Ooh I'm _really_ glad I asked now. Many thanks William.
The first time I wanted such a loop, I was beta testing your magma modular
symbols code in 2000 or so :-)
Kevin
On Monday, 4 August 2014 15:01:05 UTC+1, William wrote:
>
> On Mon, Aug 4, 2014 at 5:11 AM, Kevin Buzzard <kevin.m...@gmail.com
> <javascript:>> wrote:
> > 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?
>
> Yes, I implemented a robust way to do this long ago. Use the @fork
> decorator, and do *NOT* try to mutate a global variable in the
> function you're calling -- this makes no sense because it happens in a
> subprocess.
>
> @fork
> def g(N):
> f=ModularSymbols(N,2,1).cuspidal_subspace().hecke_
> operator(3).matrix().change_ring(GF(5)).charpoly('t')
> print N,f; sys.stdout.flush()
> return f
>
> N=Integer(1)
> R.<t>=PolynomialRing(GF(5))
> charpolys=[]
> while N<=10000:
> charpolys.append(g(N))
> N += 1
> print get_memory_usage(), charpolys # for testing
>
>
> If you want to do several in parallel, you can easily do that too as
> follows. This will both completely eliminate memory leak issues, and
> use all processors on your computer.
>
> @parallel
> def g(N):
> f=ModularSymbols(N,2,1).cuspidal_subspace().hecke_
> operator(3).matrix().change_ring(GF(5)).charpoly('t')
> print N,f; sys.stdout.flush()
> return f
>
> R.<t>=PolynomialRing(GF(5))
> charpolys={}
> for x in g([1..10000]):
> N = x[0][0][0]
> charpolys[N] = x[1]
> save(charpolys, 'charpolys.sobj') # saves all so far to a single
> file -- load later with load('charpolys.sobj')
>
>
> The save above will save the charpolys dict to disk each time you get
> back another charpoly.
>
> Welcome to the modern world (though everything above just uses a few
> Python functions from the late 1990s -- pickle and fork). Compared to
> Magma, Sage is much, much better at this sort of stuff...
>
> -- William
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