Hi!
Matrix spaces of dense and sparse matrices are equal and are thus not
unique parents:
sage: M1 = MatrixSpace(ZZ,2,sparse=True)
sage: M2 = MatrixSpace(ZZ,2,sparse=False)
sage: M1 is M2
False
sage: M1==M2
True
Fine. But what should be really bad: They violate the assumption that
equal objects have equal hash.
sage: hash(M1)==hash(M2)
False
By consequence, the two equal matrix spaces will correspond to
different items of dictionaries:
sage: D = {M1:1,M2:2}
sage: len(D)
2
I think that it is an apparent bug. Therefore, at #12290, I am fixing
the hash values (and moreover I speed-up the hash of matrix spaces
considerably).
However, it seems that the coercion framework relies on the bug.
Namely, when fixing it, one gets
sage: A = matrix(ZZ, 5, range(30), sparse=False)
sage: B = matrix(ZZ, 5, range(30), sparse=True)
sage: C = matrix(QQ, 5, range(30), sparse=True)
sage: A.elementwise_product(C).is_dense()
True
sage: B.elementwise_product(C).is_sparse()
---------------------------------------------------------------------------
TypeError Traceback (most recent
call last)
...
TypeError: no common canonical parent for objects with parents:
'Full MatrixSpace of 5 by 6 sparse matrices over Integer Ring' and
'Full MatrixSpace of 5 by 6 sparse matrices over Rational Field'
The problem can be fixed by making matrix spaces unique parents (but I
didn't check yet whether it creates other problems).
Question to you: Do you see an obvious reason why matrix spaces should
not be unique parents?
Best regards,
Simon
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