Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[1 0 0|0 4 6]
[0 1 0|4 2 2]
[0 0 1|5 2 3]
[-----+-----]
sage: F.is_mutable()
False
sage: G = copy(F)
sage: G.subdivide([],[]); G
[1 0 0 0 4 6]
[0 1 0 4 2 2]
[0 0 1 5 2 3]
If you want to determine exactly which algorithm is used to compute the echelon form, you can add
additional keywords to pass on to the echelon_form() routine employed on the augmented matrix.
Sending the flag include_zero_rows is a bit silly, since the extended echelon form will never have
any zero rows.
sage: A = matrix(ZZ, [[1,2], [5,0], [5,9]])
sage: E = A.extended_echelon_form(algorithm=’padic’, include_zero_rows=False)
sage: E
[ 1 0 36 1 -8]
[ 0 1 5 0 -1]
[ 0 0 45 1 -10]
TESTS:
The subdivide keyword is checked.
sage: A = matrix(QQ, 2, range(4))
sage: A.extended_echelon_form(subdivide=’junk’)
Traceback (most recent call last):
...
TypeError: subdivide must be True or False, not junk
AUTHOR:
•Rob Beezer (2011-02-02)
fcp(var=’x’)
Return the factorization of the characteristic polynomial of self.
INPUT:
•var - (default: ‘x’) name of variable of charpoly
EXAMPLES:
sage: M = MatrixSpace(QQ,3,3)
sage: A = M([1,9,-7,4/5,4,3,6,4,3])
sage: A.fcp()
x^3 - 8*x^2 + 209/5*x - 286
sage: A = M([3, 0, -2, 0, -2, 0, 0, 0, 0])
sage: A.fcp(’T’)
(T - 3) * T * (T + 2)
find(f, indices=False)
Find elements in this matrix satisfying the constraints in the function f. The function is evaluated on each
element of the matrix .
INPUT:
•f - a function that is evaluated on each element of this matrix.
172 Chapter 7. Base class for matrices, part 2