Add get_part method to partition.py

[jbandlow]

Add a method to partitions to return a default value for parts that do not exist.

sage: p = Partition([2,1])
sage: p.get_part(0)
2
sage: p.get_part(5)
0

Apply: attachment: trac_11300-get_part_partition-jb.2.patch

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: partitions, days30

Author: Jason Bandlow

Reviewer: Florent Hivert

Merged: sage-4.7.1.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/11300

[jbandlow]

Attachment: trac_11300-get_part_partition-jb.patch.gz

[jbandlow]

Author: jbandlow

[hivert]

Reviewer: Florent Hivert

[hivert]

Changed author from jbandlow to Jason Bandlow

[hivert]

Changed keywords from partitions, sagedays30 to partitions, days30

[hivert]

comment:3

Looks good and is useful !

[mwhansen]

comment:4

The one issue with this is the following:

sage: p = Partition([4,3])
sage: type(p.get_part(0))
<type 'sage.rings.integer.Integer'>
sage: type(p.get_part(10))
<type 'int'>

Is there a use case for a changeable default value?

[hivert]

comment:5

Replying to @mwhansen:

The one issue with this is the following:

> sage: p = Partition([4,3])
> sage: type(p.get_part(0))
> <type 'sage.rings.integer.Integer'>
> sage: type(p.get_part(10))
> <type 'int'>

That is a very good remark !

Is there a use case for a changeable default value?

If yes this can be corrected by changing default=0 to
default=Integer(0).

[jbandlow]

comment:6

I've changed the default value to Integer(0). I don't have a specific use case for another value, but it seems like it might come in handy. Do you have a reason you think it's a bad idea? I could probably be convinced to get rid of it.

[saliola]

comment:7

Hello Jason. I'm curious: did you compare timings of using the try-except statement:

 	768	        try: 
 	769	            return self[i] 
 	770	        except IndexError: 
 	771	            return default

with an if statement, like this one:

    if i < len(self._list):
        return self._list[i]
    else: 
        return default

I would guess that try-except statements are slower, but I have not tried it.

[jbandlow]

comment:8

Attachment: trac_11300-get_part_partition-jb.2.patch.gz

Replying to @saliola:

Hello Jason. I'm curious: did you compare timings of using the try-except statement:
with an if statement, like this one:

I would guess that try-except statements are slower, but I have not tried it.

I tried it and you're right--'if' is significantly faster. I've replaced the patch.

[saliola]

comment:9

Thanks for testing that. Positive review.

[jdemeyer]

Merged: sage-4.7.1.alpha1