#17965: Uniformization of the API to compute the inverse of an element.
------------------------------+------------------------
Reporter: nthiery | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: categories | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
------------------------------+------------------------
Description changed by nthiery:
Old description:
> Some classes in Sage implement the inverse of an element through the
> inverse method:
> {{{
> mistral-/opt/sage/src/sage>grep "def inverse(" **/*.py
> algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.py:
> def inverse(self):
> algebras/iwahori_hecke_algebra.py: def inverse(self):
> categories/coxeter_groups.py: def inverse(self):
> combinat/affine_permutation.py: def inverse(self):
> combinat/permutation.py: def inverse(self):
> combinat/tableau_tuple.py: def inverse(self,k):
> crypto/classical_cipher.py: def inverse(self):
> crypto/classical_cipher.py: def inverse(self):
> crypto/classical_cipher.py: def inverse(self):
> crypto/classical_cipher.py: def inverse(self):
> dynamics/interval_exchanges/iet.py: def inverse(self):
> groups/abelian_gps/element_base.py: def inverse(self):
> groups/abelian_gps/values.py: def inverse(self):
> groups/affine_gps/group_element.py: def inverse(self):
> modules/matrix_morphism.py: def inverse(self):
> rings/number_field/class_group.py: def inverse(self):
> rings/universal_cyclotomic_field/universal_cyclotomic_field.py:
> def inverse(self):
> schemes/elliptic_curves/formal_group.py: def inverse(self, prec=20):
> schemes/elliptic_curves/weierstrass_transform.py: def inverse(self):
> }}}
>
> Some other through the ``__invert__`` method:
> {{{
> mistral-/opt/sage/src/sage>grep "def __invert__(" **/*.py
> categories/algebras_with_basis.py: def __invert__(self):
> categories/magmas.py: def __invert__(self):
> categories/modules_with_basis.py: def __invert__(self):
> categories/modules_with_basis.py: def __invert__(self):
> combinat/combinatorial_algebra.py: def __invert__(self):
> combinat/sf/dual.py: def __invert__(self):
> combinat/species/generating_series.py: def __invert__(self):
> groups/indexed_free_group.py: def __invert__(self):
> groups/indexed_free_group.py: def __invert__(self):
> groups/matrix_gps/group_element.py: def __invert__(self):
> groups/raag.py: def __invert__(self):
> libs/coxeter3/coxeter_group.py: def __invert__(self):
> logic/boolformula.py: def __invert__(self):
> misc/sage_input.py: def __invert__(self):
> modular/dirichlet.py: def __invert__(self):
> modular/local_comp/smoothchar.py: def __invert__(self):
> modules/matrix_morphism.py: def __invert__(self):
> rings/continued_fraction.py: def __invert__(self):
> rings/finite_rings/element_ext_pari.py: def __invert__(self):
> rings/function_field/function_field_ideal.py: def __invert__(self):
> rings/infinity.py: def __invert__(self):
> rings/multi_power_series_ring_element.py: def __invert__(self):
> rings/number_field/morphism.py: def __invert__(self):
> rings/number_field/number_field_ideal.py: def __invert__(self):
> rings/number_field/number_field_ideal_rel.py: def __invert__(self):
> rings/pari_ring.py: def __invert__(self):
> rings/polynomial/polynomial_quotient_ring_element.py: def
> __invert__(self):
> rings/qqbar.py: def __invert__(self):
> rings/quotient_ring_element.py: def __invert__(self):
> rings/universal_cyclotomic_field/universal_cyclotomic_field.py:
> def __invert__(self):
> sandpiles/sandpile.py: def __invert__(self):
> schemes/elliptic_curves/heegner.py: def __invert__(self):
> schemes/elliptic_curves/height.py: def __invert__(self):
> schemes/elliptic_curves/weierstrass_morphism.py: def __invert__(self):
> schemes/elliptic_curves/weierstrass_morphism.py: def __invert__(self):
> schemes/hyperelliptic_curves/monsky_washnitzer.py: def
> __invert__(self):
> structure/factorization.py: def __invert__(self):
> }}}
>
> Usually they provide a crosslink so that ``__invert__`` and
> ``inverse`` are equivalent, but this is done on a case by case bases,
> so of course such links are missing here and there:
> {{{
> sage: ~AA(sqrt(~2))
> 1.414213562373095?
> sage: AA(sqrt(~2)).inverse()
> ...
> AttributeError: 'AlgebraicReal' object has no attribute 'inverse'
> }}}
>
> {{{
> sage: R.<u,v,w> = QQ[]
> sage: f = EllipticCurve_from_cubic(u^3 + v^3 + w^3, [1,-1,0],
> morphism=True)
> sage: f.inverse()
> Scheme morphism:
> ...
> sage: ~f
> ...
> TypeError: bad operand type for unary ~:
> 'WeierstrassTransformationWithInverse_class'
> }}}
>
> Shall we change the code to systematically implement ``__invert__`` as
> per Python's convention, and then implement the cross link ``inverse``
> -> ``__invert__`` once for all high up in the class hierarchy,
> typically in Magmas.ElementMethods?
>
> Caveat: this won't cover all cases since we have invertible elements
> that don't belong to a magma; e.g. a isomorphisms between two
> different parents; so it will still be necessary to handle a couple
> special cases by hand.
>
> See also comment about ``__inverse__`` in
> sage.categories.coxeter_groups.py around line 699.
>
> Note: the default implementation ~f = 1/f provided by Element should
> probably be implemented in Monoids.ElementMethods; see also #17692.
>
> Note: the qqbar classes also implement an "invert" method, but that's
> for a slightly different use case. So we may, or not, want to make
> this uniform too. `invert` does not fit Sage's usual verb/noun
> convention since it's a verb while it is not inplace.
New description:
Some classes in Sage implement the inverse of an element through the
inverse method:
{{{
mistral-/opt/sage/src/sage>grep "def inverse(" **/*.py
algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.py:
def inverse(self):
algebras/iwahori_hecke_algebra.py: def inverse(self):
categories/coxeter_groups.py: def inverse(self):
combinat/affine_permutation.py: def inverse(self):
combinat/permutation.py: def inverse(self):
combinat/tableau_tuple.py: def inverse(self,k):
crypto/classical_cipher.py: def inverse(self):
crypto/classical_cipher.py: def inverse(self):
crypto/classical_cipher.py: def inverse(self):
crypto/classical_cipher.py: def inverse(self):
dynamics/interval_exchanges/iet.py: def inverse(self):
groups/abelian_gps/element_base.py: def inverse(self):
groups/abelian_gps/values.py: def inverse(self):
groups/affine_gps/group_element.py: def inverse(self):
modules/matrix_morphism.py: def inverse(self):
rings/number_field/class_group.py: def inverse(self):
rings/universal_cyclotomic_field/universal_cyclotomic_field.py: def
inverse(self):
schemes/elliptic_curves/formal_group.py: def inverse(self, prec=20):
schemes/elliptic_curves/weierstrass_transform.py: def inverse(self):
}}}
Some other through the `__invert__` method:
{{{
mistral-/opt/sage/src/sage>grep "def __invert__(" **/*.py
categories/algebras_with_basis.py: def __invert__(self):
categories/magmas.py: def __invert__(self):
categories/modules_with_basis.py: def __invert__(self):
categories/modules_with_basis.py: def __invert__(self):
combinat/combinatorial_algebra.py: def __invert__(self):
combinat/sf/dual.py: def __invert__(self):
combinat/species/generating_series.py: def __invert__(self):
groups/indexed_free_group.py: def __invert__(self):
groups/indexed_free_group.py: def __invert__(self):
groups/matrix_gps/group_element.py: def __invert__(self):
groups/raag.py: def __invert__(self):
libs/coxeter3/coxeter_group.py: def __invert__(self):
logic/boolformula.py: def __invert__(self):
misc/sage_input.py: def __invert__(self):
modular/dirichlet.py: def __invert__(self):
modular/local_comp/smoothchar.py: def __invert__(self):
modules/matrix_morphism.py: def __invert__(self):
rings/continued_fraction.py: def __invert__(self):
rings/finite_rings/element_ext_pari.py: def __invert__(self):
rings/function_field/function_field_ideal.py: def __invert__(self):
rings/infinity.py: def __invert__(self):
rings/multi_power_series_ring_element.py: def __invert__(self):
rings/number_field/morphism.py: def __invert__(self):
rings/number_field/number_field_ideal.py: def __invert__(self):
rings/number_field/number_field_ideal_rel.py: def __invert__(self):
rings/pari_ring.py: def __invert__(self):
rings/polynomial/polynomial_quotient_ring_element.py: def
__invert__(self):
rings/qqbar.py: def __invert__(self):
rings/quotient_ring_element.py: def __invert__(self):
rings/universal_cyclotomic_field/universal_cyclotomic_field.py: def
__invert__(self):
sandpiles/sandpile.py: def __invert__(self):
schemes/elliptic_curves/heegner.py: def __invert__(self):
schemes/elliptic_curves/height.py: def __invert__(self):
schemes/elliptic_curves/weierstrass_morphism.py: def __invert__(self):
schemes/elliptic_curves/weierstrass_morphism.py: def __invert__(self):
schemes/hyperelliptic_curves/monsky_washnitzer.py: def
__invert__(self):
structure/factorization.py: def __invert__(self):
}}}
Usually they provide a crosslink so that `__invert__` and
`inverse` are equivalent, but this is done on a case by case bases,
so of course such links are missing here and there:
{{{
sage: ~AA(sqrt(~2))
1.414213562373095?
sage: AA(sqrt(~2)).inverse()
...
AttributeError: 'AlgebraicReal' object has no attribute 'inverse'
}}}
{{{
sage: R.<u,v,w> = QQ[]
sage: f = EllipticCurve_from_cubic(u^3 + v^3 + w^3, [1,-1,0],
morphism=True)
sage: f.inverse()
Scheme morphism:
...
sage: ~f
...
TypeError: bad operand type for unary ~:
'WeierstrassTransformationWithInverse_class'
}}}
Shall we change the code to systematically implement `__invert__` as
per Python's convention, and then implement the cross link `inverse`
-> `__invert__` once for all high up in the class hierarchy,
typically in `Magmas.ElementMethods`?
Caveat: this won't cover all cases since we have invertible elements
that don't belong to a magma; e.g. a isomorphisms between two
different parents; so it will still be necessary to handle a couple
special cases by hand.
See also comment about `__inverse__` in
sage.categories.coxeter_groups.py around line 699.
Note: the default implementation ~f = 1/f provided by Element should
probably be implemented in `Monoids.ElementMethods`; see also #17692.
Note: the qqbar classes also implement an `invert` method, but that's
for a slightly different use case. So we may, or not, want to make
this uniform too. `invert` does not fit Sage's usual verb/noun
convention since it's a verb while it is not inplace.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17965#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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