PARI/GP Control Statements

break ({\(n\)})

Exit \(n\) innermost enclosing loops.

for…

for (\(x\) = \(a\), \(b\), \(seq\))

Evaluate \(seq\) for \(a \le x \le b\).

forcomposite (\(x\) = \(a\), \(b\), \(seq\))

Evaluate \(seq\) for composites \(a \le x \le b\).

fordiv (\(n\), \(x\), \(seq\))

Evaluate \(seq\) for \(x\) dividing \(n\).

fordivfactored (\(n\), \(x\), \(seq\))

Evaluate \(seq\) for \(x = [d, factor(d)], d | n\).

forfactored (\(x\) = \(a\), \(b\), \(seq\))

Evaluate \(seq\) for \(x = [n, factor(n)]\), \(a \le n \le b\).

Evaluates \(seq\), where the formal variable \(x\) is [\(n\), factor(\(n\))] and \(n\) goes from \(a\) to \(b\); \(a\) and \(b\) must be integers. Nothing is done if \(a > b\).

To do: Why are some of the results in different forms like [1, matrix(0,2)], [2, Mat([2, 1])], or [6, [2, 1; 3, 1]]?

forpart (\(p\) = \(n\), \(seq\))

Loop over partitions of \(n\).

forperm (\(s\), \(p\), \(seq\))

Loop over permutations of \(s\).

forprime (\(x\) = \(a\), \(b\), \(seq\))

Evaluate \(seq\) for primes \(a \le x \le b\).

forprimestep (\(x\) = \(a\), \(b\), \(seq\))

Evaluate \(seq\) for primes \(\equiv a\space(mod\space q)\).

forqfvec (\(v\), \(q\), \(b\), \(seq\))

Loop over vectors \(v\), \(q(v) \le b\), \(q > 0\).

forsquarefree (\(x\) = \(a\), \(b\), \(seq\))

— : : : as above, \(n\) squarefree

Evaluates \(seq\), where the formal variable \(x\) is [\(x\), factor(\(x\))] and \(x\) goes through squarefree integers from \(a\) to \(b\); \(a\) and \(b\) must be integers of the same sign. Nothing is done if \(a \ge b\).

forstep (\(x\) = \(a\), \(b\), \(s\), \(seq\))

Evaluate \(seq\) for \(a \le x \le b\) stepping \(s\).

forsubgroup (\(h\) = \(g\))

Loop over \(h < g\) finite abelian group.

forsubset (\(n\), \(p\), \(seq\))

Loop over subsets of \(\lbrace1, …, n\rbrace\).

forsubset ([\(n\), \(k\)], \(p\), \(seq\))

Loop over \(k\)-subsets of \(\lbrace1, …, n\rbrace\).

forvec (\(x\) = \(v\), \(seq\))

Multivariable for, lex ordering.

if (\(a\), {\(seq1\)}, {\(seq2\)})

If \(a ≠ 0\), evaluate \(seq1\), else \(seq2\).

next ({\(n\)})

Start new iteration of \(n\)-th enclosing loop.

return ({\(n\)})

Return \(n\) from current subroutine.

until (\(a\), \(seq\))

Evaluate \(seq\) until \(a \ne 0\).

while (\(a\), \(seq\))

While \(a \ne 0\), evaluate \(seq\).