# Row reduction modulo prime powers

Has any kind of row reduction been implemented modulo prime powers? Right now I'm simply trying to write a particular element of (Z/9Z)^d as a linear combination of a handful of other elements in this space. (I happen to know for other reasons that the original element is in the span of these handful of elements.)

I tried to do this by working with matrices over pAdicField(3,2), but this didn't work. (I guess some division by 3 messes things up.)

Is there anyway to do this without writing my own row reduction code??

Have you tried working with matrices over GF(9,'a')? I believe you can get the row space of such matrices ( A.row_space() ) and also the reduced row echelon form ( A.rref() ) of a matrix A.

But I want to be working in Z/9Z -- not over a finite field! I really want characteristic 9 not 3.