Opened 11 years ago

# Matrices can be "constructed" from matrices of wrong dimensions — at Version 13

Reported by: Owned by: vbraun jason, was critical sage-4.7.2 linear algebra sd31 rbeezer, kcrisman Andrey Novoseltsev Volker Braun N/A #11200

Let's make a matrix and use it to define a morphism:

```sage: projection = matrix(ZZ,[[1,0,0],[0,1,0]])
sage: projection
[1 0 0]
[0 1 0]
sage: H = Hom(ZZ^3, ZZ^2)
sage: H(projection)
Free module morphism defined by the matrix
[1 0]
[0 0]
[1 0]
Domain: Ambient free module of rank 3 over the principal ideal domain ...
Codomain: Ambient free module of rank 2 over the principal ideal domain ...
```

As we see, the matrix of the morphism is very unlikely to be what it should be. Here is the source of the problem:

```sage: projection.parent()
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
sage: M = MatrixSpace(ZZ, 3 , 2)
sage: M
Full MatrixSpace of 3 by 2 dense matrices over Integer Ring
sage: M(projection)
[1 0]
[0 0]
[1 0]
```

So the matrix space converts the input to the matrix no matter what (same with `matrix` command, but inside morphisms matrix spaces are used). I suppose this will work any time the number of entries in the original and in the destination is matching. I think that if one really wants to do it, then this one is very welcome to insert an explicit conversion of a matrix to a list and then back to a matrix, but the above should raise exceptions.

Apply trac_10793_bug_in_matrix_construction.patch, trac_10793_fixing_existing_bugs.patch

### comment:1 Changed 11 years ago by novoselt

• Component changed from algebraic geometry to linear algebra
• Description modified (diff)
• Owner changed from AlexGhitza to jason, was
• Priority changed from major to critical
• Summary changed from FanMorphism defined by matrices are dangerous to Matrices can be "constructed" from matrices of wrong dimensions
• Type changed from PLEASE CHANGE to defect

I have completely replaced the original Volker's description since the problem is unrelated to fan morphisms themselves.

Also I think that this is an extremely dangerous bug and will take the liberty to elevate its priority...

### comment:2 follow-up: ↓ 4 Changed 11 years ago by jason

So it seems that the problem here is that in converting to an element of the matrix space, it views the entries of the matrix (or indeed, the entries of a nested list as well) as a flattened list:

```sage: M
Full MatrixSpace of 3 by 2 dense matrices over Integer Ring
sage: M([[1,2,3],[4,5,6]])
[1 2]
[3 4]
[5 6]
```

So I guess you're saying that MatrixSpace? shouldn't flatten the list, but instead should throw an error?

### comment:3 Changed 11 years ago by jason

Around line 361 in `matrix/matrix_space.py`, we see:

```        if isinstance(entries, (list, tuple)) and len(entries) > 0 and \
sage.modules.free_module_element.is_FreeModuleElement(entries[0]):
#Try to determine whether or not the entries should
#be rows or columns
if rows is None:
#If the matrix is square, default to rows
if self.__ncols == self.__nrows:
rows = True
elif len(entries[0]) == self.__ncols:
rows = True
elif len(entries[0]) == self.__nrows:
rows = False
else:
raise ValueError, "incorrect dimensions"

if self.__is_sparse:
e = {}
zero = self.base_ring()(0)
for i in xrange(len(entries)):
for j, x in entries[i].iteritems():
if x != zero:
if rows:
e[(i,j)] = x
else:
e[(j,i)] = x
entries = e
else:
entries = sum([v.list() for v in entries],[])
```

So:

1. I think it tries to be too intelligent about guessing whether you have rows or columns. That leads to inconsistent behavior when you have code dealing with different matrix spaces with different dimensions.
1. It indeed does flatten the list if all else fails (that's the sum([v.list()... line). I agree that that looks dangerous as well.

### comment:4 in reply to: ↑ 2 Changed 11 years ago by novoselt

So it seems that the problem here is that in converting to an element of the matrix space, it views the entries of the matrix (or indeed, the entries of a nested list as well) as a flattened list:

```sage: M
Full MatrixSpace of 3 by 2 dense matrices over Integer Ring
sage: M([[1,2,3],[4,5,6]])
[1 2]
[3 4]
[5 6]
```

So I guess you're saying that MatrixSpace? shouldn't flatten the list, but instead should throw an error?

Absolutely! I see no reason why such flattening can make sense, so even if there some - I think they should do it explicitly.

I find it a bit confusing that Sage uses right matrix action, so in the description I tend to think that `projection` itself is the matrix of the morphism, not its transpose. I suspect I am not the only one who can fall into this trap: it is accepted as an input, but some other not-very-related matrix is then used in the morphism.

### comment:5 Changed 10 years ago by novoselt

• Cc rbeezer added; novoselt removed

Hi Rob, this is the ticket I was talking about!

### comment:6 Changed 10 years ago by novoselt

• Authors set to Andrey Novoseltsev
• Status changed from new to needs_review

### comment:8 Changed 10 years ago by novoselt

• Status changed from needs_review to needs_work
• Work issues set to doctest failures

There are doctest failures that have to be addressed. I suspect that all places that are affected were just kind of wrong. For Nx1 and 1xN matrices nothing too horrible is going on, hopefully there are no other cases.

### comment:9 Changed 10 years ago by novoselt

Here is the list of offenders:

```	sage -t -long devel/sage-main/sage/crypto/mq/sr.py # 15 doctests failed
sage -t -long devel/sage-main/sage/interfaces/sage0.py # 2 doctests failed
sage -t -long devel/sage-main/sage/crypto/mq/mpolynomialsystem.py # 50 doctests failed
sage -t -long devel/sage-main/sage/geometry/fan_morphism.py # 4 doctests failed
sage -t -long devel/sage-main/sage/rings/polynomial/multi_polynomial_sequence.py # 33 doctests failed
sage -t -long devel/sage-main/sage/categories/map.pyx # 16 doctests failed
sage -t -long devel/sage-main/sage/interfaces/magma.py # 2 doctests failed
sage -t -long devel/sage-main/sage/modules/matrix_morphism.py # 9 doctests failed
```

IMHO, all these files are full of bugs!

### comment:10 Changed 10 years ago by novoselt

• Status changed from needs_work to needs_review
• Work issues doctest failures deleted

OK, it turned out to be not as scary as it seemed to me originally. Most of the errors were due to forgetting that matrices act from the right. In crypto I have added explicit conversion of matrices to lists since it seems that they wanted it. I don't understand that code to make sure that this is indeed correct, but at the very least I didn't introduce a new bug ;-)

### comment:11 Changed 10 years ago by novoselt

• Dependencies set to #11200

Patches should apply fine on top of sage-4.7.1.alpha4, as #11200 (and other patches modifying fan morphisms) was merged.