Bill Allombert on Mon, 17 Dec 2012 17:46:58 +0100

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Re: matdet vs. matdetint for large square matrices

On Mon, Dec 17, 2012 at 11:26:45AM -0500, Max Alekseyev wrote:
> Dear pari-users,
> Description of matdetint(x) says that "when x is square, the exact
> determinant is obtained".
> I noticed that for large binary square matrices (of order several
> hundreds), matdetint(x) gives roughly a triple speedup.
> Btw, it turns out that for square matrices, matdetint(x) gives the
> value of determinant up to a sign not exact (the description should
> have reflected this fact).

No it is a bug in matdetint(), please report it.

> In general, I'm interested in a fast way of testing whether matdet(x)
> == 0 for an integer matrix x.
> In my case among
> matdet(x) == 0
> matrank(x) < matsize(x)[1]
> matdetint(x) == 0
> the best performance is given by the last variant.
> Is there anything better?

Probably, it depends on the input distribution. 
For example you could compute the discriminant mod p for a set of small primes.
If one the result is not 0, then you know matdet()!=0.
Otherwise you can call matdetint.

In the development branch, matdet should be much faster for integer matrix.
Please test it.