Below is a matrix diagram, produced in Mathematica. In this case it's a $956\times 950$ rectangular matrix. The white parts are all zero.
sa = Import["https://pastebin.com/raw/fiErKrhU", "Package"]; MatrixPlot[sa]
I'm wondering if there is a way to efficiently compute the null space of this matrix. From a different calculation entirely (using a Molien series), I know in advance there should be 6 linearly independent vectors in this null space, and I already know one of them.
NullSpace routine takes too long to be feasible. I am hoping that there is a better way. I know that using
NullSpace[N[m]] will return the answer rather quickly, but I am hoping to be able to do this symbolically.
Any help would be appreciated.
SparseArray data for this matrix. It was too large for this message so I put it on pastebin.