Function: _forsubset_init
Class: gp2c_internal
Help: Initialize forsubset_t
Description:
 (forsubset,small):void            forallsubset_init(&$1, $2)
 (forsubset,gen):void              forsubset_init(&$1, $2)

Function: _forsubset_next
Class: gp2c_internal
Help: Compute the next subset
Description:
 (forsubset):vecsmall              forsubset_next(&$1)

Function: forsubset
Section: programming/control
C-Name: forsubset0
Prototype: vGVI
Iterator:
 (gen,gen)         (forsubset, _forsubset_init, _forsubset_next)
Wrapper: (,vG,,)
Help: forsubset(nk,s,seq): if nk is an integer n, the sequence is evaluated,
  s going through all subsets of {1, 2, ..., n}; if nk is a pair [n,k]
  of integers s goes through k-subsets of {1, 2, ..., n}.
  The order is lexicographic among subsets of the same size and smaller
  subsets come first.
Doc: if \var{nk} is an integer $n$, evaluates \kbd{seq}, where
 the formal variable $s$ goes through all subsets of $\{1, 2, \ldots, n\}$;
 if \var{nk} is a pair $[n,k]$ of integers, $s$ goes through subsets
 of size $k$ of $\{1, 2, \ldots, n\}$. In both cases $s$ goes through subsets
 in lexicographic order among subsets of the same size and smaller subsets
 come first.
 \bprog
 ? forsubset([5,3], s, print(s))
 Vecsmall([1, 2, 3])
 Vecsmall([1, 2, 4])
 Vecsmall([1, 2, 5])
 Vecsmall([1, 3, 4])
 Vecsmall([1, 3, 5])
 Vecsmall([1, 4, 5])
 Vecsmall([2, 3, 4])
 Vecsmall([2, 3, 5])
 Vecsmall([2, 4, 5])
 Vecsmall([3, 4, 5])
 @eprog

 \bprog
 ? forsubset(3, s, print(s))
 Vecsmall([])
 Vecsmall([1])
 Vecsmall([2])
 Vecsmall([3])
 Vecsmall([1, 2])
 Vecsmall([1, 3])
 Vecsmall([2, 3])
 Vecsmall([1, 2, 3])
 @eprog\noindent The running time is proportional to the number
 of subsets enumerated, respectively $2^{n}$ and \kbd{binomial}$(n,k)$:
 \bprog
 ? c = 0; forsubset([40,35],s,c++); c
 time = 128 ms.
 %4 = 658008
 ? binomial(40,35)
 %5 = 658008
 @eprog
 The function is not useful for negative $n$ or $k$, but these corner cases
 are supported nonetheless. When $n \leq 0$, we iterate through subsets of
 the empty set, i.e., the empty set; when $k < 0$ no subset of the required
 length exist and nothing happens.
