Exact integer nullspace of integer matrix?

问题:

nullspace(A) finds a basis for the null-space of a matrix A. The returned vectors have floating-point coordinates. If the matrix A is an integer-matrix, the basis can be found in integer coordinates.

For example, in Mathematica,

NullSpace[RandomInteger[{-10, 10}, {3, 4}]]

always returns integer vectors.

Is there a way to compute an integer basis for an integer matrix in Julia?

Update: I get build errors with Nemo.jl (see comments to Dan Getz's answer). In the mean time, is there an alternative?

回答1:

Nemo.jl is a package for algebra in Julia. It has a lot of functionality and should also allow to compute the null space. One way to go about it would be:

using Nemo   # install with Pkg.add("Nemo")

S = MatrixSpace(ZZ, 3, 4)
mm = rand(-10:10,3,4)
m = S(mm)
(bmat,d) = nullspace(m)

After which d is the dimension of the nullspace and bmat has a basis in its columns.

Hope this helps (I would be happy to see alternative solutions possibly using other algebra packages).