Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
... [ 0, 0,a^3, 0],
... [a^2 +4 , 0, 0,a + 2]])
sage: A.zigzag_form(subdivide=False)
[ 0 a^3 + 2*a^2 + 2*a + 2 0 0]
[ 1 2*a + 2 0 0]
[ 0 0 a^3 0]
[ 0 0 0 a^2 + 1]
TESTS:
sage: A = matrix(QQ, 2, 3, range(6))
sage: A.zigzag_form()
Traceback (most recent call last):
...
TypeError: matrix must be square, not 2 x 3
sage: A = matrix(Integers(6), 2, 2, range(4))
sage: A.zigzag_form()
Traceback (most recent call last):
...
TypeError: matrix entries must come from an exact field, not Ring of integers modulo 6
sage: A = matrix(RDF, 2, 2, range(4))
sage: A.zigzag_form()
Traceback (most recent call last):
...
TypeError: matrix entries must come from an exact field, not Real Double Field
sage: A = matrix(QQ, 2, range(4))
sage: A.zigzag_form(transformation=’junk’)
Traceback (most recent call last):
...
ValueError: ’transformation’ keyword must be True or False, not junk
sage: A = matrix(QQ, 2, range(4))
sage: A.zigzag_form(subdivide=’garbage’)
Traceback (most recent call last):
...
ValueError: ’subdivide’ keyword must be True or False, not garbage
Citations
AUTHOR:
•Rob Beezer (2011-06-09)
sage.matrix.matrix2.cmp_pivots(x, y)
Compare two sequences of pivot columns.
•If x is shorter than y, return -1, i.e., x < y, “not as good”.
•If x is longer than y, x > y, “better”.
•If the length is the same then x is better, i.e., x > y if the entries of x are correspondingly >= those of y
with one being greater.
sage.matrix.matrix2.decomp_seq(v)
This function is used internally be the decomposition matrix method. It takes a list of tuples and produces a
sequence that is correctly sorted and prints with carriage returns.
268 Chapter 7. Base class for matrices, part 2