Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

CHAPTER
THIRTEEN
SPARSE MATRICES OVER A GENERAL
RING
Sparse Matrices over a general ring
EXAMPLES:
sage: R. = PolynomialRing(QQ)
sage: M = MatrixSpace(QQ[’x’],2,3,sparse=True); M
Full MatrixSpace of 2 by 3 sparse matrices over Univariate Polynomial Ring in x over Rational Field
sage: a = M(range(6)); a
[0 1 2]
[3 4 5]
sage: b = M([x^n for n in range(6)]); b
[ 1 x x^2]
[x^3 x^4 x^5]
sage: a * b.transpose()
[ 2*x^2 + x 2*x^5 + x^4]
[ 5*x^2 + 4*x + 3 5*x^5 + 4*x^4 + 3*x^3]
sage: pari(a)*pari(b.transpose())
[2*x^2 + x, 2*x^5 + x^4; 5*x^2 + 4*x + 3, 5*x^5 + 4*x^4 + 3*x^3]
sage: c = copy(b); c
[ 1 x x^2]
[x^3 x^4 x^5]
sage: c[0,0] = 5; c
[ 5 x x^2]
[x^3 x^4 x^5]
sage: b[0,0]
1
sage: c.dict()
{(0, 1): x, (1, 2): x^5, (0, 0): 5, (1, 0): x^3, (0, 2): x^2, (1, 1): x^4}
sage: c.list()
[5, x, x^2, x^3, x^4, x^5]
sage: c.rows()
[(5, x, x^2), (x^3, x^4, x^5)]
sage: TestSuite(c).run()
sage: d = c.change_ring(CC[’x’]); d
[5.00000000000000 x x^2]
[ x^3 x^4 x^5]
sage: latex(c)
\left(\begin{array}{rrr}
5 & x & x^{2} \\
x^{3} & x^{4} & x^{5}
\end{array}\right)
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