block sums
Robert Miller
sage: B = Matrix( GF(2), [[0]] )
sage: A
[]
sage: B
[0]
sage: A.block_sum(B)
[0]
[0]
sage: A = Matrix( GF(2), [] )
sage: A
[]
sage: A.block_sum(B)
[0]
David Harvey
I don't understand the problem. In all cases, the number of rows of A
plus the number of rows of B equals the number of rows of
A.block_sum(B), and similarly for columns. What am I missing?
david
Robert Miller
especially if they're printing as the same matrix. There is no
mathematical reason for having a matrix consisting of one row and zero
columns. Even if there were, there doesn't seem to be a way to create
a matrix with zero rows and one column. I'm of the opinion that [[]]
should be treated as having zero rows *and* zero columns.
William Stein
> There should be no difference between the matrices [[]] and [],
> especially if they're printing as the same matrix. There is no
> mathematical reason for having a matrix consisting of one row and zero
> columns.
Yes there is. Most matrix algorithms have as corner cases either
the number of rows or number of columns equal to 0. Two years
ago John Cremona advocated strongly that I allow both cases, so
SAGE would be much more pleasant to use than, say, LiDIA. I've done
so, even though in many cases it was a surprising amount of extra work.
For the record, MAGMA takes the same approach:
sage: magma.RMatrixSpace(RationalField(),0,1)
Full KMatrixSpace of 0 by 1 matrices over Rational Field
> Even if there were, there doesn't seem to be a way to create
> a matrix with zero rows and one column.
Yes there is.
sage: a = matrix(QQ,0,1,[]);
sage: a.nrows(), a.ncols()
(0, 1)
> I'm of the opinion that [[]]
> should be treated as having zero rows *and* zero columns.
No. It has one row [], which has 0 columns.
Printing doesn't determine objects in SAGE, so that a 0,1 and a 0,0 matrix
print the same way isn't convincing.
-- William
> On Apr 13, 11:18 am, David Harvey <dmhar...@math.harvard.edu> wrote:
> > On Apr 13, 2007, at 2:08 PM, Robert Miller wrote:
> >
> > > sage: A = Matrix( GF(2), [[]] )
> > > sage: B = Matrix( GF(2), [[0]] )
> > > sage: A
> > > []
> > > sage: B
> > > [0]
> > > sage: A.block_sum(B)
> >
> > > [0]
> > > [0]
> > > sage: A = Matrix( GF(2), [] )
> > > sage: A
> > > []
> > > sage: A.block_sum(B)
> > > [0]
> >
> > I don't understand the problem. In all cases, the number of rows of A
> > plus the number of rows of B equals the number of rows of
> > A.block_sum(B), and similarly for columns. What am I missing?
> >
> > david
>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://www.williamstein.org