Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Full MatrixSpace of 10 by 2147483648 dense matrices over Integer Ring # 64-bit
sage: MatrixSpace(ZZ,2^31,10)
... # 32-bit
ValueError: number of rows and columns must be less than 2^31 (on a 32-bit computer -- use a 64-
Full MatrixSpace of 2147483648 by 10 dense matrices over Integer Ring # 64-bit
sage: MatrixSpace(ZZ,10,10).category()
Category of algebras over Integer Ring
sage: MatrixSpace(QQ,10).category()
Category of algebras over Rational Field
base_extend(R)
Return base extension of this matrix space to R.
INPUT:
•R - ring
OUTPUT: a matrix space
EXAMPLES:
sage: Mat(ZZ,3,5).base_extend(QQ)
Full MatrixSpace of 3 by 5 dense matrices over Rational Field
sage: Mat(QQ,3,5).base_extend(GF(7))
Traceback (most recent call last):
...
TypeError: no base extension defined
basis()
Returns a basis for this matrix space.
Warning: This will of course compute every generator of this matrix space. So for large matrices,
this could take a long time, waste a massive amount of memory (for dense matrices), and is likely not
very useful. Don’t use this on large matrix spaces.
EXAMPLES:
sage: Mat(ZZ,2,2).basis()
[
[1 0] [0 1] [0 0] [0 0]
[0 0], [0 0], [1 0], [0 1]
]
cached_method(f, name=None)
EXAMPLES:
In the following examples, one can see how a cached method works in applicationy. Below, we demonstrate
what is done behind the scenes:
sage: class C:
....: @cached_method
....: def __hash__(self):
....: print "compute hash"
....: return int(5)
....: @cached_method
....: def f(self, x):
....: print "computing cached method"
....: return x*2
sage: c = C()
sage: type(C.__hash__)
4 Chapter 1. Matrix Spaces