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 \(a > b\).
time = 2,844 ms.
time = 704 ms.
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]]?
[1, matrix(0,2)]
[2, Mat([2, 1])]
[3, Mat([3, 1])]
[4, Mat([2, 2])]
[5, Mat([5, 1])]
[6, [2, 1; 3, 1]]
[7, Mat([7, 1])]
[8, Mat([2, 3])]
[9, Mat([3, 2])]
[10, [2, 1; 5, 1]]
[11, Mat([11, 1])]
[12, [2, 2; 3, 1]]
[13, Mat([13, 1])]
[14, [2, 1; 7, 1]]
[15, [3, 1; 5, 1]]
[16, Mat([2, 4])]
[17, Mat([17, 1])]
[18, [2, 1; 3, 2]]
[19, Mat([19, 1])]
[20, [2, 2; 5, 1]]
time = 16 ms.
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 \(seq\).