Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[0|1|0 1|2]
[2|3|3 4|5]
[4|5|6 7|8]
Row subdivisions can be preserved, but only if they are identical. Otherwise, this information is discarded
and must be managed separately.
sage: A = matrix(QQ, 3, range(6))
sage: A.subdivide([1,3], None)
sage: B = matrix(QQ, 3, range(9))
sage: B.subdivide([1,3], None)
sage: A.augment(B, subdivide=True)
[0 1|0 1 2]
[---+-----]
[2 3|3 4 5]
[4 5|6 7 8]
[---+-----]
sage: A.subdivide([1,2], None)
sage: A.augment(B, subdivide=True)
[0 1|0 1 2]
[2 3|3 4 5]
[4 5|6 7 8]
The result retains the base ring of self by coercing the elements of right into the base ring of self.
sage: A = matrix(QQ, 2, [1,2])
sage: B = matrix(RR, 2, [sin(1.1), sin(2.2)])
sage: C = A.augment(B); C
[ 1 183017397/205358938]
[ 2 106580492/131825561]
sage: C.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: D = B.augment(A); D
[0.89120736006... 1.00000000000000]
[0.80849640381... 2.00000000000000]
sage: D.parent()
Full MatrixSpace of 2 by 2 dense matrices over Real Field with 53 bits of precision
Sometimes it is not possible to coerce into the base ring of self. A solution is to change the base ring
of self to a more expansive ring. Here we mix the rationals with a ring of polynomials with rational
coefficients.
sage: R = PolynomialRing(QQ, ’y’)
sage: A = matrix(QQ, 1, [1,2])
sage: B = matrix(R, 1, [’y’, ’y^2’])
sage: C = B.augment(A); C
[ y y^2 1 2]
sage: C.parent()
Full MatrixSpace of 1 by 4 dense matrices over Univariate Polynomial Ring in y over Rational
sage: D = A.augment(B)
Traceback (most recent call last):
...
TypeError: not a constant polynomial
sage: E = A.change_ring(R)
99