Hi all,
I am fighting with the same problem for too much time... I want to
invert matrices (squares and invertibles especially because they
represent basis change of a finite dimensional quotient : K[X] /
Sym(X)^+ ). We begin to have a large bunch of combinatorial ring in
sage-combinat and most of them use a combinatorial free module data
structure but the sage matrices doesn't like combinatorial free modules...
For all such matrix M, in a perfect world : I just want :
(1/M.det)*M.adjoint() ( --> and all algorithms are already here and
work fine, It is just a branching question between different features).
For now :
***************************************************************
sage: SF = SymmetricFunctions(QQ).schur()
sage: Id = identity_matrix(SF, 2); Id
[s[] 0]
[ 0 s[]]
sage: Id.inverse()
Traceback (most recent call last):
...
AttributeError: 'SymmetricFunctionAlgebra_schur_with_category' object
has no attribute 'fraction_field'
sage: ~Id.det()
s[]
sage: ~Id.det()*Id.adjoint()
Traceback (most recent call last):
...
TypeError: unsupported operand parent(s) for '*': 'Symmetric Functions
over Rational Field in the Schur basis' and 'Full MatrixSpace of 2 by 2
dense matrices over Symmetric Functions over Rational Field in the Schur
basis'
***************************************************************
Perhaps due to the fact that :
***************************************************************
sage: Id
[s[] 0]
[ 0 s[]]
sage: P = Id.parent(); P
Full MatrixSpace of 2 by 2 dense matrices over Symmetric Functions over
Rational Field in the Schur basis
sage: P.has_coerce_map_from(SF)
False
***************************************************************
Let's fix some compatibility bug with Combinatorial free module (because
SF['x'] doesn't means polynomial in x over SF in combinat world but
return a ValueError explaining that ['x'] is not a valid partition) and
had a nice coercion, I still have the same error. But the sage matrix
spaces use "some" category (the "some" is very important I guess but
that already go further than my knowledge... I do not know anything with
old category framework...):
***************************************************************
sage: SF = SymmetricFunctions(QQ).schur()
sage: Id = identity_matrix(SF, 2); Id
[s[] 0]
[ 0 s[]]
sage: P = Id.parent()
sage: P.category()
Category of algebras over Symmetric Functions over Rational Field in the
Schur basis
sage: P.__class__.mro()
[sage.matrix.matrix_space.MatrixSpace,
sage.structure.unique_representation.UniqueRepresentation,
sage.structure.unique_representation.CachedRepresentation,
sage.misc.fast_methods.WithEqualityById,
sage.structure.parent_gens.ParentWithGens,
sage.structure.parent_base.ParentWithBase,
sage.structure.parent_old.Parent,
sage.structure.parent.Parent,
sage.structure.category_object.CategoryObject,
sage.structure.sage_object.SageObject,
object]
sage: SF(1)
s[]
sage: SF(1)*Id
Traceback (most recent call last):
...
TypeError: unsupported operand parent(s) for '*': 'Symmetric Functions
over Rational Field in the Schur basis' and 'Full MatrixSpace of 2 by 2
dense matrices over Symmetric Functions over Rational Field in the Schur
basis'
***************************************************************
So, I need some advises to fix that... And currently, I find very hard
to evaluate the difficulty to do it without an horrible hack since :
- the class sage/matric/matrix_space.MatrixSpace seems to present
problem with inheritance...
- this code seems to not be new category framework compatible
- tests in this file only concerns : ZZ, QQ, GF(11), GF(2), SR, RDF,
CDF, CyclotomicField(7), QQ['x,y'] (inversion tests are at the end of
the file matrix_space.py) (not any combinatorial free module ring...)
I also didn't find where was implemented usual coercions between rings
and their corresponding matrix_space (ZZ, QQ, ...) and I do not manage
to find where (internal/external) products are implemented. I am lost in
a lot of code. If someone can help, feel free to give me some advises. I
will still try to dig in...
Cheers,
Nicolas B.
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