Joerg Arndt on Sat, 01 Jun 2013 19:46:23 +0200

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Re: new GP loop: forpart()

* Bill Allombert <> [May 30. 2013 14:06]:
> Dear PARI developers,
> I have commited a patch by Pascal and myself that adds GP function
> to loop over partitions:
> forpart(v=5,print(v))
> Vecsmall([1,1,1,1,1])
> Vecsmall([1,1,1,2])
> Vecsmall([1,2,2])
> Vecsmall([1,1,3])
> Vecsmall([2,3])
> Vecsmall([1,4])
> Vecsmall([5])
> Also I have changed the partitions function to provide the same interface
> as forpart. An unfortunate side effect is that the order of the partitions
> is reversed.

With "reversed" you mean: they are lists in ascending order?

For descending lists see

Contrary to recent publications, the generator is
faster than the one for ascending lists, at the price
of a single extra integer recording the position of the
(second) last descent.

The partitions appear ordered wrt. to their largest
part, which can be convenient.

> This could be fixed if someone provide a forpart_previous()
> function.

Please see
programmed and uploaded a minute ago.  There, in
see the method prev()

Benchmarks at end of the demo-code

> [...]

I can offer a significantly more general generator:
It can generate compositions (as list of parts)
wrt. to a given condition.  This gives you partitions
as decreasing or increasing lists, into odd parts,
distinct parts, with max rise/fall, modulo conditions...
Indeed any condition that is a condition on prefixes
(this is _quite_ general in practice).

Best,   jj