On 2014-11-13 22:17, Ursula Whitcher wrote:
2^23, so the largest prime number is 8388593.
This is fixed as in "the old, bad constant", rather than "an improved
bound which fixed the problem", right?
I meant "fixed" as synonym for "constant".
Let me try to explain it one more time:
(1) *very old situation*:
(i) Determinants of dimension n over GF(p) are computed using LinBox for
p <= f(n). If p > f(n), they are computed by lifting to ZZ.
(ii) Determinants of dimension n > 50 over ZZ are computed with a
multi-modular algorithm by reducing mod primes p with p <= f(n) (but p
close to f(n))
(2) *broken situation after LinBox upgrade*:
(i) Determinants of dimension n over GF(p) are computed using LinBox for
p <= C. If p > C, they are computed by lifting to ZZ.
(ii) Determinants of dimension n > 50 over ZZ are computed with a
multi-modular algorithm by reducing mod primes p with p <= f(n) (but p
close to f(n)).
Note that this is broken in the case that C < f(n): given a matrix over
ZZ, in (ii) we pick a prime C < p <= f(n) and compute the determinant
mod p to apply a multi-modular algorithm. By (i), this determinant is
computed by lifting to ZZ. This is an infinite loop.
The constant C equals 2^23. The condition C < f(n) is equivalent to n <=
63. For n >= 64, we have C >= f(n) and there is no problem.
(3) *fixed situation after #14032*:
(i) Determinants of dimension n over GF(p) are computed using LinBox for
p <= C. If p > C, they are computed by lifting to ZZ.
(ii) Determinants of dimension n > 50 over ZZ are computed with a
multi-modular algorithm by reducing mod primes p with p <= C (but p
close to C)
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