Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
subdivide(row_lines=None, col_lines=None)
Divides self into logical submatrices which can then be queried and extracted. If a subdivision already
exists, this method forgets the previous subdivision and flushes the cache.
INPUT:
•row_lines - None, an integer, or a list of integers
•col_lines - None, an integer, or a list of integers
OUTPUT: changes self
Note: One may also pass a tuple into the first argument which will be interpreted as (row_lines, col_lines)
EXAMPLES:
sage: M = matrix(5, 5, prime_range(100))
sage: M.subdivide(2,3); M
[ 2 3 5| 7 11]
[13 17 19|23 29]
[--------+-----]
[31 37 41|43 47]
[53 59 61|67 71]
[73 79 83|89 97]
sage: M.subdivision(0,0)
[ 2 3 5]
[13 17 19]
sage: M.subdivision(1,0)
[31 37 41]
[53 59 61]
[73 79 83]
sage: M.subdivision_entry(1,0,0,0)
31
sage: M.subdivisions()
([2], [3])
sage: M.subdivide(None, [1,3]); M
[ 2| 3 5| 7 11]
[13|17 19|23 29]
[31|37 41|43 47]
[53|59 61|67 71]
[73|79 83|89 97]
Degenerate cases work too.
sage: M.subdivide([2,5], [0,1,3]); M
[| 2| 3 5| 7 11]
[|13|17 19|23 29]
[+--+-----+-----]
[|31|37 41|43 47]
[|53|59 61|67 71]
[|73|79 83|89 97]
[+--+-----+-----]
sage: M.subdivision(0,0)
[]
sage: M.subdivision(0,1)
[ 2]
[13]
sage: M.subdivide([2,2,3], [0,0,1,1]); M
[|| 2|| 3 5 7 11]
257