it's a good plan, unless your A has exotic entries, so that a Singular 
polynomial ring with coefficients in this ring cannot be made. E.g. the 
following works:

sage: R.<x,y>=QQ[]
sage: A=matrix(R,[[1,2],[3,4]])
sage: singular.symmetricPower(A._singular_(),3).sage()

[64 48 36 27]
[96 64 42 27]
[48 28 16  9]
[ 8  4  2  1]


On Monday, May 22, 2017 at 1:34:55 PM UTC+1, Chris Brav wrote:
>
> I'd like to be able to compute symmetric powers of matrices in Sage. 
> Singular has a function for the kth symmetric power of a matrix A, namely 
> symmetricPower(A,k) (
> https://www.singular.uni-kl.de/Manual/4-0-3/sing_1107.htm#SEC1182). So it 
> seems one should just take a Sage matrix, convert it to a singular matrix, 
> take its symmetric power, and then convert back. I tried 
> singular.symmetricPower(A._singular_(),k) for A a Sage matrix, but the 
> interface complains that A is not of the correct type. It seems that 
> A._singular_() should be a matrix over a specified ring, and ._singular_() 
> doesn't create that ring. Any suggestions? 

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