Max Alekseyev on Mon, 17 Dec 2012 17:26:53 +0100

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matdet vs. matdetint for large square matrices

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).

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?