Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Mutable matrices are not hashable, so can’t be used as keys for dictionaries:
sage: hash(A)
Traceback (most recent call last):
...
TypeError: mutable matrices are unhashable
sage: v = {A:1}
Traceback (most recent call last):
...
TypeError: mutable matrices are unhashable
If we make A immutable it suddenly is hashable.
sage: A.set_immutable()
sage: A.is_mutable()
False
sage: A[0,0] = 10
Traceback (most recent call last):
...
ValueError: matrix is immutable; please change a copy instead (i.e., use copy(M) to change a
sage: hash(A) #random
12
sage: v = {A:1}; v
{[10 1]
[ 2 3]: 1}
set_row_to_multiple_of_row(i, j, s)
Set row i equal to s times row j.
EXAMPLES: We change the second row to -3 times the first row:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.set_row_to_multiple_of_row(1,0,-3)
sage: a
[ 0 1 2]
[ 0 -3 -6]
If we try to multiply a row by a rational number, we get an error message:
sage: a.set_row_to_multiple_of_row(1,0,1/2)
Traceback (most recent call last):
...
TypeError: Multiplying row by Rational Field element cannot be done over Integer Ring, use c
str(rep_mapping=None, zero=None, plus_one=None, minus_one=None)
Return a nice string representation of the matrix.
INPUT:
•rep_mapping - a dictionary or callable used to override the usual representation of elements.
If rep_mapping is a dictionary then keys should be elements of the base ring and values the desired
string representation. Values sent in via the other keyword arguments will override values in the
dictionary. Use of a dictionary can potentially take a very long time due to the need to hash entries of
the matrix. Matrices with entries from QQbar are one example.
If rep_mapping is callable then it will be called with elements of the matrix and must return a
string. Simply call repr() on elements which should have the default representation.
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