_vector_, vector and vector_space

[videlec]

This ticket stands for creating a fixed and common semantic for the vector and _vector_ methods (on elements) and vector_space (on parents). Currently the arguments of these methods depend too much on the context. Moreover, in some situation the parent also provides specific methods to generate an associated "natural" vector space (eg relative_vector_space for number fields).

$ grep -R "def vector("
media/wav.py:    def vector(self, npoints=None, channel=0):
geometry/polyhedron/representation.py:    def vector(self, base_ring=None):
modules/fg_pid/fgp_element.py:    def vector(self):
modules/free_module_element.pyx:def vector(arg0, arg1=None, arg2=None, sparse=None):
combinat/e_one_star.py:    def vector(self):
crypto/mq/sr.py:    def vector(self, d=None):
crypto/mq/sr.py:    def vector(self, d=None):
finance/time_series.pyx:    def vector(self):
homology/chain_complex.py:    def vector(self, degree):
rings/number_field/number_field_element.pyx:    def vector(self):
libs/gap/element.pyx:    def vector(self, ring=None):
libs/pari/pari_instance.pyx:    def vector(self, long n, entries=None):
functions/spike_function.py:    def vector(self, samples=2**16, xmin=None, xmax=None):
algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.py:    def vector(self):
algebras/free_algebra_quotient_element.py:    def vector(self):

and

$ grep -R "def _vector_("
modules/fg_pid/fgp_element.py:    def _vector_(self, base_ring=None):
modules/free_module_element.pyx:    def _vector_(self, R=None):
combinat/free_module.py:    def _vector_(self, new_base_ring=None):
interfaces/interface.py:    def _vector_(self, R):
interfaces/octave.py:    def _vector_(self, R=None):
modular/hecke/element.py:    def _vector_(self, R=None):
rings/finite_rings/element_givaro.pyx:    def _vector_(FiniteField_givaroElement self, reverse=False):
rings/finite_rings/element_ntl_gf2e.pyx:    def _vector_(FiniteField_ntl_gf2eElement self, reverse=False):
rings/finite_rings/element_base.pyx:    def _vector_(self, reverse=False):
schemes/toric/divisor.py:    def _vector_(self, ring=None):

and

$ grep -R "def vector_space("
groups/affine_gps/affine_group.py:    def vector_space(self):
modules/free_module.py:    def vector_space(self, base_field=None):
modules/free_module.py:    def vector_space(self, base_field=None):
modules/free_module.py:    def vector_space(self, base_field=None):
combinat/words/paths.py:    def vector_space(self):
modular/abvar/abvar.py:    def vector_space(self):
rings/number_field/number_field_rel.py:    def vector_space(self):
rings/number_field/number_field.py:    def vector_space(self):
rings/finite_rings/finite_field_base.pyx:    def vector_space(self):
rings/function_field/function_field.py:    def vector_space(self, base=None):
rings/function_field/function_field.py:    def vector_space(self):
rings/function_field/function_field.py:    def vector_space(self, base=None):
algebras/quatalg/quaternion_algebra.py:    def vector_space(self):
algebras/finite_dimensional_algebras/finite_dimensional_algebra_ideal.py:    def vector_space(self):

CC: @tscrim @kwankyu

Component: algebra

Branch: #21723

Issue created by migration from https://trac.sagemath.org/ticket/21737