Standard bases of free submodules of tensor modules defined by some monoterm symmetries¶
AUTHORS:
- Matthias Koeppe (2020-2022): initial version 
- class sage.tensor.modules.tensor_free_submodule_basis.TensorFreeSubmoduleBasis_sym(tensor_module, symbol, latex_symbol=None, indices=None, latex_indices=None, symbol_dual=None, latex_symbol_dual=None)[source]¶
- Bases: - Basis_abstract- Standard basis of a free submodule of a tensor module with prescribed monoterm symmetries. - EXAMPLES: - sage: M = FiniteRankFreeModule(ZZ, 3, name='M') sage: T11 = M.tensor_module(1,1) sage: e11 = T11.basis('e') sage: for a in e11: a.display() e_0⊗e^0 e_0⊗e^1 e_0⊗e^2 e_1⊗e^0 e_1⊗e^1 e_1⊗e^2 e_2⊗e^0 e_2⊗e^1 e_2⊗e^2 - >>> from sage.all import * >>> M = FiniteRankFreeModule(ZZ, Integer(3), name='M') >>> T11 = M.tensor_module(Integer(1),Integer(1)) >>> e11 = T11.basis('e') >>> for a in e11: a.display() e_0⊗e^0 e_0⊗e^1 e_0⊗e^2 e_1⊗e^0 e_1⊗e^1 e_1⊗e^2 e_2⊗e^0 e_2⊗e^1 e_2⊗e^2 - keys()[source]¶
- Return an iterator for the keys (indices) of the family. - EXAMPLES: - sage: M = FiniteRankFreeModule(ZZ, 3, name='M') sage: T11 = M.tensor_module(1,1) sage: e11 = T11.basis('e') sage: list(e11.keys()) [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)] - >>> from sage.all import * >>> M = FiniteRankFreeModule(ZZ, Integer(3), name='M') >>> T11 = M.tensor_module(Integer(1),Integer(1)) >>> e11 = T11.basis('e') >>> list(e11.keys()) [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)] 
 - values()[source]¶
- Return an iterator for the elements of the family. - EXAMPLES: - sage: M = FiniteRankFreeModule(ZZ, 3, name='M') sage: T11 = M.tensor_module(1,1) sage: e11 = T11.basis('e') sage: [b.disp() for b in e11.values()] [e_0⊗e^0, e_0⊗e^1, e_0⊗e^2, e_1⊗e^0, e_1⊗e^1, e_1⊗e^2, e_2⊗e^0, e_2⊗e^1, e_2⊗e^2] - >>> from sage.all import * >>> M = FiniteRankFreeModule(ZZ, Integer(3), name='M') >>> T11 = M.tensor_module(Integer(1),Integer(1)) >>> e11 = T11.basis('e') >>> [b.disp() for b in e11.values()] [e_0⊗e^0, e_0⊗e^1, e_0⊗e^2, e_1⊗e^0, e_1⊗e^1, e_1⊗e^2, e_2⊗e^0, e_2⊗e^1, e_2⊗e^2]