forpart

Function: _forpart_init
Class: gp2c_internal
Help: Initialize forpart_t
Description:
 (forpart,small,?gen,?gen):void      forpart_init(&$1, $2, $3, $4)

Function: _forpart_next
Class: gp2c_internal
Help: Compute the next part
Description:
 (forpart):vecsmall                  forpart_next(&$1)

Function: forpart
Section: programming/control
C-Name: forpart0
Prototype: vV=GIDGDG
Iterator:
 (gen,small,?gen,?gen)         (forpart, _forpart_init, _forpart_next)
Wrapper: (,vG,,)
Description:
 (small,closure,?gen,?gen):void forpart(${2 cookie}, ${2 wrapper}, $1, $3, $4)
Help: forpart(X=k,seq,{a=k},{n=k}): evaluate seq where the Vecsmall X
 goes over the partitions of k. Optional parameter n (n=nmax or n=[nmin,nmax])
 restricts the length of the partition. Optional parameter a (a=amax or
 a=[amin,amax]) restricts the range of the parts. Zeros are removed unless one
 sets amin=0 to get X of fixed length nmax (=k by default).
Doc: evaluate \var{seq} over the partitions $X=[x_1,\dots x_n]$ of the
 integer $k$, i.e.~increasing sequences $x_1\leq x_2\dots \leq x_n$ of sum
 $x_1+\dots + x_n=k$. By convention, $0$ admits only the empty partition and
 negative numbers have no partitions. A partition is given by a
 \typ{VECSMALL}, where parts are sorted in nondecreasing order. The
 partitions are listed by increasing size and in lexicographic order when
 sizes are equal:
 \bprog
 ? forpart(X=4, print(X))
 Vecsmall([4])
 Vecsmall([1, 3])
 Vecsmall([2, 2])
 Vecsmall([1, 1, 2])
 Vecsmall([1, 1, 1, 1])
 @eprog\noindent Optional parameters $n$ and $a$ are as follows:

 \item $n=\var{nmax}$ (resp. $n=[\var{nmin},\var{nmax}]$) restricts
 partitions to length less than $\var{nmax}$ (resp. length between
 $\var{nmin}$ and $nmax$), where the \emph{length} is the number of nonzero
 entries.

 \item $a=\var{amax}$ (resp. $a=[\var{amin},\var{amax}]$) restricts the parts
 to integers less than $\var{amax}$ (resp. between $\var{amin}$ and
 $\var{amax}$).

 By default, parts are positive and we remove zero entries unless $amin\leq0$,
 in which case we fix the size $\#X = \var{nmax}$:
 \bprog
 \\ at most 3 nonzero parts, all <= 4
 ? forpart(v=5,print(Vec(v)), 4, 3)
 [1, 4]
 [2, 3]
 [1, 1, 3]
 [1, 2, 2]

 \\ between 2 and 4 parts less than 5, fill with zeros
 ? forpart(v=5,print(Vec(v)),[0,5],[2,4])
 [0, 0, 1, 4]
 [0, 0, 2, 3]
 [0, 1, 1, 3]
 [0, 1, 2, 2]
 [1, 1, 1, 2]

 \\ no partitions of 1 with 2 to 4 nonzero parts
 ? forpart(v=1,print(v),[0,5],[2,4])
 ?
 @eprog\noindent
 The behavior is unspecified if $X$ is modified inside the loop.

 \synt{forpart}{void *data, long (*call)(void*,GEN), long k, GEN a, GEN n}.