Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: q = t^5 + t - 17
sage: A = block_diagonal_matrix( companion_matrix(p),
... companion_matrix(p^2),
... companion_matrix(q),
... companion_matrix(q) )
sage: A.charpoly(var=t).factor()
(t^3 + 3*t - 8)^3 * (t^5 + t - 17)^2
sage: A.minpoly(var=t).factor()
(t^3 + 3*t - 8)^2 * (t^5 + t - 17)
TESTS:
sage: companion_matrix([4, 5, 1], format=’junk’)
Traceback (most recent call last):
...
ValueError: format must be ’right’, ’left’, ’top’ or ’bottom’, not junk
sage: companion_matrix(sin(x))
Traceback (most recent call last):
...
TypeError: input must be a polynomial (not a symbolic expression, see docstring), or other itera
sage: companion_matrix([2, 3, 896])
Traceback (most recent call last):
...
ValueError: polynomial (or the polynomial implied by coefficients) must be monic, not a leading
sage: F. = GF(2^2)
sage: companion_matrix([4/3, a+1, 1])
Traceback (most recent call last):
...
TypeError: unable to find common ring for coefficients from polynomial
sage: A = companion_matrix([1])
sage: A.nrows(); A.ncols()
0
0
sage: A = companion_matrix([])
Traceback (most recent call last):
...
ValueError: polynomial cannot be specified by an empty list
AUTHOR:
•Rob Beezer (2011-05-19)
sage.matrix.constructor.diagonal_matrix(arg0=None, arg1=None, arg2=None,
sparse=True)
This function is available as diagonal_matrix(...) and matrix.diagonal(...).
Return a square matrix with specified diagonal entries, and zeros elsewhere.
FORMATS:
1.diagonal_matrix(entries)
2.diagonal_matrix(nrows, entries)
3.diagonal_matrix(ring, entries)
4.diagonal_matrix(ring, nrows, entries)
28 Chapter 2. Matrix Constructor