Suppose I have a real matrix with integer entries
A = matrix(RR,[[1,2,3],[4,5,6]])
I would like to convert it to an Integer matrix (ZZ). I can do it element by element but is there a function that will do this for the entire matrix. Doing B=ZZ(A) will return an error message
unable to coerce <type 'sage.matrix.matrix_generic_dense.matrix_generic_dense'=""> to an integer.
First, the "standard" way to do this is to change the base ring of the matrix as follows;
sage: B = A.change_ring(ZZ) ; B
[1 2 3]
[4 5 6]
sage: B.parent()
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
If P is a parent and E is some element, P(E) tries to convert E as an element of P. Hence, when you do B = ZZ(A), Sage tries to transform the matrix into an integer, which leads to an error. If you want to use such a conversion, the parent P you are looking for is the space of integer matrices of size 2*3 :
sage: P = MatrixSpace(ZZ,2,3)
sage: P
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
sage: P(A)
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[4 5 6]
Or directly:
sage: MatrixSpace(ZZ,2,3)(A)
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[4 5 6]
Note that it leads to the same result as with the change_ring method:
sage: P(A) == B
True
sage: P == B.parent()
True
It seems that the most efficient method is A.apply_map(ZZ,ZZ) (in terms of running time).
Note this will not work if you have non-integers in the matrix, then you can use A.apply_map(int,ZZ) or A.apply_map(round,ZZ) to round the entries.
You should be very careful with timings here, since in all cases, most of the time is spent in creating the parent ; compare:
sage: A = matrix(RR,[[1,2,3],[4,5,6]])
sage: %time A.apply_map(ZZ,ZZ)
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 1.49 ms
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[4 5 6]
And in another fresh Sage session (to avoid possible caching):
sage: A = matrix(RR,[[1,2,3],[4,5,6]])
sage: P = MatrixSpace(ZZ,2,3)
sage: %time A.apply_map(ZZ,ZZ)
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 367 µs
[1 2 3]
[4 5 6]
Note that each parent is only created once in a session. Once it is created, calling P(A) seems slightly faster than A.apply_map(ZZ,ZZ), probably because Sage does not even have to guess an ...
Asked: 2019-01-27 16:34:47 +0100
Seen: 1,777 times
Last updated: Jan 27 '19
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