Merge #30229

Author: Matthias Koeppe

src/sage/tensor/modules/finite_rank_free_module.py

@@ -38,10 +38,11 @@ class :class:`~sage.modules.free_module.FreeModule_generic`
 AUTHORS:
 
 - Eric Gourgoulhon, Michal Bejger (2014-2015): initial version
-- Travis Scrimshaw (2016): category set to Modules(ring).FiniteDimensional()
+- Travis Scrimshaw (2016): category set to ``Modules(ring).FiniteDimensional()``
   (:trac:`20770`)
 - Michael Jung (2019): improve treatment of the zero element
 - Eric Gourgoulhon (2021): unicode symbols for tensor and exterior products
+- Matthias Koeppe (2022): ``FiniteRankFreeModule_abstract``, symmetric powers
 
 REFERENCES:
 
@@ -519,16 +520,19 @@ class :class:`~sage.modules.free_module.FreeModule_generic`
     [2, 0, -5]
 
 """
-#******************************************************************************
-#       Copyright (C) 2015-2021 Eric Gourgoulhon <[email protected]>
-#       Copyright (C) 2015 Michal Bejger <[email protected]>
-#       Copyright (C) 2016 Travis Scrimshaw <[email protected]>
+# ******************************************************************************
+#       Copyright (C) 2014-2021 Eric Gourgoulhon <[email protected]>
+#                     2014-2016 Travis Scrimshaw <[email protected]>
+#                     2015      Michal Bejger <[email protected]>
+#                     2016      Frédéric Chapoton
+#                     2020      Michael Jung
+#                     2020-2022 Matthias Koeppe
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
-#******************************************************************************
+# ******************************************************************************
 from __future__ import annotations
 
 from typing import Generator, Optional
@@ -645,13 +649,70 @@ def tensor_product(self, *others):
             sage: M.tensor_module(1,1).tensor_product(M.tensor_module(1,2))
             Free module of type-(2,3) tensors on the 2-dimensional vector space over the Rational Field
 
+            sage: Sym2M = M.tensor_module(2, 0, sym=range(2)); Sym2M
+            Free module of fully symmetric type-(2,0) tensors on the 2-dimensional vector space over the Rational Field
+            sage: Sym01x23M = Sym2M.tensor_product(Sym2M); Sym01x23M
+            Free module of type-(4,0) tensors on the 2-dimensional vector space over the Rational Field,
+             with symmetry on the index positions (0, 1), with symmetry on the index positions (2, 3)
+            sage: Sym01x23M._index_maps
+            ((0, 1), (2, 3))
+
+            sage: N = M.tensor_module(3, 3, sym=[1, 2], antisym=[3, 4]); N
+            Free module of type-(3,3) tensors on the 2-dimensional vector space over the Rational Field,
+             with symmetry on the index positions (1, 2),
+             with antisymmetry on the index positions (3, 4)
+            sage: NxN = N.tensor_product(N); NxN
+            Free module of type-(6,6) tensors on the 2-dimensional vector space over the Rational Field,
+             with symmetry on the index positions (1, 2), with symmetry on the index positions (4, 5),
+             with antisymmetry on the index positions (6, 7), with antisymmetry on the index positions (9, 10)
+            sage: NxN._index_maps
+            ((0, 1, 2, 6, 7, 8), (3, 4, 5, 9, 10, 11))
         """
         from sage.modules.free_module_element import vector
+        from .comp import CompFullySym, CompFullyAntiSym, CompWithSym
+
         base_module = self.base_module()
         if not all(module.base_module() == base_module for module in others):
             raise NotImplementedError('all factors must be tensor modules over the same base module')
-        tensor_type = sum(vector(module.tensor_type()) for module in [self] + list(others))
-        return base_module.tensor_module(*tensor_type)
+        factors = [self] + list(others)
+        result_tensor_type = sum(vector(factor.tensor_type()) for factor in factors)
+        index_maps = []
+        running_indices = vector([0, result_tensor_type[0]])
+        result_sym = []
+        result_antisym = []
+        for factor in factors:
+            tensor_type = factor.tensor_type()
+            index_map = tuple(i + running_indices[0] for i in range(tensor_type[0]))
+            index_map += tuple(i + running_indices[1] for i in range(tensor_type[1]))
+            index_maps.append(index_map)
+
+            if tensor_type[0] + tensor_type[1] > 1:
+                basis_sym = factor._basis_sym()
+                all_indices = tuple(range(tensor_type[0] + tensor_type[1]))
+                if isinstance(basis_sym, CompFullySym):
+                    sym = [all_indices]
+                    antisym = []
+                elif isinstance(basis_sym, CompFullyAntiSym):
+                    sym = []
+                    antisym = [all_indices]
+                elif isinstance(basis_sym, CompWithSym):
+                    sym = basis_sym._sym
+                    antisym = basis_sym._antisym
+                else:
+                    sym = antisym = []
+
+                def map_isym(isym):
+                    return tuple(index_map[i] for i in isym)
+
+                result_sym.extend(tuple(index_map[i] for i in isym) for isym in sym)
+                result_antisym.extend(tuple(index_map[i] for i in isym) for isym in antisym)
+
+            running_indices += vector(tensor_type)
+
+        result = base_module.tensor_module(*result_tensor_type,
+                                           sym=result_sym, antisym=result_antisym)
+        result._index_maps = tuple(index_maps)
+        return result
 
     def rank(self) -> int:
         r"""
@@ -760,7 +821,7 @@ def is_submodule(self, other):
         EXAMPLES::
 
             sage: M = FiniteRankFreeModule(ZZ, 3, name='M')
-            sage: N = FiniteRankFreeModule(ZZ, 4, name='M')
+            sage: N = FiniteRankFreeModule(ZZ, 4, name='N')
             sage: M.is_submodule(M)
             True
             sage: M.is_submodule(N)

src/sage/tensor/modules/tensor_free_submodule.py

@@ -1,15 +1,19 @@
 r"""
 Free submodules of tensor modules defined by monoterm symmetries
+
+AUTHORS:
+
+- Matthias Koeppe (2020-2022): initial version
 """
 
-#******************************************************************************
+# ******************************************************************************
 #       Copyright (C) 2020-2022 Matthias Koeppe
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  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/
-#******************************************************************************
+# ******************************************************************************
 
 import itertools
 

src/sage/tensor/modules/tensor_free_submodule_basis.py

@@ -1,15 +1,19 @@
 r"""
 Standard bases of free submodules of tensor modules defined by some monoterm symmetries
+
+AUTHORS:
+
+- Matthias Koeppe (2020-2022): initial version
 """
 
-#******************************************************************************
+# ******************************************************************************
 #       Copyright (C) 2020-2022 Matthias Koeppe
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  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/
-#******************************************************************************
+# ******************************************************************************
 
 from sage.tensor.modules.free_module_basis import Basis_abstract