#5557: implement ridiculously fast 4x4 determinant
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Reporter: boothby | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.1
Component: linear algebra | Keywords:
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Comment(by boothby):
cwitty, this wasn't quite ready -- but thanks for your diligence! The new
patch makes this method default for dimension 4, and removes the
algorithm='4x4' option. Also, I put the code used to generate this code
into the matrix_integer_dense.pyx file. Finally, the _det_4x4 method has
been changed to _det_4x4_unsafe.
Timings:
{{{
Sage 3.4:
sage: S = MatrixSpace(ZZ,4)
sage: M = S.random_element(1,10000^200)
sage: timeit("M.determinant()")
5 loops, best of 3: 1.75 s per loop
Updated...
sage: S = MatrixSpace(ZZ,4)
sage: M = S.random_element(1,10000^200)
sage: timeit("M.determinant()")
625 loops, best of 3: 175 µs per loop
Using Pari:
sage: N = pari(M)
sage: timeit("N.matdet();")
625 loops, best of 3: 337 µs per loop
}}}
So in general, this is hugely faster than the previous version of Sage,
and twice as fast as Pari.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5557#comment:2>
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