# It takes so long to generate dictionary of GL elements.

The following command

GL4dicthash={hash(g):None for g in GL(4,2)}


takes 9 seconds to execute. On the other hand

GL4dict={g:None for g in GL(4,2)}


takes minutes and does not seem to terminate.

If I understand python dictionary correctly, they should take about the same time. So what happened?

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It seems hash(g) lies between 0 and 15 for all g. It does not make any sense to me.

( 2018-02-06 02:21:25 +0100 )edit

Found this https://trac.sagemath.org/ticket/10950. Maybe I should update my Sage.

( 2018-02-06 02:36:48 +0100 )edit

What version of Sage were you using?

( 2018-02-06 06:12:52 +0100 )edit

Mutability and hashability are two different things. In the above case, for instance:

sage: G = GL(4,2)
sage: g = G.one()
sage: g.__hash__()
0


There is a __hash__ method, so g is hashable. There are $16$ different hash-values:

sage: list( set( [ g.__hash__() for g in G ] ) )
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]


But $G$ has order

sage: prod( [ 2^4-2^k for k in [0..3] ] )
20160
sage: G.order()
20160


In order to define a dictionary where gis a key, this element should be immutable. Then for each new key one has to check if the key is already used. This takes time. And before we try to understand the time problem, why do we need to work with such a complicated dictionary?

( 2018-02-06 09:50:18 +0100 )edit

@slelievre before 8.0 now 8.1 and everything is good now. @dan_fulea: I am implementing a group action that is quite tedious. GL(4,2) acts on [0..15] by left-multiplying its binary expression as a column vector in GF(2)^4. And then act on Subsets([0..15]). I would like to cache the action as there are only 20160·16 possibilities. Moreover, if there is a (fast) way to turn g into 16-bit int then I need an array of size 65536·16, which is still affordable. What would make it triumph is that looking up array entry takes ~100ns.

( 2018-02-07 01:14:04 +0100 )edit

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The generation took on my slow linux machine approximatively 10s CPU time...

sage: %timeit -n1 GL4dict = { g : None for g in GL(4,2) }
1 loop, best of 3: 9.29 s per loop


This is

sage: version()
'SageMath version 8.1, Release Date: 2017-12-07'


Please update to the new version, if there is such a big run time difference.

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Thank you. I did update from 8.0 to 8.1. I was not aware of the version-issue because I thought I was quite new. Now everything works fine. hash(g) gives crazy numbers such as -32759827368972486.

( 2018-02-07 01:05:00 +0100 )edit

@Symbol 1 -- you can accept the answer if it solves the problem in your question.

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( 2018-09-22 09:31:58 +0100 )edit