TL;DR: I am going to write a bash loop which loops through 1<=N<=10000 and
feeds the number N into a function in a sage session, one session per N.
Has anyone written a robust way of doing this already?
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Gory details: I have memory management issues with sage, of a similar
nature to memory management issues I had with magma 10 years ago, and I'm
going to solve them by running multiple sage sessions because I am too lazy
to learn about memory management issues.
Here is a simple loop:
N=Integer(1)
R.<t>=PolynomialRing(GF(5))
charpolys=[]
while N<=10000:
f=ModularSymbols(N,2,1).cuspidal_subspace().hecke_operator(3).matrix().change_ring(GF(5)).charpoly('t')
charpolys=charpolys+[f]
print N,f
N=N+1
sage.modular.modform.constructor.ModularForms_clear_cache()
It's collecting characteristic polynomials of T_3 mod 5 on spaces of weight
2 cusp forms of level N=1,2,3,... and adding them to a list . [this is not
what I actually want to do, it's just a simple example indicating the
issues I'm having]. The point I'm trying to indicate is that there's a
complicated (but standard) modular forms calculation in the middle, but the
result (and all I want to keep track of) is a polynomial of relatively
small degree. The last line is a naive attempt on my part to persuade sage
to forget all the modular form calculations that it has done.
On my machine, by the time N=1200, the underlying python session is
occupying about 10 gigs of memory and my machine is swapping like crazy. On
the other hand, performing the commands within the loop for N=1200 takes
far less memory.
In my mind there are two ways to deal with this issue (because I would like
to go far further than N=1200). The first is to actually understand what is
going on and try to kill the spaces of modular forms that are presumably
piling up in memory. For me this is not an ideal solution because it's the
sort of thing where if next week I want to do some other loop of this
nature I'll have to come and ask again.
The second is what I'm far keener on; instead of running the loop in sage,
I want to run it in something else, e.g. a bash shell, and fire up lots of
separate sage sessions, each of which just does the calculation for one
value of N and then dies. This might sound like a far more amateur approach
to some, but basically at the end of the day it's an extremely efficient
way of doing the memory management issues that I'm struggling with, because
you 100% kill everything you're not interested in when the session dies, so
the bottom line is that it will work.
When I did this before with magma I just wrote my own routines; they were
rather amateurish but they worked. I would write all magma output to a file
and then extract the lines I wanted (flagged in the magma output by my
printing "THE NEXT LINE IS THE LINE YOU WANT" in my magma program just
before printing out the polynomial I wanted to keep etc etc) and write it
all to another file -- a real mishmash of bad shell script programming and
bad magma programming, but because all of this stuff was only taking a few
seconds per loop and the actual modular forms calculations were taking
several minutes (or longer) it didn't really matter.
Has someone written such scripts already? In short, I have a program
function.sage, defining a function m(N), and I want to loop from N=1 to
10000 in a bash shell and for each N, fire up a sage session, load
function.sage, compute m(N) and write the result to a file (one file in
total, for all values of N). This seems like a sufficiently generic problem
that perhaps someone has solved it already; if no-one has done it I'll
write some amateurish code to do it myself but I thought there was no harm
in asking first.
Kevin
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