## 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 \(seq\).