Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: A.right_kernel_matrix().parent()
Full MatrixSpace of 0 by 0 dense matrices over Finite Field of size 7
TESTS:
The “usual” quaternions are a non-commutative ring and computations of kernels over these rings are not
implemented.
sage: Q. = QuaternionAlgebra(-1,-1)
sage: A = matrix(Q, 2, [i,j,-1,k])
sage: A.right_kernel_matrix()
Traceback (most recent call last):
...
NotImplementedError: Cannot compute a matrix kernel over Quaternion Algebra (-1, -1) with ba
We test error messages for improper choices of the ‘algorithm’ keyword.
sage: matrix(ZZ, 2, 2).right_kernel_matrix(algorithm=’junk’)
Traceback (most recent call last):
...
ValueError: matrix kernel algorithm ’junk’ not recognized
sage: matrix(GF(2), 2, 2).right_kernel_matrix(algorithm=’padic’)
Traceback (most recent call last):
...
ValueError: ’padic’ matrix kernel algorithm only available over the rationals and the intege
sage: matrix(QQ, 2, 2).right_kernel_matrix(algorithm=’pari’)
Traceback (most recent call last):
...
ValueError: ’pari’ matrix kernel algorithm only available over non-trivial number fields and
sage: matrix(Integers(6), 2, 2).right_kernel_matrix(algorithm=’generic’)
Traceback (most recent call last):
...
ValueError: ’generic’ matrix kernel algorithm only available over a field, not over Ring of
sage: matrix(QQ, 2, 2).right_kernel_matrix(algorithm=’pluq’)
Traceback (most recent call last):
...
ValueError: ’pluq’ matrix kernel algorithm only available over integers mod 2, not over Rati
We test error messages for improper basis format requests.
sage: matrix(ZZ, 2, 2).right_kernel_matrix(basis=’junk’)
Traceback (most recent call last):
...
ValueError: matrix kernel basis format ’junk’ not recognized
sage: matrix(ZZ, 2, 2).right_kernel_matrix(basis=’pivot’)
Traceback (most recent call last):
...
ValueError: pivot basis only available over a field, not over Integer Ring
sage: matrix(QQ, 2, 2).right_kernel_matrix(basis=’LLL’)
Traceback (most recent call last):
...
ValueError: LLL-reduced basis only available over the integers, not over Rational Field
Finally, error messages for the ‘proof’ keyword.
sage: matrix(ZZ, 2, 2).right_kernel_matrix(proof=’junk’)
Traceback (most recent call last):
...
ValueError: ’proof’ must be one of True, False or None, not junk
sage: matrix(QQ, 2, 2).right_kernel_matrix(proof=True)
248 Chapter 7. Base class for matrices, part 2