Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: matrix(ZZ,m).hermite_form(algorithm=’padic’, include_zero_rows=False)
[ 1 0 2 0 13 5 1 166 72 69]
[ 0 1 1 0 20 4 15 195 65 190]
[ 0 0 4 0 24 5 23 22 51 123]
[ 0 0 0 1 23 7 20 105 60 151]
[ 0 0 0 0 40 4 0 80 36 68]
[ 0 0 0 0 0 10 0 100 190 170]
[ 0 0 0 0 0 0 25 0 100 150]
[ 0 0 0 0 0 0 0 200 0 0]
[ 0 0 0 0 0 0 0 0 200 0]
[ 0 0 0 0 0 0 0 0 0 200]
index_in_saturation(proof=None)
Return the index of self in its saturation.
INPUT:
•proof - (default: use proof.linear_algebra()); if False, the determinant calculations are done with
proof=False.
OUTPUT:
•positive integer - the index of the row span of this matrix in its saturation
ALGORITHM: Use Hermite normal form twice to find an invertible matrix whose inverse transforms a
matrix with the same row span as self to its saturation, then compute the determinant of that matrix.
EXAMPLES:
sage: A = matrix(ZZ, 2,3, [1..6]); A
[1 2 3]
[4 5 6]
sage: A.index_in_saturation()
3
sage: A.saturation()
[1 2 3]
[1 1 1]
insert_row(index, row)
Create a new matrix from self with.
INPUT:
•index - integer
•row - a vector
EXAMPLES:
sage: X = matrix(ZZ,3,range(9)); X
[0 1 2]
[3 4 5]
[6 7 8]
sage: X.insert_row(1, [1,5,-10])
[ 0 1 2]
[ 1 5 -10]
[ 3 4 5]
[ 6 7 8]
sage: X.insert_row(0, [1,5,-10])
[ 1 5 -10]
[ 0 1 2]
[ 3 4 5]
329