Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
lift()
Return the lift of this matrix to the integers.
EXAMPLES:
sage: a = matrix(GF(7),2,3,[1..6])
sage: a.lift()
[1 2 3]
[4 5 6]
sage: a.lift().parent()
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
Subdivisions are preserved when lifting:
sage: a.subdivide([], [1,1]); a
[1||2 3]
[4||5 6]
sage: a.lift()
[1||2 3]
[4||5 6]
matrix_window(row=0, col=0, nrows=-1, ncols=-1, check=1)
Return the requested matrix window.
EXAMPLES:
sage: a = matrix(GF(7),3,range(9)); a
[0 1 2]
[3 4 5]
[6 0 1]
sage: type(a)
We test the optional check flag.
sage: matrix(GF(7),[1]).matrix_window(0,1,1,1)
Traceback (most recent call last):
...
IndexError: matrix window index out of range
sage: matrix(GF(7),[1]).matrix_window(0,1,1,1, check=False)
Matrix window of size 1 x 1 at (0,1):
[1]
minpoly(var=’x’, algorithm=’generic’, proof=None)
Returns the minimal polynomial of self.
INPUT:
•var - a variable name
•algorithm - ‘generic’ (default)
•proof – (default: True); whether to provably return the true minimal polynomial; if False, we only
guarantee to return a divisor of the minimal polynomial. There are also certainly cases where the
computed results is frequently not exactly equal to the minimal polynomial (but is instead merely a
divisor of it).
WARNING: If proof=True, minpoly is insanely slow compared to proof=False.
EXAMPLES:
296 Chapter 14. Dense matrices over Z/nZ for n small