Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Companion matrices may be selected as any one of four different types. See the documentation for the
companion matrix constructor, sage.matrix.constructor.companion_matrix(), for more
information.
sage: A = matrix(QQ, [[35, -18, -2, -45],
... [22, -22, 12, -16],
... [ 5, -12, 12, 4],
... [16, -6, -4, -23]])
sage: A.rational_form(format=’right’)
[ 2| 0 0 0]
[--+--------]
[ 0| 0 0 10]
[ 0| 1 0 -1]
[ 0| 0 1 0]
sage: A.rational_form(format=’bottom’)
[ 2| 0 0 0]
[--+--------]
[ 0| 0 1 0]
[ 0| 0 0 1]
[ 0|10 -1 0]
sage: A.rational_form(format=’left’)
[ 2| 0 0 0]
[--+--------]
[ 0| 0 1 0]
[ 0|-1 0 1]
[ 0|10 0 0]
sage: A.rational_form(format=’top’)
[ 2| 0 0 0]
[--+--------]
[ 0| 0 -1 10]
[ 0| 1 0 0]
[ 0| 0 1 0]
TESTS:
sage: A = matrix(QQ, 2, 3, range(6))
sage: A.rational_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.rational_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.rational_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.rational_form(format=’junk’)
Traceback (most recent call last):
...
ValueError: ’format’ keyword must be ’right’, ’bottom’, ’left’, ’top’ or ’invariants’, not j
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