Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
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act_on_polynomial(f )
Returns the polynomial f(self*x).
INPUT:
•self - an nxn matrix
•f - a polynomial in n variables x=(x1,...,xn)
OUTPUT: The polynomial f(self*x).
EXAMPLES:
sage: R. = QQ[]
sage: x, y = R.gens()
sage: f = x**2 - y**2
sage: M = MatrixSpace(QQ, 2)
sage: A = M([1,2,3,4])
sage: A.act_on_polynomial(f)
-8*x^2 - 20*x*y - 12*y^2
add_multiple_of_column(i, j, s, start_row=0)
Add s times column j to column i.
EXAMPLES: We add -1 times the third column to the second column of an integer matrix, remembering
to start numbering cols at zero:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.add_multiple_of_column(1,2,-1)
sage: a
[ 0 -1 2]
[ 3 -1 5]
To add a rational multiple, we first need to change the base ring:
sage: a = a.change_ring(QQ)
sage: a.add_multiple_of_column(1,0,1/3)
sage: a
[ 0 -1 2]
[ 3 0 5]
If not, we get an error message:
sage: a.add_multiple_of_column(1,0,i)
Traceback (most recent call last):
...
TypeError: Multiplying column by Symbolic Ring element cannot be done over Rational Field, u
add_multiple_of_row(i, j, s, start_col=0)
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]
70 Chapter 5. Base class for matrices, part 0