整数矩阵的确切整数零空间? [英] Exact integer nullspace of integer matrix?

问题描述

nullspace(A) 为矩阵 A 的空空间找到一个基.返回的向量具有浮点坐标.如果矩阵 A 是整数矩阵，则可以在整数坐标中找到基.

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.

例如，在Mathematica中，

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

总是返回整数向量.

有没有办法在 Julia 中计算整数矩阵的整数基?

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

更新: Nemo.jl 出现构建错误(请参阅 Dan Getz 回答的评论).同时，还有其他选择吗?

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

推荐答案

Nemo.jl 是 Julia 中的代数包.它有很多功能，还应该允许计算空空间.一种方法是:

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)

之后，d 是空空间的维度，bmat 在其列中有一个基础.

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

希望这会有所帮助(我很高兴看到可能使用其他代数包的替代解决方案).

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

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