Solve equation efficiently

[chandra chowdhury]

I have matrices B and C of size (m,n) over integer with m>n. 

I know there is matrix A of size (m,m) such that 

AB=C. How to find A efficiently in Sage?

[Kwankyu]

I guess there is no special way in Sage to solve your kind of problem. Just solve for each row of A. 

[John Cremona]

On Tue, 30 Jul 2019 at 05:56, Kwankyu <ekwa...@gmail.com> wrote:

On Thursday, July 25, 2019 at 12:08:20 AM UTC+9, chandra chowdhury wrote:

I have matrices B and C of size (m,n) over integer with m>n. 

I know there is matrix A of size (m,m) such that 

AB=C. How to find A efficiently in Sage?

Try B.solve_left(C).  For example:

sage: B = Matrix(2,3,[1,2,3,4,5,6]); B
[1 2 3]
[4 5 6]
sage: A = Matrix(2,2,[1,1,1,2]); A
[1 1]
[1 2]
sage: C = A*B; C
[ 5  7  9]
[ 9 12 15]
sage: B.solve_left(C)
[1 1]
[1 2]
sage: B.solve_left(C) == A
True

 

I guess there is no special way in Sage to solve your kind of problem. Just solve for each row of A. 

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