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__init__(self,
A,
R,
gens=[],
basis=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...,
rank=0)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature |
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__call__(self,
x,
check=True)
File: sage/rings/ring.pyx (starting at line 37)
Coerce x into the ring. |
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ambient_algebra(self)
Return the ambient algebra of this algebra order |
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__compute_order_basis(self)
Compute a basis as an order. |
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basis(self)
Return the basis of this algebra order |
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algebra_basis_elements(self)
Return the basis of this algebra order as a tuple |
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embedding_matrix(self)
Return the $n\times n$ matrix whose rows are the vectors
expressing the basis elements of this algebra order in terms
of the ambient algebra's basis. |
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inverse_embedding_matrix(self)
Return the inverse of the $n\times n$ matrix whose rows are
the vectors expressing the basis elements of this algebra
order in terms of the ambient algebra's basis. |
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module(self)
Convert this algebra order into a module over the base ring. |
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gen(self,
i)
Return the i'th generator of this algebra order |
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gens(self)
Return the generators of this algebra order as a tuple |
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rank(self)
Return the rank of this algebra order |
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Inherited from rings.ring.Algebra:
__new__,
characteristic
Inherited from rings.ring.Ring:
__getitem__,
__hash__,
__iter__,
__len__,
__mul__,
__rmul__,
__rxor__,
__xor__,
_ideal_class_,
base_extend,
category,
ideal,
is_atomic_repr,
is_commutative,
is_exact,
is_field,
is_finite,
is_integral_domain,
is_noetherian,
is_prime_field,
is_ring,
is_subring,
one_element,
order,
principal_ideal,
random_element,
unit_ideal,
zero_element,
zero_ideal,
zeta,
zeta_order
Inherited from structure.parent_gens.ParentWithGens:
__getslice__,
__getstate__,
__setstate__,
_is_valid_homomorphism_,
gens_dict,
hom,
inject_variables,
injvar,
latex_name,
latex_variable_names,
list,
objgen,
objgens,
variable_name,
variable_names
Inherited from structure.parent_base.ParentWithBase:
Hom,
base,
base_extend_canonical,
base_extend_canonical_sym,
base_extend_recursive
Inherited from structure.parent.Parent:
_coerce_,
coerce_map_from,
coerce_map_from_impl,
construction,
get_action,
get_action_impl,
has_coerce_map_from,
has_coerce_map_from_impl,
init_coerce
Inherited from structure.sage_object.SageObject:
_axiom_,
_axiom_init_,
_gap_,
_gap_init_,
_gp_,
_gp_init_,
_interface_,
_interface_init_,
_interface_is_cached_,
_kash_,
_kash_init_,
_macaulay2_,
_macaulay2_init_,
_magma_,
_magma_init_,
_maple_,
_maple_init_,
_mathematica_,
_mathematica_init_,
_maxima_,
_maxima_init_,
_octave_,
_octave_init_,
_pari_,
_pari_init_,
_r_init_,
_sage_,
_singular_,
_singular_init_,
db,
dump,
dumps,
plot,
rename,
reset_name,
save,
version
Inherited from object:
__delattr__,
__getattribute__,
__reduce__,
__reduce_ex__,
__setattr__,
__str__
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