CoCalc Public Filestmp / 2014-11-02-214954.sagews
m = matrix(0)

File: /usr/local/sage/sage-6.3.beta6/src/sage/matrix/matrix0.pyx
Signature : m.add_multiple_of_row(self, i, j, s, start_col=0)
Docstring :
Add s times row j to row i.

EXAMPLES: We add -3 times the first row to the second row of an
integer matrix, remembering to start numbering rows at zero:

sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a
[ 0  1  2]
[ 3  1 -1]

To add a rational multiple, we first need to change the base ring:

sage: a = a.change_ring(QQ)
sage: a
[   0    1    2]
[   3  4/3 -1/3]

If not, we get an error message:

Traceback (most recent call last):
...
TypeError: Multiplying row by Symbolic Ring element cannot be done over Rational Field, use change_ring or with_added_multiple_of_row instead.   Docstring:
Signature : m.add_multiple_of_row(self, i, j, s, start_col=0)
Docstring :
Add s times row j to row i.

EXAMPLES: We add -3 times the first row to the second row of an
integer matrix, remembering to start numbering rows at zero:

sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a
[ 0  1  2]
[ 3  1 -1]

To add a rational multiple, we first need to change the base ring:

sage: a = a.change_ring(QQ)