Index

A

additive_order() (sage.modules.fg_pid.fgp_element.FGP_Element method) (sage.modules.free_module_element.FreeModuleElement method) alternating_form() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) ambient() (sage.modules.with_basis.subquotient.QuotientModuleWithBasis method) (sage.modules.with_basis.subquotient.SubmoduleWithBasis method) ambient_module() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic method) ambient_vector_space() (sage.modules.free_module.FreeModule_ambient_domain method) (sage.modules.free_module.FreeModule_ambient_field method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) (sage.modules.free_quadratic_module.FreeQuadraticModule_ambient_domain method)

annihilator() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) apply_map() (in module sage.modules.vector_symbolic_dense) (sage.modules.free_module_element.FreeModuleElement method) are_linearly_dependent() (sage.modules.free_module.FreeModule_generic method) automorphism() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method)

B

base_extend() (sage.modules.module.Module method) base_field() (sage.modules.free_module.FreeModule_ambient_field method) (sage.modules.free_module.FreeModule_generic method) base_ring() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.matrix_morphism.MatrixMorphism_abstract method) bases() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method)

basis() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) (sage.modules.free_module_homspace.FreeModuleHomspace method) (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) basis_matrix() (sage.modules.free_module.FreeModule_generic method) basis_seq() (in module sage.modules.free_module) BKZ() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method)

C

calculate_voronoi_cell() (in module sage.modules.diamond_cutting) canonicalize_radical() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) cardinality() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic method) change_of_basis() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) change_ring() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_morphism.FreeModuleMorphism method) (sage.modules.free_quadratic_module.FreeQuadraticModule_submodule_with_basis_pid method) (sage.modules.module.Module method) characteristic_polynomial() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) charpoly() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) closest_vector() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) co_kernel_projection() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) co_reduced() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) cokernel_basis_indices() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) cokernel_projection() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) column() (sage.modules.free_module_element.FreeModuleElement method) complement() (sage.modules.free_module.FreeModule_generic_field method)

complex_vector() (sage.modules.vector_double_dense.Vector_double_dense method) ComplexDoubleVectorSpace_class (class in sage.modules.free_module) conjugate() (sage.modules.free_module_element.FreeModuleElement method) construction() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) coordinate_module() (sage.modules.free_module.FreeModule_generic method) coordinate_ring() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_element.FreeModuleElement method) coordinate_vector() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_ambient_domain method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_field method) (sage.modules.free_module.FreeModule_submodule_pid method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) coordinates() (sage.modules.free_module.ComplexDoubleVectorSpace_class method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.RealDoubleVectorSpace_class method) coreduced() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) cover() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) create_key() (sage.modules.free_module.FreeModuleFactory method) create_object() (sage.modules.free_module.FreeModuleFactory method) cross_product() (sage.modules.free_module_element.FreeModuleElement method) curl() (sage.modules.free_module_element.FreeModuleElement method)

D

decomposition() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) default_basis() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) degree() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_element.FreeModuleElement method) denominator() (sage.modules.free_module.FreeModule_generic_pid method) (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method) dense_module() (sage.modules.free_module.FreeModule_generic method) dense_vector() (sage.modules.free_module_element.FreeModuleElement method) derivative() (sage.modules.free_module_element.FreeModuleElement method) det() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) determinant() (sage.modules.free_quadratic_module.FreeQuadraticModule_generic method) DiagonalModuleMorphism (class in sage.modules.with_basis.morphism)

diamond_cut() (in module sage.modules.diamond_cutting) dict() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method) diff() (sage.modules.free_module_element.FreeModuleElement method) dimension() (sage.modules.free_module.FreeModule_generic method) direct_sum() (sage.modules.free_module.FreeModule_generic method) discriminant() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic method) div() (sage.modules.free_module_element.FreeModuleElement method) dot_product() (sage.modules.free_module_element.FreeModuleElement method) dual() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) dual_exterior_power() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method)

E

echelon_coordinate_vector() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) echelon_coordinates() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_submodule_field method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) echelon_to_user_matrix() (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) echelonized_basis() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) echelonized_basis_matrix() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) eigenspaces() (sage.modules.free_module_morphism.FreeModuleMorphism method) eigenvalues() (sage.modules.free_module_morphism.FreeModuleMorphism method)

eigenvectors() (sage.modules.free_module_morphism.FreeModuleMorphism method) Element (sage.modules.fg_pid.fgp_module.FGP_Module_class attribute) (sage.modules.fg_pid.fgp_morphism.FGP_Homset_class attribute) (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule attribute) element() (sage.modules.free_module_element.FreeModuleElement method) element_class() (in module sage.modules.free_module) endomorphism() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) endomorphism_ring() (sage.modules.module.Module method)

F

fcp() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) fft() (sage.modules.vector_double_dense.Vector_double_dense method) FGP_Element (class in sage.modules.fg_pid.fgp_element) FGP_Homset() (in module sage.modules.fg_pid.fgp_morphism) FGP_Homset_class (class in sage.modules.fg_pid.fgp_morphism) FGP_Module() (in module sage.modules.fg_pid.fgp_module) FGP_Module_class (class in sage.modules.fg_pid.fgp_module) FGP_Morphism (class in sage.modules.fg_pid.fgp_morphism) FiniteFieldsubspace_iterator (class in sage.modules.finite_submodule_iter) FiniteFieldsubspace_projPoint_iterator (class in sage.modules.finite_submodule_iter) FiniteRankFreeModule (class in sage.tensor.modules.finite_rank_free_module) FiniteZZsubmodule_iterator (class in sage.modules.finite_submodule_iter) free_module() (sage.modules.free_module.FreeModule_generic method) free_module_element() (in module sage.modules.free_module_element) FreeModule_ambient (class in sage.modules.free_module) FreeModule_ambient_domain (class in sage.modules.free_module) FreeModule_ambient_field (class in sage.modules.free_module) FreeModule_ambient_field_quotient (class in sage.modules.quotient_module) FreeModule_ambient_pid (class in sage.modules.free_module) FreeModule_generic (class in sage.modules.free_module) FreeModule_generic_field (class in sage.modules.free_module) FreeModule_generic_pid (class in sage.modules.free_module) FreeModule_submodule_field (class in sage.modules.free_module)

FreeModule_submodule_pid (class in sage.modules.free_module) FreeModule_submodule_with_basis_field (class in sage.modules.free_module) FreeModule_submodule_with_basis_integer (class in sage.modules.free_module_integer) FreeModule_submodule_with_basis_pid (class in sage.modules.free_module) FreeModuleElement (class in sage.modules.free_module_element) FreeModuleElement_generic_dense (class in sage.modules.free_module_element) FreeModuleElement_generic_sparse (class in sage.modules.free_module_element) FreeModuleFactory (class in sage.modules.free_module) FreeModuleHomspace (class in sage.modules.free_module_homspace) FreeModuleMorphism (class in sage.modules.free_module_morphism) FreeQuadraticModule() (in module sage.modules.free_quadratic_module) FreeQuadraticModule_ambient (class in sage.modules.free_quadratic_module) FreeQuadraticModule_ambient_domain (class in sage.modules.free_quadratic_module) FreeQuadraticModule_ambient_field (class in sage.modules.free_quadratic_module) FreeQuadraticModule_ambient_pid (class in sage.modules.free_quadratic_module) FreeQuadraticModule_generic (class in sage.modules.free_quadratic_module) FreeQuadraticModule_generic_field (class in sage.modules.free_quadratic_module) FreeQuadraticModule_generic_pid (class in sage.modules.free_quadratic_module) FreeQuadraticModule_submodule_field (class in sage.modules.free_quadratic_module) FreeQuadraticModule_submodule_pid (class in sage.modules.free_quadratic_module) FreeQuadraticModule_submodule_with_basis_field (class in sage.modules.free_quadratic_module) FreeQuadraticModule_submodule_with_basis_pid (class in sage.modules.free_quadratic_module) function() (sage.modules.free_module_element.FreeModuleElement_generic_dense method)

G

gen() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) general_linear_group() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) gens() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic method)

get() (sage.modules.free_module_element.FreeModuleElement method) gram_matrix() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic method) gram_schmidt() (in module sage.modules.misc)

H

hamming_weight() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method) (sage.modules.vector_mod2_dense.Vector_mod2_dense method) has_canonical_map_to() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) has_user_basis() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_field method) (sage.modules.free_module.FreeModule_submodule_pid method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method)

hermitian_inner_product() (sage.modules.free_module_element.FreeModuleElement method) HKZ() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) hom() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method)

I

identity() (sage.modules.free_module_homspace.FreeModuleHomspace method) identity_map() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) im_gens() (sage.modules.fg_pid.fgp_morphism.FGP_Morphism method) image() (sage.modules.fg_pid.fgp_morphism.FGP_Morphism method) (sage.modules.matrix_morphism.MatrixMorphism_abstract method) index_in() (sage.modules.free_module.FreeModule_generic_pid method) index_in_saturation() (sage.modules.free_module.FreeModule_generic_pid method) inner_product() (sage.modules.free_module_element.FreeModuleElement method) inner_product_matrix() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic method) InnerProductSpace() (in module sage.modules.free_quadratic_module) IntegerLattice() (in module sage.modules.free_module_integer) integral() (sage.modules.free_module_element.FreeModuleElement method) integrate() (sage.modules.free_module_element.FreeModuleElement method) intersection() (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method) inv_fft() (sage.modules.vector_double_dense.Vector_double_dense method) invariants() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) inverse() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) inverse_image() (sage.modules.fg_pid.fgp_morphism.FGP_Morphism method) (sage.modules.free_module_morphism.FreeModuleMorphism method) irange() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) is_ambient() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module.FreeModule_submodule_with_basis_field method) is_bijective() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) is_dense() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_element.FreeModuleElement method) is_equal_function() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) is_FGP_Module() (in module sage.modules.fg_pid.fgp_module) is_finite() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic method)

is_FreeModule() (in module sage.modules.free_module) is_FreeModuleElement() (in module sage.modules.free_module_element) is_FreeModuleHomspace() (in module sage.modules.free_module_homspace) is_FreeModuleMorphism() (in module sage.modules.free_module_morphism) is_FreeQuadraticModule() (in module sage.modules.free_quadratic_module) is_full() (sage.modules.free_module.FreeModule_generic method) is_identity() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) is_immutable() (sage.modules.free_module_element.FreeModuleElement method) is_injective() (sage.modules.matrix_morphism.MatrixMorphism method) is_invertible() (sage.modules.vector_space_morphism.VectorSpaceMorphism method) is_MatrixMorphism() (in module sage.modules.matrix_morphism) is_Module() (in module sage.modules.module) is_mutable() (sage.modules.free_module_element.FreeModuleElement method) is_sparse() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_element.FreeModuleElement method) is_submodule() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic method) (sage.modules.with_basis.subquotient.SubmoduleWithBasis method) is_subspace() (sage.modules.free_module.FreeModule_generic_field method) is_surjective() (sage.modules.matrix_morphism.MatrixMorphism method) is_unimodular() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) is_vector() (sage.modules.free_module_element.FreeModuleElement method) is_VectorSpace() (in module sage.modules.module) is_VectorSpaceHomspace() (in module sage.modules.vector_space_homspace) is_VectorSpaceMorphism() (in module sage.modules.vector_space_morphism) is_zero() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) iteritems() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method)

J

jacobi() (in module sage.modules.diamond_cutting)

K

kernel() (sage.modules.fg_pid.fgp_morphism.FGP_Morphism method) (sage.modules.matrix_morphism.MatrixMorphism_abstract method)

L

lift() (sage.modules.fg_pid.fgp_element.FGP_Element method) (sage.modules.fg_pid.fgp_morphism.FGP_Morphism method) (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_morphism.FreeModuleMorphism method) (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) (sage.modules.with_basis.subquotient.QuotientModuleWithBasis method) (sage.modules.with_basis.subquotient.SubmoduleWithBasis method) lift_map() (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) linear_combination_of_basis() (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) linear_combination_of_smith_form_gens() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) linear_dependence() (sage.modules.free_module.FreeModule_generic_field method)

linear_form() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) linear_transformation() (in module sage.modules.vector_space_morphism) list() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_dense method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method) (sage.modules.vector_integer_dense.Vector_integer_dense method) (sage.modules.vector_mod2_dense.Vector_mod2_dense method) (sage.modules.vector_rational_dense.Vector_rational_dense method) list_from_positions() (sage.modules.free_module_element.FreeModuleElement method) LLL() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method)

M

make_FreeModuleElement_generic_dense() (in module sage.modules.free_module_element) make_FreeModuleElement_generic_dense_v1() (in module sage.modules.free_module_element) make_FreeModuleElement_generic_sparse() (in module sage.modules.free_module_element) make_FreeModuleElement_generic_sparse_v1() (in module sage.modules.free_module_element) matrix() (sage.modules.free_module.FreeModule_generic method) (sage.modules.matrix_morphism.MatrixMorphism method) (sage.modules.matrix_morphism.MatrixMorphism_abstract method) MatrixMorphism (class in sage.modules.matrix_morphism) MatrixMorphism_abstract (class in sage.modules.matrix_morphism) mean() (sage.modules.vector_double_dense.Vector_double_dense method) minimal_polynomial() (sage.modules.free_module_morphism.FreeModuleMorphism method)

minpoly() (sage.modules.free_module_morphism.FreeModuleMorphism method) Mod() (sage.modules.free_module_element.FreeModuleElement method) Module (class in sage.modules.module) Module_old (class in sage.modules.module) ModuleMorphism (class in sage.modules.with_basis.morphism) ModuleMorphismByLinearity (class in sage.modules.with_basis.morphism) ModuleMorphismFromFunction (class in sage.modules.with_basis.morphism) ModuleMorphismFromMatrix (class in sage.modules.with_basis.morphism) monic() (sage.modules.free_module_element.FreeModuleElement method)

N

n() (sage.modules.vector_mod2_dense.Vector_mod2_dense method) next() (sage.modules.finite_submodule_iter.FiniteFieldsubspace_projPoint_iterator method) (sage.modules.finite_submodule_iter.FiniteZZsubmodule_iterator method) ngens() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic method) nintegral() (sage.modules.free_module_element.FreeModuleElement method) nintegrate() (sage.modules.free_module_element.FreeModuleElement method) nonembedded_free_module() (sage.modules.free_module.FreeModule_generic method)

nonzero_positions() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.free_module_element.FreeModuleElement_generic_sparse method) norm() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.vector_double_dense.Vector_double_dense method) normalized() (sage.modules.free_module_element.FreeModuleElement method) nullity() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) numpy() (sage.modules.free_module_element.FreeModuleElement method) (sage.modules.vector_double_dense.Vector_double_dense method)

O

on_basis() (sage.modules.with_basis.morphism.ModuleMorphismByLinearity method) optimized() (sage.modules.fg_pid.fgp_module.FGP_Module_class method)

outer_product() (sage.modules.free_module_element.FreeModuleElement method)

P

pairwise_product() (sage.modules.free_module_element.FreeModuleElement method) plane_inequality() (in module sage.modules.diamond_cutting) plot() (sage.modules.free_module_element.FreeModuleElement method) plot_step() (sage.modules.free_module_element.FreeModuleElement method) pointwise_inverse() (sage.modules.with_basis.morphism.PointwiseInverseFunction method) pointwise_inverse_function() (in module sage.modules.with_basis.morphism) PointwiseInverseFunction (class in sage.modules.with_basis.morphism)

preimage() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) preimage_representative() (sage.modules.free_module_morphism.FreeModuleMorphism method) prepare() (in module sage.modules.free_module_element) print_bases() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) prod() (sage.modules.vector_double_dense.Vector_double_dense method) pushforward() (sage.modules.free_module_morphism.FreeModuleMorphism method)

Q

QuadraticSpace() (in module sage.modules.free_quadratic_module) quotient() (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method) quotient_abstract() (sage.modules.free_module.FreeModule_generic_field method)

quotient_map() (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) QuotientModuleWithBasis (class in sage.modules.with_basis.subquotient)

R

random_element() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_ambient method) (sage.modules.free_module.FreeModule_generic method) random_fgp_module() (in module sage.modules.fg_pid.fgp_module) random_fgp_morphism_0() (in module sage.modules.fg_pid.fgp_module) random_vector() (in module sage.modules.free_module_element) rank() (sage.modules.free_module.FreeModule_generic method) (sage.modules.matrix_morphism.MatrixMorphism_abstract method) (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) RealDoubleVectorSpace_class (class in sage.modules.free_module) reduce() (sage.modules.with_basis.subquotient.SubmoduleWithBasis method)

reduced_basis (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer attribute) relations() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) restrict() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) restrict_codomain() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) restrict_domain() (sage.modules.matrix_morphism.MatrixMorphism_abstract method) retract() (sage.modules.with_basis.subquotient.QuotientModuleWithBasis method) (sage.modules.with_basis.subquotient.SubmoduleWithBasis method) row() (sage.modules.free_module_element.FreeModuleElement method)

S

sage.modules.complex_double_vector (module) sage.modules.diamond_cutting (module) sage.modules.fg_pid.fgp_element (module) sage.modules.fg_pid.fgp_module (module) sage.modules.fg_pid.fgp_morphism (module) sage.modules.finite_submodule_iter (module) sage.modules.free_module (module) sage.modules.free_module_element (module) sage.modules.free_module_homspace (module) sage.modules.free_module_integer (module) sage.modules.free_module_morphism (module) sage.modules.free_quadratic_module (module) sage.modules.matrix_morphism (module) sage.modules.misc (module) sage.modules.module (module) sage.modules.quotient_module (module) sage.modules.real_double_vector (module) sage.modules.vector_callable_symbolic_dense (module) sage.modules.vector_complex_double_dense (module) sage.modules.vector_double_dense (module) sage.modules.vector_integer_dense (module) sage.modules.vector_mod2_dense (module) sage.modules.vector_modn_dense (module) sage.modules.vector_rational_dense (module) sage.modules.vector_real_double_dense (module) sage.modules.vector_space_homspace (module) sage.modules.vector_space_morphism (module) sage.modules.vector_symbolic_dense (module) sage.modules.with_basis.__init__ (module) sage.modules.with_basis.morphism (module) sage.modules.with_basis.subquotient (module) sage.tensor.modules.finite_rank_free_module (module) saturation() (sage.modules.free_module.FreeModule_generic_pid method) scale() (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method)

section() (sage.modules.with_basis.morphism.TriangularModuleMorphism method) set() (sage.modules.free_module_element.FreeModuleElement method) set_change_of_basis() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) set_default_basis() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) set_immutable() (sage.modules.free_module_element.FreeModuleElement method) shortest_vector() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) simplify() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_exp() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_factorial() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_full() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_log() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_radical() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_rational() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) simplify_trig() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) smith_form_gen() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) smith_form_gens() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) span() (in module sage.modules.free_module) (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic_field method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic_pid method) span_of_basis() (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic_field method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic_pid method) sparse_module() (sage.modules.free_module.FreeModule_generic method) sparse_vector() (sage.modules.free_module_element.FreeModuleElement method) standard_deviation() (sage.modules.vector_double_dense.Vector_double_dense method) stats_kurtosis() (sage.modules.vector_double_dense.Vector_double_dense method) stats_skew() (sage.modules.vector_real_double_dense.Vector_real_double_dense method) submodule() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.free_module.FreeModule_generic_pid method) submodule_with_basis() (sage.modules.free_module.FreeModule_generic_pid method) SubmoduleWithBasis (class in sage.modules.with_basis.subquotient) subs() (sage.modules.free_module_element.FreeModuleElement method) subspace() (sage.modules.free_module.FreeModule_generic_field method) subspace_with_basis() (sage.modules.free_module.FreeModule_generic_field method) subspaces() (sage.modules.free_module.FreeModule_generic_field method) sum() (sage.modules.vector_double_dense.Vector_double_dense method) support() (sage.modules.free_module_element.FreeModuleElement method) sym_bilinear_form() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method)

T

tensor() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) tensor_from_comp() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) tensor_module() (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) tensor_product() (sage.modules.free_module_element.FreeModuleElement method) test_morphism_0() (in module sage.modules.fg_pid.fgp_module) trace() (sage.modules.matrix_morphism.MatrixMorphism_abstract method)

TriangularModuleMorphism (class in sage.modules.with_basis.morphism) TriangularModuleMorphismByLinearity (class in sage.modules.with_basis.morphism) TriangularModuleMorphismFromFunction (class in sage.modules.with_basis.morphism) trig_expand() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method) trig_reduce() (sage.modules.vector_symbolic_dense.Vector_symbolic_dense method)

U

unpickle_v0() (in module sage.modules.vector_complex_double_dense) (in module sage.modules.vector_integer_dense) (in module sage.modules.vector_mod2_dense) (in module sage.modules.vector_modn_dense) (in module sage.modules.vector_rational_dense) (in module sage.modules.vector_real_double_dense) unpickle_v1() (in module sage.modules.vector_complex_double_dense) (in module sage.modules.vector_integer_dense) (in module sage.modules.vector_modn_dense) (in module sage.modules.vector_rational_dense) (in module sage.modules.vector_real_double_dense) update_reduced_basis() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method)

user_to_echelon_matrix() (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) uses_ambient_inner_product() (sage.modules.free_module.FreeModule_generic method)

V

V() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.quotient_module.FreeModule_ambient_field_quotient method) variance() (sage.modules.vector_double_dense.Vector_double_dense method) vector() (in module sage.modules.free_module_element) (sage.modules.fg_pid.fgp_element.FGP_Element method) Vector_callable_symbolic_dense (class in sage.modules.vector_callable_symbolic_dense) Vector_complex_double_dense (class in sage.modules.vector_complex_double_dense) Vector_double_dense (class in sage.modules.vector_double_dense) Vector_integer_dense (class in sage.modules.vector_integer_dense) Vector_mod2_dense (class in sage.modules.vector_mod2_dense) Vector_modn_dense (class in sage.modules.vector_modn_dense) Vector_rational_dense (class in sage.modules.vector_rational_dense) Vector_real_double_dense (class in sage.modules.vector_real_double_dense)

vector_space() (sage.modules.free_module.FreeModule_ambient_domain method) (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_submodule_with_basis_pid method) vector_space_span() (sage.modules.free_module.FreeModule_generic_pid method) vector_space_span_of_basis() (sage.modules.free_module.FreeModule_generic_pid method) Vector_symbolic_dense (class in sage.modules.vector_symbolic_dense) VectorSpace() (in module sage.modules.free_module) VectorSpaceHomspace (class in sage.modules.vector_space_homspace) VectorSpaceMorphism (class in sage.modules.vector_space_morphism) volume() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) voronoi_cell() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method) voronoi_relevant_vectors() (sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer method)

W

W() (sage.modules.fg_pid.fgp_module.FGP_Module_class method) (sage.modules.quotient_module.FreeModule_ambient_field_quotient method)

Z

zero() (sage.modules.free_module.FreeModule_generic method) (sage.modules.free_module_homspace.FreeModuleHomspace method) (sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule method) zero_at() (sage.modules.vector_double_dense.Vector_double_dense method) zero_submodule() (sage.modules.free_module.FreeModule_generic_field method) (sage.modules.free_module.FreeModule_generic_pid method) (sage.modules.free_quadratic_module.FreeQuadraticModule_generic_pid method)

zero_subspace() (sage.modules.free_module.FreeModule_generic_field method) zero_vector() (in module sage.modules.free_module_element) (sage.modules.free_module.FreeModule_generic method)