Wrong results in vector matrix multiplication

[simonbrandhorst]

sage: M = FreeModule(ZZ,1).span([vector([1/3])])
sage: x = M([1/3])
sage: x
(1/3)
sage: A = Matrix(QQ,[1])
sage: x*A , A*x
((1/3), (1/3))

This is good.

sage: B = Matrix(ZZ,[1])
sage: x*B , B*x
((1), (1/3))

The first entry is clearly wrong.
Somehow the first product is carried out in a wrong basis representation for x.

CC: @tscrim

Component: linear algebra

Keywords: sd91

Branch/Commit: u/roed/vmat_action @ 6021daa

Issue created by migration from https://trac.sagemath.org/ticket/23576

[simonbrandhorst]

Changed keywords from none to sd91

[roed314]

comment:2

The problem appears in line 1122 of sage.matrix.matrix_integer_dense.pyx, inside the function cdef _vector_times_matrix_(self, Vector v):

w = <Vector_integer_dense> v

If you change that to

w = <Vector_integer_dense?> v

you'll get an error, because v is a Vector_rational_dense, and if you change it to

try:
    w = <Vector_integer_dense?> v
except TypeError:
    return Matrix_dense._vector_times_matrix_(self, v)

you get (1/3).

This function is replacing a more general implementation in sage.matrix.matrix0, but it only replaces _vector_times_matrix_, not _matrix_times_vector_, thus the disparity based on whether B is acting on the left or right.

I don't know if the try/except block is the right answer. I'll think about it....

[roed314]

comment:3

There's maybe a separate issue in sage.matrix.action, since it detects the base ring of the result by checking the base ring of the inputs. But here x and B both have base ring ZZ, and indeed

sage: from sage.structure.element import coercion_model
sage: from operator import mul
sage: coercion_model.explain(x.parent(), B.parent(), mul)
Action discovered.
    Right action by Full MatrixSpace of 1 by 1 dense matrices over Integer Ring on Free module of degree 1 and rank 1 over Integer Ring
    Echelon basis matrix:
    [1/3]
Result lives in Ambient free module of rank 1 over the principal ideal domain Integer Ring
Ambient free module of rank 1 over the principal ideal domain Integer Ring

The result should probably have rational entries....

[roed314]

Branch: u/roed/vmat_action

[roed314]

comment:5

There are segfaults in the new implementation that multiplies a non-square integral matrix times a rational vector. Still working on them...

---

New commits:

6021daa

Correct base ring for matrices acting on submodules, implement multiplication for Vector_rational_dense times an integral matrix.

[roed314]

Commit: 6021daa

[simonbrandhorst]

comment:6

ping :)
Maybe #24031 is related to this? After all that bug occurs for vectors as well.
Does this one for matrices too?

[mkoeppe]

comment:7

Still unresolved as of 9.2.beta2

[slel]

comment:8

There is a possibility that #28544 will solve this,
see comment 10 there.

[mkoeppe]

comment:10

Moving to 9.4, as 9.3 has been released.