Null space of matrix over GF(2)

[Chris Dawson]

Hi all,

I am just starting out with ffpack and as an exercise was trying to call NullSpaceBasis on a a matrix over Z2. I'm getting the following error message

Assertion failed: (_p >= minCardinality()), function ModularBalanced, file /usr/local/include/givaro/modular-balanced-double.h, line 54

The relevant parts of the code that produced this are adapted from the solve example (see below). It looks like I should be using some other givaro field type for the specific case of GF(2), but I was unable to figure out how to get this to work.

Can anyone assist with this.

Many thanks,

Chris

typedef Givaro::Modular<int64_t> Field;

Field F(2);

int h_[] = {1,0,1,0,1,0,1, 0,1,1,0,0,1,1, 0,0,0,1,1,1,1};

Field::Element_ptr G, H;

H = fflas_new(F,3,7);

G = fflas_new(F,4,7);

for (unsigned i=0; i<21; i++)

        F.init(H[i], h_[i]);

size_t dim = NullSpaceBasis (F, FflasLeft, 7, 3, H, 7, G, ldn, NSdim);

[Clement Pernet]

Hi,

This is indeed a bug: FFLAS detects that Modular<int64_t> is not efficient for small cardinality and
therefore converts automatically to ModularBalanced<float>.
But then ModularBalanced is a representation of modular finite rings with cardinality p between
-(p-1)/2 and (p-1)/2, hence it requires p>=3.

This is now an open issue: https://github.com/linbox-team/fflas-ffpack/issues/151
I'll add a fix to it.

Meanwhile, you could simply replace Modular<int64_t> by Modular<float> in your code.

Best.

Clément

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[Chris Dawson]

Aha, I'd tried Modular<double> (which is also converted to ModularBalanced<float>) but not Modular<float>. All works as expected now.

Many thanks,

Chris

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