#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 | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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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>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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