I'm trying to find asymptotic bounds for the number of polynomials of
degree $n$ and height $\leq N$ with a specific Galois group (e.g.
$Syl_2(S_n)$, or in the example below $S_n$). I build all monic polynomials
with the given parameters, then ask pari for the order of their Galois
groups using the command
gp.polgalois(p)[1]
The problem is, when both $n$ and $N$ are both still relatively small, some
sort of data structure seems to be filling up, thereby causing a strange
error. It appears that this structure is saving the commands I have passed
to gp. The problem is cumulative, meaning this data structure is not
cleared unless I quit my Sage session and restart.
Perhaps the problem is best explained via an example. I can run the
function I constructed for $n=4, 2 \leq N \leq 4$, but when I try to run it
for $n=4, N=5$, the error appears:
sage: E4(5)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-5-06eb9bccdf87> in <module>()
----> 1 E4(Integer(5))
<string> in E4(N)
/opt/sage/local/lib/python2.7/site-packages/sage/interfaces/interface.py
in__getitem__
(self, n)
945 P = self._check_valid()
946 if not isinstance(n, tuple):
--> 947 return P.new('%s[%s]'%(self._name, n))
948 else:
949 return P.new('%s[%s]'%(self._name, str(n)[1:-1]))
............................................
/opt/sage/local/lib/python2.7/site-packages/sage/interfaces/gp.py in set(
self, var, value)
509 out = self.eval(cmd)
510 if out.find('***') != -1:
--> 511 raise TypeError, "Error executing code in
GP:\nCODE:\n\t%s\nPARI/GP ERROR:\n%s"%(cmd, out)
512
513
TypeError: Error executing code in GP:
CODE:
sage[65536]=sage[65535][1];
PARI/GP ERROR:
*** at top-level: sage[65536]=sage[65535][1]
*** ^---
*** _[_]: not a vector.
The ellipses denote the error being traced through several different
methods within the file
/opt/sage/local/lib/python2.7/site-packages/sage/interfaces/gp.py
If you would like to see the entire example session in which I produced the
error message above, go to:
http://sharetext.org/GlBk
Noting that $65536=2^16$, it seems that this is quite a natural place for
this data structure (denoted by 'sage[]' in the example) to be filling up.
Unfortunately, this structure is essentially inaccessible from the Sage
command line.
I should also note that I attempted to fix the problem with the command
gp.eval('allocatemem()')
but this did not fix the problem.
Any sort of explanation of what this data structure is, how I can clear it
between calls to pari, or even some sort of black box workaround, would be
greatly appreciated.
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