Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
OUTPUT:
A new matrix formed by appending right onto the right side of self. If right is a vector (or free
module element) then in this context it is appropriate to consider it as a column vector. (The code first
converts a vector to a 1-column matrix.)
EXAMPLES:
sage: A = matrix(ZZ, 4, 5, range(20))
sage: B = matrix(ZZ, 4, 3, range(12))
sage: A.augment(B)
[ 0 1 2 3 4 0 1 2]
[ 5 6 7 8 9 3 4 5]
[10 11 12 13 14 6 7 8]
[15 16 17 18 19 9 10 11]
A vector may be augmented to a matrix.
sage: A = matrix(ZZ, 3, 5, range(15))
sage: v = vector(ZZ, 3, range(3))
sage: A.augment(v)
[ 0 1 2 3 4 0]
[ 5 6 7 8 9 1]
[10 11 12 13 14 2]
The subdivide option will add a natural subdivision between self and right.
For more details about how subdivisions are managed when augmenting, see
sage.matrix.matrix1.Matrix.augment().
sage: A = matrix(ZZ, 3, 5, range(15))
sage: B = matrix(ZZ, 3, 3, range(9))
sage: A.augment(B, subdivide=True)
[ 0 1 2 3 4| 0 1 2]
[ 5 6 7 8 9| 3 4 5]
[10 11 12 13 14| 6 7 8]
Errors are raised if the sizes are incompatible.
sage: A = matrix(ZZ, [[1, 2],[3, 4]])
sage: B = matrix(ZZ, [[10, 20], [30, 40], [50, 60]])
sage: A.augment(B)
Traceback (most recent call last):
...
TypeError: number of rows must be the same, not 2 != 3
charpoly(var=’x’, algorithm=’linbox’)
INPUT:
•var - a variable name
•algorithm - ‘linbox’ (default) ‘generic’
Note: Linbox charpoly disabled on 64-bit machines, since it hangs in many cases.
EXAMPLES:
sage: A = matrix(ZZ,6, range(36))
sage: f = A.charpoly(); f
x^6 - 105*x^5 - 630*x^4
sage: f(A) == 0
318 Chapter 17. Dense matrices over the integer ring