algebra import DifferentialWeylAlgebra
-
-lazy_import('sage.algebras.commutative_dga', 'GradedCommutativeAlgebra')
-
-lazy_import('sage.algebras.rational_cherednik_algebra',
-            'RationalCherednikAlgebra')
-
-lazy_import('sage.algebras.tensor_algebra', 'TensorAlgebra')
-
-lazy_import('sage.algebras.q_system', 'QSystem')
+# *****************************************************************************
 
-lazy_import('sage.algebras.cluster_algebra', 'ClusterAlgebra')
+from sage.algebras.all__sagemath_modules import *
+from sage.algebras.all__sagemath_combinat import *
 
-lazy_import('sage.algebras.yangian', 'Yangian')
+from sage.algebras.quatalg.all import *
+from sage.algebras.fusion_rings.all import *
+from sage.algebras.lie_algebras.all import *
+from sage.algebras.lie_conformal_algebras.all import *

src/sage/algebras/all__sagemath_combinat.py

@@ -0,0 +1,37 @@
+from sage.misc.lazy_import import lazy_import
+
+
+# Algebra base classes
+from sage.algebras.free_algebra import FreeAlgebra
+from sage.algebras.free_algebra_quotient import FreeAlgebraQuotient
+
+from sage.algebras.steenrod.all import *
+from sage.algebras.quantum_groups.all import *
+
+lazy_import('sage.algebras.iwahori_hecke_algebra', 'IwahoriHeckeAlgebra')
+lazy_import('sage.algebras.affine_nil_temperley_lieb',
+            'AffineNilTemperleyLiebTypeA')
+lazy_import('sage.algebras.nil_coxeter_algebra', 'NilCoxeterAlgebra')
+lazy_import('sage.algebras.schur_algebra', ['SchurAlgebra',
+                                            'SchurTensorModule'])
+
+lazy_import('sage.algebras.hall_algebra', 'HallAlgebra')
+
+lazy_import('sage.algebras.jordan_algebra', 'JordanAlgebra')
+
+lazy_import('sage.algebras.shuffle_algebra', 'ShuffleAlgebra')
+
+lazy_import('sage.algebras.commutative_dga', 'GradedCommutativeAlgebra')
+
+lazy_import('sage.algebras.rational_cherednik_algebra',
+            'RationalCherednikAlgebra')
+
+lazy_import('sage.algebras.tensor_algebra', 'TensorAlgebra')
+
+lazy_import('sage.algebras.q_system', 'QSystem')
+
+lazy_import('sage.algebras.cluster_algebra', 'ClusterAlgebra')
+
+lazy_import('sage.algebras.yangian', 'Yangian')
+
+del lazy_import

src/sage/algebras/all__sagemath_modules.py

@@ -0,0 +1,14 @@
+from sage.misc.lazy_import import lazy_import
+
+lazy_import('sage.algebras.group_algebra', 'GroupAlgebra')
+
+# old-style class for associative algebras, use Parent instead
+from sage.rings.ring import Algebra
+
+from sage.algebras.finite_dimensional_algebras.all import FiniteDimensionalAlgebra
+from sage.algebras.clifford_algebra import CliffordAlgebra, ExteriorAlgebra
+from sage.algebras.weyl_algebra import DifferentialWeylAlgebra
+lazy_import('sage.algebras.octonion_algebra', 'OctonionAlgebra')
+
+import sage.algebras.catalog as algebras
+del lazy_import

src/sage/algebras/finite_dimensional_algebras/all.py

@@ -1 +1 @@
-from .finite_dimensional_algebra import FiniteDimensionalAlgebra
+from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import FiniteDimensionalAlgebra

src/sage/algebras/fusion_rings/all.py

@@ -15,3 +15,4 @@
 
 lazy_import('sage.algebras.fusion_rings.fusion_ring', ['FusionRing'])
 lazy_import('sage.algebras.fusion_rings.fusion_double', ['FusionDouble'])
+del lazy_import

src/sage/algebras/hecke_algebras/all.py

@@ -1,4 +1,3 @@
 """
 Hecke Algebras
 """
-#from sage.misc.lazy_import import lazy_import

src/sage/algebras/lie_algebras/all.py

@@ -2,7 +2,7 @@
 Lie Algebras
 """
 
-#*****************************************************************************
+# *****************************************************************************
 #       Copyright (C) 2013 Travis Scrimshaw <tscrim at ucdavis.edu>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
@@ -14,10 +14,11 @@
 #
 #  The full text of the GPL is available at:
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# *****************************************************************************
 from sage.misc.lazy_import import lazy_import
 
 lazy_import('sage.algebras.lie_algebras.lie_algebra', 'LieAlgebra')
-#from kac_moody import KacMoodyAlgebra
+# from kac_moody import KacMoodyAlgebra
 lazy_import('sage.algebras.lie_algebras', 'examples', 'lie_algebras')
+del lazy_import

src/sage/algebras/lie_conformal_algebras/all.py

@@ -1,14 +1,17 @@
-#******************************************************************************
+# ******************************************************************************
 #       Copyright (C) 2020 Reimundo Heluani <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# *****************************************************************************
 
 
 from sage.misc.lazy_import import lazy_import
-lazy_import('sage.algebras.lie_conformal_algebras.lie_conformal_algebra','LieConformalAlgebra')
-lazy_import('sage.algebras.lie_conformal_algebras', 'examples', 'lie_conformal_algebras')
+lazy_import('sage.algebras.lie_conformal_algebras.lie_conformal_algebra',
+            'LieConformalAlgebra')
+lazy_import('sage.algebras.lie_conformal_algebras',
+            'examples', 'lie_conformal_algebras')
+del lazy_import

src/sage/algebras/quantum_groups/all.py

@@ -5,3 +5,4 @@
 from sage.misc.lazy_import import lazy_import
 lazy_import('sage.algebras.quantum_groups.fock_space', 'FockSpace')
 lazy_import('sage.algebras.quantum_groups.quantum_group_gap', 'QuantumGroup')
+del lazy_import

src/sage/algebras/quatalg/all.py

@@ -1 +1 @@
-from .quaternion_algebra import QuaternionAlgebra
+from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra

src/sage/algebras/steenrod/all.py

@@ -1,8 +1,9 @@
 """
 The Steenrod algebra
 """
-from .steenrod_algebra import SteenrodAlgebra, Sq
 from sage.misc.lazy_import import lazy_import
+lazy_import('sage.algebras.steenrod.steenrod_algebra', ['SteenrodAlgebra', 'Sq'])
 lazy_import('sage.algebras.steenrod.steenrod_algebra_bases',
             'steenrod_algebra_basis',
             deprecation=(32647, 'removed from namespace'))
+del lazy_import