I wanted to draw a little extra attention to
https://github.com/sagemath/sage/issues/40147 in case there are people
on this mailing list with knowledge of how Singular works and/or how
Sage interfaces with it who don't monitor the GitHub issues closely, as
I'm not sure if this performance issue is the fault of Sage or of Singular.
Two fairly important computations for function fields appear to be
bottlenecked by the _maximal_order_basis function in the
FunctionField_integral class. These computations are computing the
genus, and finding the places at infinity. The specific line in the
_maximal_order_basis that causes the performance issue is when it calls
the normalize function in Singular. I've experimented with some monkey
patching to make the _maximal_order_basis faster since I'm in a case
where I know a basis for the maximal order of my function fields, and
modifying the _maximal_order_basis function to immediately return the
correct value (since I happen to know it in my case) is enough to
greatly speed up the process of finding the infinite places of the
function field, so this is definitely the culprit. Computing the genus
is still somewhat slow, but it does appear to be sped up significantly
by having a faster _maximal_order_basis function.
For comparison, Magma is able to compute the genus and the places at
infinity of function fields of comparable size to the ones I've tried to
compute in Sage much faster. Sage takes several seconds to minutes for
small examples and doesn't finish after letting it run for several hours
on larger examples. Magma does the small examples virtually instantly,
and the larger examples in a couple seconds.
Does anyone know if this is a bug in Singular, or perhaps is Sage asking
Singular to do an unnecessarily complicated computation?
--
Vincent Macri (he/him)
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